Mathematics · Year 7 · The Power of Number · Autumn Term

Addition and Subtraction Strategies

Developing efficient mental and written methods for addition and subtraction of whole numbers and integers.

• National Curriculum Attainment Targets
• KS3: Mathematics - Number

About This Topic

The order of operations (BIDMAS/BODMAS) provides the essential grammar of mathematics. Without these rules, mathematical expressions would be ambiguous and inconsistent. This topic teaches students to navigate complex calculations by prioritising brackets, indices, and the specific hierarchy of division, multiplication, addition, and subtraction. It is a fundamental skill that underpins all future work in algebra and arithmetic.

In Year 7, the focus is on moving from simple two-step problems to multi-layered expressions. Students learn that the order is not just a list to follow blindly but a logical structure that ensures everyone, anywhere in the world, reaches the same answer. This topic particularly benefits from structured discussion and peer explanation, as students can debate the 'correct' path through a problem and identify where others might go wrong.

Key Questions

1. Differentiate between various addition strategies and assess their efficiency.
2. Explain how inverse operations can be used to check subtraction calculations.
3. Construct a scenario where estimation is more appropriate than exact calculation for addition.

Learning Objectives

• Compare the efficiency of different mental addition strategies, such as partitioning and bridging, for whole numbers up to 1000.
• Explain how the inverse relationship between addition and subtraction can be used to verify the accuracy of subtraction calculations.
• Calculate the sum or difference of integers, including negative numbers, using a chosen strategy.
• Construct a word problem where estimation is a more appropriate method for finding an approximate sum than exact calculation.

Before You Start

Place Value of Whole Numbers

Why: Understanding place value is essential for strategies like partitioning, which involves breaking numbers down into hundreds, tens, and ones.

Addition and Subtraction of Whole Numbers

Why: Students need a foundational understanding of adding and subtracting positive whole numbers before tackling more complex strategies and integers.

Introduction to Integers

Why: Familiarity with positive and negative numbers is necessary for applying addition and subtraction strategies to integer calculations.

Key Vocabulary

Mental Mathematics	Performing calculations in your head without the use of written methods or calculators.
Partitioning	Breaking down a number into its place value components (e.g., 345 becomes 300, 40, and 5) to simplify addition or subtraction.
Bridging	Adding or subtracting to the nearest multiple of 10 or 100 to make calculations easier, often used in mental strategies.
Inverse Operation	An operation that reverses the effect of another operation, such as addition reversing subtraction.
Estimation	Finding an approximate answer to a calculation by rounding numbers to make them easier to work with.

Watch Out for These Misconceptions

Common Misconception

Thinking that addition must always come before subtraction because 'A' comes before 'S' in BIDMAS.

What to Teach Instead

Explain that addition and subtraction have equal priority and should be performed from left to right. Use a 'tug-of-war' analogy or number line jumps in a group setting to show that the order of these two operations doesn't change the result if done correctly from left to right.

Common Misconception

Ignoring brackets or thinking they are optional.

What to Teach Instead

Students often calculate from left to right regardless of brackets. Use a simulation where two groups solve the same numbers but with different bracket placements to show how the 'priority' physically shifts the result.

Active Learning Ideas

Formal Debate: The Viral Equation

Present a controversial 'internet' maths problem (e.g., 8 ÷ 2(2+2)). Divide the class into teams to argue for different answers based on their interpretation of BIDMAS, eventually reaching a consensus through logical proof.

20 min·Whole Class

Inquiry Circle: Target Number

Give small groups four numbers and a target total. Students must use brackets and different operations to create an expression that equals the target, testing their understanding of how operation priority changes the outcome.

30 min·Small Groups

Peer Teaching: Error Detectives

Provide pairs with 'completed' worksheets full of common BIDMAS errors. Students must act as teachers to find the mistakes, explain why they happened, and provide the correct solution using a step-by-step breakdown.

25 min·Pairs

Real-World Connections

• Budgeting for a family holiday involves estimating costs for flights, accommodation, and activities. A travel agent might quickly calculate a rough total to give clients an idea of the expense, rather than precise figures that could change.
• Retail inventory management uses addition and subtraction strategies. A shopkeeper might mentally add incoming stock to existing inventory or subtract sales to get a quick idea of remaining items, especially for fast-moving goods.

Assessment Ideas

Quick Check

Present students with three addition problems: 45 + 67, 132 + 89, 567 + 234. Ask them to solve the first using partitioning, the second by bridging, and the third using a written method, then state which strategy they found most efficient for each and why.

Exit Ticket

Give students the calculation 73 - 28. Ask them to solve it using a mental strategy and then write one sentence explaining how they could use addition to check their answer.

Discussion Prompt

Pose the scenario: 'You need to buy ingredients for a bake sale. You have a list of 15 items with prices ranging from £0.50 to £4.00. Would you calculate the exact total cost or estimate it? Explain your reasoning, considering the purpose of the calculation.'

Frequently Asked Questions

How can active learning help students understand the order of operations?

Active learning encourages students to justify their steps. Instead of just memorising an acronym, students engage in 'error analysis' or 'target number' games where they must explain *why* a certain operation must happen first. This verbalisation of the logic helps move the rules from short-term memory into a deeper conceptual understanding of mathematical hierarchy.

What does BIDMAS stand for in the UK curriculum?

It stands for Brackets, Indices, Division and Multiplication, and Addition and Subtraction. Some schools use BODMAS (Orders instead of Indices), but the principle remains the same: it defines the hierarchy of mathematical operations.

Why is the order of operations so important for algebra?

Algebra involves manipulating expressions with variables. If a student doesn't understand that a coefficient (multiplication) takes priority over addition, they will consistently simplify expressions incorrectly, leading to errors in solving equations.

How do I teach students to handle indices within BIDMAS?

Start by ensuring they understand what an index (power) is. Then, provide examples where an index is inside a bracket versus outside, using peer discussion to model how the priority changes in each case.