AC9M5A02

Elaborations

• AC9M5A02_E1using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3×5=15 and 30÷2=15 then 3×5=30÷2 therefore the solution to 3×5=30÷□ is 2
• AC9M5A02_E2using relational thinking, an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6
• AC9M5A02_E3using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not; for example, using arrays to demonstrate that 2 ×3 = 3 ×2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 ×2 ×3 = 12 and 2 ×3 ×2 = 12 and 3 ×2 ×2 = 12; understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8
• AC9M5A02_E4using materials, diagrams or arrays to recognise and explain the distributive property; for example, where 4 ×13 = 4 ×10 + 4 ×3
• AC9M5A02_E5constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering 3 ×4 = 12 and knowing 2 ×2 = 4 then 3 ×4 can be written as 3× (2 ×2) and using the associative property (3 ×2) ×2 so 3 ×4 = 6 ×2 and so 6 is the solution to 3 ×4 = □×2