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Word Problems Explained For Elementary School Parents & Teachers
Sophie Bartlett
Solving word problems in elementary school is an essential part of the math curriculum. Here are over 30 math word problems to practice with children, plus expert guidance on how to solve them.
This blog is part of our series of blogs designed for teachers, schools and parents supporting home learning .
What is a word problem?
A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a ‘real-life’ scenario.
This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem.
For example:
Isn’t brilliant arithmetic enough?
In short, no. Students need to build good reading comprehension, even in math. Overtime math problems become increasingly complex and require students to possess deep conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
As students progress through their mathematical education, they will need to be able to apply mathematical reasoning and develop mathematical arguments and proofs using math language. They will also need to be dynamic, applying their math knowledge to a variety of increasingly sophisticated problems.
To support this schools are adopting a ‘mastery’ approach to math
“Teaching for mastery”, is defined with theses component:
- Math teaching for mastery rejects the idea that a large proportion of people ‘just can’t do math’.
- All students are encouraged by the belief that by working hard at math they can succeed.
- Procedural fluency and conceptual understanding are developed in tandem because each supports the development of the other.
- Significant time is spent developing deep knowledge of the key ideas that are needed to support future learning. The structure and connections within the mathematics are emphasized, so that students develop deep learning that can be sustained.
(The Essence of Maths Teaching for Mastery, 2016)
Mastery helps children to explore math in greater depth
Fluency in arithmetic is important; however, with this often lies the common misconception that once a child has learned the number skills appropriate to their grade level/age, they should be progressed to the next grade level/age of number skills.
The mastery approach encourages exploring the breadth and depth of these math concepts (once fluency is secure) through reasoning and problem solving.
How to teach children to solve word problems?
Here are two simple strategies that can be applied to many word problems before solving them.
- What do you already know?
- How can this problem be drawn/represented pictorially?
Let’s see how this can be applied to word problems to help achieve the answer.
Solving a simple word problem
There are 28 students in a class.
The teacher has 8 liters of orange juice.
She pours 225 milliliters of orange juice for every student.
How much orange juice is left over?
1. What do you already know?
- There are 1,000ml in 1 liter
- Pours = liquid leaving the bottle = subtraction
- For every = multiply
- Left over = requires subtraction at some point
2. How can this problem be drawn/represented pictorially?
The bar model , also known as strip diagram , is always a great way of representing problems. However, if you are not familiar with this, there are always other ways of drawing it out.
Read more: What is a bar model
For example, for this question, you could draw 28 students (or stick man x 28) with ‘225 ml’ above each one and then a half-empty bottle with ‘8 liters’ marked at the top.
Now to put the math to work. This is a 5th grade multi-step problem, so we need to use what we already know and what we’ve drawn to break down the steps.
Solving a more complex, mixed word problem
Mara is in a bookshop.
She buys one book for $6.99 and another that costs $3.40 more than the first book.
She pays using a $20 bill.
What change does Mara get? (What is the remainder?)
- More than = add
- Using decimals means I will have to line up the decimal points correctly in calculations
- Change from money = subtract
See this example of bar modelling for this question:
Now to put the math to work using what we already know and what we’ve drawn to break down the steps.
Mara is in a bookshop.
She buys one book for $6.99 and another that costs $3.40 more than the first book. 1) $6.99 + ($6.99 + $3.40) = $17.38
What change does Mara get? 2) $20 – $17.38 = $2.62
Math Word Problems For Kindergarten to Grade 5
The more children learn about math as they go through elementary school, the trickier the word problems they face will become.
Below you will find some information about the types of word problems your child will be coming up against on a year by year basis, and how word problems apply to each elementary grade.
Word problems in kindergarten
Throughout kindergarten a child is likely to be introduced to word problems with the help of concrete resources (manipulatives, such as pieces of physical apparatus like coins, cards, counters or number lines) to help them understand the problem.
An example of a word problem for kindergarten would be
Chris has 3 red bounce balls and 2 green bounce balls. How many bounce balls does Chris have in all?
Word problems 1st grade
First grade is a continuation of kindergarten when it comes to word problems, with children still using concrete resources to help them understand and visualize the problems they are working on
An example of a word problem for first grade would be:
A class of 10 children each have 5 pencils in their pencil cases. How many pencils are there in total?
Word problems in 2nd grade
In second grade, children will move away from using concrete resources when solving word problems, and move towards using written methods. Teachers will begin to demonstrate the adding and subtracting within 100, adding up to 4- two-digit numbers at a time.
This is also the year in which 2-step word problems will be introduced. This is a problem which requires two individual calculations to be completed.
Second grade word problem: Geometry properties of shape
Shaun is making shapes out of plastic straws.
At the vertices where the straws meet, he uses blobs of modeling clay to fix them together
Here are some of the shapes he makes:
One of Sean’s shapes is a triangle. Which is it? Explain your answer.
Answer: shape B as a triangle has 3 sides (straws) and 3 vertices, or angles (clay)
Second grade word problem: Statistics
2nd grade is collecting pebbles. This pictogram shows the different numbers of pebbles each group finds.
Word problems in 3rd grade
At this stage of their elementary school career, children should feel confident using the written method for addition and subtraction. They will begin multiplying and dividing within 100.
This year children will be presented with a variety of problems, including 2-step problems and be expected to work out the appropriate method required to solve each one.
3rd grade word problem: Number and place value
My number has four digits and has a 7 in the hundreds place.
The digit which has the highest value in my number is 2.
The digit which has the lowest value in my number is 6.
My number has 3 fewer tens than hundreds.
What is my number?
Answer: 2,746
Word problems in 4th grade
One and two-step word problems continue in fourth grade, but this is also the year that children will be introduced to word problems containing decimals.
Fourth grade word problem: Fractions and decimals
Stan, Frank and John are washing their cars outside their houses.
Stan has washed 0.5 of his car.
Frank has washed 1/5 of his car.
Norm has washed 2/5 of his car.
Who has washed the most?
Explain your answer.
Answer: Stan (he has washed 0.5 whereas Frank has only washed 0.2 and Norm 0.4)
Word problems in 5th grade
In fifth grade children move on from 2-step word problems to multi-step word problems . These will include fractions and decimals.
Here are some examples of the types of math word problems in fifth grade will have to solve.
5th grade word problem – Ratio and proportion
The Angel of the North is a large statue in England. It is 20 meters tall and 54 meters wide.
Ally makes a scale model of the Angel of the North. Her model is 40 centimeters tall. How wide is her model?
Answer: 108cm
Fifth grade word problem – Algebra
Amina is making designs with two different shapes.
She gives each shape a value.
Calculate the value of each shape.
Answer: 36 (hexagon) and 25.
Fifth grade word problem: Measurement
Answer: 1.7 liters or 1,700ml
Topic based word problems
The following examples give you an idea of the kinds of math word problems your child will encounter in elementary school
Place value word problem fourth grade
This machine subtracts one hundredth each time the button is pressed. The starting number is 8.43. What number will the machine show if the button is pressed six times? Answer: 8.37
Download free number and place value word problems for grades 2, 3, 4 and 5
Addition and subtraction word problem grade 2
Sam has 64 sweets. He gets given 12 more. He then gives 22 away. How many sweets is he left with? Answer: 54
Download free addition and subtraction word problems for for grades 2, 3, 4 and 5
Addition word problem grade 2
Sammy thinks of a number. He subtracts 70. His new number is 12. What was the number Sammy thought of? Answer: 82
Subtraction word problem fifth grade
The temperature at 7pm was 4oC. By midnight, it had dropped by 9 degrees. What was the temperature at midnight? Answer: -5oC
Multiplication word problem third grade
Eggs are sold in boxes of 12. The egg boxes are delivered to stores in crates. Each crate holds 9 boxes. How many eggs are in a crate? Answer: 108
Download free multiplication word problems for grades 2, 3, 4 and 5.
Division word problem fifth grade
A factory produces 3,572 paint brushes every day. They are packaged into boxes of 19. How many boxes does the factory produce every day? Answer: 188
Download free division word problems for grades 2, 3, 4 and 5.
Free resource: Use these four operations word problems to practice addition, subtraction, multiplication and division all together.
Fraction word problem fourth grade
At the end of every day, a chocolate factory has 1 and 2/6 boxes of chocolates left over. How many boxes of chocolates are left over by the end of a week? Answer: 9 and 2/6 or 9 and 1/3
Download free fractions and decimals word problems for grades 2, 3, 4 and 5.
Money word problem second grade
Lucy and Noor found some money on the playground at recess. Lucy found 2 dimes and 1 penny, and Noor found 2 quarters and a dime. How many cents did Lucy and Noor find? Answer: Lucy = $0.21, Noor = $0.60; $0.21 + $0.61 = $0.81
Area word problem 3rd grade
A rectangle measures 6cm by 5cm.
What is its area? Answer: 30cm2
Perimeter word problem 3rd grade
The swimming pool at the Sunshine Inn hotel is 20m long and 7m wide. Mary swims around the edge of the pool twice. How many meters has she swum? Answer: 108m
Ratio word problem 5th grade (crossover with measurement)
A local council has spent the day painting double yellow lines. They use 1 pot of yellow paint for every 100m of road they paint. How many pots of paint will they need to paint a 2km stretch of road? Answer: 20 pots
PEMDAS word problem fifth grade
Draw a pair of parentheses in one of these calculations so that they make two different answers. What are the answers?
50 – 10 × 5 =
Volume word problem fifth grade
This large cuboid has been made by stacking shipping containers on a boat. Each individual shipping container has a length of 6m, a width of 4m and a height of 3m. What is the volume of the large cuboid? Answer: 864m3
Remember: The word problems can change but the math won’t
It can be easy for children to get overwhelmed when they first come across word problems, but it is important that you remind them that while the context of the problem may be presented in a different way, the math behind it remains the same.
Word problems are a good way to bring math into the real world and make math more relevant for your child. So help them practice, or even ask them to turn the tables and make up some word problems for you to solve.
Do you have students who need extra support in math? Give your fourth and fifth grade students more opportunities to consolidate learning and practice skills through personalized elementary math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Programs are available for fourth grade and fifth grade , and you can try 6 lessons absolutely free .
Individual packs for Kindergarten to Grade 5 containing fun math games and activities to complete independently or with a partner.
The activities are designed to be fun, flexible and suitable for a range of abilities.
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Addition and Subtraction Word Problems- Year 1- DIFFERENTIATED
Subject: Mathematics
Age range: 5-7
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Last updated
22 February 2018
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What is a word problem?
A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Word problems are seen as a crucial part of learning in the primary curriculum, because they require children to apply their knowledge of various different concepts to 'real-life' scenarios.
Word problems also help children to familiarise themselves with mathematical language (vocabulary like fewer, altogether, difference, more, share, multiply, subtract, equal, reduced, etc.).
Teachers tend to try and include word problems in their maths lessons at least twice a week.
What is RUCSAC?
In the classroom children might be taught the acronym RUCSAC (Read, Understand, Choose, Solve, Answer, Check) to help them complete word problems.
By following the acronym step by step children learn to apply a structured, analytical strategy to their calculations. They will need to understand what the problem is asking them to find out by reading the question carefully, choosing the correct mathematical operation to help them solve the query and finally checking their answer by using the inverse operation .
Word problem examples for Years 1 to 6
The following are example word problems that apply to each primary year group.
In Year 1 a child would usually been given apparatus to help them with a problem (counters, plastic coins, number cards, number lines or picture cards).
Sarah wants to buy a teddy bear costing 30p. How many 10p coins will she need?
Brian has 3 sweets. Tom has double this number of sweets. How many sweets does Tom have?
In Year 2, children continue to use apparatus to help them with problem-solving.
Faye has 12 marbles. Her friend Louise has 9 marbles. How many marbles do they both have altogether?
Three children are each given 5 teddy bears. How many teddy bears do they have altogether?
In Year 3, some children may use apparatus, but on the whole children will tend to work out word problems without physical aids. Teachers will usually demonstrate written methods for the four operations (addition, subtraction, multiplication and division) to support children in their working out of the problems.
A jumper costs £23. How much will 4 jumpers cost?
Sarah has 24 balloons. She gives a quarter of them away to her friend. How many balloons does she give away?
Children will also start to do two-step problems in Year 3. This is a problem where finding the answer requires two separate calculations, for example:
I have £34. I am given another £26. I divide this money equally into four different bank accounts. How much money do I put in each bank account?
- In this case, the first step would be to add £34 and £26 to make £60.
- The second step would be to divide £60 by 4 to make £15.
Children should feel confident in an efficient written method for each operation at this stage. They will continue to be given a variety of problems and have to work out which operation and method is appropriate for each. They will also be given two-step problems.
I have 98 marbles. I share them equally between 6 friends. How many marbles does each friend get? How many marbles are left over?
Children will continue to do one-step and two-step problems. They will start to carry out problem-solving involving decimals .
My chest of drawers is 80cm wide and my table is 1.3m wide. How much wall space do they take up when put side by side?
There are 24 floors of a car park. Each floor has room for 45 cars. How many cars can the car park fit altogether?
In Year 6 children solve 'multi-step problems' and problems involving fractions , decimals and percentages .
Sarah sees the same jumper in two different sales: In the first sale, the original price of the jumper is £36.15, but has been reduced by a third. In the second sale, the jumper was priced at £45, but now has 40% off. How much does each jumper cost and which one is the cheapest?
In the past, calculators were sometimes used for solving two-step problems like the one above, but the new curriculum does not include the use of calculators at any time during primary school.
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Looking for more mastery resources? Check out our collection of KS1 mastery maths materials. What are the benefits of solving Maths problems? There are as many
Make maths fun with these addition word problems! Great for group activities, whole-class teaching or guided teaching rotations.
This video is aimed at Year 1, and introduces the topic of word ... words in a word problem and suggests different ways they can solve word
In this video, Twinkl Teacher Izzy, shows how to use these addition and subtraction word problem activities with Year 2 children.
Solving word problems in elementary school is an essential part of math. Here are over 30 math word problems to practice with children.
Word Problems using a numberline 2 (Joanne Robson) MS Powerpoint; Red Clowns Problem Solving (Dot Hullah) ActivStudio; Problem Solving Steps (Ali McNamara)
Children can cut and stick each question into their books and work it out underneath! NC Guidance: "They discuss and solve problems in familiar practical
Year 1 children will focus on solving one step problems, whilst year 2 children can practise some 2 step problems. Year 1. Addition Word
In Year 2, children continue to use apparatus to help them with problem-solving. Faye has 12 marbles. Her friend Louise has 9 marbles. How many marbles do they
This feature details how NRICH can help you embed a problem-solving approach in your ... Tasks for KS1 children which focus on working systematically.