Mathematics · Year 1 · Additive Reasoning · Autumn Term

Number Bonds to 10

Understanding how numbers can be broken into parts and recombined to form a whole up to 10.

• National Curriculum Attainment Targets
• KS1: Mathematics - Addition and Subtraction

About This Topic

Addition and subtraction strategies in Year 1 focus on developing a toolkit of mental and physical methods. The National Curriculum expects pupils to read, write, and interpret mathematical statements involving addition (+), subtraction (-), and equals (=) signs. Students move from 'counting all' (counting every object in two groups) to 'counting on' from the largest number, which is a significant milestone in mathematical efficiency.

This topic also introduces the concept of commutativity in addition (that 3 + 2 is the same as 2 + 3) and the fact that subtraction is not commutative. Understanding these properties helps students solve problems more flexibly. This topic comes alive when students can physically model the patterns using number lines, bead strings, and collaborative problem-solving tasks.

Key Questions

1. Construct all possible number bonds for the number 10.
2. Justify why knowing number bonds helps with addition and subtraction.
3. Compare different strategies for finding number bonds.

Learning Objectives

• Identify all pairs of numbers that sum to 10.
• Calculate the missing number in a number bond to 10.
• Explain how knowing number bonds to 10 supports addition calculations.
• Demonstrate how number bonds to 10 can be used to solve subtraction problems.
• Compare strategies for finding number bonds to 10, such as counting on or using manipulatives.

Before You Start

Counting to 10

Why: Students need to be able to count reliably up to 10 to identify and construct number bonds.

Recognizing Numbers 0-10

Why: Students must be able to recognize and name numerals up to 10 to work with number bonds effectively.

Key Vocabulary

Number Bond	A visual representation showing how a whole number can be broken down into two parts. For example, 7 and 3 are parts of the whole 10.
Part	One of the two numbers that make up a whole number when using a number bond. For the number bond of 10, the parts are the two numbers that add up to 10.
Whole	The total number that is made up of two parts. In this topic, the whole is always the number 10.
Addition	The process of combining two or more numbers to find a total. For example, 4 plus 6 equals 10.
Subtraction	The process of taking away one number from another to find the difference. For example, 10 minus 3 equals 7.

Watch Out for These Misconceptions

Common Misconception

Counting the starting number

What to Teach Instead

When counting on, students often count the number they start with (e.g., for 5 + 3, they say '5, 6, 7'). Use a number line and emphasize that the first 'jump' is the first count, so they start counting from the next number.

Common Misconception

Subtraction can be done in any order

What to Teach Instead

Students might think 3 - 5 is the same as 5 - 3. Use physical objects to show that if you have 3 sweets, you cannot give away 5, highlighting that the order matters in subtraction.

Active Learning Ideas

Peer Teaching: Strategy Swap

In pairs, one student solves an addition problem by 'counting all' with cubes, while the other 'counts on' using a number line. They then explain to each other which way was faster and why.

15 min·Pairs

Simulation Game: The Addition Shop

Set up a small shop with items priced 1p to 10p. Students take turns being the shopkeeper and the customer, adding the cost of two items together and 'taking away' the money from their purse to practice subtraction.

25 min·Small Groups

Think-Pair-Share: True or False?

The teacher shows a card like '5 - 2 = 7'. Pairs must discuss if it is true or false, use cubes to prove their answer, and then share their reasoning with the class.

10 min·Pairs

Real-World Connections

• When counting items in a shop, like 10 apples, a cashier might quickly recognize that 4 apples and 6 apples make a full bag of 10, speeding up the transaction.
• A child playing with building blocks might learn that if they have 10 blocks and give 3 to a friend, they have 7 left, understanding the relationship between 10, 3, and 7.

Assessment Ideas

Exit Ticket

Give each student a card with a number from 1 to 9. Ask them to write the number that completes the number bond to 10. Then, ask them to write one sentence explaining how they found their answer.

Quick Check

Display a large number 10 with two empty circles below it. Ask students to call out pairs of numbers that fit into the circles to make 10. Record their suggestions on the board, discussing the commutative property if 3+7 and 7+3 are offered.

Discussion Prompt

Pose the question: 'If you know that 6 and 4 make 10, how does that help you figure out 10 take away 4?' Facilitate a discussion where students explain the inverse relationship between addition and subtraction using number bonds.

Frequently Asked Questions

What is 'counting on' and why is it important?

'Counting on' is when a child starts with the largest number and then counts up the remaining amount. It is more efficient than 'counting all' because it requires less counting and shows a deeper understanding of number value. It is a key step toward mental math.

How can active learning help students understand addition and subtraction?

Active learning, such as role-playing a shop or using physical number lines, makes the operations meaningful. When students simulate real-world scenarios, they understand why we add or subtract. Collaborative tasks allow them to hear different strategies from their peers, which helps them move beyond basic counting to more advanced mental methods.

When should children stop using their fingers to add?

Fingers are a great natural manipulative, but we want students to move toward mental strategies and number bonds by the end of Year 1. Encourage the use of number lines and counters as a bridge away from finger counting.

How do I explain the minus sign?

Explain the minus sign as an instruction to 'take away', 'remove', or 'find the difference'. Using a variety of words helps children understand that subtraction applies to many different situations.