# Mathematics / Year 4 / Algebra

Version 9
Curriculum content descriptions

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator (AC9M4A02)

Elaborations
• using arrays on grid paper or created with blocks or counters to develop, represent and explain patterns in the $$10 \times 10$$ multiplication facts; using the arrays to explain the related division facts
• using materials or diagrams to develop and record multiplication strategies such as doubling, halving, commutativity, and adding one more or subtracting from a group to reach a known fact; for example, creating multiples of $$3$$ on grid paper and doubling to find multiples of $$6$$; recording and explaining the connections to the $$\times3$$ and $$\times6$$ multiplication facts: $$3, 6, 9,$$ … doubled is $$6, 12, 18,$$ …
• using known multiplication facts for $$2, 3, 5$$ and $$10$$ to establish multiplication facts for $$4, 6, 7, 8$$ and $$9$$ in different ways; for example, using multiples of $$10$$ to establish the multiples of $$9$$ as “to multiply a number by $$9$$ you multiply by $$10$$ then take the number away”; $$9 \times 4 = 10 \times 4\space – \space4$$, so $$9 \times 4$$ is $$40 \space– \space4 = 36$$; using multiple of $$3$$ as “to multiply a number by $$9$$ you multiply by $$3$$, and then multiply the result by $$3$$ again”
• using arrays and known multiplication facts for twos and fives to develop the multiplication facts for sevens, applying the distributive property of multiplication; for example, when finding $$6 \times 7$$, knowing that $$7$$ is made up of $$2$$ and $$5$$, and using an array to show that $$6 \times 7$$ is the same as $$6 \times 2 + 6 \times 5 = 12 + 30$$ which is $$42$$
• using known multiplication facts up to $$10 \times 10$$ and the inverse relationship of multiplication and division to establish corresponding division facts
• designing, creating and playing instructive card games that involve the recall, recognition and explanation of the $$10 \times 10$$ multiplication facts and related division facts
General capabilities
• Critical and creative thinking Critical and Creative Thinking
• Numeracy Numeracy
ScOT terms

Commutativity,  Distributivity,  Division,  Multiplication tables

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