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

How Bloomi helps with this

This is a NAPLAN-year topic. Bloomi teaches it with a short explainer, guided practice, and NAPLAN-style questions — every one traceable to this exact code.

What this looks like in the classroom

• 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 \(2\)
• 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 \(15 ÷ 3 = 30 ÷ 6\)
• 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 \(8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8\)