1. Intelligent Grouping (teacher notes): 1.The students know that 3 chairs and 7 chairs make 10 chairs. But they may not realise that this works for all kinds of ‘objects’. For example, 3 tens and 7 tens make 10 tens (30+70=100). And if you group things in eights then 3 eights and 7 eights make 10 eights (24+56=80). 2.This previous problem can be thought of as: (3x8)+(7x8)=(3+7)x8=10x8=80 (just to emphasise we do it in the same order as the chairs example (the 3+7, don’t worry about the fact we’re adding eights instead of chairs. 3.Try to get the students to use this idea to answer the following problems. 4.In particular, for Problem 0a, we need the students to realise they have 11 eights, so 88; and in 0b, they have 12 sevens, so 84. 5.Problem 9d combines knowledge from the previous multiplication numeracy VMG.

2. Intelligent Grouping: 9.These are extension problems that use exactly the same maths: a.(17 x 12) + (13 x 12) = b.(14 x 15) + (15 x 16) = c.(6 x 67) + (33 x 6) = d.(12 x 14) + (6 x 32) = 1.(13x8) – (3x8) = __ x 8 = 2.(14x7) – (4x7) = 3.(13x7) + (7x7) = 4.(13x8) + (7x8) = 5.(23x6) – (3x6) = 6.(13x6) + (7x6) = 7.(6x27) + (6x3) = 8.(4x17) + (6x17) = Problem 0: a.(7x8) + (4x8) = b.(14x7) – (2x7) =

3. Intelligent Grouping: 9.These are extension problems that use exactly the same maths: a.(17 x 12) + (13 x 12) = 30x12 = 360 b.(14 x 15) + (15 x 16) = 30x15 = 450 c.(6 x 67) + (33 x 6) = 100x6 = 600 d.(12 x 14) + (6 x 32) = (2x6x14) + (6x32) = (6x28) + (6x32) = 6x60 = 360 1.(13x8) – (3x8) = 10 x 8 = 80 2.(14x7) – (4x7) = 70 3.(13x7) + (7x7) = 140 4.(13x8) + (7x8) = 160 5.(23x6) – (3x6) = 120 6.(13x6) + (7x6) = 120 7.(6x27) + (6x3) = 180 8.(4x17) + (6x17) = 170 Problem 0: a.(7x8) + (4x8) = 11 x 8 = 88 b.(14x7) – (2x7) = 12 x 7 = 84 Answers: