place value reasoning and problem solving year 2

Number & place value in Year 2 (age 6–7)

In Year 2, your child will learn to compare and order numbers from 1 to 100. They will recognise the place value of two-digit numbers, and will be able to use this to solve problems. They will also make more use of number lines and will be able to use less than (<), more than (>), and equals (=) symbols.

The key words for this section are number and place value .

What your child will learn

Take a look at the National Curriculum expectations for number and place value in Year 2 (ages 6–7):

Count in 2s, 3s, and 5s from 0, and in 10s from any number

Recognise the place value of two-digit numbers.

For example, in ’25’, they will understand that the first number (2) shows the number of tens, and the second number (5) shows the number of ones. So there are two tens and five ones in the number 25. Note that your child will say ones and not units when talking about place value.

Identify, represent, and estimate numbers shown in different ways

Your child will be expected to use objects, drawings/diagrams/pictures, number lines and 100 squares , and symbols to represent numbers. They will make these representations themselves, and will also be able to understand them when someone else has made them.

Your child will also start to estimate numbers based on different representations. For example, they will be able to say, ‘each of those piles of sticks has about 10 sticks, so we have about 30 sticks.’

Compare and order numbers from 0 to 100

Your child will be able to compare two numbers to say which one is bigger and which one is smaller. They will also be able to explain why:

47 is more than 29 as 47 has 4 tens compared with 29 which only has 2 tens.

Your child will learn to put a selection of numbers between 0 and 100 in order:

46, 19, 3, 76, 43, 79 in order from smallest to largest are 3, 19, 43, 46, 76, 79.

Your child will use the words will use the words  more , less , fewer , more than , less than , equal to , equivalent to , and the same value as when comparing numbers. They will use the word  fewer  when working with things that can be counted, and less when working with abstract numbers and things that are  continuous .

‘I have 3   fewer   sweets than you.’   ‘There is   less   water in the glass than in the bottle.’   ‘25 is   less  than 42.’

They will also be able to use the more than (>), less than (<) and equals (=) symbols to compare numbers.

Read and write numbers up to at least 100

Your child will read and write numbers to at least 100 in numerals (1, 2, 3, and so on) as well as in words (one, two, three, and so on).

Writing out the numbers 10–20 can be particularly tricky for children, so your child might need a bit more focus on these numbers to start with.

Use place value and number facts to solve problems

‘If I have 6 apples and you have 4 apples, how many apples do we have altogether?’

To solve this problem, your child needs to understand that zero can be used as a placeholder in numbers like 10, where the ‘1’ means that there is one ten, and the ‘0’ means there are no ones.

How to help at home

There are lots of ways you can help your child to understand number and place value. Here are just a few ideas:

1. Represent numbers creatively

Showing numbers in interesting ways really helps your child to understand number and place value. Objects from around the home like buttons, dried pasta shapes, marbles, or pencils are great to practise counting and organising numbers. For example, ’32’ could be represented by 32 marbles arranged into three groups of ten and two ones.

As well as objects, your child can use drawings, diagrams, or symbols to represent numbers. For example, you could draw 23 stick figures, then draw a circle around each group of ten, with three left outside of the circles. This shows that 23 is made from two tens and three ones.

Video: What is number?

Get a simple definition of the concept of number and the difference between cardinal, ordinal and nominal numbers with this fun animation.

2. Play a matching game

Your child will be expected to write numbers up to 100 using numerals and words. You could support their learning by playing a matching game.

Make two sets of simple cards or pieces of paper. On one set of cards, write numbers in numerals (for example, ’67’). On another set of cards, write the matching number names (for example, ‘sixty-seven’). Mix all the cards up and play snap.

Activity: Number words

3. Compare and order numbers

Encourage you child to talk through how they know that one number is bigger or smaller than another:

I know that 32 is smaller than 76, because 32 only has 3 tens, and 76 has 7 tens.

Encourage your child to use more than (>) and less than (<) symbols when comparing numbers. For example, they could write 32 < 76 or 76 > 32.

You could practise ordering with a card game. Write twenty two-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

When your child is counting objects, ask them to estimate how many there are before they count them. Being able to make accurate estimates within mathematics is a valuable skill we use in everyday life. It will help them to tell if their answers to maths problems are reasonable or not.

When counting more than ten objects in a set, it is an important skill for your child to be able to group objects in groups of ten. For example, if they are counting 36 buttons, encourage them to begin by counting out buttons into groups of ten. They will then have 3 groups of ten buttons and 6 buttons on their own.

Activity: Counting coins

5. Partition numbers in different ways

Partitioning means to break numbers into parts. Use practical resources, such as straws grouped in tens, to partition numbers in different ways. For example, the number 54 can be partitioned into 50 + 4, 40 + 14, 30 + 24, 20 + 34, or 10 + 44.

This will help your child to see patterns in numbers as they develop their calculation skills.

6. Using number facts

To help reinforce your child’s understanding of number, try to find everyday opportunities for them to use known number facts to solve problems.

This is a really easy thing to do at home and in the shops. For example:

‘If we buy 7 apples and 3 bananas – how many pieces of fruit do we have altogether?’   ‘If we have 10 people coming to your party and we have 5 party bags, how many more do we need to buy?’

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Problem Solving: Year 2 – Number and Place Value – Maths Challenge

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These problem-solving worksheets provide extra challenge for Y2 children. A variety of problems are spread across three sections, enabling you to use the whole sheet during a single lesson or to select specific problems for different teaching sessions, or home learning.

Y2 maths objective: use place value and number facts to solve problems.

This resource is part of the Challenge Maths collection. View more from this collection

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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.

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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 Charts - Year 2

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

15 July 2024

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In this KS1 maths teaching resource, pupils begin to use place value charts to aid understanding of place value. These activities cover the year 2 curriculum objectives in the maths programme of study (Number - number and place value) and supports the White Rose small steps guidance for year 2 - Autumn - Block 1 - Place Value. Content includes:

• Identify the number represented in the place value chart differentiated activities and accompanying worksheets
• Represent the number in the place value chart using base 10 and place value counters with accompanying worksheet and place value chart template and cut outs
• Write the number represented by the place value chart in words and complete the number sentences with accompanying worksheet
• Reasoning and problem solving activity and worksheet

‘Place Value Charts - Year 2’ is editable so teachers can adapt the resource to meet their individual teaching needs.

Not quite what you’re looking for? Click below to see more Year 2 Place Value resources:

Counting to 100 - Year 2 Representing Numbers - Year 2 Part-Whole Models - Year 2 Tens and Ones Addition - Year 2 Comparing Objects - Year 2 Comparing Numbers - Year 2 Ordering Objects and Numbers - Year 2 Counting in 2s, 5s and 10s - Year 2 Counting in Steps of 3 - Year 2

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A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

Year 2 Place Value Bundle

This year 2 maths teaching bundle contains the following 10 PowerPoint activities with accompanying worksheets: * Counting to 100 - Year 2 * Representing Numbers - Year 2 * Part-Whole Models - Year 2 * Tens and Ones Addition - Year 2 * Place Value Charts - Year 2 * Comparing Objects - Year 2 * Comparing Numbers - Year 2 * Ordering Objects and Numbers - Year 2 * Counting in 2s, 5s and 10s - Year 2 * Counting in Steps of 3 - Year 2 Each of these maths teaching resources has been designed to help deliver lessons covering the curriculum objectives of the year 2 maths programme of study Number (Number and place value) and support the White Rose small steps guidance for year 2 - Autumn - Block 1 - Place Value. For a full description and preview of each resource please click on the images below. This bundle gives you a saving of 63% when compared to buying each resource individually.

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Year 2 Place Value Problems Game

Support your child’s addition and subtraction skills by playing this Year 2 Place Value Problems Game. Children will use their knowledge of number facts and place value to solve problems. They will solve money problems, add tens and ones and add three one-digit numbers.

If you would like to access  additional resources which link to Year 2 Place Value Problems Game, you can purchase a subscription for £5.31 per month on our sister site, Classroom Secrets .

Teacher Specific Information

This Year 2 Place Value Problems Game supports pupils’ understanding of using place value knowledge and number facts to solve addition and subtraction problems. Children will solve money problems, add tens and ones and add three-one digit numbers. The five questions include fill in the blanks, single choice sets and a drag and drop question.

National Curriculum Objectives

Number & Place Value (2N6) Use place value and number facts to solve problems

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