reasoning and problem solving year 3 place value

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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.  

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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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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.

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Aim high, believe in yourself and celebrate success together..

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Place Value Problem Solving Year 3

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

1 October 2016

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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.

Teach this lesson

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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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Place Value Consolidation Year 3 Autumn Block 1 Reasoning and Problem Solving

Place value consolidation year 3 autumn block 1 questions.

This Place Value Consolidation Year 3 Autumn Block 1 resource is aimed at Year 3 Secure and has been designed to give children the opportunity to consolidate the skills they have learned in Block 1 – Place Value.

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What's included in the pack?

This pack includes:

• Place Value Consolidation Year 3 Autumn Block 1 Reasoning and Problem Solving worksheets (includes answers).

National Curriculum Objectives

Mathematics Year 3: Identify, represent and estimate numbers using different representations

Mathematics Year 3: Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number

Mathematics Year 3: Compare and order numbers up to 1000

Mathematics Year 3: Read and write numbers up to 1000 in numerals and in words

Mathematics Year 3: Recognise the place value of each digit in a three-digit number (hundreds, tens, ones)

Mathematics Year 3: Solve number problems and practical problems involving these ideas

Small Steps:

Represent numbers to 1,000

100s, 10s, 1s (1)

Number line to 1,000

Find 1, 10, 100 more or less than a given number

Order numbers

Count in 50s

​​​This resource is available to download with a Premium subscription.

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Reasoning/Problem Solving Maths Worksheets for Year 3 (age 7-8)

Money problems and challenges.

A variety of problem solving activities involving money.

50p to spend, but can you make sure you get the correct change?

Watch out when writing pence as pounds and remember to always have two digits after the decimal point.

The hardest part of these money problems is to read the question and work out what to do.

Put three items in your basket that you would like to buy and then use the money cards to work out the sum.

Solve money problems using the information provided.

Solve money problems at the skating rink.

Plenty of monkey business here!

It's a trip to the zoo to find the very best value.

Some tricky money problems to solve.

More tricky money problems to solve.

Finding different amounts from a given set of coins.

Number and calculating problems

Solve number problems and calculating using addition, subtraction, multiplication and division.

Find the 2-digit numbers that can be made using these digit cards.

Make 2-digit numbers and find the smallest and largest numbers.

More on finding 2-digit numbers from three digit cards.

Tricky little problems involving monsters' legs.

Use logic, addition and subtraction to find out how many strawberries are eaten.

Bar Model: addition and subtraction facts.

Use bar models to add and subtract.

Encourage children to make addition and subtraction come to life by writing short number stories.

What numbers can you make with digit cards?

What are the largest and smallest numbers that can be made with 3 cards?

More number stories to write: this time all about multiplication and division.

All the numbers are here, but the signs are missing! Can you work out what the signs should be?

Investigating odd and even numbers and what happens when you add them together.

Use knowledge of place value to find all possible answers.

Finding the numbers and missing digits to make number sentences correct.

Investigate statements involving odd and even numbers.

Investigate statements about multiplication and times tables.

I?m good at thinking of numbers, but can you work out what number I am thinking about ? I do give a clue!

Work out the missing value using division and addition.

Use reasoning to find the missing values.

More on finding the missing values - an early introduction to algebra.

Use division and addition to find the missing values.

Find the missing values from the information given.

More on finding the value using reasoning.

Real life and word problems

A selection of real life problems and word problems.

Tricky word problems.

More tricky word problems.

Tricky questions, but you only have to carry out one maths step to answer them.

Even trickier questions, and you have to carry out at least two steps to work them out!

More word problems, from the library to shopping and on to flying around the world.

Here we have four pages of questions all on time, including a trip to Alicante!

Solving tricky fraction problems.

More challenges and activities

A great selection of activities requiring logical thinking.

Investigation looking at possibilities when adding the digits from 1 to 5.

This time you can decide the total for the sides of the triangle.

Can you put the numbers 1 to 9 in the diagram so that the difference between each pair of joined numbers is odd?

This challenge is to find as many ways as possible of making 12 using three number cards and the add, subtract and multiply signs.

A development of the 'Caterpillar investigation' but using multiples of 10. Great for practising addition.

3 dinosaurs laid some eggs. They laid 19 altogether. How many did they each lay?

How many ways can three runners cover a distance of 19 miles? They all have to run an odd number of miles.

A book challenge here. How accurately can you guess the number of pages in books?

2D card shapes and a 3 x 3 pinboard are useful for these shape activities.

A calculator is needed to find how many different answers can be made from the numbers given. Good for working in an organised, logical way.

A brief summary of some of the most important maths concepts to be taught in Year 3 by way of challenges and investigations.

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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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