# Mathematics / Year 5 / Algebra

Version 9
Curriculum content descriptions

find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations (AC9M5A02)

Elaborations
• 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 $$8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8$$
• using materials, diagrams or arrays to recognise and explain the distributive property; for example, where $$4 \times 13 = 4 \times 10 + 4 \times 3$$
• 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 $$3 \times 4 = \square\times 2$$
General capabilities
• Numeracy Numeracy
• Critical and creative thinking Critical and Creative Thinking
ScOT terms

Mathematical expressions,  Factors

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