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Year 3 – Place Value

Welcome to Year 3 Place Value at Primary Maths Hub. Here you will find a growing library of outstanding resources and activities to support place value lessons in Year 3 and at home.  

If there’s a resource you’d like to see here, just visit our ‘Request a Resource’ page and Primary Maths Hub will create the resource and add it to the site.

Do Now Tasks / Starters

Place Value to 1,000 Do Now Tasks

10 More or Less Do Now Tasks

100 More or Less Do Now Tasks

Faded Scaffolding Strips- Count Forwards in Tens

Faded Scaffolding Strips- Count Backwards in Tens

Faded Scaffolding Strips- Count Forwards and Backwards in Tens

Faded Scaffolding Strips- Count Forwards in Tens and Hundreds

Faded Scaffolding Strips- Count Backwards in Ten and Hundred

Faded Scaffolding Strips- Count Forwards and Backwards in Tens and Hundreds

Place Value- Faded Scaffolding Strips- Count Forwards in Hundreds

Faded Scaffolding Strips- Count Backwards in Hundreds

Faded Scaffolding Strips- Count Forwards and Backwards in Hundreds

Read and write numbers.

Write Numbers to 1,000 in Digits

Write Numbers to 1,000 in Words

How to Write Numbers to 1000

Faded Scaffolding Strips- Place Value of Numbers to 1,000 Write in Digits

Faded Scaffolding Strips- Place Value of Numbers to 1,000 Write in Words

10 and 100 more, 10 and 100 less.

10 Less to 1000

10 More and 10 Less to 1000

10 More to 1000

100 Less to 1000

100 More and 100 Less to 1000

100 More to 1000

10 or 100 More or Less to 1,000

10 or 100 Less to 1,000

10 or 100 More to 1,000

Compare and order numbers.

Order Numbers to 1000

Compare Numbers to 1000

Faded Scaffolding Strips- Compare Numbers to 1,000

Faded Scaffolding Strips- Rounding 2-Digit Numbers to the Nearest 10

Faded Scaffolding Strips- Rounding 3-Digit Numbers to the Nearest 10

Expanded form and underlined digit.

Place Value of Numbers to 1000 – Expanded Form

Place Value of Numbers to 1000 – Expanded Form to Digits

Place Value of Numbers to 1000 – Value of the Underlined Digit

Faded Scaffolding Strips- Place Value of Numbers to 1,000 Expanded Form

Faded Scaffolding Strips- Place Value of Numbers to 1,000 Expanded Form to Digits

Faded Scaffolding Strips- Place Value of Numbers to 1,000 Value of Underlined Digit

Representation and number lines.

Represent Numbers to 1000 on a Number Line

Represent Number to 1000

Estimate Numbers to 1000 on a Number Line

Flexible Partitioning to 1000

Equality and inequality statements.

Equality and Inequality Statement Matching

Word problems and challenges.

Compare and Order Numbers to 1,000 – Challenges

Place Value of Numbers to 1,000 – Challenges

Resources to support place value.

Arrow Cards

Place Value Grid

Number Lines to 1000

Number Lines to 1000 (Portrait)

Use Place Value Chart

Steps to success.

Read and Write Numbers to 1,000- Steps to Success

Determine the Value of Digits in Numbers to 1,000- Steps to Success

Compare Numbers to 1,000- Steps to Success

Order Numbers to 1,000- Steps to Success

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2. Compare and order numbers

When comparing numbers up to 1000, your child should look at the digit with the largest value first. For example, if your child is comparing the numbers 765 and 276, they would first need to look at the digit with the largest value, i.e. the hundreds digit:

276 has 2 hundreds, and 765 has 7 hundreds, so 276 is less than 765.

However, if we compare the numbers 765 and 754, they both have the same number of hundreds. Therefore, we now need to look at the tens digit:

765 has 6 tens, and 754 only has 5 tens, so 765 is more than 754.

Try this game to practise comparing numbers. Write twenty two- and three-digit numbers and the ‘>’ and ‘<’ symbols on separate pieces of paper. Deal your child two numbers, face down. Ask them to turn over the pieces of paper and to use the ‘>’ and ‘<’ symbols to show which number is bigger or smaller.

Activity: Number statements

3. Practise counting

Your child should now use the word  multiples to describe counting up in steps from zero, securing their understanding of multiplication.

They will be expected to count in multiples of 2, 3, 4, 5, 8, 10, 50, and 100. You could help your child practise by taking it in turns to say the multiples of a number. For example:

You : 4 Your child : 8 You : 12 …  and so on.

Set a timer and see what number you can get to before a minute is up! Be sure to note any interesting patterns, like how multiples of five always end in a 5 or a 0.

4. Learn multiplication facts

In Year 3, it’s important that your child is able to recall multiplication facts. They will be likely to focus on the 3, 4, and 8 times tables. They will already be familiar with the 2, 5, and 10 times tables, but they will still practise them.

Video: What are multiples?

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Place Value Word Problems (Year 3)

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In this resource, children are encouraged to solve a variety of place value word problems, based on school locker codes, drink prices and the heights of different animals.

Answers are provided.

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: Addition & Subtraction
• Topic Group: Calculations
• Year(s): Year 3
• Media Type: PDF
• Resource Type: Worksheet
• Last Updated: 24/10/2023
• Resource Code: M2WAE110
• Curriculum Point(s): Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

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Year levels.

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Expected level of development

Australian Curriculum Mathematics V9 : AC9M3N03

Numeracy Progression : Additive strategies: P8, Number and place value: P5

At this level, students consolidate and deepen place value knowledge of two- and three-digit numbers. They do this by partitioning, rearranging and regrouping numbers to help in addition and subtraction calculations.

Use physical and virtual materials and visual representations to explore the proportional nature of place value parts when solving addition and subtraction problems. Provide repeated opportunities for students to explore different ways of partitioning, rearranging and regrouping when making calculations. For example: they explain that 163 + 28 can be more easily solved by breaking the numbers into place value parts, that 160 + 20 = 180 and 3 + 8 = 11, which then becomes 180 + 11 which makes 191.

Pose addition and subtraction problems horizontally (rather than vertically) to encourage students to think about problems in terms of place value parts. Ensure that students know they can rewrite and think about addition and subtraction problems horizontally, even if they are presented vertically to begin with. Use regular number talks to develop mental computation strategies. Include a focus on applying addition and subtraction strategies in a range of contexts, including through story problems.

Ensure students understand that different strategies will be more efficient at different times, for different people and across different problems.

Encourage students to value depth over speed. Celebrate sense-making, reasoning and lessons learned from mistakes when exploring and sharing strategies.

Teaching and learning summary:

• Use classroom talks and play-based explorations, in conjunction with explicit teaching, to support key understandings.
• Encourage reasoning, and emphasise the similarities and differences between different computation strategies used.

• justify choices when partitioning and regrouping numbers to perform addition and subtraction
• mentally solve addition and subtraction problems using partitioning, rearranging and regrouping, and explain the strategy used
• use written recordings to clearly display the solution used
• apply strategies involving partitioning, rearranging and regrouping when solving worded problems.

Some students may:

• be able to identify place value parts and count orally to 100 and beyond but still think about two- and/or three-digit collections additively in terms of ones (for example, understand 468 as the sum of 400 ones, 60 ones and 8 ones). To address this, consolidate place value understanding by comparing and ordering two-digit numbers (for example, which is larger – 2 bundles of ten and 3 ones, or the number 41 shown on a number line), counting forward and backward by tens and ones, and by renaming (for example, 32 is 3 tens and 2 ones; it’s also 32 ones; and it can also be 2 tens and 12 ones).
• consider each digit in an addition problem as a separate number as opposed to representing a place value part. When using the vertical or column method, failing to recognise the place value of the digits leads to a lack of reasoning and precision. To address this, present addition problems horizontally and create habits of reasoning that draw on place value understanding through number talks and other activities that focus on mental computation and breaking numbers up into their place value parts.

• subtract the smaller digit, regardless of which appears first when using the vertical or column method, indicating a lack of reasoning and understanding of the operation being used. To address this, present subtraction problems horizontally and create habits of reasoning through number talks and other activities that invite mental computation strategies and involve thinking in terms of place value parts.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning how place value parts help solve addition and subtraction problems.

Why are we learning about this?

• We use addition and subtraction in everyday contexts.

Use two- and three-digit numbers every day.

• Go on a number hunt. Look for, recognise and read the numbers around you, for example, numbers you notice around you on signs, calendars, speed signs and houses.
• Use everyday opportunities to practise using mental addition and subtraction strategies, such as predicting the change you will get at the store.
• Play ‘Guess my number’ or other games to put place value understanding into practice. Player 1 writes a two- or three-digit number on a piece of paper and the Player 2 asks ‘yes/no’ questions about it until they guess it. Example questions could be, ‘Is it larger than 500? Does it have an odd number in the hundreds place?’.

See mistakes as opportunities

• Know that mistakes are normal whenever we are learning or growing.
• When you get an incorrect answer, take the time to be curious about the mistake and see if you can learn from it. Which part of your strategy doesn’t quite make sense? How else could you approach the same problem?

Success criteria

• use the relationship between addition and subtraction to make some calculations
• solve addition problems mentally and verbally (for example, without pencil and paper) using place value parts
• solve subtraction problems mentally and verbally (without pencil and paper) using place value parts.

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Teaching strategies.

A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well. 

Concrete, Representational, Abstract (CRA model)

The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.

Culturally responsive pedagogy

Mathematics is not an exclusive western construct. Therefore, it is important to acknowledge and demonstrate the mathematics to be found in all cultures.

Collaborative learning

For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.

Questioning

A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.

Multiple exposures

Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.

Classroom talks

Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.

Teaching resources

A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.

Picture Storybooks: Year 3 place value

Use picture storybooks regularly to spark curiosity and interest in place value and related concepts.

Classroom Talks: Year 3 – Place Value

Run 5- to 15-minute classroom talks regularly to consolidate and build upon the foundations of place value.

resolve: Addition: Chess – The Rook

Explore addition using place value parts using the concept of chess.

Addition and subtraction with whole numbers

Use this unit to explore situations involving addition and subtraction where students choose strategies, using place value understanding.

Which would you do in your head?

Encourage students to think about which strategies suit them best when solving different addition and subtraction problems.

Wishball challenge: hundreds

Encourage students to think about the best strategies to use when solving different addition and subtraction problems.

Composition and calculation: 1,000 and four-digit numbers

Explore the composition of 1,000 and four-digit numbers.

Relevant assessment tasks and advice related to this topic.

By the end of Year 3, students extend and use single-digit addition and related subtraction facts and apply additive strategies to model and solve problems involving two- and three-digit numbers.

Assessment: Find the Solutions

Use the problems involving addition and subtraction to assess key understandings.

How many ways can you solve?

Use this task to gauge how students generate and reflect on strategies based on place value when solving problems.

Year 3 Number and Place Value

Click on an objective for related worksheets and resources.

Problem Solving with Place Value

February 3, 2021.

Understanding place value provides the essential foundation for so many aspects of mathematics, from multiplying and dividing by powers of ten, understanding the equivalence between fractions, decimals and percentages, and learning how to write and calculate with numbers in standard form.

The videos below show how I use the place value table to teach these topics conceptually.

Writing numbers as words

Multiplying by 10, 100 and 1000

Converting between fractions, decimals and percentages

I designed this problem-solving lesson to deepen students’ understanding of place value to connect it to other aspects of mathematics, including listing permutations, odd and even numbers and money. By linking to these topics, the questions are challenging yet remain accessible to students in key stage 3 and those studying the foundation GCSE course.

The lesson consists of six problem-solving questions, all centred around place value. Here is a sample of three of the questions.

Here is a sample of three of the questions.

Linking place value to arithmetic

In this question, students link their understanding of place value to writing numbers in figures from words. Next, they use column subtraction to find the difference between two numbers.

Linking place value to permutations

In this question, students arrange the four single-digit cards to make the numbers between 230 and 430.

Students link their understanding of place value to listing permutations.

Linking place value to odd and even numbers

To work out the smallest, even number, students need to find two three-digit numbers with the least difference.

To calculate the biggest, odd number, they need to find two numbers with the greatest difference.

Both questions can be completed through a method of trial and improvement. More able students would use:

• odd + odd = even
• odd + even =odd
• even + odd = odd
• even + even = even.

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About Mr Mathematics

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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Number and Place Value Worksheets - Year 3

Updated:  08 Feb 2022

16 number worksheets linked to the Australian Curriculum.

Non-Editable:  PDF

Pages:  32 Pages

• Curriculum Curriculum:  AUS V8, NSW, VIC, AUS V9
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• No Year Level Displayed (pdf) Sign up to Plus

This teaching resource  could be used in a variety of ways when teaching number . Some suggestions include:

• pre- and post-testing
• independent classwork

This teaching resource pack includes worksheets addressing the following concepts:

• odd and even numbers
• place value to thousands
• addition and subtraction
• addition strategies
• multiplication and division facts – 2s and 5s
• multiplication and division facts – 3s and 10s
• 2 digit by 1 digit multiplication.

Answer sheets are also provided.

Download options include:

• the year level displayed at the top of the sheet
• no year level displayed at the top of the sheet to use for differentiation.

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• Place Value →
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• Worksheets →

1-10 Addition Flashcards - Monsters (Vertical)

One hundred and one addition flashcards with numbers 0-10.

4-Digit Place Value Card Game - Race to 10 000

A fun game for students to play in small groups to consolidate their understanding of adding and subtracting in groups of 10, 100 and 1000.

1-10 Addition Flashcards - Owls (Vertical)

1-10 Addition Flashcards - Stars (Horizontal)

1-10 Addition Flashcards - Stars BW (Horizontal)

Lady Beetle Adding Activity

A fun and simple adding activity to consolidate simple addition.

Polygon Puzzles - Addition

A matching game that helps students to develop their addition skills.

Double Bubble - Doubling Game

A fun, interactive maths game for students to play when doubling numbers from 1 to 12.

Polygon Puzzles - Addition Worksheets with Answers

Line the sum up with the corresponding answer.

Doubles Leap Frog - Doubling Numbers Game

A fun game for students to play when doubling two digit numbers.

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Geometry and measure

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Number and Place Value

These activities are part of our Primary collections , which are problems grouped by topic.

These lower primary challenges all focus on number and place value.

Have a go at some of these upper primary tasks which will help deepen your understanding of number and place value.

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.

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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 :

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• 5th grade math problems
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Teaching Place Value in Year 1: A Comprehensive Guide for Educators

Maths Researcher

Place value is a foundational concept in our number system, laying the groundwork for all future mathematical learning. For Year 1 pupils, grasping this concept is a key step in developing a deep understanding of numbers and their relationships.

As educators, it's our responsibility to guide these young minds through the fascinating world of place value, setting them up for success in their mathematical journey.

In this guide, we'll explore effective strategies, engaging activities, and assessment techniques to help you teach place value in Year 1, as well as how parents can get involved at home.

Whether you're a seasoned educator or new to teaching maths, you'll find practical tips and research-based methods to make place value come alive in your classroom.

Understanding place value: Key concepts for Year 1

The UK National Curriculum states that in Year 1, pupils are expected to read, write and count numbers up to 100 using a tens and ones place value through objects and other pictorial representations.

Base-10 number system

Our number system is built on the concept of base-10, which means we use ten digits (0-9) to represent all numbers. In Year 1, we introduce this concept through hands-on activities and visual representations.

Key points to remember:

• Each digit's position determines its value
• The value of a digit increases tenfold as it moves one place to the left
• Zero is an important placeholder in our number system

Try this : Use a place value chart with physical objects to demonstrate how numbers are built. Start with single digits, then progress to two-digit numbers to show how the position changes the value.

• Tens and ones

Understanding tens and ones helps pupils visualise numbers and lays the groundwork for addition and subtraction.

Key ideas to emphasise:

• A 'ten' is a group of ten ones
• Two-digit numbers are composed of tens and ones
• The first digit in a two-digit number represents tens, the second represents ones

Try this : Use base-10 materials such as blocks or linking sticks to physically represent numbers. For example, show 34 as 3 sticks and 4 individual blocks.

Developmental progression of place value understanding

Understanding place value is a journey that unfolds gradually in Year 1. Let's explore the key stages of this developmental progression, from foundational skills to more abstract thinking.

Pre-place Value Skills

Before diving into place value, pupils can benefit from certain foundational skills. These pre-place value skills set the stage for deeper understanding.

Key pre-place value skills include:

• One-to-one correspondence : matching objects to numbers
• Subitising : recognising small quantities without counting
• Conservation of numbers : understanding that the number of objects remains the same regardless of arrangement

Try this : Use dot patterns on cards for quick subitising exercises. Start with patterns up to 5, then gradually increase to 10 as pupils become more confident.

Counting and grouping

As pupils progress, they move on to counting and grouping. This supports the understanding of the base-10 system and forms the backbone of place value comprehension.

Focus on these activities:

• Counting objects in twos, fives, and tens
• Grouping objects into tens and ones
• Using ten frames to visualise numbers

Try this : Create a 'counting station' in your classroom with various objects. Encourage pupils to practise counting and grouping during free time, reinforcing these skills through play.

Transitioning from Concrete to Abstract thinking

The journey from concrete understanding to abstract thinking is at the heart of the Maths — No Problem! approach. We teach this through the Concrete-Pictorial-Abstract (CPA) approach.

Stages of the CPA approach:

• Concrete : Pupils manipulate physical objects
• Pictorial : They use drawings or images to represent numbers
• Abstract : They work with numbers and symbols

When introducing a new concept, always start with concrete materials. Gradually introduce pictorial representations alongside the concrete, before moving to abstract symbols. This layered approach ensures pupils build a solid understanding at each stage.

Effective teaching strategies

Teaching place value in Year 1 requires a thoughtful approach that engages young learners and builds a strong foundation for future mathematical understanding. We’ve already discussed the CPA method, but what about other strategies? Let’s find out.

Manipulatives: More than just toys

How we use manipulatives determines how effective they are during our lessons. We can’t just hand out counters and hope for the best. Guide pupils in using these tools purposefully. For instance, when working with place value charts, have pupils physically move objects between columns to demonstrate regrouping.

Try this : create a 'maths toolkit' for each pupil with essential manipulatives like:

• Base-10 blocks
• Place value cards
• Number line

This ensures everyone has access to these tools when needed, promoting independent exploration and reinforcing place value concepts.

Visual models: Seeing is understanding

Visual models bridge the gap between concrete objects and abstract numbers. Number lines are particularly versatile when teaching relationships between numbers.

Use them to demonstrate:

• Counting forwards and backwards
• Visualising 'one more' and 'one less'
• Comparing and ordering numbers

For a practical activity, create a long number line on the classroom floor. Have pupils physically jump forward for 'one more' and backwards for 'one less'. This kinesthetic approach reinforces the concept while adding an element of fun.

The language of maths

Precise mathematical language is key to understanding place value:

• What does the [digit] stand for?
• Place value chart
• Number bonds

Encourage pupils to use this language when explaining their thinking. This not only reinforces their understanding but also develops their mathematical communication skills.

A helpful strategy is to create a ' maths word wall ' in your classroom. Add new terms as you introduce them, and refer to the wall regularly during lessons. This visual reference helps pupils internalise the language of place value.

The goal isn't just for pupils to calculate correctly, but to truly understand the underlying concepts of place value.

Engaging activities for teaching place value

We can make teaching maths fun with these hands-on experiences and real-world connections.

Hands-on games and exercises

Try these hands-on activities:

• Place value bean bag toss : Set up buckets labelled 'Tens' and 'Ones'. Pupils throw beanbags and record the two-digit number they create.
• Number building dice : In pairs, pupils roll dice to generate digits, then use base-10 blocks to build the largest number possible.
• Swap shop : Give pupils a pair of digit number cards. They must trade with classmates to make the largest or smallest number possible.

Digital tools and interactive activities

Incorporating technology can enhance place value lessons and cater to different learning styles.

Effective digital resources include:

• Interactive number lines and hundred squares
• Place value games on educational websites
• Virtual manipulatives that mimic physical base-10 blocks

Digital tools should complement, not replace, hands-on learning. Use them to reinforce concepts and provide additional practice.

Real-world applications and problem-solving

Connecting place value to real-life situations helps pupils understand its relevance and importance.

Consider these real-world activities:

• Classroom shop : Set up a pretend shop where items cost up to £99. Pupils use play money to make purchases, reinforcing their understanding of tens and ones.
• Number treasure hunt : Hide two-digit numbers around the school or playground. Pupils must find and order them from smallest to largest.
• Daily calendar : Use a monthly calendar to discuss dates, reinforcing concepts like 'one more' and 'one less'.

Try this : Encourage pupils to spot numbers in their environment and discuss their place value. This could be house numbers, price tags, or page numbers in books.

Differentiation techniques

In your classrooms, you'll find a range of abilities when it comes to understanding place value. Effective differentiation ensures that all pupils are appropriately challenged and supported. Let's explore some techniques to cater to diverse learning needs.

Supporting struggling learners

Pupils who find place value challenging often need more concrete experiences and targeted support.

Try these strategies:

• Use smaller number ranges : Start with numbers up to 20 before moving toward 100
• Provide additional manipulatives : Make sure struggling learners have regular access to manipulatives like base-10 blocks, number lines, and ten frames
• Use visual aids : Create place value charts with pockets to physically 'build' numbers

Try this : Implement a 'maths buddy' system where struggling learners are paired with more confident peers. This peer support can boost confidence on both sides. Pupils who understand the concept can practise explaining what they learned and struggling learners get a different perspective from another student.

Challenging advanced learners

For pupils who grasp place value quickly, provide opportunities to deepen their understanding and apply their knowledge in new contexts.

Consider these extension activities:

• Introduce three-digit numbers : Challenge advanced learners to explore hundreds, tens, and ones
• Encourage problem creation : Ask pupils to create their own place value puzzles for other students to solve

Addressing common misconceptions

Identifying and addressing misconceptions early is important for building a solid understanding of place value.

Common misconceptions include:

• Confusion between place and face value : Some pupils might think the '2' in 24 means 2, not 20
• Difficulty with zero as a placeholder : Pupils might struggle to understand why 105 is larger than 15
• Reversing digits : Writing 24 as 42, for example

Addressing misconceptions:

• Use concrete materials to physically represent numbers, emphasising the difference between tens and ones
• Provide plenty of practice with numbers including zero
• Use place value cards that can be physically arranged and rearranged

Try this : Create a 'misconception station' in your classroom. Display common errors and invite pupils to spot and correct them. This not only addresses misconceptions but also develops critical thinking skills.

By implementing these differentiation techniques, pupils, regardless of their starting point, can develop a robust understanding of place value. The goal is for every child to feel successful and engaged in their learning journey.

Parent involvement

Engaging parents in their child's mathematical learning can significantly enhance understanding of all maths concepts including place value.

Let's explore some effective strategies for involving parents in place value learning.

At-home activities to reinforce place value concepts

Encourage parents to incorporate place value exercises into everyday life. These activities should be fun, simple, and require minimal resources.

Suggested activities for parents:

• Number hunt : During walks or shopping trips, spot two-digit numbers and discuss their place value
• Dice games : Roll two dice to create two-digit numbers, then compare them. Talk about their place value and discuss why they are tens or ones
• Sorting coins : Use 1p and 10p coins to represent ones and tens, building different numbers

Try this : Create a 'Maths at Home' kit for each pupil. Include items like dice, base-10 blocks, and a simple place value chart. This ensures that pupils have access to basic resources for at-home practice.

Communication strategies for parents

Clear, regular communication with parents is key to maintaining their involvement and understanding of place value concepts.

Effective communication strategies include:

• Weekly newsletters : Share what maths concepts are being taught and suggest related home activities
• Parents evenings : Demonstrate how place value is taught in class during your next parent evening so parents can experience the learning process and model it at home
• Online resources : Create a class blog or use a learning platform to share videos of place value explanations and activities

Remember, many parents may be unfamiliar with current teaching methods, especially if they learned maths differently. Be patient and provide clear explanations of your classroom’s maths approach and the importance of place value.

Addressing parental concerns

Parents might express concerns or confusion about place value teaching methods. Address these proactively to maintain their support and involvement.

Common concerns and responses:

• " Why use base-10 blocks instead of just writing numbers? ": Explain the CPA approach and how concrete understanding leads to better abstract thinking
• " This looks different from how I learned maths ": Acknowledge this, but emphasise how these methods develop deeper understanding and problem-solving skills
• " My child still counts on their fingers ": Reassure parents that this is a normal stage of development, while gradually introducing more efficient strategies

Together we can create a supportive environment that extends beyond the classroom and opens up doors for communication to set up pupils for future maths success.

Assessment strategies

You may be wondering, how do we actually know if we are on the right track with our students with all of these strategies. This is where assessment comes into play.

Formative assessment techniques

Formative assessment provides real-time insights into pupils' learning, allowing us to adjust our teaching accordingly.

Try these formative assessment techniques:

• Observation : Watch pupils as they work with manipulatives or solve problems, noting their strategies and misconceptions
• Ask open ended questions : Learning to ask open ended questions leads to a wider understanding of the pupil’s capabilities
• White board responses : Pose quick questions for pupils to answer on individual white boards, allowing for a quick scan of class understanding

Using exit tickets and quick checks

Exit tickets and quick checks provide a snapshot of understanding at the end of a lesson or learning sequence.

Effective exit ticket ideas:

• Demonstrate place value : Ask pupils to represent a two-digit number using a place value chart, base-10 blocks, or number line
• True or false : Provide a statement about place value for pupils to evaluate
• Fill in the blank : Give pupils a partially completed place value statement to complete

Exit tickets should be quick to complete and easy to assess. Use the results to inform your planning for the next lesson.

Tracking progress over time

Monitoring progress over time helps ensure all pupils are moving forward in their place value understanding.

Consider these tracking methods:

• Place value checklist : Create a list of key skills (e.g., can count in tens, can identify tens and ones in a two-digit number) and regularly update it for each pupil
• Regular journalling : Have pupils consistently journal about their place value work throughout the year to show progression
• Regular low-stakes quizzes : Use short, focused assessments to track understanding of specific place value concepts

Using assessment data

The true value of assessment lies in how we use the data to inform our teaching.

Ways to use assessment data:

• Grouping : Use assessment results to create flexible groups for targeted support or extension
• Lesson planning : Adjust your plans based on common misconceptions or gaps identified in assessments
• Individual support : Use one-to-one conferencing to address specific difficulties highlighted by assessments

Baseline from Insights

See what pupils have retained. Quickly diagnose gaps. Move your class forward. Assessment as it was meant to be.

The goal with assessment is to gain a clear picture of each pupil's place value understanding, enabling educators to provide the right support at the right time.

Empowering young mathematicians: Their place value journey begins here

Teaching place value in Year 1 is a crucial foundation for mathematical learning, requiring a thoughtful blend of concrete, pictorial, and abstract approaches to help pupils understand the base-10 number system.

Effective strategies include using manipulatives, incorporating visual models, and engaging in real-world activities, whilst differentiating instruction to support all learners and involving parents in the learning process.

By implementing these varied techniques and maintaining ongoing assessment, we can create a rich, engaging environment for our pupils to develop a robust understanding of place value, setting them up for future mathematical success.

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