Mathematics · Year 2 · Additive Thinking and Strategy · Autumn Term

Number Bonds to 20 and Beyond

Recalling and using number bonds to 20, and applying this knowledge to related facts up to 100.

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

About This Topic

The commutative property is a fundamental rule of arithmetic that states the order of numbers does not change the result in addition (a + b = b + a). In Year 2, students explore this concept to build calculation efficiency. Understanding that 2 + 8 is the same as 8 + 2 allows them to always 'start with the larger number,' which reduces the cognitive load when counting on. This topic also introduces the non-commutative nature of subtraction, helping students see that 10 - 2 is not the same as 2 - 10.

This concept is a gateway to understanding number families and the relationship between addition and subtraction. By recognizing these patterns, students begin to see maths as a system of related facts rather than a series of isolated problems. Students grasp this concept faster through structured discussion and peer explanation using concrete models like part-whole diagrams.

Key Questions

1. Explain how knowing 7 + 3 helps us solve 70 + 30.
2. Predict the missing number in an addition or subtraction sentence using number bonds.
3. Justify why mastering number bonds makes mental calculations faster.

Learning Objectives

• Calculate missing numbers in addition and subtraction sentences up to 20 using known number bonds.
• Explain the relationship between number bonds to 20 and related facts up to 100, such as 7+3 and 70+30.
• Justify how recalling number bonds to 20 aids in faster mental calculations for sums up to 100.
• Identify pairs of numbers that add up to a given total within 20.

Before You Start

Counting to 100

Why: Students need to be able to count confidently to 100 to understand related facts up to 100.

Number Bonds to 10

Why: This is the foundational skill for recalling pairs of numbers that make 10, which directly supports number bonds to 20.

Addition and Subtraction within 20

Why: Students should have prior experience with basic addition and subtraction facts within 20 before extending this knowledge.

Key Vocabulary

Number Bond	A representation showing how two smaller numbers (parts) combine to make a larger number (whole). For example, 7 and 3 are parts that make the whole 10.
Related Fact	A number sentence that uses the same digits as another but in a different order or with different place values, like 7 + 3 = 10 and 70 + 30 = 100.
Commutative Property	The property stating that the order of numbers in an addition problem does not change the answer, so 7 + 3 is the same as 3 + 7.
Mental Calculation	Solving a math problem in your head without using written methods or a calculator.

Watch Out for These Misconceptions

Common Misconception

Trying to swap the numbers in a subtraction sentence.

What to Teach Instead

This is a very common error. Use physical objects to show that if you have 3 apples, you cannot take away 5. Active modeling makes the impossibility of the operation clear.

Common Misconception

Thinking that 5 + 2 and 2 + 5 are different problems to solve.

What to Teach Instead

Students often solve both from scratch. Use 'speed rounds' where they see the first answer and must instantly provide the second, explaining the rule to a partner to solidify the concept.

Active Learning Ideas

Think-Pair-Share: The Commutative Challenge

Give students an addition sentence and ask them to find its 'twin'. Then give a subtraction sentence and ask if it has a twin. Pairs discuss why it works for one but not the other.

15 min·Pairs

Simulation Game: The Human Part-Whole Model

Three students represent the parts and the whole. They move positions to show how the two 'part' students can swap places while the 'whole' stays the same, then try to do the same for subtraction.

20 min·Small Groups

Inquiry Circle: Fact Family Houses

Groups are given three numbers (e.g., 3, 7, 10). They must build a 'house' using blocks and write all four addition and subtraction facts that belong to that family, checking each other's work.

30 min·Small Groups

Real-World Connections

• Cashiers at a supermarket use number bonds to quickly calculate change. For example, if a customer pays with £10 for an item costing £7, the cashier quickly recalls the bond 7+3 to know the change is £3.
• Construction workers use addition and subtraction facts to measure and cut materials accurately. Knowing that 100cm is made of 70cm and 30cm helps them quickly determine if pieces will fit together.

Assessment Ideas

Quick Check

Present students with a part-whole diagram where the whole is 20 and one part is 8. Ask: 'What is the missing part?' Then, present a similar diagram with the whole as 80 and one part as 50. Ask: 'What is the missing part?'

Exit Ticket

Give each student a card with a number bond fact, such as 6 + 4 = 10. Ask them to write two related facts: one addition sentence up to 20 and one addition sentence up to 100. For example, 10 - 6 = 4 and 100 - 60 = 40.

Discussion Prompt

Pose the question: 'How does knowing 9 + 1 = 10 help you solve 90 + 10?' Encourage students to use the terms 'number bond' and 'related fact' in their explanations.

Frequently Asked Questions

What does 'commutative' actually mean?

It comes from the word 'commute,' meaning to move around. In maths, it means the numbers can move or swap places without changing the total. This only works for addition and multiplication.

How can active learning help students understand the commutative property?

Active learning, like the Human Part-Whole Model, allows students to physically see that the total doesn't change when parts move. By acting out the numbers, the abstract rule becomes a concrete experience. This helps them internalize the 'why' behind the rule, making it easier to apply in mental maths.

Why is it important to know that subtraction isn't commutative?

It prevents students from making errors in column subtraction later on. It also helps them understand the concept of 'the whole', you must have enough of something before you can take a part away.

How do fact families help with fluency?

They reduce the amount of information a child needs to memorize. If they know one fact (7+3=10), they actually know four facts. This builds confidence and speed.