Q1: Give two reasons to get good at doing math in your head.
Ans: You don't need to carry around a calculator.
It's fun/interesting/strengthening.
Q2: Give two situations where you might need or want to do math in your head, not with a calculator.
Ans: Answers vary.
Q3: Explain the quick way to multiply by ten.
Ans: Move each digit once to the left.
Fill the last place with a 0.
Q4: Solve these problems without using a calculator.
(a) 4 x 10
Ans: 40
(b) 15 x 10
Ans: 150
(c) 400 x 10
Ans: 4000
(d) 23 x 10
Ans: 230
(e) 117 x 10
Ans: 1170
Q5: Explain the quick way to multiply a single digit times 9.
Ans:
Subtract 1 from the original number to get the tens digit.
Subtract this tens digit from 9 to get the ones digit.
Double check by adding the digits together to get 9.
Q6: Solve the following problems without a calculator.
(a) 4 x 9
Ans: 36
(b) 9 x 9
Ans: 81
(c) 9 x 8
Ans: 72
(d) 5 x 9
Ans: 45
(e) 7 x 9
Ans: 63
(f) 9 x 2
Ans: 18
(g) 3 x 9
Ans: 27
(h) 6 x 9
Ans: 54
Q7: What's the shortcut to multiply an even number by 5?
Ans: Get the tens digit by dividing the number by 2. The ones digit is 0.
Q8: What's the shortcut to multiply an odd number by 5?
Ans: Subtract 1 from the number. Get the tens digit by dividing that answer by 2. The ones digit is 5.
Q9: Solve these problems without a calculator.
(a) 5 x 4
Ans: 20
(b) 5 x 12
Ans: 60
(c) 5 x 19
Ans: 95
(d) 5 x 15
Ans: 75
(e) 5 x 7
Ans: 35
(f) 5 x 20
Ans: 100
(g) 5 x 13
Ans: 65
(h) 5 x 21
Ans: 105
Q10: Don't solve these problems. Instead, check whether each answer could be right or not. Explain your answer.
Example: 4 x 5 = 25
No. An even number x 5 should equal a number that ends in 0.
(a) 11 x 5 = 50
Ans: No. An odd number x 5 should end in 5.
(b) 3 x 5 = 18
Ans: No. An odd number x 5 should end in 5.
Q11: Explain the trick about multiplying by 3.
Ans: If you multiply a number by 3, the digits of the answer add up to 3, 6, or 9.
Q12: How might you get “tricked” by this trick?
Ans: If your wrong answer is another multiple of 3, the digits will add up to 3 and you'll
be fooled.
Q13: How do you use an easy problem as a shortcut for a hard one? Write an example that shows how.
Ans: Student examples may vary.
19 x 7 = ?
20 x 7 = 140
140 – 7 = 133
19 x 7 = 133
Q14: Write an example that shows how to multiply by chunks.
Ans: Student examples may vary.
32 x 8 = ?
30 x 8 = 240
2 x 8 = 16
240 + 16 = 256
32 x 8 = 256
Q15: Solve this problem by using one of the tricks you learned in this lesson. Show your work.
49 x 4
Ans:
49 x 4
50 x 4 = 200
200 – 4 = 196
49 x 4 = 196
Q16: Solve these problems by using one of the tricks. Do them in your head.
(a) 13 x 6
Ans: 78
(b) 71 x 7
Ans: 497
(c) 19 x 9
Ans: 171
Q17: Solve these problems by using one of the tricks you learned in this unit. Show your work.
(a) 11 x 7
Ans:
11 x 7
10 x 7 = 70
1 x 7 = 7
70 + 7 = 77
11 x 7 = 77
(b) 39 x 3
Ans:
39 x 3
40 x 3 = 120
120 – 3 = 117
39 x 3 = 117
Q18: Solve these problems by using one of the tricks. Do them all in your head.
(a) 9 x 8
Ans: 72
(b) 8 x 5
Ans: 40
(c) 6 x 5
Ans: 30
(e) 3 x 9
Ans: 27
(f) 51 x 4
Ans: 204
(g) 301 x 10
Ans: 3,010
(h) 7 x 9
Ans: 63
(i) 19 x 7
Ans: 133
Q19: Don't solve these problems. Instead, circle which answers can't be correct. Explain why.
(a) 8 x 5 = 44
Ans: The answer doesn't end in 5.
(b) 9 x 6 = 56
Ans: The digits of the answer don't add up to 9.
(c) 21 x 3 = 61
Ans: The digits of the answer don't add up to 3, 6, or 9.
(e) 9 x 5 = 55
Ans: The digits don't add up to 9.
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