Using estimation strategies
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Round to the place of the underlined digit. 1. 3,528 2. 24,106 3. 54 4. 131,295 5. 449 6. 4,951 7. 229,999 8. 82,729 9. 998 10. Round 3,507 to the nearest ten, nearest hundred, and nearest thousand. Solutions 1.2. round down; 3,500 round up; 24,110

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Using Estimation Strategies

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Using estimation strategies

Round to the place of the underlined digit.

1.3,5282.24,1063.54

4.131,2955.4496.4,951

7.229,9998.82,7299.998

10.Round 3,507 to the nearest ten, nearest hundred, and

nearest thousand.

Solutions

1.2.

round down; 3,500 round up; 24,110

3.504.130,0005.400 6.5,000

7.200,0008.83,0009.1,00010.3,510; 3,500; 4,000

Using Estimation Strategies

COURSE 2 LESSON 1-1

(For help, go to Skills Handbook p. 697.)

1-1


Place value

Place Value


Estimation

Estimation

There are three types of Estimation:

(that we are going to look at)

1. Estimate by rounding

2. Front-end estimation (useful for finding sums)

3. Compatible numbers (useful for division)


Estimate by rounding

78.96 + 58.31 80 + 60 Round to the nearest whole number.

140Add.

Estimate by Rounding

COURSE 2 LESSON 1-1

At the zoo, you see a Colombian black spider monkey. The length of its body is 58.31 cm. The length of its tail is 78.96 cm. To the nearest centimeter, estimate the total length of the monkey’s body and tail.

Estimation should be quick and easy and DONE IN YOUR HEAD!

1. ADD/SUB: Decide which place is best to round to and then round all numbers to that place. (Usually the highest place in the smallest number)

2. Perform the given operation using the rounded numbers.

3. Give your answer with an approximately equal to () sign and units.

The total length is about 140 cm.

1-1


Estimate by rounding1

Round each factor its highest place value.

8.75 9

18.5 20

20  9 = 180 Multiply.

Estimate by Rounding

COURSE 2 LESSON 1-1

A rectangular kitchen is 18.5 ft long and 8.75 ft wide. Use rounding to estimate the area of the kitchen in square feet.

When estimating with multiplication, round each factor to its highest place value.

You should only have to multiply a single digit times a single digit.

Remember, the zeros only hold the place value, so they can be put back when the multiplication is complete.

The area of the kitchen is about 180 ft2.

1-1


Practice

Practice


Homework

Homework

  • Homework

  • Section 1-1 # 1-6


Homework1

Homework

  • Homework

  • Section 1-1 # 7-12

  • Estimate first, then do the actual multiplication to see how close your estimate was


Front end estimation

Front-End Estimation

Very useful for finding sums of several items. (for example when shopping or in line at McD’s)

1. Add the front-end digits

2. Estimate the sum of the lesser numbers and adjust the sum appropriately.

$2.87

$6.33

$4.11

$3.95

About 1 whole

First add the front-end numbers

So add 2 to your front-end estimate

About 1 whole

So this trip to the store should cost you about $17.

$15.

+ 2

= 17


Front end estimation1

}

$3.79

$1.39

$0.89

about $1

about $1

$2 = $6

$3.79

$1.39

+ $0.89

$4

Front-End Estimation

COURSE 2 LESSON 1-1

At a snack shop, you order a taco that costs $3.79, a juice that costs $.89, and a yogurt that costs $1.39. Estimate the total cost of your order.

Step 1: Add the front-end digits.

Step 2: Estimate the total number of cents to the nearest dollar.

The total cost is about $6.

1-1


Estimation by compatible numbers

58.80

8.25

Set up the quotient.

1. Round the divisor.

2. Choose a number that

goes in evenly, (i.e. is compatible.)

___

7Simplify.

Estimation by Compatible Numbers

COURSE 2 LESSON 1-1

Suppose you have saved $58.80. About how many CDs can you buy if each costs $8.25?

56

8

You can buy about 7 CDs.

1-1


Examples

Examples


Homework assignment

Homework Assignment

Read 1-1 do #’s 20-26


Using estimation strategies

`

COURSE 2 LESSON 1-1

Pages 7–9 Exercises

1.about 11

2.about 8

3.about 19

4.about 3

5.about 3

6.about 8

7.about 60

8.about 125

9. about 891

10.about 18

11.about 168

12. about 40

13.about 660 mi

14. about 8

15. about 19

16. about 13

17.about 14

18. about 40

19.about 6

20. about 9

21. about 4

22. about 9

23. about 10

24. about 4

1-1


Using estimation strategies

`

COURSE 2 LESSON 1-1

Pages 7–9 Exercises

  • about 50

  • (59.78)

  • about 150

  • (120.33917)

  • 9. about 900

  • (900.9484)

  • about 18

  • (19.9703)

  • about 100

  • (162.7024)

  • about 40

  • (40.7745)

1-1


Using estimation strategies1

Using Estimation Strategies

COURSE 2 LESSON 1-1

34. Answers may vary. Sample: Front-end estimation would show your answer should be about 400.

35.a.Answers may vary. Sample: about 6,600 lb

b.Answers may vary. Sample: 15 of the 198.7-lb boxes and

3 of the 287.2-lb boxes for a total of 18 boxes

36. Answers may vary. Sample: about $6.80

25.about 2

26.about 8 boxes

27–32. Answers may vary. Samples are given.

27.about 43.3; estimate by rounding each number to the nearest whole number.

28.about 4,296; rounding makes it easier to get an estimate.

29.about 40; 360 is compatible with 9.

30.about 1,425; front-end estimation

31.about 8; rounding

4  2 = 8

32.4; use compatible numbers 8 ÷ 2

33.about 3 mi/h more

1-1


Using estimation strategies2

Using Estimation Strategies

COURSE 2 LESSON 1-1

37–39. Answers may vary. Samples are given.

37.about $2

38. about $1

39. about $4

40. about 36

41. about $56

42. about 175

43.Anchorage: about 45 in.

El Paso: about 24 in.

Indianapolis: about 120 in.

Miami: about 180 in.

Pago Pago: about 600 in.

San Jose: about 210 in.

South Pole Sta.: about 0 in.

44. Round one of the numbers,

then find a multiple of that number

that is near the other number.

45–48.  Answers may vary.

Samples are given.

45.about 33

46. about 200

1-1


Using estimation strategies3

53. A

54. H

55. D

56.[2] $54 with reasonable justification

[1] correct answer, without error in either estimate or justification

57. 4; 40; 403; 4,004

58.7,068, 7,618, 7,680, 7,681

47.about 100

48.about 2,634

49. The second choice; the first choice cost about $33 per dozen. The second choice cost only about $30 per dozen.

50.The first choice; the first choice is less than $3 per pair while the second choice is more than $3 per pair.

51.Answers may vary. Sample: about $18

52. 899

Using Estimation Strategies

COURSE 2 LESSON 1-1

1-1


Using estimation strategies4

Using Estimation Strategies

COURSE 2 LESSON 1-1

59.two hundred forty-eight

and nine tenths

60.four hundred thirty-one

and eighty-five hundredths

61.four and twenty-eight hundredths

62.one hundred thirty and

three hundred ninety-six thousandths

1-1


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