Unlocking Brackets in Mathematics
Year 7 Mathematics Expanding and Simplifying Algebraic Expressions
What Are Brackets in Mathematics?
Brackets group terms together They show which operations to do first Common types: ( ), [ ], { } Help us organize mathematical expressions
Quick Check: What's the Difference?
Calculate: 3 × (4 + 2) Calculate: 3 × 4 + 2 Which answer is larger? Why are the answers different?
The Distributive Property
When we multiply a number by a bracket, we distribute it to each term inside a(b + c) = ab + ac This is called 'expanding' the brackets Example: 3(x + 4) = 3x + 12
Practice: Simple Expansion
Expand these expressions: 2(x + 5) 4(y + 3) 5(2a + 1) Work in pairs and check your answers
Expanding with Positive and Negative Terms
{"left":"When expanding 3(x - 2):\nDistribute 3 to both x and -2\n3 × x = 3x","right":"3 × (-2) = -6\nResult: 3x - 6\nRemember: positive × negative = negative"}
Expanding Brackets with Variables Outside
Sometimes the multiplier is also a variable Example: x(y + 3) = xy + 3x Example: 2a(b + 4) = 2ab + 8a Apply the same distributive rule
Challenge: Mixed Practice
Expand these more complex expressions: a) -2(x + 4) b) 3y(2 + y) c) -4(2a - 3) d) 2x(3x + 5) Compare answers with a classmate
Mathematical Wisdom
"Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding." - William Paul Thurston
Summary: Key Points to Remember
The distributive property: a(b + c) = ab + ac Always distribute to every term inside the brackets Pay attention to positive and negative signs Practice makes perfect - keep working on examples Next: We'll learn to expand double brackets!
More Algebraic Expressions slide decks
Other ready-to-teach decks on algebraic expressions.
