3
Using patterns to multiply in your head
Discover Mathematics P4: Term 1, Unit 5, Lessons 4–8
GoalUse zero patterns and the commutative property to solve multiplication stories in my head.
New words
mental math · working out an answer in your headfactor · a number we multiplyround number · a number with zeros, easy to use
Explanation
Zero patterns make big multiplications easy. In a story, find the two numbers to multiply, then use the basic fact and add the zeros. A trader packs 8 boxes of 300 pencils. 8 × 3 = 24, so 8 × 300 = 2,400 pencils. If the order is awkward, swap the factors: 300 × 8 is the same as 8 × 300. Sometimes we can split a number to use a pattern. 25 × 400: 25 × 4 = 100, so 25 × 400 = 100 × 100 = 10,000. Check that the answer is reasonable: 8 boxes of about 300 should be about 2,400, not 24,000.
Worked examples
A trader packs 8 boxes of 300 pencils. 8 × 300 = 8 × 3 × 100 = 24 × 100 = 2,400 pencils.
| Story | Fact | Answer |
|---|---|---|
| 30 trips × 20 | 3 × 2 = 6 | 600 |
| 5 × 1,200 | 5 × 12 = 60 | 6,000 |
25 × 400 = 100 × 100 = 10,000 because 25 × 4 = 100. If an estimate says 8 × 300 is near 24,000, it is far too big; 8 × 300 is only 2,400.
Class activity
Spin for factors. Make two spinners: one with the numbers 2 to 9, and one with 10, 100 and 1,000. Spin both and multiply them in your head. Your partner checks with a calculator. The player with the greater product wins the round.
Practice
1
A bakery bakes 700 loaves a day. How many loaves in 6 days?
6 × 700 = 4,200 loaves.
2
A packet has 50 sheets. How many sheets are in 40 packets?
50 × 40 = 2,000 sheets.
3
Find 25 × 8 by thinking 8 × 25.
8 × 25 = 200.
4
A farmer plants 20 rows with 30 date palms in each row. How many palms are there?
20 × 30 = 600 palms.
5
Salma says 9 × 2,000 = 1,800. Is the answer reasonable? Find the right answer.
No: 9 × 2,000 is more than 9 × 1,000 = 9,000. The right answer is 18,000.