AC9M5A02 Year 5 Mathematics

Content descriptor find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations

Elaborations

• • Elaboration using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3\times5=15 and 30\div2=15 then 3\times5=30\div2 therefore the solution to 3\times5=30\div\square is 2
• • Elaboration using 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
• • Elaboration using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not; for example, using arrays to demonstrate that 2 \times 3 = 3 \times 2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 \times 2 \times 3 = 12 and 2 \times3 \times2 = 12 and 3 \times 2 \times 2 = 12; understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8
• • Elaboration using materials, diagrams or arrays to recognise and explain the distributive property; for example, where 4 \times 13 = 4 \times 10 + 4 \times 3
• • Elaboration constructing 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 \times 4 = 12 and knowing 2 \times 2 = 4 then 3 \times 4 can be written as 3\times (2 \times 2) and using the associative property (3 \times 2) \times 2 so 3 \times 4 = 6 \times 2 and so 6 is the solution to 3 \times 4 = \square\times 2