Teaching mathematics
Teaching mathematics

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Teaching mathematics

2.3 Mental multiplication and division strategies

Doubling and halving are easy for most people, so make use of these tactics:

  • doubling and doubling again is the same as multiplying by 4

  • doubling and doubling and doubling again is the same as multiplying by 8.

Use the inverse of doubling (i.e. the opposite of doubling) which is halving:

  • halving is the same as dividing by 2

  • halving and halving again is the same as dividing by 4

  • halving and halving and halving again is the same as dividing by 8.

Once we begin talking about halving being the same as dividing by 2 this connects to fractions, decimals and percentages. There will be more of this in Week 2 but for now:

  • half of 100% is 50% → to find 50% of an amount just half it

  • half of 50% is 25% → to find 25% of an amount half and half it again.

Activity 5 Finding halves and quarters

Timing: Allow 5 minutes

Try the following questions.

one divided by two postfix times of postfix times times 62
one divided by four postfix times of postfix times times 62
25 percent times of postfix times times 124
25 percent times of postfix times times 18

Discussion

multiline equation row 1 one divided by two postfix times of postfix times times 62 equals 31 row 2 one divided by four of postfix times times 62 equals 15.5
multiline equation row 1 25 percent times of postfix times times 124 equals 31 row 2 25 percent of postfix times times 18 equals 4.5

Listed below are some useful mental multiplication strategies:

Multiply by 5 by multiplying by 10 then halving

equation sequence 14 multiplication five equals 140 division two equals 70

Multiply by 20 by multiplying by 10 then doubling (or vice versa)

equation sequence 24 multiplication 20 equals 240 multiplication two equals 480 comma alternatively postfix times equation sequence 24 multiplication 20 equals 48 multiplication 10 equals 480

Multiply by 50 by multiplying by 100 and halving (or vice versa)

equation sequence 26 multiplication 50 equals 2600 division two equals 1300 comma alternatively postfix times equation sequence 26 multiplication 50 equals 13 multiplication 100 equals 1300

Multiply by 11 or 9 by multiplying by 10 and adding or subtracting

equation sequence 13 multiplication 11 equals 130 plus 13 equals 143

Multiply by 21 or 19 by multiplying by 20 and adding or subtracting

equation sequence 13 multiplication 21 equals 13 multiplication 20 plus 13 equals 273
TM_1

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