Change the order of the factors to make a multiplication problem easier.
Number Framework Stage 6
- Animal strips
- Calculators
Using Materials
Ask the students what they would do to model 4 x 3 and 3 x 4 with animal strips.
Expect responses like “Get four strips of three animals” and “Get three strips of four.”
Tell some of the students to show 4 x 3 and others to show 3 x 4. Compare the total
number in each collection and how one model might be mapped onto the other.
Some students might comment that 4 x 3 can be rotated to form 3 x 4 and vice
versa.
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Model other examples with animal strips to establish that the commutative property
holds in other cases. Good examples might be:
6 x 2 and 2 x 6, 3 x 7 and 7 x 3, 4 x 8 and 8 x 4
Develop the idea further with cubes by showing the students how four sets of three
can be transformed into three sets of four in the following way.
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One cube is taken out of each set of three to form sets of four.
This can be done three times.
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Challenge the students to use the same process to change:
5 x 2 into 2 x 5, 6 x 3 into 3 x 6, 7 x 4 into 4 x 7
Using Imaging
5 times tables, whereas 5 x 8 is comparatively diffi cult).
Provide other examples in which the choice of multiplication makes a difference to
the difficulty of finding the total. Examples might be:
9 x 2 and 2 x 9 (9 sets of 2 and 2 sets of 9: easier to think of double nine)
3 x 6 and 6 x 3 (easier to think of three fives and three more)
4 x 8 and 8 x 4 (easier to think of double eight and then double again)
Record 3 x 100 and 100 x 3 on the board or modelling book. Ask the students if they think the answers to these facts will be the same and ask them to explain why. Use calculators to check whether the commutative property holds.
Give the students other examples, like: 28 x 2 and 2 x 28
99 x 4 and 4 x 99 (99 sets of 4 and 4 sets of 99) 6 x 50 and 50 x 6
Using Number Properties
Provide the students with problems involving larger numbers where the choice of
calculation makes extreme differences to the difficulty.
Which would you rather work out?
99 x 8 or 8 x 99? 53 x 3 or 3 x 53? 12 x 25 or 25 x 12?
102 x 4 or 4 x 102? 5 x 42 or 42 x 5? 2 134 x 2 or 2 x 2 134?
Independent Activity
To reinforce the commutative property and to learn basic multiplication facts, the students can play Four in a Row Multiplication (Material Master 6–6(a)).