problem solving maths questions year 2

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Year 2 Maths Worksheets UK Hub Page

Welcome to Math Salamanders Year 2 Maths Worksheets hub page.

In our Year 2 area, you will find a wide range of printable math worksheets and Maths activities for your child to enjoy.

Come and take a look at our dot-to-dot pages, or our maths games. Perhaps you would prefer our 2d shape worksheets, or learning about numbers using our number line worksheets?

Hopefully you will find something here to meet your child's maths requirements!

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• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Year 2 Maths Learning

Here are some of the key learning objectives for the end of Year 2:

• know and use Place value up to 100
• Compare and order numbers up to 100
• Counting on and back in 1s and 10s
• count in 2s, 5s and 10s
• Position numbers on a number line up to 1000
• use addition and subtraction facts to 20
• use related facts for addition and subtraction
• add or subtract 1 or 10 from a 2-digit number
• add and subtract 2-digit numbers
• number bonds to 100 using tens only
• add three single-digit numbers
• recognise and make equal groups
• use the x symbol to write multiplication sentences
• use arrays and pictures to represent multiplication sentences
• know multiplication facts for the 2, 5 and 10 times table
• recognise and find a half, a quarter and a third
• understand and use fraction notation
• understand the equivalence of a half and two-quarters
• count on in halves, thirds and quarters up to 10
• count in pence: 1p, 2p ,5p, 10p and 20p
• count in pounds: £1, £2, £5, £10 and £20
• find a simple total or difference between two money amounts
• find the change from simple amounts
• tell the time: o'clock, half-past, quarter-past and to
• understand and compare durations of time
• compare and measure length, mass, volume, capacity and temperature
• read a variety of scales going up in 1s, 2s, 5s and 10s
• recognise 2D and 3D shapes
• count sides and vertices on 2D shapes
• count faces, edges and vertices on 3D shapes
• sort and make patterns with 2D and 3D shapes
• describe movement and turns
• make tally charts
• draw and interpret pictograms
• understand and use block diagrams

Please note:

Our site is mainly based around the US Elementary school math standards.

Though the links on this page are all designed primarily for students in the US, but they are also at the correct level and standard for UK students.

The main issue is that some of the spelling is different and this site uses US spelling.

Year 2 is generally equivalent to 1st Grade in the US.

On this page you will find link to our range of math worksheets for Year 2.

Quicklinks to Year 2 ...

• Place Value Zone

Operations Zone

• Mental Math Zone

Word Problems Zone

• Measurement Zone

Geometry Zone

Data analysis zone.

• Fun Zone: games and puzzles

Coronavirus Stay At Home Support

For those parents who have found themselves unexpectedly at home with the kids and need some emergency activities for them to do, we have started to develop some Maths Grab Packs for kids in the UK.

Each pack consists of at least 10 mixed math worksheets on a variety of topics to help you keep you child occupied and learning.

The idea behind them is that they can be used out-of-the-box for some quick maths activities for your child.

They are completely FREE - take a look!

• Free Maths Grabs Packs

Place Value & Number Sense Zone

Year 2 Place Value Charts

Here you will find a range of Free Printable Place Value Charts for Year 2.

These printable charts will help your child learn to read and write numbers.

Some of the charts are partially filled to help your child learn their place value.

Using these sheets will help your child to:

• learn to count in tens and ones;
• learn to read and write numbers.
• Printable Number Charts 0-99
• Hundred Number Charts (100 Squares)
• Number Grid up to 200

Place Value and Counting Worksheets

Here you will find a range of Year 2 Place Value Worksheets.

These Year 2 maths worksheets will help your child learn their place value, reading, writing and ordering numbers up to 100.

There are also some money worksheets involving counting in dimes and pennies to support place value learning.

• learn to order numbers to 100;
• learn to count in dimes and pennies;
• learn to read and write numbers to 100.

Year 2 Place Value Worksheets

• Place Value to 20 Worksheets
• Math Place Value Worksheets Tens and Ones
• Ordering 2-digit numbers Worksheets
• Greater than Less than Worksheets - up to 2 digit numbers
• Printable Counting Worksheets to 50
• Missing Number Chart 1-100
• Counting by 2s Worksheets
• Math Worksheets Counting by 1s 5s and 10s

Number Line Worksheets

Here is our selection of free printable number line worksheets for Year 2 pupils.

These first grade math worksheets will give your child a good grasp of place value and number sequences up to 100.

• count on and back by ones;
• position numbers to 100 on a number line.
• Number lines to 20
• Number lines to 100

Year 2 Mental Maths Zone

Here you will find a range of printable mental math sheets designed especially for Year 2 children.

Each quiz tests the children on a range of math topics from number facts and mental arithmetic to geometry, solving word problems and measures questions.

A great way to revise topics, or use as a weekly math quiz!

• Year 2 Printable Mental Maths

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Year 2 Addition Worksheets

Here you will find a range of Free Printable Addition Worksheets to support Year 2.

The following first grade math worksheets involve adding different amounts.

• learn their addition facts to 12+12;
• learn to solve an addition fact where one of the addends is missing;
• learn to add numbers in columns up to 100.
• Number Bonds to 10 and 12
• Addition Sentences to 12
• Addition Fact Practice to 12
• Addition Facts to 20 Worksheets
• Adding tens
• Addition Word Problems
• 2 Digit Addition Without Regrouping
• 2 Digit Addition Worksheets With Regrouping
• Free Addition Worksheets (randomly generated)

Year 2 Subtraction Worksheets

Here you will find a range of Year 2 Subtraction Worksheets.

The following worksheets involve using the Math skills of subtracting.

Using these Year 2 maths worksheets will help your child to:

• learn their addition and subtraction facts to 12;
• learn to subtract 2 digit numbers.
• Subtraction Facts to 12
• Subtracting tens
• Subtraction Word Problems
• Two Digit Subtraction Worksheets Without Regrouping
• 2 Digit Subtraction Worksheets With Regrouping
• Free Subtraction Worksheets (randomly generated)

Addition & Subtraction Worksheets

If you need to mix and match addition and subtraction fact questions within the same sheet, then use this section here.

The addition and subtraction worksheets involve counting on and back with numbers to 12.

• Math Activities Addition and Subtraction to 12
• Add and Subtract 10 Worksheets
• Addition Subtraction Worksheets (randomly generated)
• Addition and Subtraction Problems

Year 2 Maths Word Problems

Here you will find a range of math word problems aimed at Year 2 level. Each problem sheet is based on an interesting theme such as parties or the seaside.

• Add and subtract with numbers to 12;
• order numbers to 100;
• solve a range of math problems.
• Maths Problems for Year 2

Longer Math Problems

• Year 2 Maths Problems (1st Grade)

Year 2 Geometry Worksheets

Here is a range of free geometry worksheets for Year 2 pupils.

The following worksheets will help your child to:

• Identify and name a range of 2d and 3d shapes;
• Draw 2d shapes;
• Know some of the properties of 2d shapes.
• Year 2 Geometry Worksheets (1st Grade)

Measurement Zone, including Time & Money

Year 2 measurement worksheets.

Here is our selection of measurement worksheets for Year 2 pupils.

These sheets involve reading scales going up in ones to find the weight or liquid capacity.

Using these sheets will help children to consolidate their counting as well as learning to read a simple scale.

• Year 2 Measurement Worksheets (1st Grade)

Year 2 Money Worksheets

Here you will find a range of free printable First Grade Money Worksheets.

The following worksheets involve counting different amounts of money in pennies, nickels and dimes.

• learn the names and values of the US coins;
• learn to count up different amounts of money to £1 in coins.
• Free Counting Money Worksheets UK Coins (easier)
• Free Money Worksheets UK Coins up to £1

Printable Money Resources

• Printable Money Flashcards
• Kids Counting Money Dominoes

Telling the Time Worksheets

Here is our selection of telling the time worksheets for 1st grade.

• read o'clock and half-past times;
• convert o'clock and half-past times to digital;
• draw clock hands correctly to mark out o'clock and half-past.

The year 2 maths worksheets in this section will help your child learn to tell simple times on an analogue clock.

• Telling Time Worksheets o'clock and half-past
• Clock Worksheets - Quarter Past and Quarter To

Year 2 Bar Graph Worksheets

Here is our selection of bar graphs for first graders.

These Year 2 maths worksheets involve reading and interpreting a range of bar graphs and picture graphs with a scale going up in ones.

Using these sheets will help children to understand how bar graphs work.

• Year 2 Picture/Bar Graphs (First Grade)

Fun Zone: Puzzles, Games and Riddles

Year 2 Maths Games

Here you will find a range of free printable Math games. All children like to play Math games, and you will find a good range of Maths Games at a Year 2 level here for your child to play and enjoy.

• Year 2 Maths Games (First Grade)

Year 2 Maths Puzzles

Here you will find a range of printable Year 2 level math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition and subtraction facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

• develop thinking and reasoning skills;
• develop perseverance.
• Year 2 Maths Puzzles (1st Grade)
• Dot to Dot up to 50

Math Salamanders Year 2 Maths Games Ebook

Our Year 2 Maths Games Ebook contains all of our fun maths games, complete with instructions and resources.

This ebooklet is available in our store - use the link below to find out more!

• Year 2 Maths Games Ebook

Other UK Maths Worksheet pages

See below for our other maths worksheets hub pages designed for children in the UK.

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The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

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45 year 2 maths questions

Learn how to master year 2 maths word problems with these 45 maths questions! Answers included.

Author Michelle Griczika

Published February 2024

• Key takeaways
• Addition & Subtraction : Adding and subtracting numbers is like solving puzzles and helps us with real-life situations.
• Word Problems : Solving word problems makes maths fun and helps us become better readers and problem solvers.
• Place Value : Understanding place value helps us read and write numbers correctly and compare their values.
• Measurement & Time : Measuring objects and telling time help us understand the world around us and manage our daily routines.
• Geometry (Shapes) : Recognizing shapes and their properties helps us see the world in a new way and understand how things are put together.

Table of contents

• Addition and Subtraction
• Word Problems
• Place Value
• Geometry (Shapes)

Did you know that ladybugs have spots on their backs?

If a ladybug has 2 spots on its back and it gets 1 more spot, how many spots will the ladybug have in total?

The lady bug will have 3 spots!

Year 2 maths word problems are like fun puzzles that help us use our maths skills to solve real-life situations. They are essential to year 2 maths, and practising them can help us become maths superstars!

• We can use addition and subtraction to determine how many cookies are left in a jar, how many friends are on the playground, or even how many apples are in a basket.
• Understanding place value is like being a number detective. It helps us read big numbers and know the value of each digit, so we can count things like how many toys we have or how many days until our birthday.
• Measuring things and telling time is like being an explorer in the real world. We can measure how tall we are, how long a pencil is, or even how much water is in a glass. And knowing how to read a clock helps us know when it’s time for fun activities or when it’s time to go to bed.
• Shapes are like building blocks of the world around us. We can learn about squares, triangles, and circles by looking at objects we see every day. It’s like being a shape detective, finding out how many sides and corners they have, and how they fit together like puzzle pieces in year 2 maths questions.

All of these skills are necessary for year 2 maths practice! Use these 45 maths questions to go over important maths skills needed to strengthen your student’s understanding and knowledge.

Today, we are going to practise different year 2 maths skills that cover measurement, addition and subtraction, and more! Once you are done, check your work with our answer sheet!

Section 1: Addition & subtraction

Section 2: word problems, section 3: place value, section 4: geometry (shapes), section 5: time.

What time is the clock below telling?

Time answer sheet

Parents, sign up for a DoodleMaths subscription and see your child become a maths wizard!

Lesson credits

Michelle Griczika

Michelle Griczika is a seasoned educator and experienced freelance writer. Her years teaching first and fifth grades coupled with her double certification in elementary and early childhood education lend depth to her understanding of diverse learning stages. Michelle enjoys running in her free time and undertaking home projects.

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Problem-solving maths investigations for year 2.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 2 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor – high ceiling' activities for all.

Explore all our in-depth problem solving investigations for Year 2 .

Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

Hamilton provide a mix of our own specially commissioned investigations, that include guidance for teachers together with a child-friendly sheet to guide your pupils through the investigation, as well as links to investigations on other highly regarded websites.

I am very grateful for Hamilton Trust resources, particularly the maths investigations. Julia, teacher in Wiltshire

You can find Hamilton's investigations for Year 2:

• Individually, they are incorporated into every unit in our Year 2 flexible maths blocks .
• Collectively, they appear on our resources page where you can explore all our in-depth problem solving investigations for Year 2 .

Do read our extensive range of advice for more information about the investigations and for tips on how to use them effectively.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Hamilton’s Problem-solving Investigations provide school-wide solutions to the challenges of building investigative skills from Early Years to Year 6.

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3. Try lots of different methods

Encourage your child to use a range of methods, including using objects, drawings, diagrams, and symbols, to solve addition and subtraction problems. To solve addition problems, your child might:

• Use objects. They could count all the objects in groups being added together to find their total (so for 2 + 3, they would count all the objects together: 1, 2, 3, 4, 5 ). Then, then could begin counting on from one group to find the total (so for 2 + 3, they might start at 3 and count on: 3, 4, 5 ).
• Use drawings such as number lines .
• Use formal written methods such as column addition.

To solve subtraction problems, your child might:

• Use objects and take some away to find the difference.
• Put objects from two groups into two lines and compare them to find the difference.
• Count backwards or use number lines .
• Use written methods such as column subtraction.

Your child could use rounding to estimate their answers before calculating accurately. It can also be helpful to use more than one method to double-check calculations. For example, your child could check a subtraction question by adding up the answer and the number they subtracted to see if they get back to the number they started from.

Choose an addition or subtraction calculation to solve with your child

 We are setting the table for our family of four and one guest. How many people are eating altogether?   I’ve put out 8 forks. Is that right or is it too many? How many do we need to put back in the drawer?

You have sent 20 invitations out for your party. We have heard back from everybody and 3 people have told us they can’t come. How many people are coming to your party?

Discuss which method your child would use for these questions. Try to find as many ways as you can to solve the problems, and talk about the methods you and your child each preferred and why.

4. Make up story problems

Story problems can be a fun way to help your child understand addition and subtraction. And you can have fun making them up! Why not see if your child would like to create a story problem for you?

When creating an addition story problem, you could support your child by giving them objects to use or a picture to inspire their story. Once they’ve completed the word problem, ask them if they could write the calculations in the problem using symbols (‘+’, ‘–’, and ‘=’).

5. Try missing number problems

Missing number problems can be quite tricky for children. You can support your child by making the most of opportunities to practise missing number problems practically. For example, you can ask for your child’s help if you have a number of something but need a higher number:

‘I have 5 buttons but I need 15 buttons. How many more do I need?’

Ask your child how they worked it out. Then, you could ask them to write a calculation using numbers and symbols to explain how they did it.

5 + ? = 15.   They could have counted on from 5 to 15 to get 10. They could have counted back 5 from 15 to get 10. They may have known that 15 – 5 = 10. … and so on.

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28 Math Problems For 2nd Graders With Answers & Teaching Ideas

Melanie Doppler

Math problems for 2nd graders bridge lower elementary and upper elementary math concepts. 2nd grade math problems focus on solidifying an understanding of place value and applying this to more complex addition and subtraction problems.

This blog post looks at the key areas for 2nd grade math problems including place value, measurement, geometry and math word problems. It aims to provide teachers with math problems, solutions and strategies for teaching 2nd grade math.

What are math problems for 2nd graders? 

Math problems for 2nd graders are a type of math question designed specifically for 7-8-year-old children. They include a variety of concepts across four domains of common core math standards:

• Operations and Algebraic Thinking 
• Number and Operations in Base Ten 
• Measurement and Data 
• Geometry 

Within these domains, second grade math problems include the following 2nd grade math concepts:

• Addition and subtraction (2-digit numbers within 100) with and without regrouping
• Place value (3-digit numbers up to 1,000)
• Measurement problem solving
• Counting money

Reading digital and analog clocks

• Basic fractions
• Bar graphs and picture graphs

Each concept builds on skills that students learned in kindergarten and 1st grade.

14 Fun Math Games and Activities Pack for 2nd Grade

14 fun math games and activities for 2nd grade students to complete independently or with a partner. All activities are ready to go with no prep needed. Perfect for ‘fast finishers’ or morning work.

Math problems for 2nd graders: Math curriculum 

Second grade math is an integral part of the K-5 math progression. In kindergarten and first grade, students use knowledge of counting to learn the meaning of addition and subtraction. 

Students use hands-on math manipulatives to build understanding, solve problems and build addition and subtraction fluency within 10. They are introduced to basic math word problems and learn that math is part of the real world. 

By second grade, students are expected to have efficient problem-solving strategies for addition and subtraction within 20. Building on this foundation, 2nd graders use their knowledge of smaller addition and subtraction problems to help them solve problems with larger two-digit numbers. 

Students may use math tools and visual models to learn more abstract and efficient math problem-solving strategies . This problem solving progression of concrete representational abstract is important at every grade level when learning new math concepts. 

Second grade allows students to explore new math skills such as:

• Extend understanding of base ten to compare larger numbers up to 1,000
• Develop fluency with addition and subtraction within 100
• Describe, analyze, and partition shapes
• Understand measurement units
• Represent data using bar graphs 

These 2nd grade math skills are the foundation for 3rd grade math. They help students secure their understanding of place value and apply their knowledge to larger addition and subtraction problems. 

Developing knowledge of these math concepts also prepares children to learn multiplication and division skills in 3rd grade. 

Math problems for 2nd graders with solutions

The following is a collection of math problems for 2nd graders organized by skill. Each problem includes an answer key, and an explanation of how to answer the math question. 

Addition and subtraction (2-digit numbers)

Beginning in kindergarten children learn models for solving addition and subtraction problems. In 2nd grade, students apply this understanding to solve larger problems with two-digit numbers. 

Sometimes, these problems include regrouping (or renaming), for example, exchanging one ten for ten ones or vice versa. This is a challenging idea for students, so base-ten visual models are important when teaching this new concept.  

Second graders also solve addition and subtraction word problems that are more difficult than the word problems they solved in first grade. 

28 + 32 = _____

2nd graders learn that ten ones make one ten. In this problem, students must see that 8 + 2 = 10 which means one ten goes in the tens place and there aren’t any ones remaining in the ones place. 

Using a base-ten block model is a helpful way to show what is happening in this problem. Alternatively, students may break down both numbers using place value. 

74 – 61 = _____

Students can solve this problem using the traditional digit subtraction method. However, since the numbers are relatively close, they could also count on from 61 on a number line to find the difference between 74 and 61. 

18 + _____ = 30

This problem is designed as a missing addend problem. To solve this problem, students must use a subtraction strategy to find the difference between 30 and 18. 

Missing addend problems help students connect subtraction to addition and encourage them to add on from the lower number. 

In this case, students could subtract using the traditional standard algorithm, however, they would need to rename 30 ones as 2 tens and 10 ones. You can support this new concept in 2nd grade with base ten blocks . Adding on from 18 is likely more efficient for this particular problem. 

Additionally, the unknown being to the left of the equal sign could confuse students so it is important to emphasize the meaning of the equal sign to prevent this misconception.

Nadia had 24 white flowers and 19 yellow flowers growing in her garden. How many flowers did Nadia grow in her garden in total?

Answer: 43 total flowers

Drawing a visual model or using a story problem graphic organizer are great ways to build understanding of math word problems. 

This problem is a part-part-whole problem so a bar model or tape diagram is a great way to visualize the unknown in the problem. Then students can use an addition strategy such as breaking apart one addend to solve. 

Question 5 

There were 56 people at the swimming pool. 23 people left the pool after lunch. How many people were still at the pool after lunch? 

Answer: 33 people remained at the pool 

This is a traditional separate, result unknown problem. Because there is the action of 23 people leaving, it is easier for students to visualize the subtraction. 

The traditional standard algorithm is a good method to solve this problem without any regrouping. Students can use base ten blocks to support their understanding as needed. 

Addition and subtraction common misconceptions

Two-digit addition and subtraction introduces the added challenge of regrouping. Students often need support deciding which number needs to be regrouped. 

Additionally, students often rush to using an algorithm before they have a foundation of conceptual understanding. For example, when solving 30-17, children need to be able to take one group of 10 from the 3 groups of 10 in the number 30 to use in the ones place to find the missing addend. Then they can subtract 10-7 and the remaining 2 tens – 1 ten. 

Teachers can support children with this by using a base-ten visual model with blocks or a drawing. Educators can also encourage learners to try other strategies such as breaking apart the subtrahend. Breaking 17 apart into 10 and 7 allows students to subtract first, 30 – 10, and then subtract the remaining 20 – 7. They can use base ten blocks or a number line to support problem solving. 

Place value (3-digit numbers)

Prior to second grade, students learn place value concepts such as the meaning of the tens-place and the ones-place in the base ten number system. They use visual models such as base ten blocks and place value charts to help understand the complex concept. 

In second grade, students expand their knowledge and learn the meaning and value of the hundred and thousand places in the number system. With a secure understanding of this, second graders can then learn to compare three-digit numbers numbers up to 1,000. 

Students in 2nd grade use the expanded form to represent three-digit numbers to show the meaning of each digit in the number. 

On Saturday, 346 people went to the carnival. On Sunday, 432 went to the carnival. On which day did more people go to the carnival? 

Answer: On Sunday more people went to the carnival because 432 is greater than 346

Students can solve this problem by breaking down the numbers by place value, or by writing them in a place value chart and comparing starting with the largest place value first. Learners will notice 4 hundreds is more than 3 hundreds so 432 is greater than 346.

Compare the following two numbers using the greater than, less than and/or equal to symbols (>, <, =)

624_____398

Answer: 624 > 398

Writing both numbers in expanded form helps students compare the values. Even though 398 has a larger number in the tens place and in the ones place, it has fewer hundreds than 624. Therefore 624 is greater than 398. 

Question 8 

How many hundreds are in the number 462? Explain your thinking. 

Answer: 4 hundreds

Building a number using base ten blocks is a concrete method for students to understand the number of hundreds, tens and ones in a number. Using base ten blocks or a quick picture helps students see there are 4 hundreds in the number 462. 

Write the number 684 in expanded form. 

Answer: 600 + 80 + 4

Writing answers in the expanded form is straightforward. Students should break up the number using place value. 

A place value chart can help to organize student thinking when breaking up the numbers. As an additional challenge, students can write this number as 680 + 4 or 600 + 84. 

Common place value misconceptions

Working with three digits is new for 2nd grade students. Often, in a number such as 273, they see that the number 7 is seemingly the largest. So in comparing 273 to 341, they might say that 273 is the bigger number because 7 is greater than any digits in the other number, even though 341 is greater than 273. 

Students must learn the value of each digit and compare numbers using the largest place value first. Teachers can encourage students to write numbers in expanded form (200 + 70 + 3), and use base-ten blocks to model the numbers. Place value charts are another helpful tool to clear up this misconception. 

Measurement: problem solving  and word problems

In kindergarten and first grade, children learn basic measurement concepts such as describing measurable attributes of objects and using basic measurement units. 

In second grade, children learn to use standard units of measure. They also discover various real-world contexts for measurement as they solve measurement word problems. 2nd grade measurement word problems include addition and subtraction of double-digit numbers.

Question 10 

Josh and Simone were training for a marathon. Josh ran 22 miles on Saturday. Simone ran 16 miles on Saturday. How many more miles did Josh run than Simone on Saturday?

Answer: 6 more miles

Learners can solve this problem by counting on from 16 to 22 or subtracting back from 22 to 16. Students may also use a standard algorithm although it would require regrouping and might be less efficient. 

Using a number line or bar model is a helpful visual for students to understand that in this problem they need to find the difference between 16 and 22. 

Question 11

The maple tree is 72 inches tall. The oak tree is 13 inches taller than the maple tree. How tall is the oak tree?

Answer: 85 inches tall 

Measuring height is a context that second graders often see in measurement problems. Using a vertical number line is a helpful visual model for students to recognize that they are adding 13 to 72 in this word problem. Then they can choose a solution strategy to find the sum. 

Question 12 

The Rodrigo family went on a road trip. In the first hour, they drove 55 miles. In the second hour, they drove 42 miles. How many miles did the Rodrigo family drive in the first two hours of their trip? 

Answer: 97 miles

In this math word problem, learners could use a bar model to visualize adding 55 and 42. They can then choose a strategy to find the sum, such as adding with place value or breaking apart one addend.

Money 

Second grade is the first time that students are introduced to counting money. Students learn the value of each coin and the dollar bill. Children solve word problems to determine total quantities when coins are put together and taken apart. This sets the foundation for learning about decimals in the base-ten number system, which is introduced in 4th grade, 5th grade and 6th grade. 

Question 13

The picture below shows how much money my sister has in her piggy bank. How many cents does my sister have in her piggy bank?

Answer: 89 cents

To add the value of the coins together, students should find the total value of all the coins of one type first, or find ways to make ten. 

In this case, they would see that there are 2 quarters  (50 cents), 2 dimes (20 cents), 3 nickels (15 cents) and 4 pennies (4 cents) so a total of 89 cents. 

Question 14

William has 3 quarters. Margaret has 8 pennies. Who has more money? Explain.

Answer: William has more money because 75 cents is more than 8 cents

This problem is challenging for students because the number 8 has a larger value than the number 3. Students should label their work and use real coins where possible to build meaning. 

Skip counting or repeated addition can help students see William has 75 cents and Margaret has 8 cents.

Question 15

Mr. Hopkins had a lemonade sale. He sold 2 cups of lemonade and got 1 quarter, 2 dimes and 1 nickel. How much money did Mr. Hopkins make from selling 2 cups of lemonade? 

Answer: 50 cents

Writing an equation to match a hands-on model with coins or a pictorial model with labels is a great way for students to visualize which numbers they are adding. 

At the second grade level, students do not necessarily write these numbers as decimals since they don’t add decimals until 4th and 5th grade. However, teachers can address what these numbers would look like if we wrote them using decimal notation. 

Telling time was a new skill for students in 1st grade. They learned to read digital and analog clocks to the nearest hour and a half hour. In 2nd grade, students dive deeper and learn to read digital and analog clocks to the nearest 5 minutes, using both a.m. and p.m. 

Question 16 

What time is shown on the analog clock below? Write your answer in digital clock format.

Answer: 4:40

As 2nd grade students learn about clocks, they must realize that the hour hand moves throughout the hour as well as the minute hand. 

In this situation, the hour hand is closer to 5 than 4 because it is past the half hour. Practicing with hands-on clocks helps children understand this concept.

Question 17

Lucy’s dance class starts at 5:15pm. Circle the clock that shows the time her dance class starts.

Students must recognize the short hand as the hour hand and the long hand as the minute hand. Many students may confuse D as the correct answer when it shows 3:25. 

Teachers can facilitate connections between digital and analog clock times using a visual timeline or schedule throughout the day.

Question 18

Lee woke up earlier than Timothy. If Timothy woke up at 6:00am, what time could Lee have woken up? Choose from the digital 24-hour clocks below.

The concept of earlier and later is a fairly new concept for 2nd graders when considering time. Math problems like this prepare students for elapsed time problems in 3rd grade. 

In this problem, students must recognize that 5:00 am comes before 6:00 am, therefore 5:45 am is earlier than 6:00 am. 

Common time misconceptions:

Students often confuse the hour and the minute hands on an analog clock. They need a lot of repeated practice to build understanding. 

RELATED RESOURCE : Time word problems

2nd grade introduces students to the foundation of fractions and connects fractions to geometry. 

Students learn to partition rectangles and circles into two, three and four equal shares. They connect the size of these shares to the vocabulary half, third and fourth, setting the foundation for harder fractions in 3rd grade.

Question 19

If 4 friends share a pizza and each friend gets an equal share, what fraction of the whole pizza does each friend get?

Answer: \frac{1}{4} of the whole pizza

Using visual models that students can draw on, cut and fold is critical for building a conceptual understanding of fractions. 

Children should fold a circular piece of paper or draw a circle and ‘cut’ it into fourths by drawing lines. They may also physically model it using a real pizza or play pizza. The aim is to connect the vocabulary of ‘one-fourth’ when sharing something equally with 4 people.

Question 20

Which models below show a rectangle being partitioned into fourths? Select all that apply. 

Answer: A,C,D

This math problem shows students that rectangles and other shapes can be partitioned in multiple ways. 

As long as the size of the 4 pieces are equal, all three of these models represent a rectangle partitioned into fourths. 

If students answer B, they might not understand how to draw fourths. This misconception indicates that they think drawing 4 lines partitions into fourths, rather than fifths. 

Question 21

If you slice a pie down the middle so that each side is the same size, what fraction of the whole pie is each side? 

Answer: One half or \frac{1}{2}  

Emphasizing the same-size parts is important for setting the foundation for fraction concepts in third grade and beyond. Because of this, 2nd grade fraction concepts focus heavily on vocabulary and equal shares. 

In kindergarten and first grade math, students learn the defining attributes of various two-dimensional and three-dimensional shapes. In second grade math, students solidify their understanding of some basic 2-D and 3-D shapes and draw and identify the number of sides and angles for each shape including:

• Types of triangles
• Quadrilaterals
• Cubes 

Question 22

Draw a closed shape that has 6 sides. What is the name of the shape?

Answer: Drawings may vary but should all have 6 sides and 6 angles. This shape is called a hexagon. 

Question 23

Which shape below is a pentagon? Explain how you know.

A pentagon has 5 sides and shape C is the only 5-sided figure. 

Question 24

What is the name of a shape with 3 angles? Draw a picture of this shape.

Answer: Triangle

Question 25

Draw a quadrilateral. How many angles are in a quadrilateral? 

Answer: Drawings will vary but should be closed 4-sided shapes. There are 4 angles in a quadrilateral. 

Before 2nd grade, students learned to informally organize and represent data. In second grade, students learn a more formal method to represent data: a bar graph. 

2nd grade students must know how to represent data using a bar graph and/or a picture graph and solve simple problems using data presented in bar graphs. 

Question 26

In a class survey, the students in Mrs. Nielsen’s class voted for their favorite color. The data is represented in the bar graph below. How many more students voted for blue than voted for green? 

Answer: 4 more students voted for blue

Since 9 students voted for blue and 5 students voted for green, the difference is 4 students. 

Students must be able to read the bar graph and analyze the data to find the difference. 

Question 27

Look at the bar graph. How many total people ordered food at Pat’s Diner over the weekend? 

Answer: 90 people ordered food 

2nd graders need to understand the scale on the graph. In this math problem, the scale is 10. Children should see there were 30 orders on Friday, 40 on Saturday and Sunday there were 20 and know to add those three values together. 

Question 28

How many fewer cats are there at the shelter than dogs? Use the bar graph below to answer the question. 

Answer: 10 fewer cats than dogs

2nd graders learn about the parts of a bar graph, including the: 

• Scale 
• Title 

There is a lot of information provided about all the animals at the shelter, students must identify the information in the problem and then solve the problem using the information. 

In this case, there are 5 cats at the shelter and 15 dogs, so the difference is 10. 

You may also represent this bar graph horizontally. 

3 top tips for teaching 2nd grade math problems

Teaching 2nd grade math relies on visual models to help students build understanding and develop efficient problem solving strategies. 

To help 2nd grade students build an understanding of new math concepts these elementary teaching best practices can help:

• Teach students more than one method to solve a problem. They can then decide which strategy is most efficient. For example, base-ten blocks, a number line, breaking apart one addend, breaking apart both addends or the standard algorithm.
• Use visual models such as a base-ten block to build an understanding of regrouping when adding and subtracting.
• Follow the CRA progression and transition from hands-on concrete models, to representational or pictorial models, to abstract models.

How can Third Space Learning help with 2nd grade math?

STEM-specialist tutors help close learning gaps and address misconceptions for struggling 2nd grade math students. One-on-one online math tutoring sessions help students deepen their understanding of the math curriculum and keep up with difficult math concepts.

Each student works with a private tutor who adapts instruction and math lesson content in real-time according to the student’s needs to accelerate learning.

2nd grade math worksheets and resources

Looking for more resources? Check out our math games and selection of second grade addition and subtraction worksheets, posters and activities covering the key 2nd grade math topics and more:

• 2nd Grade Fractions Error Analysis
• 2nd Grade Addition and Subtraction Code Crackers
• Addition And Subtraction Word Problems 
• Summer Math Activities For 1st and 2nd Grade
• 25 Fun Math Problems

READ MORE :

• Math problems
• 1st grade math problems
• 3rd grade math problems
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• 6th Grade Math Problems
• 7th grade math problems
• 8th grade math problems

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized 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. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

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[FREE] Ultimate Math Vocabulary Lists (K-5)

An essential guide for your Kindergarten to Grade 5 students to develop their knowledge of important terminology in math.

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Countdown printable sheet Countdown printable sheet - cards

Here is a chance to play a version of the classic Countdown Game . The challenge is to use the numbers available and the four standard operations (addition, subtraction, multiplication and division) to hit the target.

Start by choosing any six cards. The top row always contains the numbers 25, 50, 75 and 100, and the bottom row contains the numbers 1 to 10. Alternatively you could click on "Quickstart". Then click on "Generate new target" and the computer will choose a target.

You can only use each card once in your solution, and it is always possible to find a solution.

You may like to explore different levels of the game using the Settings menu (the purple cog).

How could you get close to the target? How could you use rounding and estimation to help?

You might like to start by working on the level 1 and 2 problems initially, and then comparing your answer to the available solutions.

Why play this game?

Countdown offers a motivating context in which to practise calculation strategies.  There is usually more than one way of hitting the target, which offers an opportunity for rich discussion on the merits of alternative methods. It encourages learners to estimate and to 'tinker' with solutions as they get closer to the target number.  ('Tinkering' is one of the mathematical habits of mind referred to by Al Cuoco et al.)

Possible approach

Demonstrate the game to the class.

If the students have access to computers or tablets they can work in pairs on various examples. The Settings menu offers students the possibility of working at different challenge levels:

• level 1 can always be done using two cards
• level 2 can always be done using three cards
• level 3 can always be done using four cards
• level 4 can always be done using five cards
• level 5 can always be done using all the cards.

If students don't have access to computers or tablets you could generate several examples and write them on the board for students to have a go at with their partner using pencil and paper.

Once students have successfully completed some challenges, bring the class together to share strategies and discuss the advantages of different methods.  It may be worthwhile to collect strategies on a 'working wall' so the whole group can look back and see which prove useful time and time again. 

Finally, set aside some time for students to have a few more goes to put into practice the strategies they have discussed. Students may want to challenge themselves to always find the solution using the minimum number of cards.

If they come across a particularly difficult example you could share it with the rest of the class by using the "Replay code" which can be entered in the Settings menu (access using the purple cog in the top right). If no-one finds a solution, you can leave the challenge on the wall as a 'simmering' activity for a few days so that members of the class can come back to it in their own time.

Countdown is one of the most popular resources on NRICH, so you may like to discuss your experiences of using this activity in your classroom on Twitter, using the hashtag #NRICHcountdown.

Key questions

Possible support.

Suggest that students work on the level 1 and 2 problems initially. You could also use the "Replay code" facility to share accessible examples (e.g. 25,7,4,9,3,5,125) before letting students loose on randomly generated examples.

Possible extension

Countdown Fractions offers a much more challenging version of the game.

Some of your students might be interested in this blog post , written by Nick Berry, which describes some questions he asked himself about the traditional Countdown game, and how he used coding to help answer them. We used some of the optimisation ideas from the article in the development of the new Countdown game.

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Harris Chooses Walz

A guide to the career, politics and sudden stardom of gov. tim walz of minnesota, now vice president kamala harris’s running mate..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

Hey, it’s Michael. Before we get started, I want to tell you about another show made by “The New York Times” that pairs perfectly with “The Daily.” It’s called “The Headlines.” It’s a show hosted by my colleague, Tracy Mumford, that quickly catches you up on the day’s top stories and features insights from “The Times” reporters who are covering them, all in about 10 minutes or less.

So if you like “The Daily”— and if you’re listening, I have to assume you do — I hope that means you’re going to “The Headlines” as well. You can now find “The Headlines” wherever you get your podcasts. So find it, subscribe to it, and thank you. And now, here’s today’s “Daily.”

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.”

[MUSIC PLAYING]

Today, the story of how a little known Midwestern governor became Kamala Harris’s choice for a running mate. My colleague Ernesto Londoño walks us through the career, politics, and sudden stardom of Governor Tim Walz of Minnesota.

It’s Wednesday, August 7.

Ernesto, over the past few days, we watched Vice President Harris bring the final three contenders for her running mate to her house in Washington, DC, for a set of in-person interviews. And then we watched as she seemed to narrow her pool of choices down to a final two — the governor of Pennsylvania, Josh Shapiro, and the governor of Minnesota, Tim Walz. And now, of course, we know that she has made her choice. What has she told us about her campaign strategy, the way she views this race, in ultimately choosing Tim Walz?

Michael, I think what the choice tells us is that Kamala Harris was drawn to two qualities that Governor Walz brings to the table. And what’s interesting is they may seem to be in tension. For starters, here’s the ultimate everyday man, somebody who grew up in a small town in Middle America, served in the National Guard, was a high school teacher, a football coach, very plain-spoken, goes to campaign events wearing T-shirts and baseball caps, is a gun owner and very proud about it. He sort of embodies the Midwest.

And she clearly thinks that that is going to bring the kind of moderate, white, working class voters that the campaign needs in swing states to come to them, to make this feel like a balanced ticket and something that will give her enough of the crucial votes to defeat Donald Trump in the fall.

On the other hand, as governor, he passed a slew of pretty progressive legislation in the past couple of years, everything from abortion rights to gun control. So these things are likely to appeal to bread and butter Democrats.

But the question is, when voters have examined these two facets of Tim Walz, may it bring them enough enthusiasm from the base and enough undecided voters that the campaign desperately needs, or at some point, do these two aspects of him start canceling each other out?

Right. In short, you’re saying Harris is betting on a dual appeal from Walz to two essential constituencies, but the risk is that the appeal to one of them is just much, much greater than to the other.

Right. You could definitely see a scenario where voters, once they’ve examined Tim Walz’s story and legacy, may conclude that both of these candidates are quite liberal.

OK, so tell us the story of Tim Walz, a story that I think a lot of us don’t know because we really don’t know Walz all that well, and how he has come to embody these two qualities and that tension that you just described.

Michael, the origin story of Tim Walz’s political career is quite fascinating.

He and his wife were teachers in a small city south of Minneapolis. And in 2004, when George W. Bush was running for re-election, Walz took a group of his students to a political rally in his hometown. They wanted to just see the president make his case. And a strange scuffle happened when they were trying to get in.

Well, one of the kids had a John Kerry sticker on his wallet. And this is where the individual says, well, you’re not going to be allowed to enter. You’ve been deemed a threat.

Apparently, one of the students had a sticker for Bush’s rival, John Kerry, on his wallet. And security officials at the rally didn’t want to let them in.

And I said, oh, it’s OK. They’re with me. And who are you? And I said, I’m Tim Walz. I’m their teacher here, and showed them my ID. And they said, well, you two have been deemed a threat to the president. And I said, well, that’s not true. And it kind of escalated.

And this really ticked off Tim Walz. He was really upset. There was a fight and a confrontation at the rally.

At this point in time, I’m kind of nervous. I’m getting arrested. So I’m like saying, well, I’m Teacher of the Year in Mankato. And they didn’t care about that. And it was kind of a sad epiphany moment, how it felt for people to be looked right through by people. These people didn’t see me. And this is happening.

And ultimately, he sort of walks away from this moment feeling really sick of the Bush administration, the politics of the day. And he turns around and volunteers for the Kerry campaign.

And then the more interested he becomes in politics in this era, he starts looking around his congressional district, and there’s a Republican who’s held the seat for many, many years. This was a largely rural district in southern Minnesota. And there’s no reason to believe that a newcomer to politics, somebody without a donor base, could make a run for this seat and win.

But Walz signs up for this weekend boot camp, where expert campaigners train newcomers who want to run for office. And he gets really enthused by the idea that he can pull it off. So he starts raising money with the support of an army of students who become so thrilled and energized by the prospect that their nerdy and kind geography teacher is making this uphill bid for a congressional race.

So his campaign staff is basically his former students.

That’s right. And he proves to be a formidable candidate. He draws a lot of attention to his experience in the classroom and as a coach.

When I coached football, these stands held about 3,000 people. That’s a lot. It’s also the number of American soldiers who have died fighting in Iraq.

He’s a very strong advocate for pulling out of the war in Iraq.

Serving right now are kids that I taught, coached, and trained to be soldiers. They deserve a plan for Iraq to govern itself, so they can come home.

And one thing that happens in the campaign that is really surprising to people is he comes out as being in favor of same-sex marriage. Now, it’s useful to remember that this is 2006, when the vast majority of Democrats, Democrats running for most elected office, were not ready to come out in favor of same-sex marriage.

And here’s a guy who’s new to politics, who’s trying to unseat a Republican who’s held on to his seat for more than 12 years, taking what appeared to be a reckless position on something. And when he was asked about it at the time, Tim Walz told a supporter, this just happens to be what I believe in. And I’d rather lose a race that I’ve ran being true and consistent to my values than try to run as somebody I’m not.

And of course, he wins.

Yes. To everybody’s surprise, he pulled it off.

So from the get-go, he shows a kind of maverick, “politics be damned” quality, taking stands that he knows may be unpopular among the voters he’s trying to win over. But he’s got some innate political gifts that are all making it work.

Yeah, I think that first campaign showed us that Tim Walz had real political chops. He was a very effective campaigner. And people really liked him. When he was knocking on doors, when he was introducing himself to voters, they saw him as somebody who was very genuine and who was admirable.

So once he gets elected in this conservative leaning district in Minnesota, what does he actually do in Congress?

In Congress, he develops a reputation for being somebody who can work across the aisle. And this is a period where Democrats and Republicans were deeply polarized over the Iraq War. He spends a lot of his time lobbying to expand benefits for veterans, so it’s easier for them to go to college after their service, and also becomes a leading voice in the quest to repeal Don’t Ask, Don’t Tell, the policy that prohibited openly gay servicemen from serving in uniform.

And he remained really popular. He easily won re-election five times. The last time he runs for his seat happens to be 2016, when President Trump wins his district by about 15 points.

And still, voters kept Tim Walz in office.

I think it’s important to note what you just said. Walz is distinguishing himself as a Democrat who can take some pretty progressive positions, as he did in that first campaign on gay rights, as he did with Don’t Ask, Don’t Tell, and keep winning in very Trump-friendly districts of his state.

That’s right. And as he’s serving his sixth term in office, he sets his sights on the governor’s mansion and decides to run for office in 2018. He wins that race easily. And early on, during his time as governor, the eyes of the world are on Minnesota after a police officer kills George Floyd. And what we see is massive looting and protests in Minneapolis.

Right, and remind us how Governor Walz handles that violence, those protests.

Yeah, I think that’s a crucial chapter in Tim Walz’s political career and one that will come under scrutiny in the days ahead.

After George Floyd was killed on a Monday —

People are upset, and they’re tired. And being Black in Minnesota already has a stigma and a mark on your back.

— protests took root in Minneapolis.

Y’all want to sit out here and shoot off your rubber bullets and tear gas.

And they got progressively larger and more violent.

There comes a point where the mayor and the police chief in Minneapolis plead for help. They ask the governor to send in the National Guard. And crucially, that request was not immediately heeded.

This is the third precinct here. There are fires burning to the left of it at the —

And at the height of the crisis, a police precinct building was abandoned.

There’s someone climbing up the wall right now, kicking the window in, trying to climb up the wall.

Because city officials grew concerned that protesters were about to overrun it and may attack the cops inside their own turf.

[EXPLOSIONS]

And the building is set on fire.

Right, a very memorable image. I can recall it happening in real-time.

Yeah, and in the days that followed, I think there were a lot of questions of why the governor didn’t send in troops earlier and whether a more muscular, decisive response could have averted some of the destruction that spread through the city.

And how does Walz end up explaining his decision not to send in the National Guard more quickly?

The governor and his administration have said that they were really, really dealing with an unprecedented challenge. And I think there was a concern that sending in troops into this really, really tense situation could have done more to escalate rather than pacify things on the street.

But in the weeks and months that followed, there were a lot of questions about Governor Walz’s leadership. And there were critics who said, during what may have been the most challenging week of his life, we saw a governor who was indecisive and who waited too long to send in resources that ultimately allowed the city to get to a semblance of order.

Right, and it feels like this is a moment that will almost assuredly be used against him by Donald Trump and JD Vance, the Republican ticket, which has made law and order so central to their message in this campaign.

Yeah, absolutely. And here in Minnesota, that was certainly a liability for him when he ran for re-election in 2022. But voters kept him in office, and he won that race handily. And not only did he win, but Democrats managed to flip the Senate and have full control of the legislature on his watch.

And that sets in motion one of the most productive legislative sessions in Minnesota history, where Tim Walz and his allies in the House and the Senate managed to pass a trove of really progressive legislation, oftentimes on a party vote.

Tell us about some of that legislation.

Well, Minnesota becomes the first state in the wake of the Supreme Court ending the constitutional right to abortion to actually codify this right under state statute. And they did a lot more stuff. They had a huge budget surplus, and they used that, for instance, to fund meals for all school children.

They managed to pass a couple of gun control laws that were very contentious. They gave the right to undocumented immigrants to get driver’s licenses. They legalized recreational marijuana. And finally, the governor takes a pretty bold stance on this issue of gender affirming care for transgender kids and teenagers, and says that Minnesota will be a safe haven for people who want that health care.

So, Ernesto, so how should we think about that blitz of legislation and the largely progressive tone of it, given the way that Walz had campaigned and succeeded up to that moment as somebody with such broad appeal across the political spectrum?

When the governor was asked whether this had been too much too quickly in terms of progressive legislation, his answer was that these were broadly popular policies, that these are issues Democrats had campaigned on. And here, Democrats had a window of opportunity where they were in control of the governor’s mansion and control of the House, the Senate, and that when you have political capital, you spend it.

But when you start listening to Republicans in Minnesota, they say, here’s a guy who campaigned on this mantra of “One Minnesota.” That was his campaign slogan. And he sort of came into office with this promise that he would govern in a bipartisan way, reach across the aisle.

But when they had all the votes they needed to pass their policies, Republicans felt that Walz was not bothering to bring them into the fold and to pass legislation that was going to be palatable to conservatives in the state. So I think people who once regarded him as a moderate now start seeing him as somebody who, when he had the power, acted in ways that were really progressive and liberal.

So at the height of his power, Governor Walz emerges as somebody who, when given a shot at getting done what he really wants to get done with a Democratic legislature, is a pretty progressive leader, even at the risk of being somewhat at odds with his earlier image as more moderate, because in his mind, enough people in the state are behind these policies.

Yeah, and I think he assumed that he had banked enough goodwill and that people across the state liked him enough to tolerate policies they may have disagreed with. And I think it’s safe to say, among the people who cover him here regularly, there was never any real hint that Tim Walz was eyeing a run for higher office. He’s not somebody who has written the kind of political memoir that oftentimes serves as a case of what you would bring to a national ticket or to the White House. And he seems pretty happy with a state job.

So it was a huge surprise when Tim Walz starts going viral through a string of cable news appearances right after President Biden drops out of the race, and the Democrats are scrambling to put Harris at the top of the ticket. And what becomes clear is that Walz is very forcefully auditioning for the role of vice president, and Vice President. Harris starts taking him very seriously.

We’ll be right back.

So, Ernesto, tell us about this cable news audition that Governor Walz undertakes over the past few weeks and how, ultimately, it seemed to help him land this job of being Harris’s running mate.

I think Walz does something really interesting, and that is that he says that Democrats shouldn’t be talking about Trump and Vance as existential threats. He kind of makes the case that Democrats have been in this state of fear and paralysis for too long, and that it’s not serving them well. So the word he latches onto is “weird.”

Well, it’s true. These guys are just weird.

It is. It is.

And they’re running for he-man women hater’s club or something. That’s what they go at. That’s not what people are interested in.

And I think one other thing we see in Walz is somebody who’s putting himself out there as a foil to JD Vance.

That angst that JD Vance talks about in “Hillbilly Elegy,” none of my hillbilly cousins went to Yale, and none of them went on to be venture capitalists or whatever. It’s not —

I think the case he’s making is that Tim Walz is a more authentic embodiment of small town values.

What I know is, is that people like JD Vance know nothing about small town America. My town had 400 people in it, 24 kids in my graduating class. 12 were cousins. And he gets it all wrong. It’s not about hate.

And behind the scenes, people from Tim Walz’s days on Capitol Hill start calling everybody they know in the Harris campaign and the Harris orbit and saying, here’s a guy who has executive experience as governor, but also somebody who has a really impressive record from his time on Capitol Hill and somebody who could be an asset in helping a Harris administration pass tough legislation. So you should take a hard look at this guy.

Which is, of course, exactly what Harris ends up doing. And I want to talk for a moment about how Harris announces Walz as her running mate on Tuesday morning. She did it in an Instagram message. And it felt like the way she did it very much embraced this idea that you raised earlier, Ernesto, that Walz contains these two appeals, one to the Democratic base, one to the white working class.

Harris specifically cites the work that Walz did with Republicans on infrastructure and then cites his work on gun control. She mentions that he was a football coach and the founder of the high school Gay Straight Alliance. She’s straddling these two versions of Walz.

But I want to linger on the idea for a moment of Walz’s vulnerabilities, because once he becomes Harris’s running mate, Harris and Walz are going to lose a fair amount of control over how they present him to the country, because he’s going to become the subject of very fierce attacks from the Republicans in this race. So talk about that for just a moment.

Yeah, I mean, it’s important to keep in mind that Governor Walz has never endured the scrutiny of a presidential race. So the questions he’s going to be asked and the way his record is going to be looked at is going to be different and sharper. I think the Harris campaign is billing him as, first and foremost, a fighter for the middle class. And I think that certainly will have some appeal.

But I think in coming days, there’s going to be a lot of attention drawn to parts of his record that may be unpopular with many voters. For instance, giving undocumented immigrants driver’s licenses, which Governor Walz championed. It’s likely to provide fodder for an attack ad.

The very dramatic footage of Minneapolis burning in 2020 is also something that I think people will be drawn to. And there’s going to be interest in reexamining what the governor did and what he could have done differently to avert the chaos.

And on Tuesday, we saw that the Trump campaign wasted no time in trying to define Tim Walz as soft on crime, permissive on immigration policy. And they also made clear they wanted to relitigate the era of George Floyd’s killing. And specifically, they want to try to tie him to the effort at the time to defund the police, which is a movement that Walz personally never endorsed.

So the Republican attack here will be pretty simple. Walz is liberal. Harris is liberal. So, in their efforts to speak to especially white working class and rural voters in swing states, the Trump campaign is going to say this is not the ticket for that group of voters. This is the ticket of burning police precincts and gun control. And of course, that may not be fair, but that’s very likely going to be the message over the next couple of months.

Right. I think there’s going to be effort to portray him as a radical liberal who has used his small town roots to put on this sort of veneer of being a moderate and a really sort of understanding and being part of the segments of the electorate that I think are critical in this election.

I want to speak for just a moment about the person Harris did not pick when she chose Walz because many Democrats had felt that Walz was a potentially too liberal seeming running mate for a candidate, Kamala Harris, who herself comes from a blue state and is caricatured by the Republicans as liberal herself.

And the person she didn’t choose was Governor Josh Shapiro of Pennsylvania, who was seen as having a huge appeal in that particular key swing state, but also presented risks of his own of alienating parts of the Democratic base with his well-documented support for Israel and his criticism of campus protesters. How should we think about the fact that, ultimately, Harris chose Walz over Shapiro?

Yeah, I think in the final stretch of this campaign to be the vice presidential pick, we started seeing a lot of acrimony in pockets of the Democratic base, drawing attention to the fact that Governor Shapiro could be divisive on Gaza, which has really sort of split the party in recent months.

So I think at the end of the day, they made a calculation that Tim Walz would be more of a unifying figure and would be somebody who would inspire and energize enough pockets of the electorate that they need, particularly in the Midwest, to make him the stronger and more exciting pick and somebody who wouldn’t force them to go back to defending and relitigating the Biden administration’s record on Israel and on the war in Gaza.

Right, and then, on Tuesday night, we got our first glimpse of Harris and Walz together on stage for the first time at a campaign rally. I’m curious, what struck you about their debut together.

Good evening, Philadelphia.

I think everybody was watching the opening scene of this rally to see what the chemistry between these two people was going to be like. And they both seemed giddy. They were literally, at times, bouncing with enthusiasm.

Since the day that I announced my candidacy, I set out to find a partner who can help build this brighter future.

So Pennsylvania, I’m here today because I found such a leader.

Governor Tim Walz of the great state of Minnesota.

They soon got down to business. And that business was how to define Tim Waltz for voters who don’t know him well.

To those who know him best, Tim is more than a governor.

And right off the bat, we saw that Kamala Harris really highlighted a lot of pieces of his pre-political career.

To his former high school football players, he was Coach.

She repeatedly called him Coach Walz, Mr. Walz, evoking his time in the classroom, and even used his military title from his days in the Army.

To his fellow veterans, he is Sergeant Major Walz.

And then when it came time for Tim Walz to introduce himself on this massive stage —

Welcome the next vice president of the United States, Tim Walz.

— he drew a lot of attention to his small town roots.

I was born in West Point, Nebraska. I lived in Butte, a small town of 400.

He said something that he said repeatedly recently in campaign appearances, which is —

In Minnesota, we respect our neighbors and their personal choices that they make. Even if we wouldn’t make the same choice for ourselves, there’s a golden rule — mind your own damn business.

The golden rule of small towns is you mind your own damn business, which is something he said in the context of his argument that Republicans have been limiting, rather than expanding, people’s rights. But he also drew attention to the fact that he’s a gun owner.

By the way, as you heard, I was one of the best shots in Congress. But in Minnesota, we believe in the Second Amendment, but we also believe in common sense gun violence laws.

And then when it came time to draw a sharp contrast with their opponents, Tim Walz said, these guys are phonies.

Donald Trump is not fighting for you or your family. He never sat at that kitchen table like the one I grew up at, wondering how we were going to pay the bills. He sat at his country club in Mar-a-Lago, wondering how he can cut taxes for his rich friends.

He said it’s actually people like me and Kamala Harris who come from humble origins and showed what is possible in America when you hail from a working class background, and you seize opportunities that were available to you.

Thank you, Philadelphia. Thank you, Vice President. God bless America.

So when it comes to this question of Walz’s dual identities and dual appeals, what did we learn on day one of this new Democratic ticket, do you think?

I think the campaign is trying to convey that these two facets of Tim Walz’s life are not mutually exclusive, that they don’t need to be in tension. They don’t cancel each other out. They’re both part of Tim Walz’s story. And I think that’s how they’re going to present him from now until Election Day.

Ernesto, thank you very much. We appreciate it.

It’s my pleasure, Michael.

Here’s what else you need to know today. On Tuesday, Hamas said that Yahya Sinwar, one of the masterminds behind the deadly October 7 attacks on Israel, had consolidated his power over the entire organization. Until now, Sinwar had held the title of Hamas’s leader in Gaza. But with the assassination of Hamas’s top political leader by Israel last week, Hamas said that Sinwar would take on that title as well. Sinwar remains a major target of Israel and is believed to have been hiding in tunnels underneath Gaza since October 7.

And the US Department of Justice has charged a Pakistani man with ties to Iran with trying to hire a hitman to assassinate political figures in the United States. The man recently traveled to the US and was arrested in New York last month. American authorities believe that his potential targets likely included former President Trump.

Today’s episode was produced by Alex Stern, Eric Krupke, and Olivia Natt. It was edited by Lisa Chow and Patricia Willens, contains original music by Pat McCusker and Marion Lozano, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Nick Pittman and Minnesota Public Radio.

That’s it for “The Daily.” I’m Michael Barbaro. See you tomorrow.

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Earlier this summer, few Democrats could have identified Gov. Tim Walz of Minnesota.

But, in a matter of weeks, Mr. Walz has garnered an enthusiastic following in his party, particularly among the liberals who cheer on his progressive policies. On Tuesday, Vice President Kamala Harris named him as her running mate. Ernesto Londoño, who reports for The Times from Minnesota, walks us through Mr. Walz’s career, politics and sudden stardom.

On today’s episode

Ernesto Londoño , a reporter for The Times based in Minnesota, covering news in the Midwest.

Background reading

Who is Tim Walz , Kamala Harris’s running mate?

Mr. Walz has faced criticism for his response to the George Floyd protests.

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Michael Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Maddy Masiello, Isabella Anderson, Nina Lassam and Nick Pitman.

An earlier version of this episode misstated the subject that Walz’s wife taught. She taught English, not Social Studies.

How we handle corrections

Ernesto Londoño is a Times reporter based in Minnesota, covering news in the Midwest and drug use and counternarcotics policy. More about Ernesto Londoño

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