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Multiplication and Division Progressions Progression Example CA Solve simple problems by counting all the objects from one. Rote skip count in 2’s 5’s,10’s (then 3’s, 4’s) 3 x 2 = 1,2, 3,4, 5,6 5,10, 15, 20, 25, 30, 35, 40, 45, 50 AC Use skip counting to solve multiplication problems (involving 2’s,5’s10s) 6 x 5 = 5, 10, 15, 20, 25, 30 Understand meaning of “x” using arrays. See that 3 x 6 and 6 x 3 may have the same answer but ‘look’ different. 3 x 6 = ****** ****** ****** Understand the link between addition and multiplication and use repeated addition to solve problems. 5x3=3+3+3+3+3 =6+6+3 Understand division as a ‘sharing” context. 8 4 = ** ** ** ** 8 lollies shared between 4 children, how many lollies does each child have? 8 4 = **** **** 8 lollies put into sets of 4, how many sets? EA Stage 5 Understand division as a ‘grouping“ context. AA Stage 6 AM Stage 7 Solve division problems by skip counting or repeated addition 12 3 = 3,6,9,12 therefore the answer is 4. Understand x 2 by doubling, Understand x5 by halving x 10 KNOWLEDGE: Recall x 2 x 5 and x 10 mult and div facts 2 x 8 = double 8, or 8 + 8 5 x 8 = half of 10 x 8 Derive unknown basic multiplication facts from known facts using: commutative property to make problems easier (change the order) 6x3=3x6 distributive property x 6, x7, x8 from x5 known facts (splitting) x4 and x9 facts from x5 or x10 known facts (tidy numbers) 8 x 6 = (8 x 5) + (8 x 1) 9 x 7 = (10 x 7) – (1 x 7) associative property x4, x8 by doubling and doubling again Apply these strategies to larger numbers. e.g. 6 x 19 = (6 x 20 ) - 6 8 x 6 = 2 x 2 x (2 x 6) Multiply by tens and hundreds 28 x 10=280, 36 x 100=3600 Solve division problems by reversing into a multiplication problem (inverse operations) 36 4 is the same as 4 x ? = 36 KNOWLEDGE: Recall all basic multiplication facts to 10x10 & some division facts (all division facts to be learnt at Stage 7). 6 x 7, 4x3, 9x8 Choose efficiently from a range of mult/div strategies to a full range of contexts and whole numbers. Division Example Multiplication Example 76 4 is the same as (80 4) – (4 4) = 20 – 1 = 19 Tidy Numbers 29 x 6 = (30 x 6) – (1 x 6) 76 4 is the same as (40 4) + (36 4) = 10 + 8 108 12 is the same as (108 2) 6 Place Value 24 x 6 = (20 x 6) + (4 x 6) Splitting Factors 23 x 12 = 23 x 3 x 2 x2 Adjusting both numbers proportionally by finding a common factor. 108 12 is the same as 54 6 = 9 Proportional Adjustment (associative Property) 18 x 3 = 9 x 6 (doubling and halving) 33 x 27 = 99 x 9 (thirding and trebling) Standard Written Forms AP 108 12 is the same as 12 x ? = 108 Reversibility (inverse) Not Applicable 39 4 = Express remainders as whole numbers, fractions, or decimals Not Applicable Divisible by.. 3 and 9 if sum of digits are divisible by 9. Use divisibility rules for 2,3,5 9 (then 4,6,8), Not Applicable 9 = 3 Use exponents (powers and roots of numbers) 32 = 3 x 3 = 9 9r3 or 9 ¾ or 9.75 Apply properties of multiplication and division across a full range of contexts with fractions and decimals and manipulating relationships algebraically. Marie Hirst, Numeracy Facilitator, Facilitator name, Month, year [version ie. Draft v3] 2