problem solving interests

SIMPLE INTEREST PROBLEMS WITH SOLUTIONS

Problem 1 :

A person deposits $5,000 in a bank account which pays 6% simple interest per year. Find the value of his deposit after 4 years.

Formula for simple interest is

Substitute P = 5000, t = 4, r = 6%.

I = 5000 ⋅ 6/100 ⋅ 4

Accumulated value = Principal + Interest

= 5000 + 1200

Problem 2 :

Glen received $2,250 loan from bank. After six months, he paid back $2,295 and closed the loan. Find the rate of interest.

Interest = Amount - Principal

I = 2295 - 2250

Given : Time period is 6 months.

In simple interest formula, we use time period in years. But, the time period given in the question is in months.

So, let us change the given time period in years.

6 months = 6/12 year = 1 /2 years

So, the time period is 1/2 year.

Formula for simple interest :

Substitute I = 45, P = 2250, t = 1/2.

45 = 2250 ⋅ r ⋅ 1/2

45 = 1125 ⋅ r

Divide both sides by 1125.

45/1125 = r

To convert the decimal 0.04 into percentage, multiply it by 100.

0.04 ⋅ 100% = r

Problem 3 :

A man invests $16,500 in two kinds treasury notes, which yield 7.5% and 6% annually. After two years year, he earns $2442 in interest. How much does he invest at the 6 % rate ?

Let x be the amount invested at 6% rate.

Then, the amount invested in 7.5% account is

= 16500 - x

Given : After two years, total interest earned in both the accounts is $2,442.

Interest at 6% rate + Interest at 7.5% rate = 2442

x ⋅ 6/100 ⋅ 2 + (16500 - x) ⋅ 7.5/100 ⋅ 2 = 2442

x ⋅ 0.06 ⋅ 2 + (16500 - x) ⋅ 0.075 ⋅ 2 = 2442

0.12x + (16500 - x) ⋅ 0.15 = 2442

0.12x + 2475 - 0.15x = 2442

2475 - 0.03x = 2442

2475 - 2442 = 0.03x

Divide both sides by 0.03.

33/0.03 = x

Hence, the amount invested at 6% rate is $1100.

Problem 4 :

A person invested $25,200 in two accounts, which pay 5 % and 10% interest annually. The amount invested at 10% rate is 110% of the amount invested at 5% rate. After three years year, he earns $5760 in interest. How much did he invest at the 5% rate ?

Let x be the amount invested at 5% rate.

Then, the amount invested in 10% account is

= 110% of x

= 1.10 ⋅ x

Given : After three years, total interest earned in both the accounts is $5,760.

Interest at 5% rate + Interest at 10% rate = 5760

x ⋅ 5/100 ⋅ 3 + 1.1x ⋅ 10/100 ⋅ 3 = 5760

x ⋅ 0.05 ⋅ 3 + 1.1x ⋅ 0.1 ⋅ 3 = 5760

0.15x + 0.33x = 5760

0.48x = 5760

Divide both sides by 0.48.

x = 5760/0.48

x = 576000/48

Hence, the amount invested at 5% rate is $12000.

Problem 5 :

In simple interest, a sum of money doubles itself in 10 years. Find the number of years it will take to triple itself.

Let P be the sum of money invested.

Given : Sum of money doubles itself in 10 years.

Then, P will become 2P in 10 years.

Now we can calculate interest for ten years as given below.

From the above calculation, P is the interest for the first 10 years.

In simple interest, interest earned will be same for every year.

So, interest earned in the next 10 years also will be P.

It has been explained below.

Hence, it will take 20 years for the principal to become triple itself.

Problem 6 :

In simple interest, a sum of money amounts to $ 6200 in 2 years and $ 7400 in 3 years. Find the principal.

At the end of 2 years, we get $6200

At the end of 3 years, we get $7400

From these two information, we can get the interest earned in the 3rd year as given below.

In simple interest, interest will be same for every year.

Based on this, we can calculate the principal as given below.

Hence, the principal is $3800.

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Algebra: Interest Word Problems

In these lessons, we will how to solve • word problems that involve a single Simple Interest • word problems that involve more that one Simple Interest. • word problems that involve Simple Interest with discounted loan.

Related Pages Simple Interest Formula Simple and Compound Interest Compound Interest Word Problems

Interest Problems are word problems that use the formula for Simple Interest . There is also another type of interest word problems called Compound Interest Word Problems .

The following tables give the formulas for Simple Interest, Compound Interest, and Continuously Compounded Interest. Scroll down the page for examples and solutions on how to use the Simple Interest Formula.

Simple Interest Word Problems

Interest represents a change of money.

If you have a saving account, the interest will increase your balance based upon the interest rate paid by the bank.

If you have a loan, the interest will increase the amount you owe based upon the interest rate charged by the bank.

The formula for Simple Interest is:

I = prt where I is the interest generated. p is the principal amount that is either invested or owed. r is the rate at which the interest is paid. t is the time that the principal amount is either invested or owed.

This type of word problem is not difficult. Just remember the formula and make sure you plug in the right values. The rate is usually given in percent , which you will need to change to a decimal value.

Word Problems With One Simple Interest

Example 1: John wants to have an interest income of $3,000 a year. How much must he invest for one year at 8%?

Solution: Step 1: Write down the formula I = prt

Step 2: Plug in the values 3000 = p × 0.08 × 1 3000 = 0.08p p = 37,500

Answer: He must invest $37,500

Example 2: Jane owes the bank some money at 4% per year. After half a year, she paid $45 as interest. How much money does she owe the bank?

Answer: She owes $2,250

How To Solve Simple Interest Word Problems (Investment Problems)?

Find the amount of interest earned by $8000 invested at 5% annual simple interest rate for 1 year.
To start a mobile dog-grooming service, a woman borrowed $2,500. If the loan was for two years and the amount of interest was $175, what simple interest rate was she charged?
A student borrowed some money from his father at 2% simple interest to buy a car. He paid his father $360 in interest after 3 years, how much did he borrow?
A couple invested $6,000 of his $20,000 lottery earning in bonds. How much do they have left to invest in stocks?
A college student wants to invest the $12,000 inheritance he received and use the annual interest earned to pay for his tuition cost of $945. The highest interest offered by a bank is 6% annual simple interest. At this rate, he cannot earn the needed $945, so he decides to invest some of the money in a riskier, but more profitable, investment offering a 9% return. How much should he invest in each rate?
A credit union loaned out $50,000, part at an annual rate of 6% and the rest at an annual rate of 12% . The collected combined interest was $3,600 that year. How much did the credit union loan out at each rate?

How To Solve Interest Problems Using The Simple Interest Formula?

If you invest $3,500 in a savings account that pays 4% in simple interest, how much interest will you earn after 3 years? What will the new balance be?
You borrow $6,000 from a loan shark. If you owe $7,200 in 18 months, what would be the simple interest rate?

How to use the Simple Interest Formula to solve Word Problems?

Example: Jenna invests $13,000 into separate bank accounts, one earning 6% simple interest and the other earning 3% simple interest. If at the end of one year she earns $682.50 in interest, how much did she invest in each account?

Word Problems With More Than One Simple Interest Rate

How To Solve Word Problems With More Than One Simple Interest?

Example: Pam invested $5000. She earned 14% on part of her investment and 6% on the rest. If she earned a total of $396 in interest for the year, how much did she invest at each rate? Note that this problem requires a chart to organize the information.

The chart is based on the interest formula, which states that the amount invested times the rate of interest = interest earned. The chart is then used to set up the equation.

How To Solve Word Problems With Two Simple Interest Rates?

Example: Johnny is a shrewd eight-year-old. For Christmas, his grandparents gave him ten thousand dollars. Johnny decides to invest some of the money in a savings account that pays two percent per annum and the rest in a stock fund that pays ten percent per annum. Johnny wants his investments to yield seven percent per annum. How much should he put in each account?

How To Solve A Real Life Problem Involving Interest?

Example: Suppose $7,000 is divided into two bank accounts. One account pays 10% simple interest per year and the other pays 5%. After three years there is a total of $1451.25 in interest between the two accounts. How much was invested into each account (rounded to the nearest cent)?

Simple Interest Discounted Loan

A discounted loan is a loan that collects interest from the amount of the loan or face value of the loan when the loan is made.

The interest is deducted from the loan amount so you don’t receive the full loan amount or face value of the loan when you receive the loan. The deducted interest is the discount.

Example: You borrow $2,000 on a 12% discount loan for 12 months. 1. What is the loan discount? 2. Determine the net amount of money that you will actually receive. 3. What is the loan’s actual annual simple interest rate?

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6.4 Solve Simple Interest Applications

Learning objectives.

Use the simple interest formula
Solve simple interest applications

Be Prepared 6.4

Before you get started, take this readiness quiz.

Solve 0.6 y = 45 . 0.6 y = 45 . If you missed this problem, review Example 5.43 .
Solve n 1.45 = 4.6 . n 1.45 = 4.6 . If you missed this problem, review Example 5.44 .

Use the Simple Interest Formula

Do you know that banks pay you to let them keep your money? The money you put in the bank is called the principal , P , P , and the bank pays you interest , I . I . The interest is computed as a certain percent of the principal; called the rate of interest , r . r . The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable for time, t , t , represents the number of years the money is left in the account.

Simple Interest

If an amount of money, P , P , the principal, is invested for a period of t t years at an annual interest rate r , r , the amount of interest, I , I , earned is

Interest earned according to this formula is called simple interest .

The formula we use to calculate simple interest is I = P r t . I = P r t . To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information by listing all four variables and filling in the given information.

Example 6.33

Find the simple interest earned after 3 3 years on $500 $500 at an interest rate of 6%. 6%.

Organize the given information in a list.

I = ? P = $500 r = 6% t = 3 years I = ? P = $500 r = 6% t = 3 years

We will use the simple interest formula to find the interest.

Try It 6.65

Find the simple interest earned after 4 4 years on $800 $800 at an interest rate of 5%. 5%.

Try It 6.66

Find the simple interest earned after 2 2 years on $700 $700 at an interest rate of 4%. 4%.

In the next example, we will use the simple interest formula to find the principal.

Example 6.34

Find the principal invested if $178 $178 interest was earned in 2 2 years at an interest rate of 4%. 4%.

I = $178 P = ? r = 4% t = 2 years I = $178 P = ? r = 4% t = 2 years

We will use the simple interest formula to find the principal.

Try It 6.67

Find the principal invested if $495 $495 interest was earned in 3 3 years at an interest rate of 6%. 6%.

Try It 6.68

Find the principal invested if $1,246 $1,246 interest was earned in 5 5 years at an interest rate of 7% . 7% .

Now we will solve for the rate of interest.

Example 6.35

Find the rate if a principal of $8,200 $8,200 earned $3,772 $3,772 interest in 4 4 years.

Organize the given information.

I = $3,772 P = $8,200 r = ? t = 4 years I = $3,772 P = $8,200 r = ? t = 4 years

We will use the simple interest formula to find the rate.

Try It 6.69

Find the rate if a principal of $5,000 $5,000 earned $1,350 $1,350 interest in 6 6 years.

Try It 6.70

Find the rate if a principal of $9,000 $9,000 earned $1,755 $1,755 interest in 3 3 years.

Solve Simple Interest Applications

Applications with simple interest usually involve either investing money or borrowing money. To solve these applications, we continue to use the same strategy for applications that we have used earlier in this chapter. The only difference is that in place of translating to get an equation, we can use the simple interest formula.

We will start by solving a simple interest application to find the interest.

Example 6.36

Nathaly deposited $12,500 $12,500 in her bank account where it will earn 4% 4% interest. How much interest will Nathaly earn in 5 5 years?

We are asked to find the Interest, I . I .

I = ? P = $12,500 r = 4% t = 5 years I = ? P = $12,500 r = 4% t = 5 years

Try It 6.71

Areli invested a principal of $950 $950 in her bank account with interest rate 3%. 3%. How much interest did she earn in 5 5 years?

Try It 6.72

Susana invested a principal of $36,000 $36,000 in her bank account with interest rate 6.5% . 6.5% . How much interest did she earn in 3 3 years?

There may be times when you know the amount of interest earned on a given principal over a certain length of time, but you don't know the rate. For instance, this might happen when family members lend or borrow money among themselves instead of dealing with a bank. In the next example, we'll show how to solve for the rate.

Example 6.37

Loren lent his brother $3,000 $3,000 to help him buy a car. In 4 years 4 years his brother paid him back the $3,000 $3,000 plus $660 $660 in interest. What was the rate of interest?

We are asked to find the rate of interest, r . r .

I = 660 P = $3,000 r = ? t = 4 years I = 660 P = $3,000 r = ? t = 4 years

Try It 6.73

Jim lent his sister $5,000 $5,000 to help her buy a house. In 3 3 years, she paid him the $5,000 , $5,000 , plus $900 $900 interest. What was the rate of interest?

Try It 6.74

Hang borrowed $7,500 $7,500 from her parents to pay her tuition. In 5 5 years, she paid them $1,500 $1,500 interest in addition to the $7,500 $7,500 she borrowed. What was the rate of interest?

There may be times when you take a loan for a large purchase and the amount of the principal is not clear. This might happen, for instance, in making a car purchase when the dealer adds the cost of a warranty to the price of the car. In the next example, we will solve a simple interest application for the principal.

Example 6.38

Eduardo noticed that his new car loan papers stated that with an interest rate of 7.5% , 7.5% , he would pay $6,596.25 $6,596.25 in interest over 5 5 years. How much did he borrow to pay for his car?

We are asked to find the principal, P . P .

I = 6,596.25 P = ? r = 7.5% t = 5 years I = 6,596.25 P = ? r = 7.5% t = 5 years

Try It 6.75

Sean's new car loan statement said he would pay $4,866.25 $4,866.25 in interest from an interest rate of 8.5% 8.5% over 5 5 years. How much did he borrow to buy his new car?

Try It 6.76

In 5 5 years, Gloria's bank account earned $2,400 $2,400 interest at 5%. 5%. How much had she deposited in the account?

In the simple interest formula, the rate of interest is given as an annual rate, the rate for one year. So the units of time must be in years. If the time is given in months, we convert it to years.

Example 6.39

Caroline got $900 $900 as graduation gifts and invested it in a 10-month 10-month certificate of deposit that earned 2.1% 2.1% interest. How much interest did this investment earn?

We are asked to find the interest, I . I .

I = ? P = $900 r = 2.1% t = 10 months I = ? P = $900 r = 2.1% t = 10 months

Try It 6.77

Adriana invested $4,500 $4,500 for 8 8 months in an account that paid 1.9% 1.9% interest. How much interest did she earn?

Try It 6.78

Milton invested $2,460 $2,460 for 20 20 months in an account that paid 3.5% 3.5% interest How much interest did he earn?

Section 6.4 Exercises

Practice makes perfect.

In the following exercises, use the simple interest formula to fill in the missing information.

In the following exercises, solve the problem using the simple interest formula.

Find the simple interest earned after 5 5 years on $600 $600 at an interest rate of 3%. 3%.

Find the simple interest earned after 4 4 years on $900 $900 at an interest rate of 6%. 6%.

Find the simple interest earned after 2 2 years on $8,950 $8,950 at an interest rate of 3.24% . 3.24% .

Find the simple interest earned after 3 3 years on $6,510 $6,510 at an interest rate of 2.85% . 2.85% .

Find the simple interest earned after 8 8 years on $15,500 $15,500 at an interest rate of 11.425% . 11.425% .

Find the simple interest earned after 6 6 years on $23,900 $23,900 at an interest rate of 12.175% . 12.175% .

Find the principal invested if $656 $656 interest was earned in 5 5 years at an interest rate of 4% . 4% .

Find the principal invested if $177 $177 interest was earned in 2 2 years at an interest rate of 3% . 3% .

Find the principal invested if $70.95 $70.95 interest was earned in 3 3 years at an interest rate of 2.75%. 2.75%.

Find the principal invested if $636.84 $636.84 interest was earned in 6 6 years at an interest rate of 4.35%. 4.35%.

Find the principal invested if $15,222.57 $15,222.57 interest was earned in 6 6 years at an interest rate of 10.28% . 10.28% .

Find the principal invested if $10,953.70 $10,953.70 interest was earned in 5 5 years at an interest rate of 11.04%. 11.04%.

Find the rate if a principal of $5,400 $5,400 earned $432 $432 interest in 2 2 years.

Find the rate if a principal of $2,600 $2,600 earned $468 $468 interest in 6 6 years.

Find the rate if a principal of $11,000 $11,000 earned $1,815 $1,815 interest in 3 3 years.

Find the rate if a principal of $8,500 $8,500 earned $3,230 $3,230 interest in 4 4 years.

Casey deposited $1,450 $1,450 in a bank account with interest rate 4%. 4%. How much interest was earned in 2 2 years?

Terrence deposited $5,720 $5,720 in a bank account with interest rate 6%. 6%. How much interest was earned in 4 4 years?

Robin deposited $31,000 $31,000 in a bank account with interest rate 5.2% . 5.2% . How much interest was earned in 3 3 years?

Carleen deposited $16,400 $16,400 in a bank account with interest rate 3.9% . 3.9% . How much interest was earned in 8 8 years?

Hilaria borrowed $8,000 $8,000 from her grandfather to pay for college. Five years later, she paid him back the $8,000 , $8,000 , plus $1,200 $1,200 interest. What was the rate of interest?

Kenneth lent his niece $1,200 $1,200 to buy a computer. Two years later, she paid him back the $1,200 , $1,200 , plus $96 $96 interest. What was the rate of interest?

Lebron lent his daughter $20,000 $20,000 to help her buy a condominium. When she sold the condominium four years later, she paid him the $20,000 , $20,000 , plus $3,000 $3,000 interest. What was the rate of interest?

Pablo borrowed $50,000 $50,000 to start a business. Three years later, he repaid the $50,000 , $50,000 , plus $9,375 $9,375 interest. What was the rate of interest?

In 10 10 years, a bank account that paid 5.25% 5.25% earned $18,375 $18,375 interest. What was the principal of the account?

In 25 25 years, a bond that paid 4.75% 4.75% earned $2,375 $2,375 interest. What was the principal of the bond?

Joshua's computer loan statement said he would pay $1,244.34 $1,244.34 in interest for a 3 3 year loan at 12.4% . 12.4% . How much did Joshua borrow to buy the computer?

Margaret's car loan statement said she would pay $7,683.20 $7,683.20 in interest for a 5 5 year loan at 9.8%. 9.8%. How much did Margaret borrow to buy the car?

Caitlin invested $8,200 $8,200 in an 18-month 18-month certificate of deposit paying 2.7% 2.7% interest. How much interest did she earn form this investment?

Diego invested $6,100 $6,100 in a 9-month 9-month certificate of deposit paying 1.8% 1.8% interest. How much interest did he earn form this investment?

Airin borrowed $3,900 $3,900 from her parents for the down payment on a car and promised to pay them back in 15 15 months at a 4% 4% rate of interest. How much interest did she owe her parents?

Yuta borrowed $840 $840 from his brother to pay for his textbooks and promised to pay him back in 5 5 months at a 6% 6% rate of interest. How much interest did Yuta owe his brother?

Everyday Math

Interest on savings Find the interest rate your local bank pays on savings accounts.

ⓐ What is the interest rate?
ⓑ Calculate the amount of interest you would earn on a principal of $8,000 $8,000 for 5 5 years.

Interest on a loan Find the interest rate your local bank charges for a car loan.

ⓑ Calculate the amount of interest you would pay on a loan of $8,000 $8,000 for 5 5 years.

Writing Exercises

Why do banks pay interest on money deposited in savings accounts?

Why do banks charge interest for lending money?

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

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Compound Interest Problems with Detailed Solutions

Compound interest problems with answers and solutions are presented.

Free Practice for SAT, ACT and Compass Maths tests

A principal of $2000 is placed in a savings account at 3% per annum compounded annually. How much is in the account after one year, two years and three years?
What would $1000 become in a saving account at 3% per year for 3 years when the interest is not compounded (simple interest)? What would the same amount become after 3 years with the same rate but compounded annually?
$100 is the principal deposited in a 5% saving account not compounded (simple interest). The same amount of $100 is placed in a 5% saving account compounded annually. Find the total amount A after t years in each saving plan and graph both of them in the same system of rectangular axes. Use the graphs to approximate the time it takes each saving plan to double the initial amount.
If $3000 is placed in an account at 5% and is compounded quarterly for 5 years. How much is in the account at the end of 5 years?
$1200 is placed in an account at 4% compounded annually for 2 years. It is then withdrawn at the end of the two years and placed in another bank at the rate of 5% compounded annually for 4 years. What is the balance in the second account after the 4 years.
$1,200 is placed in an account at 4% compounded daily for 2 years. It is then withdrawn and placed in another bank at the rate of 5% compounded daily for 4 years. What is the balance in the second account after the 4 years. (compare with the previous problem)
$1200 is placed in an account at 4% compounded continuously for 2 years. It is then withdrawn and placed in another bank at the rate of 5% compounded continuously for 4 years. What is the balance in the second account after the 4 years. (compare with the two previous problem)
What principal you have to deposit in a 4.5% saving account compounded monthly in order to have a total of $10,000 after 8 years?
A principal of $120 is deposited in a 7% account and compounded continuously. At the same time a principal of $150 is deposited in a 5% account and compounded annually. How long does it take for the amounts in the two accounts to be equal?
A first saving account pays 5% compounded annually. A second saving account pays 5% compounded continuously. Which of the two investments is better in the long term?
What interest rate, compounded annually, is needed for a principal of $4,000 to increase to $4,500 in 10 year?
A person deposited $1,000 in a 2% account compounded continuously. In a second account, he deposited $500 in a 8% account compounded continuously. When will the total amounts in both accounts be equal? When will the total amount in the second accounts be 50% more than the total amount in the second account?
A bank saving account offers 4% compounded on a quarterly basis. A customer deposit $200, in this type of account, at the start of each quarter starting with the first deposit on the first of January and the fourth deposit on the first of October. What is the total amount in his account at the end of the year?
An amount of $1,500 is invested for 5 years at the rates of 2% for the first two years, 5% for the third year and 6% for the fourth and fifth years all compounded continuously. What is the total amount at the end of the 5 years?

Solutions to the Above Questions

Solution When interest is compounded annually, total amount A after t years is given by: A = P(1 + r) t , where P is the initial amount (principal), r is the rate and t is time in years. 1 year: A = 2000(1 + 0.03) 1 = $2060 2 years: A = 2000(1 + 0.03) 2 = $2121.80 3 years: A = 2000(1 + 0.03) 3 = $2185.45
Solution Not compounded: A = P + P(1 + r t) = 1000 + 1000(1 + 0.03 · 3) = $1090 Compounded: A = P(1 + r) t = 1000(1 + 0.03) 3 = $1092.73 Higher return when compounded.
Solution Compounded n times a year and after t years, the total amount is given by: A = P(1 + r/n) n t quarterly n = 4: Hence A = P(1 + r/4) 4 t = 3000(1 + 0.05/4) 4 × 5 = $3846.11
Solution Annual compounding First two years: A = P(1 + r) t = 1200(1 + 0.04) 2 = $1297.92 Last four years : A = P(1 + r) t = 1297.92(1 + 0.05) 4 = $1577.63
Solution Daily compounding (assuming 365 days per year) First two years: A = P(1 + r / 365) 365 t = 1200(1 + 0.04 / 365) 365 × 2 = $1299.94 Last four years : A = P(1 + r / 365) 365 t = 1299.94 (1 + 0.05 / 365) 365 ×4 = $1587.73 Higher final balances compared to annual compounding in last problem.
Solution In continuous compounding, final balance after t years is given by: A = P e r t . First two years: A = P e r t = 1200 e 0.04 × 2 = $1299.94 Last four years : A = P e r t = $1299.94 e 0.05 × 4 = $1587.75 Same balances compared to daily compounding in last problem.
Solution P initial balance to find and final balance A known and equal to $10,000. A = P(1 + 0.045 / 12) 12 × 8 = 10,000 P = 10,000 / ( (1 + 0.045 / 12) 12 × 8 ) = $6981.46
Solution P initial balance is equal to $4,000 and final balance is equal to $4,500. A = P(1 + r) t = 4,500 4000(1 + r) 10 = 4,500 (1 + r) 10 = 4500 / 4000 Take ln of both sides. 10 ln(1 + r) = ln(4500 / 4000) ln(1 + r) = ln(4500 / 4000) / 10 1 + r = e 0.1 ln(4500 / 4000) r = e 0.1 ln(4500 / 4000) - 1 ? 0.012
Solution A 1 = 1000 e 0.02 t A 2 = 500 e 0.08 t A 1 = A 2 gives 1000 e 0.02 t = 500 e 0.08 t Divide both sides by 500 e 0.02 t and simplify 100 / 500 = e 0.08 t - 0.02 t 2 = e 0.06 t Take ln of both sides. 0.06 t = ln 2 t = ln 2 / 0.06 ? 11.5 years A 2 is 50% more than A 1 gives the equation: A 2 = 1.5 A 1 500 e 0.08 t = 1.5 × 1000 e 0.02 t e 0.08 t - 0.02 t = 3 0.06 t = ln 3 t ? 18.5 years
Solution A = P(1 + r/n) n t First quarter deposit, t = 1 year: A 1 = 200 (1 + 0.04 / 4) e 4 × 1 = $208.12 Second quarter deposit, t = 3/4 of 1 year : A 2 = 200 (1 + 0.04 / 4) e 4 × 3/4 = $206.06 Third quarter deposit , t = 1/2 of 1 year : A 3 = 200 (1 + 0.04 / 4) e 4 × 1/2 = $204.02 Fourth quarter deposit, t = 1/4 of 1 year : A 4 = 200 (1 + 0.04 / 4)e 4 × 1/4 = $202 Total amount = $208.12 + $206.06 + $204.02 + $202 = $820.2
Solution A = P e r t End of first two years: A 1 = 1500 e 0.02 × 2 End of third year: A 2 = A 1 e 0.05 × 1 End of fifth year (last two years): A 3 = A 2 e 0.06 × 2 = 1500 e 0.02 × 2 + 0.05 × 1 + 0.06 × 2 = $1850.51

GMAT Math : Interest Problems

Study concepts, example questions & explanations for gmat math, all gmat math resources, example questions, example question #1 : interest problems.

Grandpa Jack wants to help pay for college for his grandson, Little Jack. Little Jack is currently 8 years old. Grandpa Jack makes a one-time deposit into an account that earns simple interest every year. Grandpa Jack invests $10,000 now and in ten years, that will grow to $15,000. What rate of simple interest did Grandpa Jack receive?

To calculate simple interest, the formula is

$problem solving interests$

ALTERNATE SOLUTION:

Another way of finding this is to calculate the amount of interest per year. Since this is simple interest, Grandpa Jack earns the same amount of interest per year. The total interest earned is 15,000-10,000= 5,000. $5,000 over 10 years, equates to $500 per year. $500 divided by the original $10,000 is .05, or 5%.

Example Question #2 : Interest Problems

$problem solving interests$

Example Question #3 : Interest Problems

$problem solving interests$

Example Question #101 : Gmat Quantitative Reasoning

A bank offers a business a loan in the amount of $13,000 with a simple annual interest rate of 9%. How much will the business owe the bank after 3 years?

$problem solving interests$

The accrual of simple interest can be found in two steps. First, multiply the principal amount by the interest rate. Second, multiply that result by the number of years during which interest will accrue.

$problem solving interests$

The question asks for the total amount that the business will owe the bank, so we must add the interest accrued to the principal amount.

$problem solving interests$

Example Question #6 : Interest Problems

$problem solving interests$

Therefore, solving for the time factor:

$problem solving interests$

Example Question #7 : Interest Problems

$problem solving interests$

Therefore, solving for the principal factor in the equation:

$problem solving interests$

Example Question #8 : Interest Problems

$problem solving interests$

Therefore, solving for the rate factor in the equation:

$problem solving interests$

Example Question #10 : Interest Problems

$problem solving interests$

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How to Solve Compound Interest Problems?

Compound interest is an interest that is accumulated on the principal and interest together over a given time. In this article, let's familiarize ourselves with solving compound interest problems.

Simple interest is interest that is paid only on the principal of money, while compound interest is interest that is paid on principal and compound interest at regular intervals.

A step-by-step guide to solving compound interest problems

Compound interest is the interest paid on principal and interest that is combined at regular intervals. At regular intervals, the interest so far accumulated is added to the existing principal amount and then the interest is calculated for the new principal. The new principal is equal to the sum of the Initial principal, and the interest accumulated so far.

Compound interest $=$ interest on principal $+$ compounded interest at regular intervals

The compound interest is calculated at regular intervals like annually( yearly), semi-annually, quarterly, monthly, etc.

Compound interest formula

The compound interest is calculated after calculating the total amount over some time, based on the interest rate and the initial principle. For an initial principal of $P$, rate of interest per annum of $r$, period $t$ in years, frequency of the number of times the interest is compounded annually $n$, the formula for calculation of amount is as follows.

$\color{blue}{A=P\left(1+\frac{r}{n}\right)^{nt}}$

The above formula represents the total amount at the end of the period and includes compound interest and principal. In addition, we can calculate the compound interest by subtracting the principal from this amount. The formula for calculating compound interest is as follows:

$\color{blue}{CI=P\left(1+\frac{r}{n}\right)^{nt}-P}$

In the above expression:

$P$ is the principal amount
$r$ is the rate of interest (decimal)
$n$ is the frequency or no. of times the interest is compounded annually
$t$ is the overall tenure.

It should be noted that the above formula is a general formula when the principal is compounded $n$ several times in a year. If the given principal is compounded annually, the amount after the period at the percent rate of interest, $r$, is given as:

$\color{blue}{A=P\left(1+\frac{r}{100}\right)^t}$

$\color{blue}{C.I.=P\left(1+\frac{r}{100}\right)^t-P}$

Compound interest formula for different periods

The compound interest for a given principle can be calculated for different periods using different formulas.

Compound interest formula – quarterly

If the period for calculating the interest is quarterly, the profit is calculated every three months and the amount is combined $4$ times a year. The formula to calculate the compound interest when the principal is compounded quarterly is given:

$\color{blue}{C.I.=P\left(1+\frac{\frac{r}{4}}{100}\right)^{4t}-P}$

Here the compound interest is calculated for the quarterly period, so the interest rate r is divided by $4$ and the period is quadrupled. The formula to calculate the amount when the principal is compounded quarterly is given:

$\color{blue}{A=P\left(1+\frac{\frac{r}{4}}{100}\right)^{4t}}$

In the above expression,

$A$ is the amount at the end of the period
$P$ is the initial principal value, $r$ is the rate of interest per annum
$t$ is the period
$C.I.$ is the compound interest.

Compound interest formula – half-yearly

Profit for compound interest varies based on the calculation period. If the profit calculation period is half-yearly, the profit is calculated once every six months and is combined twice a year. The formula for calculating compound interest if the principal is compounded semi-annually or half-yearly is given as:

$\color{blue}{C.I.=P\left(1+\frac{\frac{r}{2}}{100}\right)^{2t}-P}$

Here the compound interest is calculated for six months, so the interest rate $r$ is divided by $2$ and the period is doubled. The formula to calculate the amount when the principal is compounded semi-annually or half-yearly is given:

$\color{blue}{A=P\left(1+\frac{\frac{r}{2}}{100}\right)^{2t}}$

Compound Interest – Example 1:

Davide lends $$3,000$ to John at an interest rate of $10%$ per annum, compounded half-yearly for $2$ years. Can you help him find out how much amount he gets after $2$ years from John?

The principal amount $P$ is $$3,000$. The rate of interest $r$ is $10%$ per annum. Conversion period $=$ Half-year, Rate of interest per half-year $= \frac{10%}{2}= 5%$. The time period $t$ is $2$ years. The compounding frequency $n$ is $2$.

Now, substitute the given data in the compound interest formula: $A\:=\:P\left(1+\frac{\frac{r}{2}}{100}\right)^{2n}$

$A=3,000\left(1+\frac{\frac{10}{2}}{100}\right)^{2\times 2}$

$=3646.51$

Exercises for Solving Compound Interest Problems

What interest rate do you need to turn $$1,000$ into $$5,000$ in $20$ Years?
If you deposit $$5,000$ into an account paying $6%$ annual interest compounded monthly, how long until there is $$8,000$ in the account?
$\color{blue}{8.38%}$
$\color{blue}{7.9}$

by: Effortless Math Team about 2 years ago (category: Articles )

Effortless Math Team

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6.2.1: Compound Interest (Exercises)

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Rupinder Sekhon and Roberta Bloom
De Anza College

SECTION 6.2 PROBLEM SET: COMPOUND INTEREST

Do the following compound interest problems involving a lump-sum amount.

Do the following compound interest problems.

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Earth and space

Simple Interest Problems

Key concepts.

Simple interest, percent of interest and principal.
Find simple interest.
Find the percent of interest.
Find the principal.

Solve simple interest problems

What is principal.

When an individual or business borrows a certain sum of money through a loan, the amount borrowed is referred to as the principal amount.

Example: Maddy wants to construct his house; the estimation was calculated to be $40000. He decides to borrow $10000 from the bank. This borrowed amount is termed as principal.

What is simple interest?

Simple interest is the method of calculating the interest amount for some principal amount of money. We generally borrow money from our siblings or friends when our pocket money gets exhausted or lend money. We use that money for our purpose and return it when we receive the next month’s pocket money to them. This is how lending and borrowing works at home.

But in the real world, money is not free to borrow. We often borrow money from banks in the form of a loan. During payback, apart from the loan amount, we pay an extra amount that depends on the loan amount and the time period for which we borrowed. This additional amount being paid is called simple interest.

What is percent of interest?

An interest rate is a percent used to calculate interest on the principal.

Maddy borrows $10000 at 4% interest for a period of two years.

Here, we understand that principal = $10000 and rate of interest = 4%.

Let us understand, what does 4% mean?

4% is written as 4/100

The banker here wants to convey that if Maddy borrows $100, then he must pay $4 extra during the payback. But, Maddy here borrows $10000.

The interest to be paid = 10000 × 4%

= 10000 × 0.04

= $400.

Therefore, Maddy must pay $400 during the payback additionally along with the principal of $10000.

Find simple interest

Example 1: Ann opens a saving account with a deposit of $670. She will earn 1.5% interest each year on her money. How much interest will she earn over a period of 10 years? (assuming she does not add or take out any money).

Use the percent equation to find the amount of interest earned in one year.

We know that, part = percent × whole

Let us take the interest amount as I, part = I, percent = 1.5% and whole = amount deposited.

I = 1.5% × 670

I = 0.015 × 670

Step 2:Multiply the interest earned in one year by 10 to calculate the total interest Ann will earn over a 10-year period.

Total interest earned by Ann in 10 years = 10.05 × 10

= 100.5

Therefore, Ann gets $100.5 in ten years’ time.

Example 2: Dave borrows $1500 to repair his house. He will pay off the loan after 3 years by paying back the principal plus 3.5% interest for each year. How much will he pay in interest, and how much will she pack back altogether

Let us take the interest amount as I, part = I, percent = 3.5% and whole = amount borrowed.

I = 3.5% × 1500

I = 0.035 × 1500

Step 2: Multiply the interest to be paid in one year by 3 to calculate the total interest Dave will have to pay over a 3-year period.

Total interest in 3 years = 52.5 × 3

= 157.5

Total amount to be paid back = principal + interest

= 1500 + 157.5

= 1657.5

Therefore, the interest to be paid by Dave is $157.5, and the total amount altogether is $1657.5

Find the percent of interest

Example 1: A bank lends $4000 on loan to a businessman in simple interest. If he promises to pay $20 every month for a period of two years. What is the interest rate on the loan per annum?

Multiply the interest by 12 to get the interest for 1 year.

20 × 12 = $240

Interest to be paid in two years = 240 × 2

= $480.

Step 2: Use the percent equation to find the interest rate.

Here we understand that, part = interest, whole = principal and percent rate = p.

Let us take interest rate as p, which we are about to find.

Interest = interest rate × principal.

480 = p × 4000

Divide the equation by 4000 on both sides.

480/4000 = p

Express the decimal as a percent by multiplying by 100.

Therefore, the interest rate levied on the loan by the bank is 12%.

Example 2: A person deposits $5000 in a bank in simple interest; he finds $6200 after two years in the account. What is the rate of interest per annum?

Find the interest paid by the bank in those two years

Interest paid in two years = 6200 – 5000

= $1200.

Interest paid in one year = 1200/2

Interest paid in one year = 600

600 = p × 5000

Divide the equation by 1200 on both sides.

600/5000 = p

Therefore, the interest rate levied on the deposit by the bank is 12%

Find the principal

Example 1: Brit opened a savings account that fetches him 4% interest. Brit estimates that assuming he neither adds to nor withdraws from his account, he will earn $300 in interest after 5 years. How much did Brit deposit when he opened the account?

Firstly, find the interest he earns in 1 year.

300 ÷ 4 = 75

Interest earned per year is $75.

Step 2: Use the percent equation to find the deposit or principal.

Let us take principal as p, which we are about to find.

Here we understand that, part = interest amount, whole = principal and percent = interest rate.

Interest amount per year = interest rate × principal.

75 = 4% × P

75 = 0.04 × P

Divide the equation by 0.04 on both sides.

75/0.04 = 0.04/0.04 = × P

P × 1 =1875

Therefore, Brit deposits $1875 in the account at 4% simple interest to earn $300 interest over a period of 4 years.

Example 2: Alex borrowed money for school. He took out a loan that charges 5% simple interest. He will end up paying $800 in interest after 5 years. How much did Alex borrow for school?

800 ÷ 5 = 160

Interest earned per year is $160.

160 = 5% × P

160 = 0.05 × P

Divide the equation by 0.05 on both sides.

160/0.05 = 0.05/0.05 = × P

P × 1 =3300

Therefore, Alex borrows $3300 for school at 5% simple interest over a period of 5 years and pays $800 interest.

A bank lends $1000 at 2.5% in simple interest. After 5 years, how much money should be paid back to the bank?
Adam borrows $6600 from his friend at 1.5% in simple interest; he promises to pay it back in 3 years. How much interest does he pay?
Calculate the interest earned on lending $500 for two years at 3% per annum in simple interest?
Greg pays $100 in interest per year for 8 years for borrowing $12000 in simple interest; what is the interest rate?
A bank asks to pay $50 per year for 2 years on borrowing $1000. Determine the rate of interest.
A company lends Maya $4000. Every month she will pay $11.88 interest for 1 year. What is the interest rate?
The interest earned at 2% is $320 for 2 years. What is the principal?
The interest earned at 5% is $1000 for a period of 10 years. Determine the principal.
Rebecca borrows money to pay for her medical expenses. She paid $400 over a period of 10 years borrowing at 2% in simple interest. How much did she borrow?
Adam decided to deposit $8000 in a bank at a simple interest of 3% till 12 years so that he can use it for his business expansion later. How much money will he have in his account after 12 years, assuming that he neither draws nor adds any amount?

What have we learned?

Understanding simple interest, percent of interest and principal.
Finding simple interest.
Finding the percent of interest.
Finding the principal.

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Compound Interest Questions

Compound interest questions are provided here to help the students understand the applications of compound interest in our daily existence. As we know, compound interest is one of the important mathematical concepts that can be applied in many financial transactions.

Below are some situations where we can use the formula of CI to calculate the required results.

Increase or decrease in population
The growth of a bacteria (when the rate of growth is known)
The value of an item, if its price increases or decreases in the intermediate years

What is Compound Interest?

Interest is the additional money paid by organisations like banks or post offices on money deposited (kept) with them. Interest is also paid by people when they borrow money. When the interest is calculated on the previous year’s amount, the interest is called compounded or Compound Interest (C.I.).

The formula for finding the amount on compound interest is given by:

A = P[1 +(R/100)] n

This is the amount when interest is compounded annually.

Compound interest (CI) = A – P

Compound Interest Questions and Answers

1. Find the compound interest (CI) on Rs. 12,600 for 2 years at 10% per annum compounded annually.

Principal (P) = Rs. 12,600

Rate (R) = 10

Number of years (n) = 2

= 12600[1 + (10/100)] 2

= 12600[1 + (1/10)] 2

= 12600 [(10 + 1)/10] 2

= 12600 × (11/10) × (11/10)

= 126 × 121

Total amount, A = Rs. 15,246

= Rs. 15,246 – Rs. 12,600

2. At what rate of compound interest per annum, a sum of Rs. 1200 becomes Rs. 1348.32 in 2 years?

Let R% be the rate of interest per annum.

Principal (P) = Rs. 1200

Total amount after 2 years (A) = Rs. 1348.32

We know that,

A = P[1 + (R/100)] n

Rs. 1348.32 = Rs. 1200[1 + (R/100)] 2

1348.32/1200 = [1 + (R/100)] 2

1 + (R/100) = 53/50

R/100 = (53/50) – 1

R/100 = (53 – 50)/50

Hence, the rate of interest is 6%.

3. A TV was bought for Rs. 21,000. The value of the TV was depreciated by 5% per annum. Find the value of the TV after 3 years. (Depreciation means the reduction of value due to use and age of the item)

Principal (P) = Rs. 21,000

Rate of depreciation (R) = 5%

Using the formula of CI for depreciation,

A = P[1 – (R/100)] n

A = Rs. 21,000[1 (5/100)] 3

= Rs. 21,000[1 – (1/20)] 3

= Rs. 21,000[(20 – 1)/20] 3

= Rs. 21,000 × (19/20) × (19/20) × (19/20)

= Rs. 18,004.875

Therefore, the value of the TV after 3 years = Rs. 18,004.875.

4. Find the compound interest on Rs 48,000 for one year at 8% per annum when compounded half-yearly.

Principal (P) = Rs 48,000

Rate (R) = 8% p.a.

Time (n) = 1 year

Also, the interest is compounded half-yearly.

So, A = P[1 + (R/200)] 2n

= Rs. 48000[1 + (8/200)] 2(1)

= Rs. 48000[1 + (1/25)] 2

= Rs. 48000[(25 + 1)/25] 2

= Rs. 48,000 × (26/25) × (26/25)

= Rs. 76.8 × 26 × 26

= Rs 51,916.80

Therefore, the compound interest = A – P

= Rs (519,16.80 – 48,000)

= Rs 3,916.80

5. Find the compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.

Principal (P) = Rs. 8000

Rate of interest (R) = 15% p.a

Time (n) = 2 years 4 months

4 months = 4/12 years = 1/3 years

= Rs. 8000 × (23/20) × (23/20) × (21/20)

= Rs. 11,109

Therefore, the compound interest = A – P = Rs. 11,109 – Rs. 8000 = Rs. 3109

6. If principal = Rs 1,00,000. rate of interest = 10% compounded half-yearly. Find

(i) Interest for 6 months.

(ii) Amount after 6 months.

(iii) Interest for the next 6 months.

(iv) Amount after one year.

P = Rs 1,00,000

(i) A = P[1 + (R/200)] 2n

Here, 2n is the number of half years.

Let us find the interest compounded half-yearly for 6 months, i.e., one half year.

So, A = Rs. 1,00,000 [1 + (10/200)] 1

= Rs. 1,00,000 × 21/20

= Rs. 1,05,000

Compounded interest for 6 months = Rs. 1,05,000 – Rs. 1,00,000 = Rs. 5000

(ii) Amount after 6 months = Rs. 1,05,000

(iii) To find the interest for the next 6 months, we should consider the principal amount as Rs. 1,05,000.

Thus, A = Rs. 1,05,000 [1 + (10/200)] 1

= Rs. 1,05,000 × (21/20)

= Rs. 1,10,250

Compound interest for next 6 months = Rs. 1,10,250 – Rs. 1,05,000 = Rs. 5250

(iv) Amount after one year = Rs. 1,10,250

7. The population of a place increased to 54,000 in 2003 at a rate of 5% per annum.

(i) Find the population in 2001.

(ii) What would be its population in 2005?

(i) Let P be the population in the year 2001.

Thus, population in the year 2003 = A = 54000 (given)

Also, n = 2

54000 = P[1 + (5/100)] 2

54000 = P[1 + (1/20)] 2

54000 = P × [(20 + 1)/20] 2

54000 = P × (21/20) × (21/20)

P = 54000 × (20/21) × (20/21)

P = 48979.6

The population in 2001 = 48980 (approx.)

(ii) Given that the population in the year 2003 = P = 54000

= 54000[1 + (5/100)] 2

= 54000[1 + (1/20)] 2

= 54000 × [(20 + 1)/20] 2

= 54000 × (21/20) × (21/20)

Therefore, the population in 2005 = 59535

8. What is the difference between the compound interests on Rs. 5000 for 1 ½ year at 4% per annum compounded yearly and half-yearly?

P = Rs. 5000

Time (n) = 1 ½ years

When the interest is compounded yearly,

= Rs. 5000 × (26/25) × (51/50)

CI = A – P = Rs. 5304 – Rs. 5000 = Rs. 304

When the interest is compounded half-yearly,

n = 1 ½ years = 3 half-years

A = P[1 + (R/200)] 2n

Here, 2n = 3

A = Rs. 5000 [1 + (4/200)] 3

= Rs. 5000 [1 + (1/50)] 3

= Rs. 5000 [(50 + 1)/50] 3

= Rs. 5000 × (51/50) × (51/50) × (51/50)

= Rs. 5306.04

CI = A – P = Rs. 5306.04 – Rs. 5000 = Rs. 306.04

Difference between compound interest = Rs. 306.04 – Rs. 304 = Rs. 2.04

9. The population of a town decreased every year due to migration, poverty and unemployment. The present population of the town is 6,31,680. Last year the migration was 4%, and the year before last, it was 6%. What was the population two years ago?

The present population of the town (A) = 631680

Last year migration rate was 4%, and the year before, the previous migration rate was 6%.

Let P be the population of a town, two years ago.

Thus, R 1 = 4%

According to the given situation, the total population is:

631680 = P × (24/25) × (47/50)

P = 631680 × (25/24) × (50/47)

Therefore, the population of the town, two years ago = 700000

10. Find the amount and the compound interest on Rs. 1,00,000 compounded quarterly for 9 months at the rate of 4% per annum.

P = Rs. 1,00,000

Time = 9 months

A = P[1 + (R/400)] 4n

Here, R/400 is the quarterly interest rate.

4n = 9 months = 3 quarters

So, A = Rs. 1,00,000 [1 + (4/400)] 3

= Rs. 1,00,000 [1 + (1/100)] 3

= Rs. 1,00,000 [(100 + 1)/100] 3

= Rs. 1,00,000 × (101/100) × (101/100) × (101/100)

= Rs. 103030.10

Practice Questions on Compound Interest

The population of a city was 20,000 in the year 1997. It increased at the rate of 5% p.a. Find the population at the end of the year 2000.
Find the compound interest on Rs. 16,000 at 20% per annum for 9 months, compounded quarterly.
Vasudevan invested Rs. 60,000 at an interest rate of 12% per annum, compounded half-yearly. What amount would he get- (i) after 6 months? (ii) after 1 year?
Kamala borrowed Rs. 26,400 from a bank to buy a scooter at a rate of 15% p.a., compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?
Find CI paid when a sum of Rs. 10,000 is invested for 1 year and 3 months at 8 1/2 % per annum, compounded annually.

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EVERYTHING IS PERSONAL. INCLUDING THIS BLOG.

Larry Ray Esq.

Jan 19, 2021
10 min read

Distinguishing Between Positions and Interests: A Vital Step in Problem Solving.

A vital step in effective problem solving is to distinguish between positions and interests.

The next step is to prioritize the issues searching for commonalities, for interdependence between the parties involved. This sets the stage for step three: Creativity leading to a plan of action or agreement.

What Are Positions?

Positions are statements of what you will or will not do. What you can or cannot do. The Yes’s and No’s.

-I cannot sign that agreement.

-I will not go on that trip.

-I cannot pay that amount.

-I will not rent that apartment.

-I will not modernize this house.

-I will buy this car.

-I can afford this rent.

-I need two months to research.

-I need to make a stop.

These are the “yes’s” and “no’s.” I can or cannot. I will or will not.

What Are Interests?

The Positions are clear and now parties need to uncover their interests. One does this by asking questions: What? How? Why? Interests include needs, emotions, values, underlying motivations and aspirations.

Example: I cannot sign that agreement.

Response: What are the reasons you cannot sign that agreement?

EX: I cannot pay that amount.

Response: Why can you not pay that amount?

Response: My hours at my job were cut so I have reduced income?

EX: I will buy this car.

Response: What attracts you to purchase this car?

Once these questions are asked, parties really need to listen fully to the responses and summarize them. One may need to ask more questions or follow up questions.

Sometimes the first response reveals an interest but not the real underlying interests which means more questions.

Think of the metaphor of “peeling the onion” or “unnesting the dolls.” It should be noted that in a typical Nesting Dolls item, there are usually five dolls. So, maybe one needs to ask five questions to discover the underlying issues.

This is similar to the Five Why’s Theory. Sometimes one needs to ask “why” five times to discover what is really going on.

An excellent example of this process is the issue of pricing or dollar amount which is often the first position. Most of the time when questioned, parties will admit the the dollar amount is not the highest priority but instead, value and quality are the real issues.

(See Blog Entry on Questioning Skills: https://www.larryrayesq.com/post/questioning-skills-essential-for-effective-negotiation

How Do Parties Prioritize?

This step is challenging in two ways:

One, many parties have not thought about prioritization. This will require of each party reflection, research and discernment so they can effectively place issues in order.

Second, after each parties discerns their priorities there must be a trusting, open environment to set the stage for them to share such. Thus, each party must practice behaviors that create this environment. These include effective listening, summarizing, asking questions and ensuring all parties realize that their perspectives are valued, even if there is not agreement.

(See Blog on Liking and Trusting: https://www.larryrayesq.com/post/trust-must-be-earned-trust-is-fragile

How Do Parties Discover Commonalities or Interdependence?

This is a vital step. It is often easier if the issues and priorities are clearly posted on a board or screen. The parties can then step back, use their critical thinking skills to identify where the issues overlap. Once, they find this overlap-this linking, this interdependence, they realize even more so why there is a need to negotiate.

Interdependency is a mutual dependency situation characterized by interlocking goals. The structure of these interests determines the range of outcomes. If all goals can be achieved, it is integrative negotiation with mutual gains.

Setting the Stage for Creativity.

Most folks pride themselves on being creative but the research demonstrates that most lose their childlike creativity as they mature. So, for this stage to be successful, the creative atmosphere must be established.

Secondly, most folks instantly connect creativity with brainstorming so they open the door widely to suggestions, ideas and options. This can work but only in a step by step fashion:

-Solicit ideas. Value each idea. Do not evaluate. Do not question during this stage.

-Explain for further delineate each idea so all is understandable.

-Now, prioritize each idea and again look for commonalities. If there is agreement by all parties that a particular idea or ideas are workable, start the discussion there. Don’t discard the other ideas. They might be useful in the future or maybe part of an idea can be combined.

-Finally, integrate the ideas into a plan of action of agreement.

(Children are often willing to criticize and don’t mind asking stupid questions since they are not into “saving face.” As adults, they often lose those qualities.)

https://www.inc.com/yoram-solomon/3-reasons-children-are-more-creative-than-adults.html

(See Blog entry on Creativity: https://www.larryrayesq.com/post/creativity-is-vital-for-effective-negotiation-mediation )

Creating a Plan of Action or Agreement.

Many parties rush through this stage because they are so excited that they have reached such. Don’t! Instead take the time to craft an agreement that will work for the long term (usually, this is desired). This is the time to ask, the “What if’s.”

-What if this deadline is not reach?

-What if these resources cannot be located.

In this way, when the parties leave, they will have the same understanding of the plan of action.

Goal and Steps:

So the goal in distinguishing between positions and interests is clear:

To discover the underlying issues leading to a better understanding leading to creative options and ultimately an enduring and creative agreement.

-Question to get to underlying issues.

-Prioritize the issues searching for commonalities and interdependence.

-General and test creative options.

-Craft an enduring agreement.

Exercise: This Exercise is often conducted in the Negotiation class at The George Washington University School of Law.

Issue: Installation of bullet proof glass in taxis in the District of Columbia between the drivers and passengers.

-NO, say the Taxi Drivers and the Taxi Unions.

-YES, say the DC Taxicab Commission.

Interests: The students than brainstorm to discover the underlying interests of each party. The result?

Interests of Taxi Drivers and Unions:

Communication issues.

Self-employed-independence

Environmental issues

Windows ineffective

Not involved in decision-making

No respect for commission

Cost of installation

Time to install-cab out of service

Increase weight of cab-more gas

Appearance may intimidate passenger

Will tips be impaired-psychological barrier

Don’t want another regulation

Cleaning and vandalism of glass

Will the glass really make them safer?

Will the glass extend to the floor?

Interests of Taxi Commission:

-Safety of Taxi Drivers

-Safety of Tourists/Guests

-Liability issues

-Public Perception of safety

-Influence of glass lobby?

-Low respect for taxi unions.

-Need to show actions.

-Avoid charges of discrimination.

-Need to reduce crime.

-Bullet proof glass is a trend in major cities.

Issues Priorities: Since this was a real life case, real life interviews were conducted with the taxi drivers to discern their priorities. On the surface, they stated Communication and Safety. Based on further probing questions, they admitted that compensation/tips and the feeling of self-employed; that is, independence, were the underlying top priorities.

Based on real life interviews of the Taxi Commission, they initially stated, Safety but again, after probing questions, they admitted that “taking action” was their underlying motive so they would be re-appointed and possibly run for political offices.

Finding Interdependence: The students then found it easy to find commonalities between the politically appointed Commission and the Taxi Drivers/Unions.

-Promoting Tourism

-Communication

-Costs and reducing Liability.

Creating a Plan of Action: I all parties had been in the problem solving mood, they could have easily crafted a creative plan of action. Possibly, the city could have paid for the glass installation. Possibly, the glass could have been designed to promote communication. All stakeholders could have touted progress.

Other Position versus Interests Examples:

District of Columbia Street Cleaning: DC has not had street cleaning for 25 years and then they started it. The DC Street Cleaners indicated that they had chosen the Dupont neighborhood to be the first experiment. They also said that they needed to clean weekly so the residents get into the habit of moving their cars from side to side. This was based on the experiences of other cities. This seemed interesting.

One of the Neighborhood Commissioners got curious and discovered the underlying interest was not street cleaning but giving parking tickets. DC Street Cleaning had done their own research and found out the Dupont residents pay their tickets more loyally than any other neighborhood. So, a revelation?

Position-Many Jurisdictions Require Voter ID: Why? On the surface, the politicians state that their interest is decreasing voter fraud.

But many believe the underlying interest is, voter suppression.

Example: Yahoo CEO Marissa Mayer 2013 position: No more telecommuting.

What’s the interest? Mayer stated that she wanted “One Yahoo” and that many ideas emanate from being side by side in the hallways, etc.

Many wondered about the real underlying interest. Is it to make her mark? Does she merely want to go against the trend? Does she want to test who is really serious about their jobs?

Some recent research indicates that telecommuting and increased productivity may be nuanced. It might indicate that those who telecommute 20% of less might be more productive than not.

https://money.com/telecommuting-what-marissa-mayer-got-right-and-wrong/

Example: Opposition to Red Light (Stop) Cameras: Many take the position of, Yes; and others, No. Politicians usually state the reason is safety, but many wonder if the interest is really raising revenue. So what is the real interest? The research varies and so one believes whichever research agrees with their position.

https://www.fhwa.dot.gov/publications/research/safety/05049/

Red Light Cameras (Red Light Safety Cameras) Distinguishing between Interests and Positions.

Positions: Some say YES and others say NO.

Interests of the Ones who say Yes:

-Enforcement of law

-Reduces angle crashes

-Encourages safe driving

-Spill over safety to other intersections

-Unbias ticketing

-System pays for itself

Interests of those who say NO:

-Tickets mailed to registered car

-Owner-may not be driver

-Many tickets give to illegal right

-Are illegal turns-not as serious

-This is all about finances.

-Increases rear-end crashes

Example: Back Car Window Stickers/Decals/Hangers:

Most, most likely have not given much thought to the car back window. There was a trend for awhile of having dangling signs in the rear window saying,

-My kid is an A student.

-My kid is on the honor role.

-My kid is in the Scouts.

Most seemed mildly amused by this publicity.

Then some playful folks began putting other dangles or stickers saying,

-Life s-cks.

-Things stink

-What the f-ck.

Several state legislators found these messages objectionable and began offering bills to ban such stickers. The proposed bills limited nontransparent stickers to 7-15 square inches of the back window farthest from the driver. That was their position. Their stated interest: Safety.

But, was it really?

Example: Sagging Pants Legislative Laws and Proposals.

During the past 20 years, many conservative legislators, mostly in the South began introducing and passing laws against “sagging pants.” They even criminalized the situation along with up to $1000 fines.

So the Position : No sagging pants 3 inches below the waist. One proposed law even referred to “ilevin” which is the widest bone of the pelvis.

What is the Interests? Some legislators declare that they want the youngsters to dress according to standards so that they can get good jobs in the future. Some say it is all about “proper dress.”

But is it? Some think that these legislators are connecting sagging pants to the prison culture, the gang culture or the drug culture. Some, go so far as saying the interest may be racially motivated animus.

Whatever the interest, many of these laws are being repealed due to the disproportionate impact on Black and Brown Male Teenagers, sometimes even giving them a criminal record.

It should also be noted that none of the laws talk about bare skin or possibly one with saggy pants could be wearing a speedo under them-perfectly legal?

https://www.motherjones.com/crime-justice/2019/06/why-it-matters-that-a-city-council-in-louisiana-repealed-a-ban-on-saggy-pants/

Example: Training Institute and Number of Continuing Education Hours (CEU):

Sharon offers training at the Institute. The Institute demands 7 hours of instruction per day to offer CEU’s, 9-5 with an hour for lunch. That is their position. Sharon called them indicating that all 20 of the trainees wanted to take the training on Friday from 8-4AM with an hour lunch so they could get “on the road” driving an hour earlier. This time equaled 7 hours.

The training director said, No! For CLE, one must train for 7 hours per day. The training is advertise from 9-5PM and that is how it must stay.

What is the underlying interest? Most likely Control.

Case Study: Hannah and Emma

Hannah and Emma are sisters and own a successful printing and copying business. They are having troubles. The sisters are going in different directions. Emma is more family oriented and Hannah is focusing on her health. On the side the business also supports a charity for children.

Emma’s Positions:

-Emma is tired and wants out of the partnership.

-She wants Hannah to buy her out.

Emma’s Interests:

- Having a work situation conducive to her child-care needs.

-Getting rest.

-Getting capital for the Husband’s new business.

-Getting a fair “buy-out” for her investment.

-Getting this resolved for the sake of the family.

-She wants recognition that the business was her idea and that because of Hannah’s health, Emma has devoted more than 50% to the business.

-She loves her sister, wants to help her and sustain their relationship.

Hannah’s Positions:

-She cannot afford to buy Hannah out.

-She wants the partnership to continue.

-Because of her health, she cannot run the business on her own.

-Hannah needs a job and this is the only one she can do.

Hannah’s Interests:

- Hannah needs to financially support herself including health insurance.

-Having a work situation conducive to her health needs.

-Continuing a successful business.

-Hannah wants recognition that she has brought in most of the clients.

-Hannah loves her sister and wants to retain the relationship.

Interdependence of Hanna’s and Emma’s Issues.

After Hannah and Emma identified their issues they easily discerned the commonalities:

-They both want a Sisterly loving relationship.

-They both want Hannah to have health insurance and to take care of Hannah’s depression.

-They both want the charity to be sustained.

-They both want a fair financial arrangement accommodating both of their different directions.

-They both want this situation resolved.

Cite: This case study was created by Internationally Acclaimed Mediator and Executive Coach Melinda Ostermeyer. She was the director of the Houston Justice Center and the DC Multi-Door Dispute Resolution Center.

Case Study: The PowerScreen Negotiation aka HackerStar .

Hacker and Star started a business together ten years ago. They were drinking buddies and shared lots of ideas. Hacker is a program developer and Star is a dentist. Hacker provides expertise; Star provides the revenue. They fell out of communication and began having many fights and issues.

One day, each of them took the positions: Close the Business or a New Partnership Agreement.

They each hired representatives who assisted them in identifying the interests:

Hacker’s interests:

-Freedom to develop

-Creative range

-Recognition of expertise

-Increased communication.

-Recognition of 50/50 partnership.

Star’s Interests:

-ROI (return on investment)

-Respect as an investor.

-Open communication, no secrets about developing new programs.

-Easy ways to resolve disputes as they arise.

Once these interests were identified, both Hacker and Star realized their common interests-their independence. Because of this, they crafted a creative new partnership agreement bringing in a third partner, satisfying all interests and including a dispute resolution clause.

https://law.justia.com/codes/wisconsin/2011/346/346.88.html

This case study was created by the Harvard Law School Program on Negotiation.

https://www.pon.harvard.edu/shop/powerscreen-problem/

Conclusion:

Distinguishing between positions and interests is a vital process in decision-making, problem solving and negotiation. First, identify positions which are usually Yes’s and No’s. Then probe to discern what is underlying those positions. Sometimes the interests initially stated are only surface so probing deeper might be necessary. After all the interests are identified and explained including being written on a board or screen, the next step is finding commonalities or interdependence. All of this opens the door to creativity and in the ideal, crafting an agreement that meets all of the interests.

Essentials of Negotiation, 6th Edition, Roy Lewicki, The Ohio State School of Business. (This textbook is used by Professor Larry Ray in his Negotiation course at The George Washington University School of Law).

https://www.prioritytextbook.com/essentials-of-negotiation-6th-edition-lewicki/

Getting to Yes by Roger Fisher et al. This book was first published in the 1980’s. There are many reasons to read this basic book. One reason is that so many attorneys and negotiators are following the basic principles of this book. These principles include,

-Separating the people from the problem.

-Distinguishing between interests and positions.

-Creating options.

· Getting to Yes: Negotiating Agreement Without Giving In

· by Penguin Books

https://amzn.to/2U3tsb3

How to Win Friends and Influence Enemies by Dale Carnegie. This was first published in 1936 and republished each 5 year period. The principles still hold true. One principle is negotiators need to exhibit behaviors to get people to “like” them so they are more persuadable.

Malcolm Gladwell , Talking to Strangers.

https://amzn.to/389ST2W

Malcolm Gladwell, Outliers-Secret to Success

https://amzn.to/3erzv2f

Malcolm Gladwell, Tipping Point

https://amzn.to/3mOXbAO

David and Goliath , Malcolm Gladwell

https://amzn.to/3kUiKiB

Apollo’s Arrow , Nicholas Christakis

https://amzn.to/363Y0P8

Emotional Intelligence , Travis Bradberry

https://amzn.to/3jSBHB1

Seagull Manager , Travis Bradberry

https://amzn.to/2HXPauf

Engaging Problem-Solving Activities That Spark Student Interest

In today’s educational landscape, fostering critical thinking and problem-solving skills is paramount. As educators, we aim to cultivate a generation of students who excel not only academically but also in navigating real-world challenges with creativity and confidence. In this article, we’ll explore a range of engaging problem-solving activities crafted to captivate students’ interest and promote active learning across various subjects. From STEM design challenges to literature-based dilemmas, these hands-on activities are meticulously tailored to inspire curiosity, collaboration, and critical thinking in the classroom .

1. Escape Room Challenge: The Lost Treasure

Follow the steps below to implement this activity in the class:

Introduce the escape room challenge and set the scene with a captivating treasure hunt theme.
Transform the classroom into an immersive escape room environment with hidden clues and puzzles.
Divide students into teams and provide instructions for the challenge, emphasizing teamwork and problem-solving skills.
Allow teams to explore the room and uncover hidden clues and puzzles.
Encourage observation and collaboration as teams work together to solve challenges.
Present teams with a variety of puzzles and obstacles to overcome.
Challenge them to solve each puzzle to progress through the adventure.
Set a time limit for the challenge to create urgency and excitement.
Encourage teams to work efficiently to unlock the secrets of the treasure before time runs out.
Foster effective communication and teamwork among team members.
Emphasize the importance of listening and leveraging each other’s strengths.
Throughout the challenge, students will develop critical thinking, communication, and problem-solving skills.
Encourage reflection on their strategies and teamwork dynamics.
Celebrate each team’s success upon completing the challenge.
Facilitate a debrief session for students to share insights and reflect on their experiences.

With this guide, you can create an engaging escape room challenge that promotes teamwork, critical thinking, and problem-solving skills in a fun and immersive learning environment.

2. STEM Design Challenge: Build a Bridge

Here is the step by step breakdown of this activity:

Present the STEM design challenge to students, explaining that they will be tasked with building a bridge using simple materials.
Supply students with materials such as popsicle sticks, straws, tape, string, and basic construction tools.
Encourage students to inspect the materials and plan their bridge designs accordingly.
Prompt students to brainstorm ideas and sketch their bridge designs before starting construction.
Encourage them to consider factors like structural stability, weight distribution, and material durability.
Instruct students to begin building their bridges based on their designs.
Remind them to apply principles of engineering and physics as they construct their bridges.
As students build their bridges, they’ll encounter challenges and obstacles.
Encourage them to apply problem-solving strategies and make adjustments to their designs as needed.
Throughout the construction process, facilitate discussions among students.
Encourage them to reflect on their design choices and problem-solving approaches.
Provide opportunities for students to test their bridges using various weight loads or simulated environmental conditions.
Encourage them to observe how their bridges perform and make further adjustments if necessary.

8. Bridge-Building Showcase:

Conclude the challenge with a bridge-building showcase where students present their creations to their peers.
Encourage students to discuss their design process, challenges faced, and lessons learned.

9. Celebrate Achievements:

Celebrate students’ achievements and highlight the importance of their creativity and engineering prowess.
Encourage a spirit of inquiry and innovation as students showcase their bridge designs.

10. Reflect and Conclude:

Conclude the STEM design challenge with a reflection session.
Prompt students to reflect on their experiences and discuss the skills they’ve developed throughout the challenge.

By following these step-by-step instructions, students will engage in a hands-on STEM design challenge that fosters critical thinking, creativity, collaboration , and resilience while deepening their understanding of engineering and physics principles.

3. Mystery Box Inquiry: What’s Inside?

Follow these steps to carry out this activity in the class:

Introduction and Setup: Introduce the Mystery Box Inquiry activity and set up a closed mystery box in the classroom.
Group Formation and Instructions: Divide students into small groups and provide instructions emphasizing teamwork and critical thinking.
Engage the Senses: Encourage students to gather around the mystery box and use their senses (touch, smell, hearing) to gather clues about its contents.
Making Observations: Instruct students to carefully observe the exterior of the mystery box and record their observations.
Formulating Hypotheses: Prompt students to formulate hypotheses about what might be inside the mystery box based on their observations.
Testing Hypotheses: Invite students to test their hypotheses by proposing various scenarios and explanations.
Refining Problem-Solving Strategies: Encourage students to refine their problem-solving strategies based on new information and insights.
Group Discussion and Conclusion: Gather the groups for a discussion, allowing students to share their observations, hypotheses, and insights. Conclude by revealing the contents of the mystery box and discussing the problem-solving process.
Reflection and Extension: Provide students with an opportunity to reflect on their experience and optionally extend the activity by challenging them to design their own mystery box inquiries.

By following these steps, you can facilitate an engaging Mystery Box Inquiry activity that prompts students to make astute observations, test hypotheses, and refine their problem-solving strategies effectively.

4. Real-World Problem Simulation: Environmental Crisis

Introduce the environmental crisis scenario.
Explain its significance and real-world implications.
Divide students into teams with varied skill sets.
Assign roles like researcher, negotiator, presenter.
Task teams with researching causes, impacts, and solutions.
Provide access to relevant resources.
Encourage teams to negotiate with stakeholders.
Prompt the development of comprehensive strategies.
Organize a debate or town hall-style discussion.
Facilitate analysis of proposed solutions.
Allow teams to implement proposed solutions.
Monitor progress and outcomes.
Conclude with a group reflection session.
Discuss lessons learned and the importance of problem-solving skills.

This is one of the problem solving activities that can create a simulated environmental crisis scenario, fostering collaboration, critical thinking, and problem-solving skills in students.

5. Mathematical Escape Puzzle: Crack the Code

Introduce the escape puzzle, explaining the goal of unlocking a hidden code through math equations and logic puzzles.
Set up materials in the classroom.
Explain students’ task: solving math equations and logic puzzles to unlock the code.
Provide puzzle materials to teams or individuals.
Instruct on effective use.
Prompt students to solve provided math equations and logic puzzles.
Encourage collaboration and problem-solving among students.
Offer guidance as needed.
Monitor student progress and provide assistance when required.
Celebrate successful completion of puzzles.
Guide students through unlocking the hidden code.
Conclude with a reflective discussion on math concepts and problem-solving skills applied.

By following these steps, you can engage students in a challenging Mathematical Escape Puzzle that reinforces math skills and promotes problem-solving abilities.

6. Literature-Based Problem Solving Activity: Character Dilemmas

Choose literature pieces with rich character development and moral dilemmas that are suitable for your students’ age and maturity level.
Present the Literature-Based Problem Solving activity to students, explaining that they will engage in thought-provoking analysis and ethical reflection inspired by characters in literature.
Assign readings or excerpts from the selected literature to students.
Instruct students to analyze the characters’ motivations, actions, and the ethical dilemmas they face.
Encourage students to prepare for discussions by taking notes on key points, character motivations, and possible solutions to the dilemmas.
Host lively discussions where students explore the moral dilemmas presented in the literature.
Encourage students to express their thoughts, opinions, and interpretations while respecting diverse perspectives.
Organize persuasive debates where students defend their viewpoints and propose solutions to the character dilemmas.
Encourage students to use evidence from the literature to support their arguments.
Prompt students to apply problem-solving skills to analyze the consequences of different decisions and actions within the literature.
Encourage critical thinking as students navigate complex ethical situations.
Guide students in applying the lessons learned from literature to real-world scenarios.
Encourage reflection on how the problem-solving skills and ethical considerations explored in the activity can be applied in their own lives.
Conclude the Literature-Based Problem Solving activity by summarizing key insights and takeaways from the discussions and debates.
Encourage students to reflect on how their understanding of moral dilemmas and problem-solving skills has evolved through the activity.

It is one of the problem solving activities through which students will engage in thought-provoking analysis, ethical reflection, and problem-solving inspired by characters in literature, fostering critical thinking and ethical decision-making skills in a meaningful and engaging way.

Engaging problem solving activities are the cornerstone of active learning, fostering essential skills for success in today’s dynamic world. By seamlessly integrating these hands-on experiences into the classroom, educators inspire curiosity, collaboration, and critical thinking in their students. Whether through STEM design challenges, literature-based dilemmas, or coding adventures, these activities empower students to become adept problem solvers, equipped to navigate the challenges of tomorrow with confidence and ingenuity. Embrace the transformative potential of engaging problem-solving activities to unleash the full spectrum of educational possibilities and prepare students for a future brimming with possibilities.

Problem solving through values: A challenge for thinking and capability development

• This paper introduces the 4W framework of consistent problem solving through values.
• The 4W suggests when, how and why the explication of values helps to solve a problem.
• The 4W is significant to teach students to cope with problems having crucial consequences.
• The paper considers challenges using such framework of thinking in different fields of education.

The paper aims to introduce the conceptual framework of problem solving through values. The framework consists of problem analysis, selection of value(s) as a background for the solution, the search for alternative ways of the solution, and the rationale for the solution. This framework reveals when, how, and why is important to think about values when solving problems. A consistent process fosters cohesive and creative value-based thinking during problem solving rather than teaching specific values. Therefore, the framework discloses the possibility for enabling the development of value-grounded problem solving capability.The application of this framework highlights the importance of responsibility for the chosen values that are the basis for the alternatives which determine actions. The 4W framework is meaningful for the people’s lives and their professional work. It is particularly important in the process of future professionals’ education. Critical issues concerning the development of problem solving through values are discussed when considering and examining options for the implementation of the 4W framework in educational institutions.

1. Introduction

The core competencies necessary for future professionals include problem solving based on complexity and collaborative approaches ( OECD, 2018 ). Currently, the emphasis is put on the development of technical, technological skills as well as system thinking and other cognitive abilities (e.g., Barber, 2018 ; Blanco, Schirmbeck, & Costa, 2018 ). Hence, education prepares learners with high qualifications yet lacking in moral values ( Nadda, 2017 ). Educational researchers (e.g., Barnett, 2007 ; Harland & Pickering, 2010 ) stress that such skills and abilities ( the how? ), as well as knowledge ( the what? ), are insufficient to educate a person for society and the world. The philosophy of education underlines both the epistemological and ontological dimensions of learning. Barnett (2007) points out that the ontological dimension has to be above the epistemological one. The ontological dimension encompasses the issues related to values that education should foster ( Harland & Pickering, 2010 ). In addition, values are closely related to the enablement of learners in educational environments ( Jucevičienė et al., 2010 ). For these reasons, ‘ the why ?’ based on values is required in the learning process. The question arises as to what values and how it makes sense to educate them. Value-based education seeks to address these issues and concentrates on values transfer due to their integration into the curriculum. Yazdani and Akbarilakeh (2017) discussed that value-based education could only convey factual knowledge of values and ethics. However, such education does not guarantee the internalization of values. Nevertheless, value-based education indicates problem solving as one of the possibilities to develop values.

Values guide and affect personal behavior encompassing the ethical aspects of solutions ( Roccas, Sagiv, & Navon, 2017 ; Schwartz, 1992 , 2012 ; Verplanken & Holland, 2002 ). Therefore, they represent the essential foundation for solving a problem. Growing evidence indicates the creative potential of values ( Dollinger, Burke, & Gump, 2007 ; Kasof, Chen, Himsel, & Greenberger, 2007 ; Lebedeva et al., 2019) and emphasizes their significance for problem solving. Meanwhile, research in problem solving pays little attention to values. Most of the problem solving models (e.g., Newell & Simon, 1972 ; Jonassen, 1997 ) utilize a rational economic approach. Principally, the research on the mechanisms of problem solving have been conducted under laboratory conditions performing simple tasks ( Csapó & Funke, 2017 ). Moreover, some of the decision-making models share the same steps as problem solving (c.f., Donovan, Guss, & Naslund, 2015 ). This explains why these terms are sometimes used interchangeably ( Huitt, 1992 ). Indeed, decision-making is a part of problem solving, which emerges while choosing between alternatives. Yet, values, moral, and ethical issues are more common in decision-making research (e.g., Keeney, 1994 ; Verplanken & Holland, 2002 ; Hall & Davis, 2007 ; Sheehan & Schmidt, 2015 ). Though, research by Shepherd, Patzelt, and Baron (2013) , Baron, Zhao, and Miao (2015) has affirmed that contemporary business decision makers rather often leave aside ethical issues and moral values. Thus, ‘ethical disengagement fallacy’ ( Sternberg, 2017, p.7 ) occurs as people think that ethics is more relevant to others. In the face of such disengagement, ethical issues lose their prominence.

The analysis of the literature revealed a wide field of problem solving research presenting a range of more theoretical insights rather empirical evidence. Despite this, to date, a comprehensive model that reveals how to solve problems emphasizing thinking about values is lacking. This underlines the relevance of the chosen topic, i.e. a challenge for thinking and for the development of capabilities addressing problems through values. To address this gap, the following issues need to be investigated: When, how, and why a problem solver should take into account values during problem solving? What challenges may occur for using such framework of thinking in different fields of education? Aiming this, the authors of the paper substantiated the conceptual framework of problem solving grounded in consistent thinking about values. The substantiation consists of several parts. First, different approaches to solving problems were examined. Second, searching to reveal the possibilities of values integration into problem solving, value-based approaches significant for problem solving were critically analyzed. Third, drawing on the effect of values when solving a problem and their creative potential, the authors of this paper claim that the identification of values and their choice for a solution need to be specified in the process of problem solving. As a synthesis of conclusions coming from the literature review and conceptual extensions regarding values, the authors of the paper created the coherent framework of problem solving through values (so called 4W).

The novelty of the 4W framework is exposed by several contributions. First, the clear design of overall problem solving process with attention on integrated thinking about values is used. Unlike in most models of problem solving, the first stage encompass the identification of a problem, an analysis of a context and the perspectives that influence the whole process, i.e. ‘What?’. The stage ‘What is the basis for a solution?’ focus on values identification and their choice. The stage ‘Ways how?’ encourages to create alternatives considering values. The stage ‘Why?’ represent justification of a chosen alternative according particular issues. Above-mentioned stages including specific steps are not found in any other model of problem solving. Second, even two key stages nurture thinking about values. The specificity of the 4W framework allows expecting its successful practical application. It may help to solve a problem more informed revealing when and how the explication of values helps to reach the desired value-based solution. The particular significance is that the 4W framework can be used to develop capabilities to solve problems through values. The challenges to use the 4W framework in education are discussed.

2. Methodology

To create the 4W framework, the integrative literature review was chosen. According to Snyder (2019) , this review is ‘useful when the purpose of the review is not to cover all articles ever published on the topic but rather to combine perspectives to create new theoretical models’ (p.334). The scope of this review focused on research disclosing problem solving process that paid attention on values. The following databases were used for relevant information search: EBSCO/Hostdatabases (ERIC, Education Source), Emerald, Google Scholar. The first step of this search was conducted using integrated keywords problem solving model , problem solving process, problem solving steps . These keywords were combined with the Boolean operator AND with the second keywords values approach, value-based . The inclusion criteria were used to identify research that: presents theoretical backgrounds and/or empirical evidences; performed within the last 5 years; within an educational context; availability of full text. The sources appropriate for this review was very limited in scope (N = 2).

We implemented the second search only with the same set of the integrated keywords. The inclusion criteria were the same except the date; this criterion was extended up to 10 years. This search presented 85 different sources. After reading the summaries, introductions and conclusions of the sources found, the sources that do not explicitly provide the process/models/steps of problem solving for teaching/learning purposes and eliminates values were excluded. Aiming to see a more accurate picture of the chosen topic, we selected secondary sources from these initial sources.

Several important issues were determined as well. First, most researchers ground their studies on existing problem solving models, however, not based on values. Second, some of them conducted empirical research in order to identify the process of studies participants’ problem solving. Therefore, we included sources without date restrictions trying to identify the principal sources that reveal the process/models/steps of problem solving. Third, decision-making is a part of problem solving process. Accordingly, we performed a search with the additional keywords decision-making AND values approach, value-based decision-making . We used such inclusion criteria: presents theoretical background and/or empirical evidence; no date restriction; within an educational context; availability of full text. These all searches resulted in a total of 16 (9 theoretical and 7 empirical) sources for inclusion. They were the main sources that contributed most fruitfully for the background. We used other sources for the justification the wholeness of the 4W framework. We present the principal results of the conducted literature review in the part ‘The background of the conceptual framework’.

3. The background of the conceptual framework

3.1. different approaches of how to solve a problem.

Researchers from different fields focus on problem solving. As a result, there still seems to be a lack of a conventional definition of problem solving. Regardless of some differences, there is an agreement that problem solving is a cognitive process and one of the meaningful and significant ways of learning ( Funke, 2014 ; Jonassen, 1997 ; Mayer & Wittrock, 2006 ). Differing in approaches to solving a problem, researchers ( Collins, Sibthorp, & Gookin, 2016 ; Jonassen, 1997 ; Litzinger et al., 2010 ; Mayer & Wittrock, 2006 ; O’Loughlin & McFadzean, 1999 ; ect.) present a variety of models that differ in the number of distinct steps. What is similar in these models is that they stress the procedural process of problem solving with the focus on the development of specific skills and competences.

For the sake of this paper, we have focused on those models of problem solving that clarify the process and draw attention to values, specifically, on Huitt (1992) , Basadur, Ellspermann, and Evans (1994) , and Morton (1997) . Integrating the creative approach to problem solving, Newell and Simon (1972) presents six phases: phase 1 - identifying the problem, phase 2 - understanding the problem, phase 3 - posing solutions, phase 4 - choosing solutions, phase 5 - implementing solutions, and phase 6 - final analysis. The weakness of this model is that these phases do not necessarily follow one another, and several can coincide. However, coping with simultaneously occurring phases could be a challenge, especially if these are, for instance, phases five and six. Certainly, it may be necessary to return to the previous phases for further analysis. According to Basadur et al. (1994) , problem solving consists of problem generation, problem formulation, problem solving, and solution implementation stages. Huitt (1992) distinguishes four stages in problem solving: input, processing, output, and review. Both Huitt (1992) and Basadur et al. (1994) four-stage models emphasize a sequential process of problem solving. Thus, problem solving includes four stages that are used in education. For example, problem-based learning employs such stages as introduction of the problem, problem analysis and learning issues, discovery and reporting, solution presentation and evaluation ( Chua, Tan, & Liu, 2016 ). Even PISA 2012 framework for problem solving composes four stages: exploring and understanding, representing and formulating, planning and executing, monitoring and reflecting ( OECD, 2013 ).

Drawing on various approaches to problem solving, it is possible to notice that although each stage is named differently, it is possible to reveal some general steps. These steps reflect the essential idea of problem solving: a search for the solution from the initial state to the desirable state. The identification of a problem and its contextual elements, the generation of alternatives to a problem solution, the evaluation of these alternatives according to specific criteria, the choice of an alternative for a solution, the implementation, and monitoring of the solution are the main proceeding steps in problem solving.

3.2. Value-based approaches relevant for problem solving

Huitt (1992) suggests that important values are among the criteria for the evaluation of alternatives and the effectiveness of a chosen solution. Basadur et al. (1994) point out to visible values in the problem formulation. Morton (1997) underlines that interests, investigation, prevention, and values of all types, which may influence the process, inspire every phase of problem solving. However, the aforementioned authors do not go deeper and do not seek to disclose the significance of values for problem solving.

Decision-making research shows more possibilities for problem solving and values integration. Sheehan and Schmidt (2015) model of ethical decision-making includes moral sensitivity, moral judgment, moral motivation, and moral action where values are presented in the component of moral motivation. Another useful approach concerned with values comes from decision-making in management. It is the concept of Value-Focused Thinking (VFT) proposed by Keeney (1994) . The author argues that the goals often are merely means of achieving results in traditional models of problem solving. Such models frequently do not help to identify logical links between the problem solving goals, values, and alternatives. Thus, according to Keeney (1994) , the decision-making starts with values as they are stated in the goals and objectives of decision-makers. VFT emphasizes the core values of decision-makers that are in a specific context as well as how to find a way to achieve them by using means-ends analysis. The weakness of VFT is its restriction to this means-ends analysis. According to Shin, Jonassen, and McGee (2003) , in searching for a solution, such analysis is weak as the problem solver focuses simply on removing inadequacies between the current state and the goal state. The strengths of this approach underline that values are included in the decision before alternatives are created. Besides, values help to find creative and meaningful alternatives and to assess them. Further, they include the forthcoming consequences of the decision. As VFT emphasizes the significant function of values and clarifies the possibilities of their integration into problem solving, we adapt this approach in the current paper.

3.3. The effect of values when solving a problem

In a broader sense, values provide a direction to a person’s life. Whereas the importance of values is relatively stable over time and across situations, Roccas et al. (2017) argue that values differ in their importance to a person. Verplanken and Holland (2002) investigated the relationship between values and choices or behavior. The research revealed that the activation of a value and the centrality of a value to the self, are the essential elements for value-guided behavior. The activation of values could happen in such cases: when values are the primary focus of attention; if the situation or the information a person is confronted with implies values; when the self is activated. The centrality of a particular value is ‘the degree to which an individual has incorporated this value as part of the self’ ( Verplanken & Holland, 2002, p.436 ). Thus, the perceived importance of values and attention to them determine value-guided behavior.

According to Argandoña (2003) , values can change due to external (changing values in the people around, in society, changes in situations, etc.) and internal (internalization by learning) factors affecting the person. The research by Hall and Davis (2007) indicates that the decision-makers’ applied value profile temporarily changed as they analyzed the issue from multiple perspectives and revealed the existence of a broader set of values. The study by Kirkman (2017) reveal that participants noticed the relevance of moral values to situations they encountered in various contexts.

Values are tightly related to personal integrity and identity and guide an individual’s perception, judgment, and behavior ( Halstead, 1996 ; Schwartz, 1992 ). Sheehan and Schmidt (2015) found that values influenced ethical decision-making of accounting study programme students when they uncovered their own values and grounded in them their individual codes of conduct for future jobs. Hence, the effect of values discloses by observing the problem solver’s decision-making. The latter observations could explain the abundance of ethics-laden research in decision-making rather than in problem solving.

Contemporary researchers emphasize the creative potential of values. Dollinger et al. (2007) , Kasof et al. (2007) , Lebedeva, Schwartz, Plucker, & Van De Vijver, 2019 present to some extent similar findings as they all used Schwartz Value Survey (respectively: Schwartz, 1992 ; ( Schwartz, 1994 ), Schwartz, 2012 ). These studies disclosed that such values as self-direction, stimulation and universalism foster creativity. Kasof et al. (2007) focused their research on identified motivation. Stressing that identified motivation is the only fully autonomous type of external motivation, authors define it as ‘the desire to commence an activity as a means to some end that one greatly values’ (p.106). While identified motivation toward specific values (italic in original) fosters the search for outcomes that express those specific values, this research demonstrated that it could also inhibit creative behavior. Thus, inhibition is necessary, especially in the case where reckless creativity could have painful consequences, for example, when an architect creates a beautiful staircase without a handrail. Consequently, creativity needs to be balanced.

Ultimately, values affect human beings’ lives as they express the motivational goals ( Schwartz, 1992 ). These motivational goals are the comprehensive criteria for a person’s choices when solving problems. Whereas some problem solving models only mention values as possible evaluation criteria, but they do not give any significant suggestions when and how the problem solver could think about the values coming to the understanding that his/her values direct the decision how to solve the problem. The authors of this paper claim that the identification of personal values and their choice for a solution need to be specified in the process of problem solving. This position is clearly reflected in humanistic philosophy and psychology ( Maslow, 2011 ; Rogers, 1995 ) that emphasize personal responsibility for discovering personal values through critical questioning, honest self-esteem, self-discovery, and open-mindedness in the constant pursuit of the truth in the path of individual life. However, fundamental (of humankind) and societal values should be taken into account. McLaughlin (1997) argues that a clear boundary between societal and personal values is difficult to set as they are intertwined due to their existence in complex cultural, social, and political contexts at a particular time. A person is related to time and context when choosing values. As a result, a person assumes existing values as implicit knowledge without as much as a consideration. This is particularly evident in the current consumer society.

Moreover, McLaughlin (1997) stresses that if a particular action should be tolerated and legitimated by society, it does not mean that this action is ultimately morally acceptable in all respects. Education has possibilities to reveal this. One such possibility is to turn to the capability approach ( Sen, 1990 ), which emphasizes what people are effectively able to do and to be. Capability, according to Sen (1990) , reflects a person’s freedom to choose between various ways of living, i.e., the focus is on the development of a person’s capability to choose the life he/she has a reason to value. According to Webster (2017) , ‘in order for people to value certain aspects of life, they need to appreciate the reasons and purposes – the whys – for certain valuing’ (italic in original; p.75). As values reflect and foster these whys, education should supplement the development of capability with attention to values ( Saito, 2003 ). In order to attain this possibility, a person has to be aware of and be able to understand two facets of values. Argandoña (2003) defines them as rationality and virtuality . Rationality refers to values as the ideal of conduct and involves the development of a person’s understanding of what values and why he/she should choose them when solving a problem. Virtuality approaches values as virtues and includes learning to enable a person to live according to his/her values. However, according to McLaughlin (1997) , some people may have specific values that are deep or self-evidently essential. These values are based on fundamental beliefs about the nature and purpose of the human being. Other values can be more or less superficial as they are based on giving priority to one or the other. Thus, virtuality highlights the depth of life harmonized to fundamentally rather than superficially laden values. These approaches inform the rationale for the framework of problem solving through values.

4. The 4W framework of problem solving through values

Similar to the above-presented stages of the problem solving processes, the introduced framework by the authors of this paper revisits them (see Fig. 1 ). The framework is titled 4W as its four stages respond to such questions: Analyzing the Problem: W hat ? → Choice of the value(s): W hat is the background for the solution? → Search for the alternative w ays of the solution: How ? → The rationale for problem solution: W hy is this alternative significant ? The stages of this framework cover seven steps that reveal the logical sequence of problem solving through values.

The 4 W framework: problem solving through values.

Though systematic problem solving models are criticized for being linear and inflexible (e.g., Treffinger & Isaksen, 2005 ), the authors of this paper assume a structural view of the problem solving process due to several reasons. First, the framework enables problem solvers to understand the thorough process of problem solving through values. Second, this framework reveals the depth of each stage and step. Third, problem solving through values encourages tackling problems that have crucial consequences. Only by understanding and mastering the coherence of how problems those require a value-based approach need to be addressed, a problem solver will be able to cope with them in the future. Finally, this framework aims at helping to recognize, to underline personal values, to solve problems through thinking about values, and to take responsibility for choices, even value-based. The feedback supports a direct interrelation between stages. It shapes a dynamic process of problem solving through values.

The first stage of problem solving through values - ‘ The analysis of the problem: What? ’- consists of three steps (see Fig. 1 ). The first step is ‘ Recognizing the problematic situation and naming the problem ’. This step is performed in the following sequence. First, the problem solver should perceive the problematic situation he/she faces in order to understand it. Dostál (2015) argues that the problematic situation has the potential to become the problem necessary to be addressed. Although each problem is limited by its context, not every problematic situation turns into a problem. This is related to the problem solver’s capability and the perception of reality: a person may not ‘see’ the problem if his/her capability to perceive it is not developed ( Dorst, 2006 ; Dostál, 2015 ). Second, after the problem solver recognizes the existence of the problematic situation, the problem solver has to identify the presence or absence of the problem itself, i.e. to name the problem. This is especially important in the case of the ill-structured problems since they cannot be directly visible to the problem solver ( Jonassen, 1997 ). Consequently, this step allows to determine whether the problem solver developed or has acquired the capability to perceive the problematic situation and the problem (naming the problem).

The second step is ‘ Analysing the context of the problem as a reason for its rise ’. At this step, the problem solver aims to analyse the context of the problem. The latter is one of the external issues, and it determines the solution ( Jonassen, 2011 ). However, if more attention is paid to the solution of the problem, it diverts attention from the context ( Fields, 2006 ). The problem solver has to take into account both the conveyed and implied contextual elements in the problematic situation ( Dostál, 2015 ). In other words, the problem solver has to examine it through his/her ‘contextual lenses’ ( Hester & MacG, 2017 , p.208). Thus, during this step the problem solver needs to identify the elements that shape the problem - reasons and circumstances that cause the problem, the factors that can be changed, and stakeholders that are involved in the problematic situation. Whereas the elements of the context mentioned above are within the problematic situation, the problem solver can control many of them. Such control can provide unique ways for a solution.

Although the problem solver tries to predict the undesirable results, some criteria remain underestimated. For that reason, it is necessary to highlight values underlying the various possible goals during the analysis ( Fields, 2006 ). According to Hester and MacG (2017) , values express one of the main features of the context and direct the attention of the problem solver to a given problematic situation. Hence, the problem solver should explore the value-based positions that emerge in the context of the problem.

The analysis of these contextual elements focus not only on a specific problematic situation but also on the problem that has emerged. This requires setting boundaries of attention for an in-depth understanding ( Fields, 2006 ; Hester & MacG, 2017 ). Such understanding influences several actions: (a) the recognition of inappropriate aspects of the problematic situation; (b) the emergence of paths in which identified aspects are expected to change. These actions ensure consistency and safeguard against distractions. Thus, the problem solver can now recognize and identify the factors that influence the problem although they are outside of the problematic situation. However, the problem solver possesses no control over them. With the help of such context analysis, the problem solver constructs a thorough understanding of the problem. Moreover, the problem solver becomes ready to look at the problem from different perspectives.

The third step is ‘ Perspectives emerging in the problem ’. Ims and Zsolnai (2009) argue that problem solving usually contains a ‘problematic search’. Such a search is a pragmatic activity as the problem itself induces it. Thus, the problem solver searches for a superficial solution. As a result, the focus is on control over the problem rather than a deeper understanding of the problem itself. The analysis of the problem, especially including value-based approaches, reveals the necessity to consider the problem from a variety of perspectives. Mitroff (2000) builds on Linstone (1989) ideas and claims that a sound foundation of both naming and solving any problem lays in such perspectives: the technical/scientific, the interpersonal/social, the existential, and the systemic (see Table 1 ).

The main characteristics of four perspectives for problem solving

Whereas all problems have significant aspects of each perspective, disregarding one or another may lead to the wrong way of solving the problem. While analysing all four perspectives is essential, this does not mean that they all are equally important. Therefore, it is necessary to justify why one or another perspective is more relevant and significant in a particular case. Such analysis, according to Linstone (1989) , ‘forces us to distinguish how we are looking from what we are looking at’ (p.312; italic in original). Hence, the problem solver broadens the understanding of various perspectives and develops the capability to see the bigger picture ( Hall & Davis, 2007 ).

The problem solver aims to identify and describe four perspectives that have emerged in the problem during this step. In order to identify perspectives, the problem solver search answers to the following questions. First, regarding the technical/scientific perspective: What technical/scientific reasons are brought out in the problem? How and to what extent do they influence a problem and its context? Second, regarding the interpersonal/social perspective: What is the impact of the problem on stakeholders? How does it influence their attitudes, living conditions, interests, needs? Third, regarding the existential perspective: How does the problem affect human feelings, experiences, perception, and/or discovery of meaning? Fourth, regarding the systemic perspective: What is the effect of the problem on the person → community → society → the world? Based on the analysis of this step, the problem solver obtains a comprehensive picture of the problem. The next stage is to choose the value(s) that will address the problem.

The second stage - ‘ The choice of value(s): What is the background for the solution?’ - includes the fourth and the fifth steps. The fourth step is ‘ The identification of value(s) as a base for the solution ’. During this step, the problem solver should activate his/her value(s) making it (them) explicit. In order to do this, the problem solver proceeds several sub-steps. First, the problem solver reflects taking into account the analysis done in previous steps. He/she raises up questions revealing values that lay in the background of this analysis: What values does this analyzed context allow me to notice? What values do different perspectives of the problem ‘offer’? Such questioning is important as values are deeply hidden ( Verplanken & Holland, 2002 ) and they form a bias, which restricts the development of the capability to see from various points of view ( Hall & Paradice, 2007 ). In the 4W framework, this bias is relatively eliminated due to the analysis of the context and exploration of the perspectives of a problem. As a result, the problem solver discovers distinct value-based positions and gets an opportunity to identify the ‘value uncaptured’ ( Yang, Evans, Vladimirova, & Rana, 2017, p.1796 ) within the problem analyzed. The problem solver observes that some values exist in the context (the second step) and the disclosed perspectives (the third step). Some of the identified values do not affect the current situation as they are not required, or their potential is not exploited. Thus, looking through various value-based lenses, the problem solver can identify and discover a congruence between the opportunities offered by the values in the problem’s context, disclosed perspectives and his/her value(s). Consequently, the problem solver decides what values he/she chooses as a basis for the desired solution. Since problems usually call for a list of values, it is important to find out their order of priority. Thus, the last sub-step requires the problem solver to choose between fundamentally and superficially laden values.

In some cases, the problem solver identifies that a set of values (more than one value) can lead to the desired solution. If a person chooses this multiple value-based position, two options emerge. The first option is concerned with the analysis of each value-based position separately (from the fifth to the seventh step). In the second option, a person has to uncover which of his/her chosen values are fundamentally laden and which are superficially chosen, considering the desired outcome in the current situation. Such clarification could act as a strategy where the path for the desired solution is possible going from superficially chosen value(s) to fundamentally laden one. When a basis for the solution is established, the problem solver formulates the goal for the desired solution.

The fifth step is ‘ The formulation of the goal for the solution ’. Problem solving highlights essential points that reveal the structure of a person’s goals; thus, a goal is the core element of problem solving ( Funke, 2014 ). Meantime, values reflect the motivational content of the goals ( Schwartz, 1992 ). The attention on the chosen value not only activates it, but also motivates the problem solver. The motivation directs the formulation of the goal. In such a way, values explicitly become a basis of the goal for the solution. Thus, this step involves the problem solver in formulating the goal for the solution as the desired outcome.

The way how to take into account value(s) when formulating the goal is the integration of value(s) chosen by the problem solver in the formulation of the goal ( Keeney, 1994 ). For this purpose the conjunction of a context for a solution (it is analyzed during the second step) and a direction of preference (the chosen value reveals it) serves for the formulation of the goal (that represents the desired solution). In other words, a value should be directly included into the formulation of the goal. The goal could lose value, if value is not included into the goal formulation and remains only in the context of the goal. Let’s take the actual example concerning COVID-19 situation. Naturally, many countries governments’ preference represents such value as human life (‘it is important of every individual’s life’). Thus, most likely the particular country government’s goal of solving the COVID situation could be to save the lifes of the country people. The named problem is a complex where the goal of its solution is also complex, although it sounds simple. However, if the goal as desired outcome is formulated without the chosen value, this value remains in the context and its meaning becomes tacit. In the case of above presented example - the goal could be formulated ‘to provide hospitals with the necessary equipment and facilities’. Such goal has the value ‘human’s life’ in the context, but eliminates the complexity of the problem that leads to a partial solution of the problem. Thus, this step from the problem solver requires caution when formulating the goal as the desired outcome. For this reason, maintaining value is very important when formulating the goal’s text. To avoid the loss of values and maintain their proposed direction, is necessary to take into account values again when creating alternatives.

The third stage - ‘ Search for the alternative ways for a solution: How? ’ - encompasses the sixth step, which is called ‘ Creation of value-based alternatives ’. Frequently problem solver invokes a traditional view of problem identification, generation of alternatives, and selection of criteria for evaluating findings. Keeney (1994) ; Ims and Zsolnai (2009) criticize this rational approach as it supports a search for a partial solution where an active search for alternatives is neglected. Moreover, a problematic situation, according to Perkins (2009) , can create the illusion of a fully framed problem with some apparent weighting and some variations of choices. In this case, essential and distinct alternatives to the solution frequently become unnoticeable. Therefore, Perkins (2009) suggest to replace the focus on the attempts to comprehend the problem itself. Thinking through the ‘value lenses’ offers such opportunities. The deep understanding of the problem leads to the search for the alternative ways of a solution.

Thus, the aim of this step is for the problem solver to reveal the possible alternative ways for searching a desired solution. Most people think they know how to create alternatives, but often without delving into the situation. First of all, the problem solver based on the reflection of (but not limited to) the analysis of the context and the perspectives of the problem generates a range of alternatives. Some of these alternatives represent anchored thinking as he/she accepts the assumptions implicit in generated alternatives and with too little focus on values.

The chosen value with the formulated goal indicates direction and encourages a broader and more creative search for a solution. Hence, the problem solver should consider some of the initial alternatives that could best support the achievement of the desired solution. Values are the principles for evaluating the desirability of any alternative or outcome ( Keeney, 1994 ). Thus, planned actions should reveal the desirable mode of conduct. After such consideration, he/she should draw up a plan setting out the actions required to implement each of considered alternatives.

Lastly, after a thorough examination of each considered alternative and a plan of its implementation, the problem solver chooses one of them. If the problem solver does not see an appropriate alternative, he/she develops new alternatives. However, the problem solver may notice (and usually does) that more than one alternative can help him/her to achieve the desired solution. In this case, he/she indicates which alternative is the main one and has to be implemented in the first place, and what other alternatives and in what sequence will contribute in searching for the desired solution.

The fourth stage - ‘ The rationale for the solution: Why ’ - leads to the seventh step: ‘ The justification of the chosen alternative ’. Keeney (1994) emphasizes the compatibility of alternatives in question with the values that guide the action. This underlines the importance of justifying the choices a person makes where the focus is on taking responsibility. According to Zsolnai (2008) , responsibility means a choice, i.e., the perceived responsibility essentially determines its choice. Responsible justification allows for discovering optimal balance when choosing between distinct value-based alternatives. It also refers to the alternative solution that best reflects responsibility in a particular value context, choice, and implementation.

At this stage, the problem solver revisits the chosen solution and revises it. The problem solver justifies his/her choice based on the following questions: Why did you choose this? Why is this alternative significant looking from the technical/scientific, the interpersonal/social, the existential, and the systemic perspectives? Could you take full responsibility for the implementation of this alternative? Why? How clearly do envisaged actions reflect the goal of the desired solution? Whatever interests and for what reasons do this alternative satisfies in principle? What else do you see in the chosen alternative?

As mentioned above, each person gives priority to one aspect or another. The problem solver has to provide solid arguments for the justification of the chosen alternative. The quality of arguments, according to Jonassen (2011) , should be judged based on the quality of the evidence supporting the chosen alternative and opposing arguments that can reject solutions. Besides, the pursuit of value-based goals reflects the interests of the individual or collective interests. Therefore, it becomes critical for the problem solver to justify the level of responsibility he/she takes in assessing the chosen alternative. Such a complex evaluation of the chosen alternative ensures the acceptance of an integral rather than unilateral solution, as ‘recognizing that, in the end, people benefit most when they act for the common good’ ( Sternberg, 2012, p.46 ).

5. Discussion

The constant emphasis on thinking about values as explicit reasoning in the 4W framework (especially from the choice of the value(s) to the rationale for problem solution) reflects the pursuit of virtues. Virtues form the features of the character that are related to the choice ( Argandoña, 2003 ; McLaughlin, 2005 ). Hence, the problem solver develops value-grounded problem solving capability as the virtuality instead of employing rationality for problem solving.

Argandoña (2003) suggests that, in order to make a sound valuation process of any action, extrinsic, transcendent, and intrinsic types of motives need to be considered. They cover the respective types of values. The 4W framework meets these requirements. An extrinsic motive as ‘attaining the anticipated or expected satisfaction’ ( Argandoña, 2003, p.17 ) is reflected in the formulation of the goal of the solution, the creation of alternatives and especially in the justification of the chosen alternative way when the problem solver revisits the external effect of his/her possible action. Transcendent motive as ‘generating certain effects in others’ ( Argandoña, 2003, p.17 ) is revealed within the analysis of the context, perspectives, and creating alternatives. When the learner considers the creation of alternatives and revisits the chosen alternative, he/she pays more attention to these motives. Two types of motives mentioned so far are closely related to an intrinsic motive that emphasizes learning development within the problem solver. These motives confirm that problem solving is, in fact, lifelong learning. In light of these findings, the 4W framework is concerned with some features of value internalization as it is ‘a psychological outcome of conscious mind reasoning about values’ ( Yazdani & Akbarilakeh, 2017, p.1 ).

The 4W framework is complicated enough in terms of learning. One issue is concerned with the educational environments ( Jucevičienė, 2008 ) required to enable the 4W framework. First, the learning paradigm, rather than direct instruction, lies at the foundation of such environments. Second, such educational environments include the following dimensions: (1) educational goal; (2) learning capacity of the learners; (3) educational content relevant to the educational goal: ways and means of communicating educational content as information presented in advance (they may be real, people among them, as well as virtual); (5) methods and means of developing educational content in the process of learners’ performance; (6) physical environment relevant to the educational goal and conditions of its implementation as well as different items in the environment; (7) individuals involved in the implementation of the educational goal.

Another issue is related to exercising this framework in practice. Despite being aware of the 4W framework, a person may still not want to practice problem solving through values, since most of the solutions are going to be complicated, or may even be painful. One idea worth looking into is to reveal the extent to which problem solving through values can become a habit of mind. Profound focus on personal values, context analysis, and highlighting various perspectives can involve changes in the problem solver’s habit of mind. The constant practice of problem solving through values could first become ‘the epistemic habit of mind’ ( Mezirow, 2009, p.93 ), which means a personal way of knowing things and how to use that knowledge. This echoes Kirkman (2017) findings. The developed capability to notice moral values in situations that students encountered changed some students’ habit of mind as ‘for having “ruined” things by making it impossible not to attend to values in such situations!’ (the feedback from one student; Kirkman, 2017, p.12 ). However, this is not enough, as only those problems that require a value-based approach are addressed. Inevitably, the problem solver eventually encounters the challenges of nurturing ‘the moral-ethical habit of mind’ ( Mezirow, 2009, p.93 ). In pursuance to develop such habits of mind, the curriculum should include the necessity of the practising of the 4W framework.

Thinking based on values when solving problems enables the problem solver to engage in thoughtful reflection in contrast to pragmatic and superficial thinking supported by the consumer society. Reflection begins from the first stage of the 4W framework. As personal values are the basis for the desired solution, the problem solver is also involved in self-reflection. The conscious and continuous reflection on himself/herself and the problematic situation reinforce each step of the 4W framework. Moreover, the fourth stage (‘The rationale for the solution: Why’) involves the problem solver in critical reflection as it concerned with justification of ‘the why , the reasons for and the consequences of what we do’ (italic, bold in original; Mezirow, 1990, p.8 ). Exercising the 4W framework in practice could foster reflective practice. Empirical evidence shows that reflective practice directly impacts knowledge, skills and may lead to changes in personal belief systems and world views ( Slade, Burnham, Catalana, & Waters, 2019 ). Thus, with the help of reflective practice it is possible to identify in more detail how and to what extent the 4W framework has been mastered, what knowledge gained, capabilities developed, how point of views changed, and what influence the change process.

Critical issues related to the development of problem solving through values need to be distinguished when considering and examining options for the implementation of the 4W framework at educational institutions. First, the question to what extent can the 4W framework be incorporated into various subjects needs to be answered. Researchers could focus on applying the 4W framework to specific subjects in the humanities and social sciences. The case is with STEM subjects. Though value issues of sustainable development and ecology are of great importance, in reality STEM teaching is often restricted to the development of knowledge and skills, leaving aside the thinking about values. The special task of the researchers is to help practitioners to apply the 4W framework in STEM subjects. Considering this, researchers could employ the concept of ‘dialogic space’ ( Wegerif, 2011, p.3 ) which places particular importance of dialogue in the process of education emphasizing both the voices of teachers and students, and materials. In addition, the dimensions of educational environments could be useful aligning the 4W framework with STEM subjects. As STEM teaching is more based on solving various special tasks and/or integrating problem-based learning, the 4W framework could be a meaningful tool through which content is mastered, skills are developed, knowledge is acquired by solving pre-prepared specific tasks. In this case, the 4W framework could act as a mean addressing values in STEM teaching.

Second is the question of how to enable the process of problem solving through values. In the current paper, the concept of enabling is understood as an integral component of the empowerment. Juceviciene et al. (2010) specify that at least two perspectives can be employed to explain empowerment : a) through the power of legitimacy (according to Freire, 1996 ); and b) through the perspective of conditions for the acquisition of the required knowledge, capabilities, and competence, i.e., enabling. In this paper the 4W framework does not entail the issue of legitimacy. This issue may occur, for example, when a teacher in economics is expected to provide students with subject knowledge only, rather than adding tasks that involve problem solving through values. Yet, the issue of legitimacy is often implicit. A widespread phenomenon exists that teaching is limited to certain periods that do not have enough time for problem solving through values. The issue of legitimacy as an organizational task that supports/or not the implementation of the 4W framework in any curriculum is a question that calls for further discussion.

Third (if not the first), the issue of an educator’s competence to apply such a framework needs to be addressed. In order for a teacher to be a successful enabler, he/she should have the necessary competence. This is related to the specific pedagogical knowledge and skills, which are highly dependent on the peculiarities of the subject being taught. Nowadays actualities are encouraging to pay attention to STEM subjects and their teacher training. For researchers and teacher training institutions, who will be interested in implementing the 4W framework in STEM subjects, it would be useful to draw attention to ‘a material-dialogic approach to pedagogy’ ( Hetherington & Wegerif, 2018, p.27 ). This approach creates the conditions for a deep learning of STEM subjects revealing additional opportunities for problem solving through values in teaching. Highlighting these opportunities is a task for further research.

In contrast to traditional problem solving models, the 4W framework is more concerned with educational purposes. The prescriptive approach to teaching ( Thorne, 1994 ) is applied to the 4W framework. This approach focuses on providing guidelines that enable students to make sound decisions by making explicit value judgements. The limitation is that the 4W framework is focused on thinking but not executing. It does not include the fifth stage, which would focus on the execution of the decision how to solve the problem. This stage may contain some deviation from the predefined process of the solution of the problem.

6. Conclusions

The current paper focuses on revealing the essence of the 4W framework, which is based on enabling the problem solver to draw attention to when, how, and why it is essential to think about values during the problem solving process from the perspective of it’s design. Accordingly, the 4W framework advocates the coherent approach when solving a problem by using a creative potential of values.

The 4W framework allows the problem solver to look through the lens of his/her values twice. The first time, while formulating the problem solving goal as the desired outcome. The second time is when the problem solver looks deeper into his/her values while exploring alternative ways to solve problems. The problem solver is encouraged to reason about, find, accept, reject, compare values, and become responsible for the consequences of the choices grounded on his/her values. Thus, the problem solver could benefit from the 4W framework especially when dealing with issues having crucial consequences.

An educational approach reveals that the 4W framework could enable the development of value-grounded problem solving capability. As problem solving encourages the development of higher-order thinking skills, the consistent inclusion of values enriches them.

The 4W framework requires the educational environments for its enablement. The enablement process of problem solving through values could be based on the perspective of conditions for the acquisition of the required knowledge and capability. Continuous practice of this framework not only encourages reflection, but can also contribute to the creation of the epistemic habit of mind. Applying the 4W framework to specific subjects in the humanities and social sciences might face less challenge than STEM ones. The issue of an educator’s competence to apply such a framework is highly important. The discussed issues present significant challenges for researchers and educators. Caring that the curriculum of different courses should foresee problem solving through values, both practicing and empirical research are necessary.

Declaration of interests

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Both authors have approved the final article.

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Six Tips for Successful Interest-Based Problem Solving

Interest-based problem solving (IBPS) is a collaborative approach to solving problems.

Michael Hurley was the education director for the Coalition of Kaiser Permanente Unions for several years, and he and his team designed many of the LMP programs used to support unit-based team education.

1. Know why we use interest-based problem solving

Interest-based problem solving (IBPS) is a collaborative approach to solving problems, a process for negotiating differences amicably without giving in. When you’re in an ongoing partnership—whether it’s a labor-management partnership or, say, a marriage—you likely have multiple objectives you want to satisfy when resolving differences. Those include not only the desire to solve the problem in a way that meets your needs, but also to solve it in a way that doesn’t cost too much (in time, money or emotional wear and tear), and that leaves the relationship intact or even improves it. Because down the road, you know you’re going to be working together again to solve the next problem that crops up.

2. Understand key terms

Four words are at the heart of the interest-based process. The issue is the problem or subject area to be addressed. A position is a proposed solution. The interest is the underlying need, motivation or concern that may have to be addressed in order to reach a solution; you can tell an interest in part because there is usually more than one way to satisfy it. An option is a potential way to address the issue, in whole or in part.

Your position tells us what you want but not necessarily why you want it.

A spouse wants to put 5 percent of income into a retirement savings account.
A parent wants a child in bed by 9:30 on a weeknight.
A union wants a 3 percent across-the-board wage increase in collective bargaining.

Your interests tell us what is important to you.

A spouse wants enough saved to have a comfortable retirement.
A parent wants a child to be well rested for school the next day.
A union rep wants a compensation package for members that aids recruitment and retention.

3. Ask: Is that ‘interest’ really a position?

What do you do when you’ve got a position masquerading as an interest? Usually, you can get to the interests that underlie a position if you listen carefully and ask the right questions. Find out the needs and concerns behind the position. Here’s an example:

Statement by wife: “I hate living in Los Angeles. We should move to Oregon.”

Reaction to self: “Great, here we go again.”

Question to wife: “Why should we move to Oregon?”

Answer: “We’re in a rut. We’ve lived our whole lives here. I’m tired of it.”

Question: “What else appeals to you about Oregon?”

Answers: “The weather is too hot here, and we spend so much time stuck in traffic. We have to do all our exercising here at the gym. Oregon is cooler and there are prettier roads for biking. We can get to the woods and good hiking faster. People are more relaxed there. “

Interests: Change in weather, less traffic, easier access to uncrowded outdoors, less stress.

By starting with a discussion of interests, the parties can talk about what is important to them without staking out what they want the outcome to be. It opens the door to collaborative problem solving, as opposed to competition or compromise.

4. Agree on the information

Find agreement on what data to collect and how to collect it, vet it and report it—or you’ll just argue about the data.

5. Make an action plan

Create an action plan for turning solutions into reality. Be clear on who’s accountable for what. Establish a timeline.

6. Set ground rules

Remember, interest-based processes don’t always work. In my experience, they have the best chance for success if the parties agree to:

Focus on the issue, not personalities.
Share information fully and early.
Listen actively.
Work hard to meet interests, not sell positions.
Be open to options.
Look for ways to build trust.

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109 Hobbies and Interests Examples (for a Resume)

hobbies and interests examples and definition, explained below

Hobbies and interests refer to personal pursuits that are not related to professional work. They’re often requested on a resume as a way to assess your soft skills like teamwork, personal motivation, and community-mindedness.

The hobbies and interests you list need to be honest, but you should also select ones that showcase your personality, character traits, or skills that are not immediately apparent from your professional experience (Bell, 2012).

Interests that include group participation, such as playing team sports or being a part of a group, can demonstrate that you’re a good team player. Similarly, volunteering at a local charity might convey your ethical responsibility.

However, avoid presenting interests that might raise red flags for employers. Polarizing interests – those that could cause controversy or disagreement – or interests that might conflict with the company’s vision (e.g. having a side hustle that competes with the company you’re applying to be part of) might decrease your chances of getting the job.

Hobbies and Interests Examples

Creative hobbies and interests.

Graphic Design: A hobby in graphic design showcases your artistic tendencies and technical skills . It speaks to your ability to visualize concepts aesthetically. This is particularly useful in roles that require creativity and tech-savvy, like UX/UI design or advertising. And fortunately, creativity is a trait that tends to lead to pay rises .
Blogging: This hobby indicates a proficiency in written communication , digital marketing, and SEO. It can also reveal deep knowledge on particular subjects, marking you as an expert. For careers in digital marketing, journalism, or communications, this can be a sterling asset. In fact, effective communication is the most sought-after soft skill by employers
Amateur Astronomy: This interest represents a love for science and learning, pointing to a curious and observant nature. It can showcase your patience and meticulousness in understanding and interpreting details. This can be an appealing characteristic for jobs in education, research, or scientific fields.
Cooking Classes: This hobby signifies a willingness to develop new abilities, as well as a touch of creativity. It shows that you appreciate both the process and the pursuit of an excellent outcome. This can resonate well in careers involving process management, or roles in the hospitality field.
Gardening: A penchant for gardening suggests a patient character, a love for nature, and an ability to nurture and grow things over time. This can indicate responsibility and planning skills. Such attributes can be appealing for jobs in project management, education, or environmental science roles.
Homebrewing Coffee: This reveals a dedication to mastering a craft and an appreciation for details. It suggests process-oriented thinking and high standards for outcomes. Jobs in quality assurance, the food industry, or roles requiring a meticulous nature could value this hobby.
Magic Tricks: Magic as a hobby reveals strong discipline, coordination, and presentation talents. It demonstrates an ability to engage and impress audiences. This can be a unique asset for client-facing roles or careers in entertainment and sales.
Hiking: This displays your love for nature and an appreciation for physical fitness and endurance. It can suggest that you’re personally invested in maintaining health and wellness. Careers in the health and fitness industry, outdoor education, or environmental organisations may find this hobby attractive.
Learning Languages: Actively learning new languages depicts your adaptability and a love for diverse cultures. It also showcases your communication skills and patience. In fields like international business, travel, or translation services, such a hobby can be beneficial. And good news for you: research shows being bilingual can increase your chances of getting a job.
Podcasting: The production or participation in podcasts demonstrates speaking skills, technological aptitude, and confidence. It also suggests an interest in sharing knowledge or opinions. This is a useful hobby for jobs in media, education, public relations, or marketing.
Chess: Playing chess reveals an ability to strategise, anticipate competitors’ moves, and make decisive actions. This can signal a logical, strategic mindset which can be valuable for roles in business strategy, account planning, or software development.
Photography: Photography as a hobby showcases creative talent, attention to detail, and a good eye for aesthetics. It also requires an understanding of technique and equipment. Media, journalism, or creative roles may be particularly suited to someone with this interest.
Bird Watching: This hobby suggests patience, keen observational skills, and a love for nature. It can be seen as a reflective, quiet pursuit indicating a thoughtful nature. Conservation, environment, or research roles may value this hobby.
Origami: Origami showcases manual dexterity, patience, and attention towards intricate details. It reflects appreciation for the traditional arts and a meditative, focused approach. Roles in art, education, design, or therapy may find this interesting.
Archery: Practicing archery exhibits your focus, control, and precision . It reveals your discipline and an ability to aim for specific goals . Roles requiring focus and precision, such as quality control or risk management, may value this hobby.
Stand-up Comedy: Pursuing stand-up comedy speaks to your ability to engage an audience and think quickly. It hints at confidence, a sense of humor, and excellent communication skills. These traits can be beneficial in roles within public relations, customer service, or advertising.
Music Composition: If you enjoy composing music, it discloses your artistic talents and your ability to amalgamate different elements into a harmonious whole. It can denote patience, creativity, memory and focus , and deep understanding of the intricate aspects of music. Careers in the music industry, multimedia production, or creative direction can find this hobby advantageous.
Pottery: Engaging in pottery shows your capability to mold raw materials into beautiful artifacts, demonstrating your creativity and patience. It suggests a hands-on approach and a focus on producing tangible outcomes. Careers involving craftsmanship, design, and teaching arts can appreciate the skills associated with this hobby.
Calligraphy: Calligraphy can highlight your precision, patience, and admiration for aesthetic beauty. The practice demonstrates a dedication to mastering a meticulous and traditional craft, suggesting a detail-oriented character. Jobs in design, event planning, or jobs that require handwritten presentations may value this hobby.

Sporting Hobbies and Interests

Running: Choosing running as a hobby suggests discipline, commitment, and the enjoyment of personal challenge. It can reflect a goal-oriented mindset and, since running is also a solitary activity, it can imply an independent and self-motivated personality. Suitable for roles requiring focus, resilience, and individual motivation.
Yoga: Practicing yoga regularly indicates a dedication to personal well-being, patience, and control. It can also signal a preference for a balanced lifestyle and suggest a calm and focused temperament. People who do yoga also have heightened mental clarity . Useful for roles that demand patience, flexibility, and balance.
Hiking: Hiking as a hobby points to a love for nature, and often links to determination and adventurousness. It also shows a commitment to physical fitness and resilience. Particularly relevant for roles requiring physical endurance and a strong connection with the outdoors.
Tennis: Playing tennis portrays a love for strategic sports, as well as agility, speed, and hand-eye coordination. It could indicate that you thrive within a challenging, rapidly evolving environment. Suitable for roles that require quick decision-making and strategic planning.
Swimming: Regular swimming indicates stamina, discipline, and a love for solo sports. It can highlight your ability to continuously improve and push your limits. Relevant in roles where persistence and self-motivation are key.
Rock Climbing: This hobby shows daring, strength, and a desire for personal accomplishment. It can showcase your ability to face and overcome fears, highlighting determination and problem-solving skills . Rock climbing can be a valuable hobby for high-risk management or problem-solving roles.
Cycling: For those deeply into cycling, it can demonstrate a love for speed and endurance sports. It may signal a strong competitive streak, with a side of environmental consciousness. Useful in roles that require endurance, commitment, or eco-friendly awareness.
Badminton: Playing badminton regularly suggests agility, hand-eye coordination, and strategic thinking. It is a fast-paced, competitive sport that can be both singles and doubles, indicating you are comfortable both in teamwork and individual competition. Applicable to roles requiring strategic thinking , agility, and teamwork.
Chess Boxing: This unique sport combines the mental challenge of chess with the physical demands of boxing. It implies resilience, strategic planning, and adaptability skills . Useful for jobs involving high-pressure decision making and strategic assessment.
Martial Arts: Practicing martial arts depicts discipline, resilience, and respect for tradition. It shows that you can focus on long-term goals and respect others’ boundaries. Relevant for roles requiring discipline, respect, and self-defense knowledge.
Sailing: This hobby shows a love for water sports, along with navigational and survival skills. It exhibits decision-making skills under unpredictable circumstances. Noteworthy for roles that involve navigating complex situations and strategic thinking.
Rowing: Rowing displays physical strength, endurance, and a preference for group sports. It is a demanding sport that requires synchronization and fluid cooperation. Especially relevant in roles requiring teamwork, strength, and cooperative skills .
Archery: Practicing archery implies precision, focus, and consistency. It suggests you have an eye for detail and steady hands. Suitable for attention-to-detail roles or positions requiring steady hand-eye coordination.
Soccer: Playing soccer indicates teamwork, coordination, and strategic abilities. It shows your competitive spirit and your ability to work within a diverse group. This is especially relevant for roles requiring team coordination and strategic planning. Furthermore, research shows sports like soccer can increase brain health !
Skiing: Skiing suggests a sense of adventure and outdoor sports passion. It can imply risk management skills and physical fitness. Especially relevant for travel, tourism, or fitness-related roles.
Gymnastics: Engaging in gymnastics points to physical fitness, flexibility, and discipline. It can show your dedication to mastering complex routines. Useful in roles that value precision, agility, and performance under pressure.
Polo: Playing polo can highlight team spirit, coordination, and a love for traditional sports. As it is considered a luxury sport, it also signals interest in high-society community. Particular suitable for roles in luxury goods marketing, social interaction, or team-coordination fields.
Kickboxing: Regular kickboxing indicates high energy, discipline, and self-defense skills. It reflects a resilient spirit and readiness to compete. Suitable for roles requiring high energy, self-defense knowledge, and resilience.
Volleyball: Playing volleyball shows a dedication to team sports. It suggests quick reflexes, strategic skills, and an ability to collaborate. Especially relevant for roles that demand teamwork and quick decision-making under pressure.

Team Hobbies and Interests

Team Sports (e.g., basketball): Playing team sports signals working well with others, leadership skills , and competitive spirit. It demonstrates your ability to collaborate effectively towards a common goal, and can show that you thrive in a dynamic, fast-paced environment. Particularly noteworthy for roles requiring teamwork, quick thinking, and adaptability.
Drama Club: Being part of a drama club underscores your ability to collaborate, communicate, and react adaptively in performing a role. It also exhibits your creativity and presentation skills. Useful for roles involving communication, creativity, or public relations.
Orchestra or Band: Playing in an orchestra or band showcases your talent, dedication, and ability to synchronize with others. It suggests an understanding of harmony and team dynamics. Good for roles that involve teamwork and creative expression.
Debate Team: Engaging in a debate team shows your ability to present arguments convincingly and process information quickly. It demonstrates strong teamwork, analytical, and public speaking skills. Especially relevant for roles in public relations, law, or policy-making.
Relay Races: Participating in relay races reveals your speed, endurance, and teamwork skills. It also demonstrates your pass-the-baton mindset – the ability to trust team members and work cooperatively. Suitable for roles requiring teamwork, coordination, and endurance.
Volunteering Group: Active involvement in community volunteering groups displays your commitment to social issues and teamwork skills. It showcases your empathy, responsibility, and management skills. It is relevant for roles in social services, healthcare, or community development. Furthermore, research shows that volunteering and community involvement can increase your chances of employment by 27%.
Quiz Team: Being part of a quiz team exhibits your general knowledge, your ability to think quickly, and work effectively under pressure. It also reflects your ability to collaborate proficiently in a group. Applicable to jobs requiring fast thinking, information recall, and team participation.
Dance Troupe: Participating in a dance troupe illustrates your appreciation for arts and performance and the ability to work in sync with others. It showcases your expressiveness, teamwork, and dedication. Useful for roles requiring creativity, coordination, or teamwork.
Rowing Crew: Being in a rowing crew demands physical strength, endurance, and excellent teamwork. It’s a symbol of your perseverance, synchronization, and cooperative skills. Particularly relevant for roles that require teamwork, discipline, and physical fitness.
Chess Club: Partaking in a chess club can demonstrate your strategical thinking, patience, and ability to work in a group. It shows your enthusiasm for intellectual stimulation and competition. Suitable for roles requiring strategic planning, problem-solving, and logical thinking.
Book Club: Active participation in a book club displays your love for reading, discussing ideas, and respecting diverse viewpoints. It also suggests good listening and analytical skills – plus, it relieves stress . Particularly useful for roles in literature, education, or discussion moderator.
Film-Making Group: Being a member of a film-making group underscores your ability to work as part of a multifaceted team. It also showcases your creativeness and understanding of storytelling. Apt for roles in the arts, digital media, or storytelling fields.
Chorale Group: Singing in a chorale group evidences your musical appreciation, vocal skills, and team cooperation. It showcases your capacity to harmonize your part with others’. Suitable for jobs in the music industry, volunteering, or team-based roles.
Tech Club: Being part of a tech-oriented club, like a robotics team or coding club, shows your ability to collaborate on technical projects. It denotes strong problem-solving skills and a passion for technology. Particularly relevant for technological, engineering, and educational roles.
Competitive Gaming Team: Involvement in a competitive gaming team reveals your strategic thinking, teamwork, and adaptability in dynamic environments. It reflects your capability to coordinate with others in high pressure, fast-paced scenarios. Applicable for roles that involve quick decision-making, teamwork, and digital technology.
Environmental Conservation Group: Participation in an environmental conservation group shows your commitment to nature preservation and effective teamwork. It illustrates a strong sense of responsibility and eco-consciousness. Suitable for roles in environmental science, outdoor education, or community outreach.
Innovation Lab: Active involvement in an innovation lab highlights your teamwork and problem-solving skills in an innovative setting. It indicates your inventive thinking and collaborative nature. Relevant for design, engineering, or creative problem-solving roles.
DIY Crafting Club: Being part of a DIY crafting club indicates your creativity, patience, and attention to detail. It underscores your enjoyment of hands-on work and collaborative projects. Good for roles requiring creativity, precision, or craft-based abilities.

Read Also: Strong Personal Attributes to List on your Resume

Unique Hobbies and Interests for a Resume

Storm Chasing: This unique hobby demonstrates your adventurous spirit and interest in meteorology. It implies a somewhat daring nature and an appetite for hands-on learning about extreme weather phenomena.
Beekeeping: Beekeeping showcases your patience, commitment, and a fascination for the natural world. It also reflects a concern for environmental issues and ecosystem balance.
Falconry: Practicing falconry indicates a close connection with wildlife and an understanding of animal psychology. This hobby suggests a sense of adventure and an unconventional interest.
Underwater Hockey: Playing underwater hockey highlights your love for unique sports. It combines swimming skills, teamwork, and strategic game playing all in one.
Bonsai Cultivation: Cultivating bonsai plants requires patience, precision, and a deep respect for nature. It can be seen as artistic and therapeutic, reflecting a meticulous and patient character.
Capoeira: Engaging in this Brazilian martial art that combines elements of dance, acrobatics, and music suggests a love for cultural exploration, physical fitness, and artistry.
Ice Sculpting: Creating sculptures out of ice shows your artistic skills, resilience, and ability to work under challenging conditions. This unique hobby can reflect a high level of creativity and patience.
Parkour: Engaging in parkour – the intense art of traversing obstacles swiftly and fluently – suggests that you’re physically fit, agile, and adventurous. It’s indicative of an active, risk-taking personality.
Astro-Photography: This hobby indicates a fascination with the universe and a dedication to capturing its beauty. It demonstrates endurance, patience, and technical abilities.
Ghost Hunting: This unusual interest shows your adventurousness, curiosity about supernatural phenomena, and perhaps a passion for solving mysteries.
Acrobatics: Engaging in acrobatics reveals physical strength, flexibility, discipline, and daring. It can be indicative of a dynamic, performance-oriented character.
Competitive Eating: Participation in this hobby suggests your competitive nature and possibly an unusual culinary fervor. It can reflect a keen spirit of competition and tolerance for physical discomfort.
Sand Sculpting: Building sand sculptures shows a creative spirit, patience, and a unique way of expressing artistry. This suggests meticulousness and a playful attitude towards art.
Aerial Silks: This form of aerial acrobatics showcases physical strength, control, and a love for high-flying artistry. It indicates fearlessness, discipline, and a readiness to see the world from a different perspective.
LARPing (Live Action Role Playing): This hobby points to your creativity, teamwork, and love for fictional narratives. LARPing requires imagination, quick thinking, and adaptability.
Puppetry: Creating and animating puppets requires creativity, craftsmanship, and performance abilities. It suggests a love for storytelling and theatrical flair.
Cryptozoology: Having an interest in cryptozoology – the search for and study of creatures whose existence or survival is disputed, such as Bigfoot or the Loch Ness Monster – shows your fascination with mysteries and untapped areas of science.
Fencing: Engaging in fencing shows a love for traditional sports, discipline, and precision. It can indicate quick reflexes, strategic thinking, and an appreciation for the arts of dueling.
Pyrography: Practicing pyrography – the art of decorating wood or other materials with burn marks – demonstrates your artistic inclination, patience, and a unique take on craft making.
Skydiving: Going for skydiving displays your adventurous spirit, thrill-seeking tendency, and physical fitness. This high-adrenaline hobby can reflect a love for the exhilarating and extraordinary.

Analytical Hobbies and Interests

Chess: Playing chess indicates your analytical, strategic thinking and foresight. It shows your capability to anticipate opponents’ moves and adapt to changing scenarios, making it excellent for strategic planning or problem-solving roles.
Sudoku: Solving Sudoku puzzles displays your application of logic, pattern recognition, and decision-making skills. It suggests your enjoyment of challenging your brain and concentrating on complex tasks.
Programming: Engaging in programming showcases your problem-solving, logical thinking, and technical skills. It’s also indicative of your enthusiasm for creating systems or finding solutions to technical issues.
Data Analysis : Pursuing data analysis as a hobby reveals your ability to make sense of complex information. It can highlight your attention to detail, logical thinking, and quantitative skills.
Reading Scientific Journals: This interest demonstrates your love for learning, reading comprehension, and ability to understand complex scientific reports. It could be essential for roles in research, science, or academia.
Cryptozoology: The study of creatures whose existence is disputed, like Bigfoot or the Loch Ness Monster, shows your curiosity and willingness to question established beliefs. It can suggest a meticulous nature and strong research skills.
Philosophical Debates: Participating in philosophical debates exhibits your logical thinking, open-mindedness, and verbal communication skills . It reflects an appreciation for deep thought and analytical discussions.
Cryptography: Decrypting codes or cryptograms evidences your love for solving complex problems and applying logical reasoning. It might suggest capabilities in mathematics, computer science, or security.
Economic Forecasting: Forecasting economic trends as a hobby indicates your understanding of the economic landscape, analytical prowess, and predictive abilities. Valuable for roles in finance, economics, or market research.
Astronomy: Hobbyist astronomy showcases your observation skills, understanding of scientific principles, and patience. This pursuit is relevant for roles in research, analysis, or academia.
Birdwatching: Observing and identifying different bird species demonstrates your patience, attention to detail, and data recording. It may suggest a meticulous and patient personality with a keen eye for detail.
Genealogy: Tracing and studying family lineages highlights your interest in history and detailed research. This shows a capacity to analyze relationships and trends over time.
Bridge: Playing Bridge – a complex card game – requires strategic thinking, problem-solving, and cooperation. It showcases your analytical skills and ability to work within a team.
Model Building: Engaging in model building – from model trains to miniature figurines – requires detailed work, patience, and a systematic approach. It suggests precision, concentration, and an eye for accuracy.
DIY Electronics: Building electronic devices, like radios or robots, highlights your technical understanding and troubleshooting skills. It shows a systematic and practical approach, together with problem-solving abilities.
Numismatics: The collection and study of coins and currencies can show your attention to detail and research skills. This hobby can indicate your analytical capabilities, patience, and interest in financial history.

Technical Hobbies and Interests

Coding: Participating in coding projects showcases your problem-solving abilities, along with your technical acumen. It also suggests an interest in technology development and programming languages. This hobby suits roles in IT, software development, and data analysis.
Robotics: Building or programming robots demonstrates your skills in applying engineering and coding concepts. It exhibits your technical knowledge and uptake of futuristic technologies. This can be valuable for careers in robotics, engineering, or tech education.
Computer Building: Building computers from scratch demonstrates your understanding of hardware and your problem-solving skills. It exhibits your specialized technical knowledge and hands-on skills. Helpful for roles in IT support, hardware engineering, or tech consulting.
Web Development: Creating websites showcases your coding abilities, design sensibilities, and understanding of user experience. It’s an embodiment of technical and creative skills, highlighting your versatility. Particularly useful for roles in IT, digital marketing, and web design.
Amateur Radio Operation: Operating a ham radio indicates your mastery of specific technological tools and your ability to communicate effectively. It shows your technical proficiency and adherence to regulations. Applicable to roles in telecommunications, signal operating, or electronics.
Photography & Photo Editing: Engaging in photography and mastering photo editing software shows your operational knowledge of technical equipment and software. It indicates your eye for detail and appreciation for aesthetics. Suitable for digital media, graphic design, and communication roles.
Software Beta Testing: Beta testing new software applications highlights your strong understanding of user interface, debugging, and programming. It excels at exposing anomalies and faults , refining your detail orientation. Relevant for software development, product management, and user experience roles.
Video Production: Creating and editing videos shows your technical skills in operating video equipment and editing software. It depicts a blend of creativity and technical expertise. This hobby is useful for careers in media production, cinematography, or digital marketing.
Advanced Excel: Mastering and utilizing advanced Excel functionalities highlights your data processing, financial reporting, or problem-solving competence. It exposes your strong analytical prowess. Particularly relevant for roles in finance, business analysis, or data management.
Game Development: Developing video games illustrates your skills in coding, design, and storytelling. It reflects your understanding of game mechanics and creativity. Valuable for roles in game design, software development, and graphic design.
Home Networking: Building and managing home networks underscores your abilities in network configuration and management. It shows your understanding of network principles and troubleshooting. Relevant for networking, IT support, and systems administration roles.
Linux Administration: Proficiency in using the Linux operating system indicates strong technical skills and versatility. It demonstrates your open-source software knowledge. Highly beneficial for roles in IT, systems administration, and software development.
Building Drones: Constructing drones displays your understanding of aerodynamics, electronics, and often coding. It exhibits your ability to handle complex, multidimensional projects. Useful for roles in engineering, avionics, or technology education.
3D Printing: Creating 3D printed objects shows your grasp of 3D modeling software and understanding of design principles. It showcases your innovative spirit and practical application of advanced technology. Adequate for roles in product development, manufacturing, or design.
Data Analysis: Data analysis as a hobby underscores your comfort with large amounts of information and your analytical skills. It reflects your logical thinking and precision. Particularly applicable for roles in data science, market research, and strategic planning.
Cryptocurrency Trading: Trading cryptocurrencies shows your understanding of blockchain technology and your risk assessment skills. It demonstrates your up-to-date knowledge of digital finance trends. Appreciated in finance, business, or IT roles.
Machine Learning Projects: Engaging in machine learning projects depicts your grasp of complex programming constructs and algorithms. It reflects your foresight in next-generation technology applications. Relevant for AI development, data science, or technology consulting roles.

Incorporating the right hobbies and interests in your resumes should be considered a strategic move. You need to keep them associated with the job you’re applying for, portray a multi-faceted personality, and avoid potentially divisive hobbies. Above all, remain genuine and honest about the hobbies and interests you list. Assessors appreciate humility and honesty, and it’s always easier to discuss something you genuinely enjoy in an interview rather than a fabricated interest.

References and Further Reading

Clay, D. (2018) How to Write the Perfect Resume. Independently Published.

Littleford, D., Halstead, J., & Mulraine, C. (2017). Career skills: opening doors into the job market . Bloomsbury Publishing.

Sher, B. (2006). Refuse to Choose!: Use All of Your Interests, Passions, and Hobbies to Create the Life and Career of Your Dreams . Rodale Books.

Timotheou, S., Fitzgerald, C., & Dahlitz, R. (2014). Resume writing: Stand out from the crowd. Australian and New Zealand Grapegrower and Winemaker , (609), 106-107.

Wallwork, A. (2019). English for academic CVs, resumes, and online profiles . Springer.

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6.2.1: Compound Interest (Exercises)

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Simple Interest Problems

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