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Area, grouping factors and two strategies

الأسبوع 16 · المساحة وخصائص الضرب · 3 دروس
3

Two strategies, one answer

Discover Mathematics P3: Term 2, Lessons 61–70
GoalSolve a problem in one way, check it in a second way, and read a clock to the minute.
New words
strategy · a way of solving a problemdouble-check · to solve again in a different wayinverse · the opposite operation, as division undoes multiplication
Explanation

A good mathematician solves a problem one way and checks it another way. For 6 × 14, strategy one is to break 14 into 10 and 4: 6 × 10 = 60 and 6 × 4 = 24, so 60 + 24 = 84. Strategy two is to write 14 as 2 × 7: 6 × 2 × 7 = 12 × 7 = 84. Both give 84, so we trust it. For division use the inverse operation: 48 ÷ 6 = 8, and the check is 8 × 6 = 48. We can also read a clock two ways. At 7:03 the minute hand is 3 small marks after the 12, and the digital clock shows 7:03.

StrategyStepsAnswer
Break apart(6 × 10) + (6 × 4) = 60 + 2484
Change factors6 × 2 × 7 = 12 × 784
Worked examples
9999999972
Find 72 ÷ 8. Think: 8 times what number makes 72? 8 × 9 = 72, so 72 ÷ 8 = 9. Check: 9 × 8 = 72.
WayStepsAnswer
140 + 2060
230 × 260
Find 15 × 4 in two ways. Way one: (10 × 4) + (5 × 4) = 40 + 20 = 60. Way two: double and double again: 15 × 2 = 30, and 30 × 2 = 60.
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Read the clock. The hour hand is just after 7. The minute hand is 3 small marks after the 12, so it is 3 minutes past 7. The digital time is 7:03.
Class activity

Two-ways race. Write five multiplication problems such as 7 × 12 or 9 × 13. Solve each problem in two different ways. If the two answers are different, look for the mistake together. Which strategy do you like best?

Practice
1
Find 7 × 12 in two ways.
2
Find 54 ÷ 9 and check with multiplication.
3
What time does the clock show? Write it as a digital time.
123456789101112
4
Mina says 8 × 13 = 94. Check her answer with another strategy.
5
A bakery puts 9 loaves on each tray and fills 11 trays. How many loaves is that? Use two ways.