Algebra and the Laws of Numbers
Year 7 Mathematics Exploring Number Laws with Variables
Learning Intentions
Apply number laws using pronumerals and algebraic expressions Use variables with number laws Simplify algebraic expressions Recognise equivalent expressions
Warm-Up: True or False?
a + b = b + a 2(x + 3) = 2x + 3 (a + b) + c = a + (b + c) Discuss and justify your answers
From Numbers to Algebra
We use the same laws with numbers and variables Numbers: 3 + 5 = 5 + 3 Algebra: a + b = b + a Variables represent any number
The Commutative Law
Order doesn't matter for addition and multiplication Addition: a + b = b + a Multiplication: a × b = b × a Example: x + 7 = 7 + x
The Associative Law
Grouping doesn't matter for addition and multiplication (a + b) + c = a + (b + c) (a × b) × c = a × (b × c) Example: (x + 2) + 5 = x + (2 + 5) = x + 7
The Distributive Law
Multiply everything inside the brackets a(b + c) = ab + ac Example: 3(x + 4) = 3x + 12 Think: 'distribute' the multiplication
What Doesn't Work?
{"left":"Subtraction is NOT commutative\nDivision is NOT associative","right":"5 - 3 ≠ 3 - 5\n(8 ÷ 4) ÷ 2 ≠ 8 ÷ (4 ÷ 2)"}
Guided Practice
Simplify these expressions: 3(x + 4) = ? a + 7 + b = ? (2 + m) + 5 = ? Which law did you use each time?
Independent Challenge
Match each expression with its simplified form and the law used: Can you create a word problem that shows the distributive law?
More Algebraic Expressions slide decks
Other ready-to-teach decks on algebraic expressions.
