1. Created by Tania Colson (2010)
Mental Math 6
Created by Tania Colson (2010)

2. Created by Tania Colson (2010)
Mental Math Routine
Focus on 1-2 strategies each week
Practiced 3 to 5 times per week
10 questions with 5-10 seconds to record an answer
All tests are is self corrected
All results recorded by teacher
Name goes in for a draw (1, 2, 3 chances) for a small reward
Correct with a pen or lose your tickets for the day
If corrected incorrectly no chance to win during the next draw.
Take care of whiteboards and markers.
Created by Tania Colson (2010)

3. Mental Math 6: Part 1 Mental Calculation
A. Addition Basic Addition Facts Applied to Multiples of Powers of 10 Front End Focus Quick Addition- No Regrouping Finding Compatibles Break Up and Bridge Compensation (Addition) Make Multiples of Powers of 10 B. Subtraction Basic Subtraction Facts Applied to Multiples of Powers of 10 Quick Subtraction Back Through a Multiple of a Power of 10 Up Through a Multiple of a Power of 10 Compensation (Subtraction) Balancing for a Constant Difference
C. Multiplication and Division
Quick Multiplication — No Regrouping
Quick Division — No Regrouping
Multiplying by 10, 100, and 1000
Dividing by tenths (0.1), hundredths (0.01) and thousandths (0.001)
Dividing by Ten, Hundred and Thousand
Multiplication of tenths, hundredths and thousandths
Division when the divisor is a multiple of 10 and the dividend is a multiple of the divisor
Division using the Think Multiplication strategy
Compensation(Multiplication)
Halving and Doubling
Front End Multiplication or the Distributive Principle in 10s, 100s, and 1000s
Finding Compatible Factors
Using Division Facts for Tens, Hundreds and Thousands
Breaking Up the Dividend
Compensation (Division)
Balancing For a Constant Quotient
D. Computational Estimation
Quick Estimates (Front End Addition & Subtraction)
Quick Estimates (Front End Multiplication)
Rounding (Addition & Subtraction)
Rounding (Multiplication)
Quick Estimates (Adjusted Front End Division)
Front End with Clustering (Division)
Doubling for Division
Created by Tania Colson (2010)
Created by Tania Colson (2010)

4. Mental Math 6: Part 2 Measurement Estimation
Length Area and Perimeter Volume and Capacity Angles The Development of Spatial Sense
Mental Math 6: Part 3 Measurement Estimation
Created by Tania Colson (2010)

5. Created by Tania Colson (2010)
ADDITION
Created by Tania Colson (2010)

6. Strategy Intro Using Basic Addition Facts
Try These In Your Head = = = , , , _________ 0.2 s s = 0.04 cm plus 0.03 cm=
Created by Tania Colson (2010)

7. Strategy Using Basic Addition Facts
Check you Answers = = = = , , , s s = 0.8 s 0.04 cm plus 0.03 cm= 0.07 cm
How many strategies can you think of to solve addition problems?
Created by Tania Colson (2010)

8. Strategy Using Basic Addition Facts
Doubles Facts Examples: or Plus-One Facts Examples: 6 +1 or 8 +1 Near-Doubles (1-Aparts) Facts Examples: or 2 + 3
Plus-Two Facts
Examples: or 7 + 2
Plus Zero Facts
Examples or 4 +0
Make-10 Facts
Examples: 7 + 3, 2 + 8
These 6 strategies can be applied for 88 of the 100 addition facts!
Created by Tania Colson (2010)

9. Strategy Using Basic Addition Facts
Knowing your basic addition facts can help you add other problems in your head. Think: … 7 tens plus 6 tens is 13 tens or 130. Think: … 4 thousand plus 7 thousand is 11 thousand or Think: …9 hundredths plus 6 is 15 hundredths or 0.15
Created by Tania Colson (2010)

10. PB 1 : Using Basic Addition Facts=
100 more than 400 =
7 000 plus =
$ $9 000 =
0.03 cm increased by 0.09cm =
20 million and 30 million =
The sum of 8 kg and 9 kg =
0.6 mm mm =
$0.80 plus $0.90 =
0.8 billion and 0. 6 billion=
Created by Tania Colson (2010)

11. PB 1: Using Basic Addition Facts
= 170
100 more than 400 = 500
7 000 plus =
$ $9 000 = $15 000
0.03 cm increased by 0.09cm = 0.12cm
20 million and 30 million = 50 million
The sum of 8 kg and 9 kg = 17 kg
0.6 mm mm = 1.5 mm
$0.80 plus $0.90 = $1.70
0.8 billion and 0. 6 billion= 1.4 billion
Created by Tania Colson (2010)
Created by Tania Colson (2010)

12. PB 2: Using Basic Addition Facts=
200 more than 900 =
4 000 plus =
$ $3 000 =
0.05 cm increased by 0.05cm =
30 million and 80 million =
The sum of 2 kg and 6 kg =
0.7 mm mm =
$0.60 plus $0.50 =
0.7 billion and 0. 9 billion=
Created by Tania Colson (2010)

13. PB 2: Using Basic Addition Facts
= 130
200 more than 900 = 1 100
4 000 plus =
$ $3 000 = 4 000
0.05 cm increased by 0.05cm = 0.10cm
30 million and 80 million = 110 million
The sum of 2 kg and 6 kg =
0.7 mm mm = 1.4 mm
$0.60 plus $0.50 = $1.10
0.7 billion and 0. 9 billion= 1.6 billion
Created by Tania Colson (2010)

14. PB 3: Using Basic Addition Facts=
600 more than 800 =
3 000 plus =
$ $7 000 =
0.09 cm increased by 0.09cm =
30 million and 70 million =
The sum of 4 kg and 9 kg =
0.8 mg mg =
$0.30 plus $0.40 =
0.2 billion and 0. 5 billion=
Created by Tania Colson (2010)

15. PB 3: Using Basic Addition Facts
= 70
600 more than 800 = 1400
3 000 plus =
$ $7 000 =
0.09 cm increased by 0.09cm = 0.18cm
30 million and 70 million = 100 million
The sum of 4 kg and 9 kg = 13 kg
0.8 mg mg = 1.6 mg
$0.30 plus $0.40 = $0.70
0.2 billion and 0. 5 billion= 0.7 billion
Created by Tania Colson (2010)

16. PB 4: Using Basic Addition Facts=
400 more than 900 =
1 000 plus =
$ $8 000 =
0.02 cm increased by 0.06cm =
50 million and 80 million =
The sum of 3g and 6g =
0.4 mL mL =
$0.40 plus $0.70 =
0.2 s and 0. 5 s =
Created by Tania Colson (2010)

17. PB 4: Using Basic Addition Facts
= 100
400 more than 900 = 1300
1 000 plus = 8 000
$ $8 000 =
0.02 cm increased by 0.06cm = 0.08 cm
50 million and 80 million =130 million
The sum of 3g and 6g = 9g
0.4 mL mL = 1.0mL
$0.40 plus $0.70 = $1.10
0.2 s and 0. 5 s = 0.7s
Created by Tania Colson (2010)

18. PB 5: Using Basic Addition Facts=
300 more than 300 =
4 000 plus =
$ $5 000 =
0.04 cm increased by 0.03cm =
40 million and 20 million =
The sum of 7g and 8g =
0.2 L L =
$0.60 plus $0.70 = =
Created by Tania Colson (2010)

19. PB 5: Using Basic Addition Facts
= 180
300 more than 300 = 600
4 000 plus =
$ $5 000 = $9 000
0.04 cm increased by 0.03cm = 0.07cm
40 million and 20 million = 60 million
The sum of 7g and 8g = 15 g
0.2 L L = 0.5L
$0.60 plus $0.70 = 1.30
= 1.2
Created by Tania Colson (2010)

20. Strategy Intro Front End Focus Addition
Try These In Your Head = 307 and 206 = = 5.06 more than 3.05 = 7.2cm + 2.6cm = 5.8 million plus 2.5 million=
Created by Tania Colson (2010)

21. Strategy Front End Focus Addition
Check Your Answers = and 206 = = more than 3.05 = cm + 2.6cm = 56.97cm 5.8 million plus 2.5 million= 8.3 million
Did you use the same strategy to solve all of these problems?
Created by Tania Colson (2010)
Created by Tania Colson (2010)

22. Strategy Front End Focus Addition
When you need to regroup, can still start at the front end and break up the numbers to create a quick addition problem Think: …
30 plus 20 is 50.
7 plus 8 is 15.
Now add the totals…
= 65.
Created by Tania Colson (2010)

23. Strategy Front End Focus Addition
It works on really big numbers and really small numbers just the same. Try: …3 000 plus is 5 000, 600 plus 500 is 1 100, and and 1100 is Try: …5 plus 3 is 8, 6 hundredths plus 5 hundredth is 11 hundredths (0.11), and 8 and 0.11 is 8.11.
Created by Tania Colson (2010)

24. PB 1: Front End Focus Addition=
18 kg more than 56 kg =
102 plus 569 =
$660 + $270 =
102 cm and 150cm more = =
The sum of and =
4.5 km km =
$3.12 plus $1.09 =
5.4 million million =
Created by Tania Colson (2010)

25. PB 1: Front End Focus Addition
45 +36= 81
18 kg more than 56 kg= 74
102 plus 569= 671
$660 + $270= $930
102 cm and 150cm more = 252cm
=9 200
The sum of and 5 060= 7 100
4.5 km km = 7.2 km
$3.12 plus $1.09 = $4.21
5.4 million million= 7.2 million
Created by Tania Colson (2010)

26. PB 2: Front End Focus Addition=
35 km more than 29 km =
209 plus 403 =
$580 + $340 =
309 cm and 268cm more = =
The sum of and =
2.6 cm cm =
$3.12 plus $1.09 =
4.8 billion and 3. 6 billion=
Created by Tania Colson (2010)

27. PB 2: Front End Focus Addition
= 43
35 km more than 29 km = 64km
209 plus 403 = 612
$580 + $340 = 920
309 cm and 268cm more = 577 =
The sum of and = 8 160
2.6 cm cm = 6.5 cm
$3.12 plus $1.09 = $4.21
4.8 billion and 3. 6 billion = 8.4 billion
Created by Tania Colson (2010)

28. PB 3: Front End Focus Addition=
67 m + 28 m =
320 plus 490 =
$330 + $280 =
208 cm more than 409cm = =
The sum of and =
4.5 cm cm =
$6.19 plus $1.05 =
1.8 billion and 2.6 billion =
Created by Tania Colson (2010)

29. PB 3: Front End Focus Addition
= 73
67 m + 28 m = 95m
320 plus 490 = 819
$330 + $280 = $620
208 cm more than 409cm = 617cm =
The sum of and = 7 240
4.5 cm cm = 12.4 cm
$6.19 plus $1.05 = $7.24
1.8 billion and 2.6 billion = 4.4 billion
Created by Tania Colson (2010)

30. PB 4: Front End Focus Addition=
62 m + 59 m =
240 plus 690 =
$460 + $280 =
409 cm more than 601cm = =
The sum of and =
3.9 mm mm =
$7.09 plus $2.05 =
50.3 million and 2.8 million =
Created by Tania Colson (2010)

31. PB 4: Front End Focus Addition
= 93
62 m + 59 m = 121m
240 plus 690 = 930
$460 + $280 = $740
409 cm more than 601cm = 1010 cm
=32 110
The sum of and = 7 120
3.9 mm mm = 8.1 mm
$7.09 plus $2.05 = $9.14
50.3 million and 2.8 million = 53.1million
Created by Tania Colson (2010)

32. PB 5: Front End Focus Addition=
42 m + 39 m =
210 plus 390 =
$480 + $180 =
307 cm more than 409cm = =
The sum of and =
5.8 mm mm =
$12.08 plus $3.04 =
10.5 million and 3.7 million =
Created by Tania Colson (2010)

33. PB 5: Front End Focus Addition
= 73
42 m + 39 m = 81 m
210 plus 390 = 600
$480 + $180 = $660
307 cm more than 409cm = 716 cm =
The sum of and = 9 110
5.8 mm mm = 7.15mm
$12.08 plus $3.04 = $15.12
10.5 million and 3.7 million = million
Created by Tania Colson (2010)

34. Strategy Intro Quick Addition
Try These In Your Head = = = = = =
How are all these problems alike?
Created by Tania Colson (2010)

35. Strategy Intro Quick Addition
Check your Answers = = = = = = 46.47
Created by Tania Colson (2010)

36. Strategy Quick Addition
Adding can be done quickly when there is no regrouping. You can start at the front end. Think: …
4 tens plus 2 tens is
6 tens or 60 .
7 plus 1 is 8.
So… = 68 .
Created by Tania Colson (2010)

37. Created by Tania Colson (2010)
PB 1: Quick Addition =
The sum of 43 and 12
541 more than 126 =
129 plus 230 = =
231.2 increased by 152.3
The total of $4.12 and $3.36 =
1.2 m m =
Created by Tania Colson (2010)

38. Created by Tania Colson (2010)
PB 1: Quick Addition
= 48
The sum of 43 and 12 = 55
541 more than 126 = 667
= 864
129 plus 230 = 359
= 887
231.2 increased by = 383.5
The total of $4.12 and $3.36 = $7.48
= 1.586
1.2 m m = 3.9m
Created by Tania Colson (2010)

39. Created by Tania Colson (2010)
PB 2: Quick Addition =
The sum of 13 and 64
123 more than 810 =
plus = =
72.2 increased by 14.6
The total of $0.66 and $0.33 =
2.2 m m =
Created by Tania Colson (2010)

40. Created by Tania Colson (2010)
PB 2: Quick Addition
= 66
The sum of 13 and 64 = 77
123 more than 810 = 933
= 8490
plus =
= 88.7
72.2 increased by = 86.8
The total of $0.66 and $0.33 = $0.99
= 1.91
2.2 m m = 7.9m
Created by Tania Colson (2010)

41. Created by Tania Colson (2010)
PB 3: Quick Addition =
The sum of 54 and 33
154 more than 712 =
plus = =
71.36 increased by 23.60
The total of $3.29and $4.50 =
8.4 cm cm =
Created by Tania Colson (2010)

42. Created by Tania Colson (2010)
PB 3: Quick Addition
= 66
The sum of 54 and 33 = 87
154 more than 712 = 866
= 4944
plus =
= 67.9
71.36 increased by = 94.96
The total of $3.29and $4.50 = $7.79
= 4.99
8.4 cm cm = 9.9 cm
Created by Tania Colson (2010)

43. Strategy Intro Finding Compatibles
Try These In Your Head = = = = = =
Did you add each number in order?
Created by Tania Colson (2010)

44. Strategy Intro Finding Compatibles
Check Your Answers = = = = = = 1.3
Created by Tania Colson (2010)

45. Strategy Finding Compatibles
Search for pairs of numbers that add to 10, 100, 1000 or For small numbers find pairs that add to 1 or 0.1. Think:
8 plus 2 is 10.
7 plus 3 is 10.
And…10 plus 10 is 20.
Created by Tania Colson (2010)

46. PB 1: Finding Compatibles=
The total of $75, $95, and $425 =
The sum of 200, 700, 500, 800 = =
2 500 and = =
6 –tenths + 9=tenths + 4 tenths =
$0.50 more than $0.75 plus $0.25
The sum of three lengths: 0.09m, 0.13m, 0.01m =
Created by Tania Colson (2010)

47. PB 1: Finding Compatibles
= 200
The total of $75, $95, and $425 = $595
The sum of 200, 700, 500, 800 = 2200 =
2 500 and =
= 2.3
6 –tenths + 9=tenths + 4 tenths = 1.9
$0.50 more than $0.75 plus $0.25 = $1.25
The sum of three lengths: 0.09m, 0.13m, 0.01m = 0.23
= 24.0
Created by Tania Colson (2010)

48. PB 2: Finding Compatibles=
The total of $50, $25, and $350 =
The sum of 600, 600, 400, 400 = =
3 500 and = =
4 –tenths + 1=tenths + 9 tenths =
$0.75 more than $0.50 plus $0.25
The sum of three lengths: 0.04m, 0.01m, 0.06m =
Created by Tania Colson (2010)

49. PB 2: Finding Compatibles
= 200
The total of $50, $25, and $350 = $425
The sum of 600, 600, 400, 400 = 2000 =
3 500 and =
= 2.2
4 –tenths + 1=tenths + 9 tenths = 1.4
$0.75 more than $0.50 plus $0.25 = $1.50
The sum of three lengths: 0.04m, 0.01m, 0.06m = 0.11m
= 20.0
Created by Tania Colson (2010)

50. PB 3: Finding Compatibles=
The total of $50, $50, and $425 =
The sum of 300, 200, 700, = =
1 500 and = =
3 –tenths + 7=tenths + 2 tenths =
0.30 more than $0.70 plus $0.50
The sum of three lengths: 0.3 m, 0.8m, 0.2m =
Created by Tania Colson (2010)

51. PB 3: Finding Compatibles
= 200
The total of $50, $50, and $425 = $525
The sum of 300, 200, 700, = 2100 =
1 500 and =
= 2.4
3 –tenths + 7=tenths + 2 tenths = 1.2
0.30 more than $0.70 plus $0.50 = $1.50
The sum of three lengths: 0.3 m, 0.8m, 0.2m = 1.3m
= 2.3
Created by Tania Colson (2010)

52. Strategy Intro Break Up and Bridge
Try These In Your Head = 17 more than 64= = = = =
How did you break up the numbers to solve?
Created by Tania Colson (2010)

53. Strategy Intro Break Up and Bridge
Check your answers = more than 64= = = = = 9.30
Created by Tania Colson (2010)

54. Strategy Break Up and Bridge
Begin with the first number and break up the second number according to the place value of its digits. Add these on one at a time to the first number Think:
542 plus 300 is 842
842 plus 9 more is 851.
Created by Tania Colson (2010)

55. Created by Tania Colson (2010)
PB 1: Break Up and Bridge =
15 more than 76=
The sum of $340 and $440 =
365 increased by 109 = =
The total of 4070 girls and 3080 boys= =
$ and $ =
4.7 m m =
4.56 kg more than 4.40 kg =
Created by Tania Colson (2010)

56. Created by Tania Colson (2010)
PB 1: Break Up and Bridge
= 91
15 more than 76 = 91
The sum of $340 and $440 = $780
365 increased by 109 = 474
= 6 200
The total of 4070 girls and 3080 boys= 7150 =
$ and $ = $81 000
4.7 m m = 8.2 m
4.56 kg more than 4.40 kg = 8.96 kg
Created by Tania Colson (2010)

57. Created by Tania Colson (2010)
PB 2: Break Up and Bridge =
19 more than 82 =
The sum of $340 and $440 =
215 increased by 467 = =
The total of 5060 L and 2080 L = =
$ and $ =
2.7 m m =
3.56 kg more than 4.90 kg =
Created by Tania Colson (2010)

58. Created by Tania Colson (2010)
PB 2: Break Up and Bridge
= 102
19 more than 82 = 101
The sum of $340 and $440 = $780
215 increased by 467 = 682
= 6 300
The total of 5060 L and 2080 L = =
$ and $ =
2.7 m m =
3.56 kg more than 4.90 kg =
Created by Tania Colson (2010)

59. Created by Tania Colson (2010)
PB 3: Break Up and Bridge =
53 more than 27=
The sum of $760 and $260 =
653 increased by 109 = =
The total of 2312 and 1748= =
$ and $ =
4.9 million million =
3.50 L more than 4.80 L =
Created by Tania Colson (2010)

60. Created by Tania Colson (2010)
PB 3: Break Up and Bridge
= 93
53 more than 27= 80
The sum of $760 and $260 = 1 020
653 increased by 109 = 762
= 6 100
The total of 2302 and 1700= 4002
= 7.4
$ and $ =
4.9 million million = 7.4 million
3.50 L more than 4.80 L = 8.3 L
Created by Tania Colson (2010)

61. Strategy Intro Compensation (Addition)
Try These In Your Head = = = = = = =
Did you notice anything nifty about one of the addends?
Created by Tania Colson (2010)

62. Strategy Intro Compensation (Addition)
Check Your Answers = = = = = = = 0.83
One of the addends has a 8, or 9 which makes is easy to round off.
Created by Tania Colson (2010)

63. Strategy Compensation (Addition)
Round one addend up to the nearest compatible number that is a multiple of a power of ten. Use that number to carry out the addition instead. Since you added a little too much, subtract the amount of the change you made. Think:
390 rounds up to plus 400 is minus the extra 10 leaves 720
Created by Tania Colson (2010)

64. PB 1: Compensation (Addition)= =
$198 more than $465 =
3 456mm added to 999 mm= =
The total of $ and $9 900 = =
3.5 km more than 4.8 km =
$ =
2.47s more than 4.99s=
Created by Tania Colson (2010)

65. PB 1: Compensation (Addition)
= 97
= 87
$198 more than $465 = $663
3 456mm added to 999 mm= 4455mm =
The total of $ and $9 900 = $47 000
= 6.4
3.5 km more than 4.8 km = 8.3km
$ $0.39 = $0.75
2.47 s more than 4.99s = 7.46 s
Created by Tania Colson (2010)

66. PB 2: Compensation (Addition)= =
$198 more than $250 =
4 500 mL added to 900 mL= =
The total of $ and $9 000 = =
1.5 km more than 3.8 km =
$0.45+ $0.49 =
3.35 more than $2.99=
Created by Tania Colson (2010)

67. PB 2: Compensation (Addition)
= 81
= 95
$198 more than $250 = $448
4 500 mL added to 900 mL= mL =
The total of $ and $9 000 = $87 000
= 5.3
1.5 km more than 3.8 km = 5.3 km
$0.45+ $0.49 = $0.94
$3.35 more than $2.99 = $6.34
Created by Tania Colson (2010)

68. PB 3: Compensation (Addition)= =
$498 more than $300 =
4 500 L added to 900 L= =
The sum of and =
2.8 cm cm =
2.3 more than 4.9 m =
$0.50+ $1.99 =
$4.99 more than $4.99=
Created by Tania Colson (2010)

69. PB 3: Compensation (Addition)
= 81
= 98
$498 more than $300 = $698
4 500 L added to 900 L= 5 400L =
The sum of and =
2.8 cm cm = 3.8 cm
2.3 more than 4.9 m = 7.2 m
$0.50+ $1.99 = $2.49
$4.99 more than $4.99= $9.98
Created by Tania Colson (2010)

70. Strategy Intro Make Multiples of Powers of 10
Try These In Your Head = = = = = = =
Did you use a strategy other than compensation?
Created by Tania Colson (2010)

71. Strategy Intro Make Multiples of Powers of 10
Check Your Answers = = = = = = = 8.22
Created by Tania Colson (2010)

72. Strategy Make Multiples of Powers of 10
Take a little from here to put a little more there is the name of the game! Take the amount you need from one addend to make one addend a multiple of a power of ten. Add both changed numbers together. Think:
Take 6 from 237
to make 400.
237 minus 6 is 231.
Add 231 and 400.
Created by Tania Colson (2010)

73. PB 1: Make Multiples of Powers of 10= =
$198 more than $402 =
3 556 mL added to 999 mL= =
The sum of and =
1.9 m m =
5.8 cm more than 4.5 cm =
$ $0.59 =
1.46 km more than 2.99km =
Created by Tania Colson (2010)

74. PB 1: Make Multiples of Powers of 10
= 90
= 80
$198 more than $402 = $600
3 556 mL added to 999 mL= 4 555 =
The sum of and =
1.9 m m = 4.5m
5.8 cm more than 4.5 cm = 10.3cm
$ $0.59 = $0.84
1.46 km more than 2.99km = 4.45 km
Created by Tania Colson (2010)

75. PB 2: Make Multiples of Powers of 10= =
$498 more than $345 =
2 600 L added to 900 L = =
The sum of and =
10.9 m m =
3.9 cm more than 4.6 cm =
$ $0.76 =
1.27 more than 2.99 =
Created by Tania Colson (2010)

76. PB 2: Make Multiples of Powers of 10
= 91
= 100
$498 more than $302 = $800
2 600 L added to 900 L = L =
The sum of and =
10.9 m m = 13.3 m
3.9 cm more than 4.6 cm = 8.5 cm
$ $0.76 = $1.05
1.27 more than 2.99 = 4.26
Created by Tania Colson (2010)

77. PB 3: Make Multiples of Powers of 10= =
$199 more than $150 =
2 600 L added to 900 L = =
The sum of and =
1.9 m m =
3.3 cm more than 1.9 cm =
$ $0.28 =
2.07 more than 0.99 =
Created by Tania Colson (2010)

78. PB 3: Make Multiples of Powers of 10
= 71
= 40
$199 more than $150 = $349
1 600 L added to 900 L = L =
The sum of and =
1.9 m m = 4.4 m
3.3 cm more than 1.9 cm = 5.2 cm
$ $0.28 = $0.45
2.07 more than 0.99 = 3.06
Created by Tania Colson (2010)

79. Created by Tania Colson (2010)
SUBTRACTION
Created by Tania Colson (2010)

80. Strategy Intro Using Basic Subtraction Facts
Try These In Your Head = = – 600 = – 2 000= 0.8 – 0.5 = 1.4 – 0.7 = 0.17 – 0.09=
How well do you know your basic subtraction facts?
Created by Tania Colson (2010)

81. Strategy Intro Using Basic Subtraction Facts
Check Your Answers = = – 600 = – 2 000= – 0.5 = – 0.7 = – 0.09= 0.08
Created by Tania Colson (2010)

82. Strategy Using Basic Subtraction Facts
Knowing your basic subtraction facts can help you solve other problems in your head. Think: …
7 tens minus 5 tens is 2 tens or 20.
Focus on the facts!
Created by Tania Colson (2010)

83. PB 1: Using Basic Subtraction Facts
120 – 70 =
$20 less than $90 =
700 kg decreased by 300 kg =
The difference between 1100 km and 400 km =
6000 minus 1000 =
– =
0.7 kg – 0.2 kg =
1.6 less 0.9 =
$ $0.08 =
0.10 – 0.01 =
Created by Tania Colson (2010)

84. PB 1: Using Basic Subtraction Facts
120 – 70 = 50
$20 less than $90 = $70
700 kg decreased by 300 kg = 400 kg
The difference between 1100 km and 400 km = 700 km
6 000 minus = 5 000
– =
0.7 kg – 0.2 kg = 0.5 kg
1.6 less 0.9 = 0.7
$ $0.08= $0.08
0.10 – 0.01 = 0.09
Created by Tania Colson (2010)

85. PB 2: Using Basic Subtraction Facts
180 – 30 =
$40 less than $60 =
500 g decreased by 200 kg =
The difference between 1200 m and 600 m =
8000 minus 3000 =
– =
0.8 kg – 0.1 kg =
1.2 less 1.0 =
$ $0.05 =
0.10 – 0.02 =
Created by Tania Colson (2010)

86. PB 2: Using Basic Subtraction Facts
180 – 30 = 150
$40 less than $60 = $20
500 g decreased by 200 kg = 300 kg
The difference between 1200 m and 600 m = 600
8 000 minus = 5 000
– =
0.8 kg – 0.1 kg = 0.07 kg
1.2 less 1.0 = 0.2
$ $0.05 = $0.10
0.10 cm – 0.02 cm = 0.08 cm
Created by Tania Colson (2010)

87. PB 3: Using Basic Subtraction Facts
120 – 40 =
$160 less than $180 =
300 g decreased by 100 g =
The difference between 1300 m and 400 m =
9 000 minus =
– =
0.7 kg – 0.2 kg =
1.5 less 1.3 =
$ $0.05 =
0.10 km – 0.03 km =
Created by Tania Colson (2010)

88. PB 3: Using Basic Subtraction Facts
120 – 40 = 80
$160 less than $180 = $20
300 g decreased by 100 g = 200 g
The difference between m and 400 m = 900 m
9 000 minus = 3 000
– =
0.7 kg – 0.2 kg = 0.5 kg
1.5 less 1.3 = 0.2
$ $0.05 = $0.15
0.10 km – 0.03 km = 0.07 km
Created by Tania Colson (2010)

89. Strategy Intro Quick Subtraction
Try These In Your Head = 268 – 124 = 765 – 602 = 4070 – 3030 = – = – = 0.27 – 0.13 =
How are all these problems alike?
Created by Tania Colson (2010)

90. Strategy Intro Quick Subtraction
Try These In Your Head = – 124 = – 602 = – 3030 = – = – = – 0.13 = 0.14
There’s no regrouping!
Created by Tania Colson (2010)

91. Strategy Quick Subtraction
Adding can be done quickly when there is no regrouping. You can start at the front end. Think: …
7 tens minus 5 tens is 2 tens or 20.
9 minus 7 is 2
79 – 57 = 22
Created by Tania Colson (2010)

92. Created by Tania Colson (2010)
PB 1: Quick Subtraction
56 – 21 =
$604 less than $203 =
$245 less than $605 =
The difference between 1225 km and 3575 km =
Subtract 575 from 3889 =
– =
213.7 kg decreased by kg =
45.12 m less than =
$ $ =
0.29 – 0.15 =
Created by Tania Colson (2010)

93. Created by Tania Colson (2010)
PB 1: Quick Subtraction
56 – 21 = 35
$604 less than $203 = $401
$245 less than $605 = $440
The difference between 1225 km and 3575 km = 1350 km
Subtract 575 from 3889 = 3314
– =
213.7 kg decreased by kg = 112.5kg
45.12 m less than = m
$ $ = $100.25
0.29 – 0.15 = 0.14
Created by Tania Colson (2010)

94. Created by Tania Colson (2010)
PB 2: Quick Subtraction
48 – 35 =
$235 less than $115 =
340 less than 220 =
1304 fewer than 1509=
Subtract 625 from 855 =
– =
12.2 kg decreased by 10.1 kg =
67.15 m less than =
$ $ =
0.39 – 0.13 =
Created by Tania Colson (2010)

95. Created by Tania Colson (2010)
PB 2: Quick Subtraction
48 – 35 = 13
$235 less than $115 = $120
340 less than 220 = 120
1304 fewer than 1509= 205
Subtract 625 from 855 = 230
– = 5 505
12.2 kg decreased by 10.1 kg = 2.1 kg
67.15 m less than = 22.10
$ $ = $300.01
0.39 – 0.13 = 0.26
Created by Tania Colson (2010)

96. Created by Tania Colson (2010)
PB 3: Quick Subtraction
82 – 21 =
$103 less than $205 =
$425 minus $315 =
2040 km fewer than and 5050 km =
Subtract 6505 from 9999 =
– =
27.9 g decreased by 15.4 g =
26.2 m less than 56.7m =
$ $ =
0.67 – 0.42 =
Created by Tania Colson (2010)

97. Created by Tania Colson (2010)
PB 3: Quick Subtraction
82 – 21 = 61
$103 less than $205 = $102
$425 minus $315 = $110
2040 km fewer than and 5050 km = 3010km
Subtract 6505 from 9999 = 3494
– =
27.9 g decreased by 15.4 g = 12.5g
26.2 m less than 56.7m = 30.5m
$ $ = $100.25
0.67 – 0.42 = 0.25
Created by Tania Colson (2010)

98. Strategy Intro Back Through a Multiple of 10
Try These In Your Head = = – 800 = – = 4.5 – 0.9 = 1.63 – 0.07=
Which strategy did you use?
Created by Tania Colson (2010)

99. Strategy Intro Back Through a Multiple of 10
Check Your Answers = – 70 = – 800 = – = – 0.9 = – 0.07= 1.56
Created by Tania Colson (2010)

100. Strategy Back Through a Multiple of 10
Start by knocking off the amount needed to get the subtrahend to the nearest multiple of a power of ten. Then, you will have a nice number from which you can take the remaining amount. Think: …
250 minus 50 of the 80 leaves 200. Take away 30 more is 170.
Created by Tania Colson (2010)

101. PB 1: Back Through a Multiple of 10
9 fewer people than 92 =
$40 less than $210 =
$ $70 =
The difference between 630 and 80 =
Subtract 600 from =
– =
23.5 L decreased by 0.8 L =
13.2kg – 0.7kg =
0.06 m less than 1.21 m=
$2.53 – $0.07=
Created by Tania Colson (2010)

102. PB 1: Back Through a Multiple of 10
9 fewer people than 92 = 83
$40 less than $210 = $170
$ $70 = $270
The difference between 630 and 80 = 550
Subtract 600 from = 1 700
– =
23.5 L decreased by 0.8 L = 22.7 L
13.2 kg – 0.7 kg = 12.5 kg
0.06 m less than 1.21 m= 1.15 m
$2.53 – $0.07= $2.46
Created by Tania Colson (2010)

103. PB 2: Back Through a Multiple of 10
8 fewer people than 76 =
$50 less than $130 =
$ $90 =
The difference between 730 and 70 =
Subtract 500 from =
– =
31.5 L decreased by 0.6 L =
1.2kg – 0.7kg =
0.07 m less than 2.34 m =
$1.56 – $0.08 =
Created by Tania Colson (2010)

104. PB 2: Back Through a Multiple of 10
8 fewer people than 76 = 68
$50 less than $130 = $180
$ $90 = $170
The difference between 730 and 70 = 660
Subtract 500 from = 2 700
– =
31.5 L decreased by 0.6 L = 30.9 L
1.2kg – 0.7kg = 0.5 kg
0.07 m less than 2.34 m = 2.27
$1.56 – $0.08 = $1.48
Created by Tania Colson (2010)

105. PB 3: Back Through a Multiple of 10
68% - 9% =
$60 less than $240 =
$220 - $70 =
440 minus 60 =
Subtract 300 from =
– =
20.5 L decreased by 0.8 L =
2.3 g – 0.4 g =
0.06 s less than 1.61 s =
$1.03 – $0.04 =
Created by Tania Colson (2010)

106. PB 3: Back Through a Multiple of 10
68% - 9% = 59%
$60 less than $240 = $180
$220 - $70 = $150
440 minus 60 = 380
Subtract 300 from = 800
– =
20.5 L decreased by 0.8 L = 19.7 L
2.3 g – 0.4 g = 1.9 g
0.06 s less than 1.61 s = 1.55 s
$1.03 – $0.04 = $0.99
Created by Tania Colson (2010)

107. Strategy Intro Up Through a Multiple of 10
Try These In Your Head 84 – 77 = 613 – 594 = – 1800 = – = 12.4 – = 6.12 – 5.99 = – =
How are all these problems similar?
Created by Tania Colson (2010)

108. Strategy Intro Up Through a Multiple of 10
Check Your Answers 84 – 77 = – 594 = – 1800 = – = – = – 5.99 = – = 0.06
The two amounts are relatively close together.
Created by Tania Colson (2010)

109. Strategy Up Through a Multiple of 10
This is perfect for numbers that are close together. Find the difference between the smaller amount in two steps. First to the nearest multiple of a power of ten and then to the actual number. Think: …
57 is 3 from is 4 more from 64.
3 plus 4 more is 7.
The difference is 7.
Created by Tania Colson (2010)

110. PB 1: Up Through a Multiple of 10
92 – 86 =
$140 less than $210 = =
The difference between 630 and 580 =
2 400 minus =
– =
m decreased by m =
13.2 kg – 12.7 kg =
1.99 m less than 2.21 m=
$2.53 – $2.45 =
Created by Tania Colson (2010)

111. PB 1: Up Through a Multiple of 10
92 – 86 = 6
$140 less than $210 = 70
196 – 189 = 7
The difference between 630 and 580 = 50
2 400 minus = 700
– = 7 000
m decreased by m = m
13.2 kg – 12.7 kg = 0.5 kg
1.99 m less than 2.21 m= 0.22 m
$2.53 – $2.45 = $0.08
Created by Tania Colson (2010)

112. PB 2: Up Through a Multiple of 10
52 – 48 =
$190 less than $230 =
$183 - $179 =
The difference between 560 and 620 =
2 200 minus =
– =
m decreased by m =
10.3 kg – 9.7 kg =
1.99 m less than 2.33 m=
$3.54 – $3.49 =
Created by Tania Colson (2010)

113. PB 2: Up Through a Multiple of 10
52 – 48 = 4
$190 less than $230 = 40
$183 - $179 = 4
The difference between 560 and 620 = 60
2 200 minus = 600
– = 7 000
m decreased by m = m
10.3 kg – 9.7 kg = 0.6 kg
1.99 m less than 2.33 m = 0.34 m
$3.54 – $3.49 = $0.05
Created by Tania Colson (2010)

114. PB 3: Up Through a Multiple of 10
76 – 68 =
$240 less than $170 =
$172 - $167 =
The difference between 430 and 390 =
1 100 minus 800 =
– =
m decreased by m =
22.2 kg – 21.9 kg =
2.98 m less than 3.33 m=
$5.09 – $4.99 =
Created by Tania Colson (2010)

115. PB 3: Up Through a Multiple of 10
76 – 68 = 8
$240 less than $170 = $70
$172 - $167 = $5
The difference between 430 and 390 = 40
1 100 minus 800 = 300
– = 5 000
m decreased by m = m
22.2 kg – 21.9 kg = 0.3 kg
2.98 m less than 3.33 m = 0.35 m
$5.09 – $4.99 = $0.10
Created by Tania Colson (2010)

116. Strategy Intro Break Up and Bridge
Try These In Your Head 92 – 26 = 745 – 207 = 860 – 370 = – = – 680 = – = – =
How might you use a number line to solve these problems?
Created by Tania Colson (2010)

117. Strategy Intro Break Up and Bridge
Check Your Answers 92 – 26 = – 207 = – 370 = – = – 680 = – = – =
How might you use a number line to solve these problems?
Created by Tania Colson (2010)

118. Strategy Break Up and Bridge
Begin with the first number and break up the second number according to the place value of its digits. Subtract these one at a time from the first number Think: …
81 minus 30 is 51.
51 minus 7 is 44.
The difference is 44.
Created by Tania Colson (2010)

119. Created by Tania Colson (2010)
PB 1: Break Up and Bridge
53 – 25 =
$306 less than $870 =
750 km =
The difference between 640 and 170 =
5 400 minus =
71 00 – =
$8020 minus $3050 =
– =
km – km=
less than =
Created by Tania Colson (2010)

120. Created by Tania Colson (2010)
PB 1: Break Up and Bridge
53 – 25 = 28
$306 less than $870 = $564
750 km = 490
The difference between 640 and 170 = 470
5 400 minus = 3 900
7 100 – = 4 500
$8020 minus $3050 = $5030
– =
km – km = km
less than =
Created by Tania Colson (2010)

121. Created by Tania Colson (2010)
PB 2: Break Up and Bridge
48 – 29 =
$410 less than $780 =
820 km =
The difference between 530 and 170 =
6 200 minus =
4 100 – =
$5020 minus $1050 =
– =
km – km=
less than =
Created by Tania Colson (2010)

122. Created by Tania Colson (2010)
PB 2: Break Up and Bridge
48 – 29 = 19
$410 less than $780 = $370
820 km – 330 km = 490 km
The difference between 530 and 170 = 360
6 200 minus = 3 700
4 100 – = 2 400
$5020 minus $1050 = 3070
– =
km – km = km
less than = 6 000
Created by Tania Colson (2010)

123. Created by Tania Colson (2010)
PB 3: Break Up and Bridge
78 – 19 =
$380 less than $540 =
920 km – 230 km =
The difference between 450 and 180 =
3 400 minus =
8 200 – =
$4030 minus $2050 =
– =
km – km=
less than =
Created by Tania Colson (2010)

124. Created by Tania Colson (2010)
PB 3: Break Up and Bridge
78 – 19 = 59
$380 less than $540 = $160
920 km – 230 km = 690 km
The difference between 450 and 180 = 270
3 400 minus = 1 700
8 200 – = 6 800
$4030 minus $2050 = 1980
– =
km – km= km
less than =
Created by Tania Colson (2010)

125. Strategy Intro Compensation (Subtraction)
Try These In Your Head 36 – 8 = 85 – 29 = = = – 999= – 995 = – =
How can you tackle eights and nine?
Created by Tania Colson (2010)

126. Strategy Intro Compensation (Subtraction)
Check Your Answers 36 – 8 = – 29 = = = – 999= – 995 = – =
Created by Tania Colson (2010)

127. Strategy Compensation (Subtraction)
Round one number up to the nearest compatible number that is a multiple of a power of ten. Use that number to carry out the subtraction instead. Since you subtracted a little too much, add the amount of the change you made. Think:
290 rounds up to 300.
850 minus 300 is 550.
550 is 10 less than the answer.
550 plus 10 is 560.
Created by Tania Colson (2010)

128. PB 1: Compensation (Subtraction)
92 – 38 =
$399 less than $875=
298 km fewer than 630 km =
450 – 190 =
5 700 – 997 =
4 500 less =
The difference between $ and $ =
km – 2980 km =
minus 9 900=
Subtract from =
Created by Tania Colson (2010)

129. PB 1: Compensation (Subtraction)
92 – 38 = 54
$399 less than $875 = $476
298 km fewer than 630 km = 332 km
450 – 190 = 360
5 700 – 997 = 4 703
4 500 less = 2 510
The difference between $ and $ = $21 003
km – 2980 km = km
minus =
Subtract from =
Created by Tania Colson (2010)

130. PB 2: Compensation (Subtraction)
72 – 28 =
$499 less than $775 =
198 km fewer than 540 km =
340 – 180 =
6 500 – 999 =
3 500 less =
The difference between $ and $ =
km – 5990 km =
minus 9 000=
Subtract from =
Created by Tania Colson (2010)

131. Created by Tania Colson (2010)
PB 2: Compensation
72 – 28 = 44
$499 less than $775 = $276
198 km fewer than 540 km = 341 km
340 – 180 = 160
6 500 – 999 = 5501
3 500 less = 1 502
The difference between $ and $ = $40 003
km – 5990 km =
minus =
Subtract from =
Created by Tania Colson (2010)

132. Created by Tania Colson (2010)
PB 3: Compensation
58 – 29 =
$298 less than $560=
498 cm fewer than 940 cm =
240 – 199 =
3 200 – 997 =
6 600 less =
The difference between $ and $ =
m – 6980 m =
minus 9 000=
Subtract from =
Created by Tania Colson (2010)

133. PB 3: Compensation (Subtraction)
58 – 29 = 29
$298 less than $560= $262
498 cm fewer than 940 cm = 442 cm
240 – 199 = 41
3 200 – 997 = 2203
6 600 less = 2 601
The difference between $ and $ = $31 010
m – m =
minus =
Subtract from =
Created by Tania Colson (2010)

134. Strategy Intro Balancing for a Constant Difference
Try These In Your Head 87 – 19 = 345 – 198 = – = – = – = – = – =
How is 12 minus 2 like 14 minus 4? How are they different?
Created by Tania Colson (2010)

135. Strategy Intro Balancing for a Constant Difference
Check Your Answers 87 – 19 = – 198 = – = – = – = – = – =
Created by Tania Colson (2010)

136. Strategy Balancing for a Constant Difference
Changing both numbers by the same amount will always give the same answer. This can make a difficult problem easier to solve using another strategy like quick subtraction. Think:
48 is 2 from 50.
Add 2 to both numbers.
58 minus 50 is the new problem. =8
Created by Tania Colson (2010)

137. PB 1: Balancing for a Constant Difference
77 – 39 =
$53 – $28 =
$875 minus $399 =
750 less 290 =
830 decreased by 380 =
5 400 – 997 =
The difference between $ and $ =
– 2997 =
km – 4980 =
Subtract from =
Created by Tania Colson (2010)

138. PB 1: Balancing for a Constant Difference
77 – 39 = 38
$53 – $28 = $25
$875 minus $399 = $474
750 less 290 = 460
830 decreased by 380 = 450
5 400 – 997 = 4 403
The difference between $ and $ = $4 600
– 2997 =
km – 4980 =
Subtract from =
Created by Tania Colson (2010)

139. PB 2: Balancing for a Constant Difference
54 – 29 =
$68 – $49 =
$540 minus $299 =
870 less 190 =
630 decreased by 270 =
6 900 – 998 =
The difference between $ and $ =
– 1997 =
km – 5980 =
Subtract from =
Created by Tania Colson (2010)

140. PB 2: Balancing for a Constant Difference
54 – 29 = 25
$68 – $49 =19
$540 minus $299 = $241
870 less 190 = 680
630 decreased by 270 = 360
6 900 – 998 = 5 902
The difference between $ and $ = $2 700
– 1997 =
km – 5980 =
Subtract from =
Created by Tania Colson (2010)

141. PB 3: Balancing for a Constant Difference
82 – 59 =
48% – 29% =
$360 minus $299 =
820 less 160 =
500 decreased by 290 =
3 900 – 998 =
The difference between km and km =
– 1998 =
km – 2900 =
Subtract from =
Created by Tania Colson (2010)

142. PB 3: Balancing for a Constant Difference
82 – 59 = 23
48% – 29% = 19%
$360 minus $299 = $61
820 less 160 = 660
500 decreased by 290 = 210
3 900 – 998 = 2 902
The difference between km and km = km
– 1998 =
km – 2900 =
Subtract from =
Created by Tania Colson (2010)

143. Created by Tania Colson (2010)
MULTIPLICATION
and DIVISION
Created by Tania Colson (2010)

144. Strategy Intro Quick Multiplication
Try These In Your Head 43 x 2 = 1.42 x 2 = 4.2 x 4 = 3 x 12.3 = 7.2 x 3 = 41 x 2 = 23 x 3 =
Why are these sentences easier to solve than
4 x 9.5 ?
Created by Tania Colson (2010)

145. Strategy Intro Quick Multiplication
Check Your Answers 43 x 2 = x 2 = x 4 = x 12.3 = x 3 = x 2 = x 3 = 66
There is no regrouping to think about.
Created by Tania Colson (2010)

146. Strategy Quick Multiplication
Begin by multipling the one digit factor by digit of the other factor starting at the front end. Combine the totals to solve. Think: 31 x 4
4 times 3 tens is 12 tens or 120.
4 times 1 is 4.
120 plus 4 is 124.
Created by Tania Colson (2010)

147. PB 1: Quick Multiplication
123 x 3 =
$3 x $41 =
54 times 2=
The perimeter of a square with a side of 3.1 cm =
4 groups of 22 =
211 x 3=
4 sets of 121=
2 x 432=
3 times 4324 =
The product of 9 times 111=
Created by Tania Colson (2010)

148. PB 1: Quick Multiplication
123 x 3 = 369
$3 x $41 = 123
54 times 2 = 108
The perimeter of a square with a side of 3.1 cm = 12.4 cm
4 groups of 22 =88
211 x 3= 633
4 sets of 121= 484
2 x 432= 864
3 times 4321 =
The product of 9 times 111= 999
Created by Tania Colson (2010)

149. PB 2: Quick Multiplication
343 x 2 =
$2 x $32 =
51 times 2=
The perimeter of a square with a side of 1.2 m =
3 groups of 130 =
201 x 3=
4 sets of 212=
3 x 132=
2 times 1324 =
The product of 5 times 111=
Created by Tania Colson (2010)

150. PB 2: Quick Multiplication
343 x 2 = 686
$2 x $32 = $64
51 times 2= 102
The perimeter of a square with a side of 1.2 m = 4.8 m
3 groups of 130 =390
201 x 3= 603
4 sets of 212= 848
3 x 132= 396
2 times 1324 = 2648
The product of 5 times 111= 555
Created by Tania Colson (2010)

151. PB 3: Quick Multiplication
321 x 3 =
$3 x $32 =
41 times 2 =
The perimeter of a square with a side of 2.11 cm =
3 groups of 23 =
423 x 2=
4 sets of 11.2=
2 x 2.33=
2 times 1232 =
The product of 7 times 101=
Created by Tania Colson (2010)

152. PB 3: Quick Multiplication
321 x 3 = 363
$3 x $32 = $96
41 times 2 = 82
The perimeter of a square with a side of 2.11 cm = 8.44 cm
3 groups of 23 = 69
423 x 2= 846
4 sets of 11.2= 44.8
2 x 2.33= 4.66
2 times 1232 = 2464
The product of 7 times 101 = 707
Created by Tania Colson (2010)

153. Strategy Intro Quick Division
Try These In Your Head 640  2 = 1290  3 = 360  3 = 4802  2 = 7280  8 = 32.8  4 =  6 =
Why are these sentences easier to solve than
675 divided by 5 ?
Created by Tania Colson (2010)

154. Strategy Intro Quick Division
Check Your Answers 640  2 =  3 =  3 =  2 =  8 =  4 =  6 = 4.03
They can be solved without regrouping.
Created by Tania Colson (2010)

155. Strategy Quick Division
Begin by dividing the one digit factor by each
digit of the other factor starting at the front
end. Combine the totals to solve.
Think: 642  2
Hint: You can also look
at the fist two digit on the
left together to solve.
Think : 459  9…
45 tens  9 = 5 tens
And…9  9 = 1
So… the answer is 59!
6 hundreds divided by 2 is 3 hundreds or 300.
4 tens divided by 2 is 2 tens or 20.
2 divided by 2 is 1.
= 321
Created by Tania Colson (2010)

156. Created by Tania Colson (2010)
PB 1: Quick Division
68  2 =
5010  5 =
186 divided by 6=
How many groups of 8 in 1680 =
6036 kg  3 kg =
6309  9=
The quotient of 328 cm  4 cm=
153 m  3 m =
4050  5=
The length of a side of a square with a perimeter of 28.4 cm=
Created by Tania Colson (2010)

157. Created by Tania Colson (2010)
PB 1: Quick Division
68  2 = 34
5010  5 =1002
186 divided by 6 = 31
How many groups of 8 in 1680 = 210
6036 kg  3 kg = 2012 kg
6309  9= 701
The quotient of 328 cm  4 cm= 82 cm
153 m  3 m = 51 m
4050  5 = 810
The length of a side of a square with a perimeter of 28.4 cm= 7.1 cm
Created by Tania Colson (2010)

158. Created by Tania Colson (2010)
PB 2: Quick Division
147  7 =
4040  2 =
246 divided by 3=
How many groups of 9 in 279 =
8040 kg  4 kg =
729  9 =
The quotient of 126 cm  3 cm=
4907 m  7 m =
355  5=
The length of a side of a square with a perimeter of 36.8 cm=
Created by Tania Colson (2010)

159. Created by Tania Colson (2010)
PB 2: Quick Division
147  7 = 21
4040  2 = 2020
246 divided by 3= 82
How many groups of 9 in 279 = 31
8040 kg  4 kg = 2010 kg
729  9 = 81
The quotient of 126 cm  3 cm= 42 cm
4907 m  7 m = 701 m
355  5= 71
The length of a side of a square with a perimeter of 36.8 cm= 9.2 cm
Created by Tania Colson (2010)

160. Created by Tania Colson (2010)
PB 3: Quick Division
287  7 =
164  2 =
364 divided by 4=
How many groups of 6 in 546 =
2480 kg  8 kg =
5490  9 =
The quotient of 1869 cm  3 cm =
2170 km  7 km =
2005  5=
The length of a side of a equilateral triangle with a perimeter of 27.9 m=
Created by Tania Colson (2010)

161. Created by Tania Colson (2010)
PB 3: Quick Division
287  7 = 41
164  2 = 82
364 divided by 4= 91
How many groups of 6 in 546 = 91
2480 kg  8 kg = 310 kg
5490  9 = 61
The quotient of 1869 cm  3 cm = 623 cm
2170 km  7 km = 310 km
2005  5= 401
The length of a side of a equilateral triangle with a perimeter of 27.9 m= 9.3 m
Created by Tania Colson (2010)

162. Strategy Intro Multiplying by 10, 100 and 1000
Try These In Your Head 53 x 10 = 10 x 2.5 = 60 x 100 = 0.6 x 100 = 120 x 1000 = 8.36 x 1000 = 0.03 x 1000 =
How does multiply by 10, 100 and 1000 change the place value of each digit?
Created by Tania Colson (2010)

163. Strategy Intro Multiplying by 10, 100 and 1000
Check Your Answers 53 x 10 = x 2.5 = x 100 = x 100 = x 1000 = x 1000 = x 1000 = 30
Each digit shifts 1, 2, or 3 places to the left to have a higher place value.
Created by Tania Colson (2010)

164. Strategy Multiplying by 10, 100 and 1000
This strategy is all about following a pattern as easy
as 1, 2, 3!
Multiplying by 10 increases the place value of each digit by one place
To the left. Tack on 1 zero OR hop the decimal 1 space to the right.
Multiplying by 100 increase the place value of each digit by two
places to the left. Tack on 2 zeros OR hop the decimal 2 spaces to the right.
Multiplying by 1000 increases the place value of each digit by three
places to the left. Tack on 3 zeros OR hop the decimal 3 spaces to the right
Created by Tania Colson (2010)

165. Created by Tania Colson (2010)
PB 1: Multiplying by 10, 100, and 1000
10 x 53 =
92 x 10 =
0.3 x 10 =
5 cm = ______ mm
$50 x 100 =
100 x 15 =
0.12 m = ______ cm
1000 x $73=
9.9 x 1000=
234 km = _______m
10 mm = 1 cm
100 cm = 1 m
1000 m = 1km
Created by Tania Colson (2010)

166. Created by Tania Colson (2010)
PB 1: Multiplying by 10, 100, and 1000
10 x 53 = 530
92 x 10 =920
0.3 x 10 = 3
5 cm = 50 mm
$50 x 100 = $5000
100 x 15 = 1500
0.12 m = 12cm
1000 x $73 = $73 000
9.9 x 1000 = 9 900
234 km = m
10 mm = 1 cm
100 cm = 1 m
1000 m = 1km
Created by Tania Colson (2010)

167. Created by Tania Colson (2010)
PB 2: Multiplying by 10, 100, and 1000
10 x $56 =
239 x 10 =
0.5 x 10 =
_____ mg = 16 cg
$49 x 100 =
100 x 654 =
_____ cm = 0.16 g
1000 x $68=
5.8 x 1000=
471 kg = _____g
10 mg = 1 cg
100 cg = 1 g
1000 g = 1kg
Created by Tania Colson (2010)

168. Created by Tania Colson (2010)
PB 2: Multiplying by 10, 100, and 1000
10 x $56 = $560
239 x 10 =2390
0.5 x 10 = 5
160 mg = 16 cg
$49 x 100 = $4900
100 x 654 =
16 cg = 0.16 g
1000 x $68= $68 000
5.8 x 1000= 5 800
471 kg = g
10 mg = 1 cg
100 cg = 1 g
1000 g = 1kg
Created by Tania Colson (2010)

169. Created by Tania Colson (2010)
PB 3: Multiplying by 10, 100, and 1000
10 x $48 =
583 x 10 =
0.31 x 10 =
_____ mm = 39 cm
$74 x 100 =
100 x 398 =
_____ cm = 0.92 m
1000 x $432=
4.6 x 1000=
85 km = _____ m
10 mm = 1 cm
100 cm = 1 m
1000 m = 1km
Created by Tania Colson (2010)

170. Created by Tania Colson (2010)
PB 3: Multiplying by 10, 100, and 1000
10 x $48 = $480
583 x 10 =5830
0.31 x 10 = 3.1
390 mm = 39 cm
$74 x 100 = $7400
100 x 398 =
92 cm = 0.92 m
1000 x $432 = $
4.6 x 1000 = 4600
85 km = m
10 mm = 1 cm
100 cm = 1 m
1000 m = 1km
Created by Tania Colson (2010)

171. Strategy Intro Dividing by 0.1, 0.01 and 0.001
Try These In Your Head 53  0.1 = 25  0.1 = 60  0.01 = 0.6  0.01 = 120  = 8.36  = 0.03  =
Warning! Model with Base 10 blocks!
How does multiply by 0.1, 0.01 and change the place value of each digit?
Created by Tania Colson (2010)

172. Strategy Intro Dividing by 0.1, 0.01 and 0.001
Check Your Answers 53  0.1 =  0.1 =  0.01 =  0.01 =  =  =  = 30
Warning! Model with Base 10 blocks!
Where have you seen this pattern before?
Click Here!
Created by Tania Colson (2010)

173. Strategy Intro Multiplying by 10, 100 and 1000
Check Your Answers 53 x 10 = x 2.5 = x 100 = x 100 = x 1000 = x 1000 = x 1000 = 30
It’s the same!
Go Back to dividing by 0.1, 0.01 and 0.001
Created by Tania Colson (2010)

174. Strategy Dividing by 0.1, 0.01, and 0.001
This strategy is also all about following a pattern as easy
as 1, 2, 3!
Dividing by 0.1 is like multiplying by 10 and increases the place value
of each digit by one place to the left. Tack on 1 zero OR hop the decimal 1
space to the right.
Dividing by 0.01 is like multiplying by 100 and increase the place value of
each digit by two places to the left. Tack on 2 zeros OR hop the decimal 2
spaces to the right.
Dividing by is like multiplying by 1000 and increases the place value of
each digit by three places to the left. Tack on 3 zeros OR hop the decimal 3
spaces to the right
Created by Tania Colson (2010)

175. Created by Tania Colson (2010)
PB 1: Dividing by 0.1, 0.01, and 0.001
5  0.1 =
23  0.1 =
How many tenths in two tenths (0.2)?
5  0.01 =
How many hundredth in 12?
15  =
How many thousandths in 24?
1000  =
9.7  0.001=
6.5  =
Created by Tania Colson (2010)

176. Created by Tania Colson (2010)
PB 1: Dividing by 0.1, 0.01, and 0.001
5  0.1 = 50
23  0.1 = 230
How many tenths in two tenths (0.2)? 2
5  0.01 = 500
How many hundredth in 12? 1200
15  = 1500
How many thousandths in 24?
1000  =
9.7  0.001= 9700
6.5  = 6500
Created by Tania Colson (2010)

177. Created by Tania Colson (2010)
PB 2: Dividing by 0.1, 0.01, and 0.001
7  0.1 =
34  0.1 =
How many tenths in five tenths?
7 0.01 =
How many hundredths in 0.03?
28  =
How many thousandths in 3?
2500  =
5.4  0.001=
0.6  =
Created by Tania Colson (2010)

178. Created by Tania Colson (2010)
PB 2: Dividing by 0.1, 0.01, and 0.001
7  0.1 = 70
34  0.1 = 340
How many tenths in five tenths? 5
7 0.01 = 700
How many hundredths in 0.03? 3
28  = 2800
How many thousandths in 3? 3000
2500  =
5.4  0.001= 5 400
0.6  = 600
Created by Tania Colson (2010)

179. Created by Tania Colson (2010)
PB 3: Dividing by 0.1, 0.01, and 0.001
60  0.1 =
82  0.1 =
How many tenths in nine tenths?
40 0.01 =
How many hundredths in 0.05?
93  =
How many thousandths in 4?
4800  =
3.7  0.001=
0.51  =
Created by Tania Colson (2010)

180. Created by Tania Colson (2010)
PB 3: Dividing by 0.1, 0.01, and 0.001
60  0.1 = 600
82  0.1 = 820
How many tenths in nine tenths? 9
40 0.01 =4000
How many hundredths in 0.05? 5
93  = 9300
How many thousandths in 4? 4000
4800  =
3.7  0.001= 3700
0.51  = 510
Created by Tania Colson (2010)

181. Strategy Intro Dividing by 10, 100 and 1000
Try These In Your Head 50  10 = 640  10 = 720  10 =  100 =  100 =  1000 =  1000 =
How does dividing by 10, 100 and 1000 change the place value of each digit?
Created by Tania Colson (2010)

182. Strategy Intro Dividing by 10, 100 and 1000
Check Your Answers 50  10 =  10 =  10 =  100 =  100 =  1000 =  1000 = 840
Created by Tania Colson (2010)

183. Strategy Dividing by 10, 100 and 1000
This strategy is still all about following a pattern as easy
as 1, 2, 3! But this time change directions 
Dividing by 10 decreases the place value of each digit by one place
to the right. Hop the decimal space to the left.
Dividing by 100 decrease the place value of each digit by two
places to the right. Hop the decimal 2 spaces to the left.
Dividing by 1000 decreases the place value of each digit by three
places to the right. Hop the decimal 3 spaces to the left.
Created by Tania Colson (2010)

184. Created by Tania Colson (2010)
PB 1: Dividing by 10, 100, and 1000
53  10 =
290  10 =
360  10 =
______ cm = 50 mm
3 00  100 =
4 000  100 =
3 200 cm = _____ m
 1000 =
 1000 =
_____ km = m
10 mm = 1 cm
100 cm = 1 m
1000 m = 1km
Created by Tania Colson (2010)

185. Created by Tania Colson (2010)
PB 1: Dividing by 10, 100, and 1000
53  10 = 5.3
290  10 = 29
360  10 = 36
5 cm = 50 mm
3 00  100 = 3
 100 = 40
3 200 cm = 32 m
 1000 = 34
 1000 = 13
4.5 km = m
10 mm = 1 cm
100 cm = 1 m
1000 m = 1km
Created by Tania Colson (2010)

186. Created by Tania Colson (2010)
PB 2: Dividing by 10, 100, and 1000
20  10 =
340  10 =
760  10 =
______ cL = 980 mL
6 00  100 =
9 000  100 =
4 500 cL = _____ L
 1000 =
 1000 =
_____ kL = L
10 mL = 1 cL
100 cL = 1 L
1000 L = 1kL
Created by Tania Colson (2010)

187. Created by Tania Colson (2010)
PB 2: Dividing by 10, 100, and 1000
20  10 = 2
340  10 = 34
760  10 = 76
98 cL = 980 mL
6 00  100 = 6
9 000  100 = 90
4 500 cL = 45 L
 1000 = 84
 1000 = 92
2.5 kL = L
10 mL = 1 cL
100 cL = 1 L
1000 L = 1kL
Created by Tania Colson (2010)

188. Created by Tania Colson (2010)
PB 3: Dividing by 10, 100, and 1000
50  10 =
480  10 =
950  10 =
______ cg = 920 mg
7 00  100 =
4 000  100 =
8 000 cg = _____ g
 1000 =
 1000 =
_____ kg = g
10 mg = 1 cg
100 cg = 1 g
1000 g = 1kg
Created by Tania Colson (2010)

189. Created by Tania Colson (2010)
PB 3: Dividing by 10, 100, and 1000
50  10 = 5
480  10 = 48
950  10 = 95
92 cg = 920 mg
7 00  100 = 7
4 000  100 = 40
8 000 cg = 80 g
 1000 = 76
 1000 = 29
3 kg = g
10 mg = 1 cg
100 cg = 1 g
1000 g = 1kg
Created by Tania Colson (2010)

190. Strategy Intro Multiplying by 0.1, 0.01 and 0.001
Try These In Your Head 50 x 0.1 = 0.1 x 130 = 39x 0.01 = 10 x 0.01 = 900 x = 3000 x = x =
Warning! Model with Base 10 blocks!
How does multiply by 0.1, 0.01 and change the place value of each digit?
Created by Tania Colson (2010)

191. Strategy Intro Multiplying by 0.1, 0.01 and 0.001
Check Your Answers 50 x 0.1 = x 130 = x 0.01 = x 0.01 = x = x = x = 46
Warning! Model with Base 10 blocks!
How does multiply by 0.1, 0.01 and change the place value of each digit?
Created by Tania Colson (2010)

192. Strategy Multiplying by 0.1, 0.01 and 0.001
This strategy is really still just about following a pattern as easy as 1, 2, 3! The hopping is to the left 
Multiplying by 0.1 is like dividing by 10 and decreases the place value of each digit by one place to the right. Hop the decimal 1 space to the left.
Multiplying by 0.01 is like dividing by 100 and decreases the place value of each digit by two places to the right. Hop the decimal 2 spaces to the left.
Multiplying by is like dividing by and decreases the place value of each digit by three places to the right. Hop the decimal 3 spaces to the left.
Created by Tania Colson (2010)

193. PB 1: Multiplying by 0.1, 0.01, and 0.01
0.1 x 12 =
5.5 x 0.1 =
0.3 x 0.1=
0.1 x 48 =
500 x 0.01 =
150 pennies = $______
1200 x 0.01 =
0.001 x 34 =
990 x 0.001=
3400 x =
How many pennies in $1? in $10?
Created by Tania Colson (2010)

194. PB 1: Multiplying by 0.1, 0.01, and 0.01
0.1 x 12 = 1.2
5.5 x 0.1 = 0.55
0.3 x 0.1= 0.03
0.1 x 48 = 4.8
500 x 0.01 = 5
150 pennies = $1.50
1200 x 0.01 = 12
0.001 x 34 = 0.034
990 x 0.001= 0.990
3400 x = 3.4
There are 100 pennies in $1 and
1000 pennies in $10
Created by Tania Colson (2010)

195. PB 2: Multiplying by 0.1, 0.01, and 0.01
0.1 x 8 =
40 x 0.1 =
136 x 0.1=
0.1 x 3.2 =
600 x 0.01 =
300 pennies = $______
1500 x 0.01 =
0.001 x 26 =
870 x 0.001=
x =
How many pennies in $1? in $10?
Created by Tania Colson (2010)

196. PB 2: Multiplying by 0.1, 0.01, and 0.01
0.1 x 8 = 0.8
40 x 0.1 = 4
136 x 0.1= 13.6
0.1 x 3.2 =0.32
600 x 0.01 = 6
300 pennies = $3
1500 x 0.01 = 15
0.001 x 26 = 0.026
870 x 0.001= 0.870
x = 45
How many pennies in $1? in $10?
Created by Tania Colson (2010)

197. PB 3: Multiplying by 0.1, 0.01, and 0.01
0.1 x 5 =
70 x 0.1 =
180 x 0.1=
0.1 x 6.2 =
900 x 0.01 =
200 pennies = $______
2500 x 0.01 =
0.001 x 99 =
720 x 0.001=
x =
How many pennies in $1? in $10?
Created by Tania Colson (2010)

198. PB 3: Multiplying by 0.1, 0.01, and 0.01
0.1 x 5 = 0.5
70 x 0.1 = 7.0
180 x 0.1= 18.0
0.1 x 6.2 = 0.62
900 x 0.01 = 9.00
200 pennies = $2
2500 x 0.01 = 25.00
0.001 x 99 = 0.099
720 x 0.001= 0.720
x = 84
How many pennies in $1? in $10?
Created by Tania Colson (2010)

199. Strategy Intro Cancelling Common Zeros
Try These In Your Head 500  10 = 900  30 = 8000  40 =  20 = 2000  50 =  600 =  300 =
Warning! Model Shrinking with Base 10 blocks!
How do you deal with all those trailing zeros?
Created by Tania Colson (2010)

200. Strategy Intro Cancelling Common Zeros
Try These In Your Head 500  10 =  30 =  40 =  20 =  50 =  600 =  300 = 80
Warning! Model Shrinking with Base 10 blocks!
You can cancel common zeros.
Created by Tania Colson (2010)

201. Strategy Cancelling Common Zeros
When both numbers have trailing zeros, you can cancel common zeros. This shrinks both numbers by a power of 10. The problem will be simpler to solve using your division facts. Think: 400  20
Cancel common zeros and 400 divided by 20 shrinks to…
40 divided by 2.
40  2 = 20
Created by Tania Colson (2010)

202. PB 1: Cancelling Common Zeros
600  20 =
800 divided by 40 =
9000  30 =
9000  300 =
The quotient of 6900 divided by 30 =
1200  60 =
1500 divided by 500 =
1800  200 =
Divide by 3000 =
 =
Created by Tania Colson (2010)

203. PB 1: Cancelling Common Zeros
600  20 = 30
800 divided by 40 = 20
9000  30 = 300
9000  300 = 30
The quotient of 6900 divided by 30 = 230
1200  60 = 20
1500 divided by 500 = 3
1800  200 = 9
Divide by 3000 = 30
 = 4
Created by Tania Colson (2010)

204. PB 2: Cancelling Common Zeros
800  20 =
900 divided by 30 =
5000  250 =
1200  300 =
The quotient of 4500 divided by 90 =
7200  60 =
5000 divided by 500 =
2700  300 =
Divide by 200 =
 =
Created by Tania Colson (2010)

205. PB 2: Cancelling Common Zeros
800  20 = 40
900 divided by 30 = 30
5000  250 = 20
1200  300 = 4
The quotient of 4500 divided by 90 = 50
7200  60 = 120
5000 divided by 500 = 10
2700  300 = 9
Divide by 200 = 410
 = 6
Created by Tania Colson (2010)

206. PB 3: Cancelling Common Zeros
600  30 =
700 divided by 70 =
8000  400 =
9000  300 =
The quotient of 1100 divided by 110 =
3500  70 =
1600 divided by 800 =
2400  300 =
Divide by 5000 =
 =
Created by Tania Colson (2010)

207. PB 3: Cancelling Common Zeros
600  30 = 20
700 divided by 70 = 10
8000  400 = 20
9000  300 = 30
The quotient of 1100 divided by 110 = 1
3500  70 = 50
1600 divided by 800 = 2
2400  300 = 8
Divide by 5000 = 8
 = 5
Created by Tania Colson (2010)

208. Strategy Intro Think Multiplication
Try These In Your Head 240  12 = 880  40 = 1470  70 = 3600  12 = 1260  60 = 6000 12 = 6500  50 =
How can knowing your multiplication facts help you divide?
Created by Tania Colson (2010)

209. Strategy Intro Think Multiplication
Check Your Answers 240  12 =  40 =  70 =  12 =  60 =  12 =  50 = 130
How can knowing your multiplication facts help you divide?
Created by Tania Colson (2010)

210. Strategy Think Multiplication
If division troubles you, you can always think of multiplication instead. See 60  12 and think: What times 12 is 60? This strategy can be combined with many other strategies for multiplication to find the answer. Think: 920  40
What times 40 is 920?
20 groups of 400 is 800, leaving 120, which is 3 more groups of 40. That’s 23 groups in all!
Created by Tania Colson (2010)

211. PB 1: Think Multiplication
880  40 =
How many groups of 70 in 1470?
660  60 =
540  90 =
The quotient of 840 divided by 12 =
450  15 =
5400 divided by 30 =
2870  70 =
Divide by 700 =
 =
Created by Tania Colson (2010)

212. PB 1: Think Multiplication
880  40 = 22
How many groups of 70 in 1470? 21
660  60 = 11
540  90 = 6
The quotient of 840 divided by 12 = 70
450  15 = 30
5400 divided by 30 =180
2870  70 = 21
Divide by 700 = 71
 = 4
Created by Tania Colson (2010)

213. PB 2: Think Multiplication
880  80 =
How many groups of 40 in 320?
420  20 =
9090  90 =
The quotient of 480 divided by 12 =
3600  12 =
5500 divided by 50 =
2800  70 =
Divide by 700 =
 =
Created by Tania Colson (2010)

214. PB 2: Think Multiplication
880  80 = 22
How many groups of 40 in 320? 8
420  20 = 21
9090  90 = 303
The quotient of 480 divided by 12 = 40
3600  12 = 300
5500 divided by 50 = 110
2800  70 = 40
Divide by 700 = 61
 = 6
Created by Tania Colson (2010)

215. PB 3: Think Multiplication
840  40 =
How many groups of 70 in 420?
420  60 =
450  30 =
The quotient of 960 divided by 12 =
2400  20 =
5400 divided by 60 =
2800  70 =
Divide by 500 =
 =
Created by Tania Colson (2010)

216. PB 3: Think Multiplication
840  40 = 21
How many groups of 70 in 420? 6
420  60 = 7
450  30 =15
The quotient of 960 divided by 12 = 80
2400  20 = 120
5400 divided by 60 = 90
2800  70 = 40
Divide by 500 = 43
 = 71
Created by Tania Colson (2010)

217. Strategy Intro Compensation (Multiplication)
Try These In Your Head 4.98 X 2 = 9.99 x 8 = 6.99 x 9 = 5.98 x 7 = x 5 = x 6 =
During what everyday activity might you have to do this kind of calculation?
Created by Tania Colson (2010)

218. Strategy Intro Compensation (Multiplication)
Check Your Answers 4.98 X 2 = x 8 = x 9 = x 4 = x 5 = x 6 =
When buying more that one of something!
Created by Tania Colson (2010)

219. Strategy Compensation (Multiplication)
Round the decimal factor up to the nearest whole number. Use that number to carry out the multiplication instead. Since you multiplied by a little too much, adjust your answer to compensate for the amount of the change you made. . Think: 2.99 x 3
2.99 rounds to 3.00
3 times 3 is 9.00
9 is too much!
3 groups of 0.01 is 0.03
= 8.97
Created by Tania Colson (2010)

220. PB 1: Compensation (Multiplication)
$1.99 x 2 =
$4.98 x 3=
5 CDs at $11.99 each totals $_______
$14.98 x 3 =
6 groups of $24.99 =
The perimeter of a square with a side length of cm is _______ cm
$99.98 x 3 =
5 times $ =
$ x 4 =
x 3 =
Created by Tania Colson (2010)

221. PB 1: Compensation (Multiplication)
$1.99 x 2 = $3.98
$4.98 x 3= $14.94
5 CDs at $11.99 each totals $59.95
$14.98 x 3 = $44.94
6 groups of $24.99 = $149.94
The perimeter of a square with a side length of cm is cm
$99.98 x 3 = $299.94
5 times $ = $999.90
$ x 4 =
x 3 =
Created by Tania Colson (2010)

222. PB 2: Compensation (Multiplication)
$1.99 x 3 =
$3.98 x 2=
4 movie passes at $8.99 each totals $______
$11.98 x 3 =
8 groups of $19.99 =
The perimeter of a square with a side length of cm is _______ cm
$99.98 x 3 =
6 times $ =
$ x 5 =
x 2 =
Created by Tania Colson (2010)

223. PB 2: Compensation (Multiplication)
$1.99 x 3 = $5.97
$3.98 x 2= $7.96
4 movie passes at $8.99 each totals $35.96
$11.98 x 3 = $35.94
8 groups of $19.99 = $159.92
The perimeter of a square with a side length of cm is cm
$99.98 x 3 = $299.94
6 times $ = $179.88
$ x 5 = $
x 2 =
Created by Tania Colson (2010)

224. PB 3: Compensation (Multiplication)
$1.99 x 2 =
$1.98 x 4=
5 value meals at $3.99 each totals $______
$9.98 x 4 =
5 groups of $19.98 =
The perimeter of a square with a side length of 8.99 cm is _______ cm
$99.98 x 2 =
7 times $ =
$ x 9 =
x 2 =
Created by Tania Colson (2010)

225. PB 3: Compensation (Multiplication)
$1.99 x 2 = $3.98
$1.98 x 4= $7.92
5 value meals at $3.99 each totals $19.95
$9.98 x 4 = $39.92
5 groups of $19.98 = $99.90
The perimeter of a square with a side length of 8.99 cm is cm
$99.98 x 2 = $199.96
7 times $ = $
$ x 9 = $
x 2 =
Created by Tania Colson (2010)

226. Strategy Intro Halving and Doubling
Try These In Your Head 42 x 50 = 500 x 88 = 12 x 2.5 = 4.5 x 2.2 = 140 x 35 = 200 x 4.5 =
Which should you halve? Which should you double?
Created by Tania Colson (2010)

227. Strategy Intro Halving and Doubling
Check Your Answers 42 x 50 = x 88 = x 2.5 = x 2.2 = x 35 = x 4.5 = 900
Halve the evens, double the odds!
Created by Tania Colson (2010)

228. Strategy Halving and Doubling
Double the odd factor and halve the even number to get two new factors that are easier to multiply. If both factors are even decide which factor when double will be easier to work with. Think: 34 x 50
Halve 34 to get 17
Double 50 to get 100
17 times 100 is 1700.
Created by Tania Colson (2010)

229. PB 1: Halving and Doubling
86 x 50 =
50 x 28 =
64 times 50 =
70 x 500 =
18 x 2.5=
The area of a garden with dimensions of 2.5m and 2.2m =
1.5 x 6.6 =
The product of 60 and 2.5 =
180 x 45 =
160 x 35 =
Created by Tania Colson (2010)

230. PB 1: Halving and Doubling
86 x 50 = 4300
50 x 28 = 1400
64 times 50 = 3200
70 x 500 = 3500
18 x 2.5 = 45
The area of a garden with dimensions of 2.5m and 2.2m = 5.5m2
1.5 x 6.6 = 9.9
The product of 60 and 2.5 = 150
180 x 45 = 8100
160 x 35 = 5600
Created by Tania Colson (2010)

231. PB 2: Halving and Doubling
44 x 50 =
50 x 14 =
4 x 13 =
14 x 2.5 =
16 x 2.5 =
The area of a room with dimensions of 4.5m and 6 m =
125 x 8 =
The product of 6 and 65 =
8 x 225=
45 x 4=
Created by Tania Colson (2010)

232. PB 2: Halving and Doubling
44 x 50 = 2200
50 x 14 = 700
4 x 13 = 52
14 x 2.5 = 35
16 x 2.5 = 40
The area of a room with dimensions of 4.5m and 6 m = 27m2
125 x 8 = 1000
The product of 6 and 65 = 390
8 x 225= 1800
45 x 4= 180
Created by Tania Colson (2010)

233. PB 3: Halving and Doubling
4 x 75=
24 x 5 =
12 x 50=
14 x 4.5 =
16 x 3.5 =
The area of a pool with dimensions of 3.5m and 6 m =
18 x 35 =
The product of 6 and 500 =
8.8 x 500=
75 x 6 =
Created by Tania Colson (2010)

234. PB 3: Halving and Doubling
4 x 75 = 300
24 x 5 =120
12 x 50 = 600
14 x 4.5 = 63
16 x 3.5 = 56
The area of a pool with dimensions of 3.5m and 6 m = 21m2
18 x 35 = 630
The product of 6 and 500 = 3000
8.8 x 500 = 4400
75 x 6 = 450
Created by Tania Colson (2010)

235. Strategy Intro Front End Distributative Principle
Try These In Your Head 62 x 3 = 4 x 64 = 2 x 706 = 804 x 6 = 5 x = 3 x =
Take it one step at a time!
Created by Tania Colson (2010)

236. Strategy Intro Front End Distributative Principle
Check Your Answers 62 x 3 = x 64 = x 706 = x 6 = x = x = 9 600
Created by Tania Colson (2010)

237. Strategy Front End Distributive Principle
Find the product of the single digit factor and the factor in the highest place value of the second number. Then find the product of the single digit factor and the remaining digit or digits. Add together for the final answer Think: 53 x 3
3 times 50 is 150.
3 times 3 is 9.
150 plus 9 is 159.
Created by Tania Colson (2010)

238. PB 1: Front End Distributive Principle
62 x 4 =
53 x 3 =
3 x 29 =
4 glasses of milk with 250 mL =
503 x 3 =
606 x 6 =
7 groups of 309 =
3 x =
5 x =
4 300 x 2 =
Created by Tania Colson (2010)

239. PB 1: Front End Distributive Principle
62 x 4 = 248
53 x 3 = 159
3 x 29 = 87
4 glasses of milk with 250 mL = 1000 mL
503 x 3 = 1515
606 x 6 = 3636
7 groups of 309 = 2163
3 x =
5 x =
4 300 x 2 = 8 600
Created by Tania Colson (2010)

240. PB 2: Front End Distributive Principle
32 x 4 =
83 x 3 =
92 x 5 =
The area of a tile 75mm by 8 mm =
209 x 9 =
503 x 2 =
122 x 4 =
The product of 4 and =
4 300 x 2 =
2 100 x 7 =
Created by Tania Colson (2010)

241. PB 2: Front End Distributive Principle
32 x 4 = 128
83 x 3 = 249
92 x 5 = 4510
The area of a tile 75mm by 8 mm = 600
209 x 9 =1881
503 x 2 = 1006
122 x 4 = 488
The product of 4 and = 8 400
4 300 x 2 = 8 600
2 100 x 7 =
Created by Tania Colson (2010)

242. PB 3: Front End Distributive Principle
41 x 6 =
75 x 3 =
35 x 4 =
703 x 8 =
804 x 6 =
320 x 3 =
3 100 x 6 =
3 x =
4 x =
2 100 x 8 =
Created by Tania Colson (2010)

243. PB 3: Front End Distributive Principle
41 x 6 = 246
75 x 3 = 225
35 x 4 = 140
703 x 8 = 5624
804 x 6 = 4824
320 x 3 = 960
3 100 x 6 =
3 x = 9 600
4 x =
2 100 x 8 =
Created by Tania Colson (2010)

244. Strategy Intro Finding Compatible Factors
Check Your Answers 25 x 63 x 4 = 2 x 78 x 500 = 5 x 450 x 2 = 25 x 28 = 68 x 500 = 36 x 25 =
How can you turn a two factor multiplication sentence into a 3 product multiplication sentence?
Created by Tania Colson (2010)

245. Strategy Intro Finding Compatible Factors
Check Your Answers 25 x 63 x 4 = x 78 x 500 = x 450 x 2 = x 28 = 700 Think (25 x 4 x 7) 68 x 500 = 3400 Think (500 x 2 x 34) 36 x 25 = 900 Think (25 x 4 x 9)
Created by Tania Colson (2010)

246. Strategy Finding Compatibles
Look for pairs of factors whose product will be 10, 100, or Then multiply by the remaining factor. Think: 25 x 68 x 4
25 and 4 are compatible. The product is 100.
68 times 100 is 6800.
Created by Tania Colson (2010)

247. PB 1: Finding Compatibles
5 x 19 x 2 =
2 x 43 x 50 =
4 x 38 x 25 =
40 x 25 x 33 =
250 x 56 x 4 =
500 x 86 x 2 =
25 x 32 =
24 x 500 =
250 x 8 =
36 x 25 =
Created by Tania Colson (2010)

248. PB 1: Finding Compatibles
5 x 19 x 2 = 190
2 x 43 x 50 = 4300
4 x 38 x 25 = 3800
40 x 25 x 33 =
250 x 56 x 4 =
500 x 86 x 2 =
25 x 32 = 800
24 x 500 =
250 x 8 = 2000
36 x 25 = 900
Created by Tania Colson (2010)

249. PB 2: Finding Compatibles
5 x 31 x 2 =
2 x 62 x 50 =
4 x 15 x 25 =
40 x 25 x 42 =
250 x 92 x 4 =
500 x 54 x 2 =
25 x 16 =
62 x 500 =
250 x 32 =
48 x 25 =
Created by Tania Colson (2010)

250. PB 2: Finding Compatibles
5 x 31 x 2 = 3100
2 x 62 x 50 = 6200
4 x 15 x 25 = 1500
40 x 25 x 42 =
250 x 92 x 4 =
500 x 54 x 2 =
25 x 16 = 400
62 x 500 =
250 x 32 = 8000
48 x 25 = 1200
Created by Tania Colson (2010)

251. PB 3: Finding Compatibles
5 x 70 x 2 =
2 x 41 x 50 =
4 x 55 x 25 =
40 x 37 x 25=
4 x 38 x 25=
5000 x 9 x 2 =
250 x 24 =
34 x 500 =
250 x 28 =
48 x 50 =
Created by Tania Colson (2010)

252. PB 3: Finding Compatibles
5 x 70 x 2 = 700
2 x 41 x 50 = 4100
4 x 55 x 25 = 5500
40 x 37 x 25=
4 x 38 x 25= 3800
5000 x 9 x 2 =
250 x 24 = 6000
34 x 500 =
250 x 28 = 7000
48 x 50 = 2400
Created by Tania Colson (2010)

253. Strategy Intro Using Division Facts
Try These In Your Head 60  3 = 80  4 = 90  3 = 120  6 = 180  9 = 250  5 =
How can division facts help you solve these?
Created by Tania Colson (2010)

254. Strategy Intro Using Division Facts
Check Your Answers 60  3 =  4 =  3 =  6 =  9 =  5 = 5 000
Created by Tania Colson (2010)

255. Strategy Using Division Facts
Look for familiar division facts. Then decide if the dividend is 10, 100, or 1000 times greater. The quotient will be 10, 100, or 1000 times greater too. See how the number of zeros In the dividend reappears in the quotient. Think: 150  5
15 divided by 5 is 3.
150 is 10 times greater.
So,150 divided by 5 is 30.
Created by Tania Colson (2010)

256. PB 1: Using Division Facts
60  2 =
210  7 =
450  9 =
240  6 =
800  4 =
3 500  7 =
1600  4 =
 8 =
 3 =
 8 =
Created by Tania Colson (2010)

257. PB 1: Using Division Facts
60  2 = 30
210  7 = 30
450  9 = 50
240  6 = 40
800  4 = 200
3 500  7 = 500
1600  4 = 400
 8 = 9 000
 3 = 8 000
 8 = 5 000
Created by Tania Colson (2010)

258. PB 2: Using Division Facts
80  2 =
210  3 =
450  5 =
240  4 =
800  2 =
3 600  6 =
2800  7 =
 6 =
 8 =
 7 =
Created by Tania Colson (2010)

259. PB 2: Using Division Facts
80  2 = 40
210  3 = 70
450  5 = 90
240  4 = 60
800  2 = 400
3 600  6 = 600
2800  7 = 400
 6 = 9 000
 8 = 3 000
 7 = 6 000
Created by Tania Colson (2010)

260. PB 3: Using Division Facts
60  2 =
280  4 =
630  9 =
300  6 =
1200  4 =
4900  7 =
2000  4 =
 9 =
 7 =
 12 =
Created by Tania Colson (2010)

261. PB 3: Using Division Facts
60  2 = 30
280  4 = 70
630  9 = 70
300  6 = 50
1200  4 = 300
4900  7 = 700
2000  4 = 500
 9 = 9 000
 7 = 8 000
 12 = 4 000
Created by Tania Colson (2010)

262. Strategy Intro Breaking Up the Dividend
Try These In Your Head 372  6 = 496  4 = 90  3 = 120  6 = 180  9 = 250  5 =
How could you separate the dividend to make it easier to solve?
Created by Tania Colson (2010)

263. Strategy Intro Breaking Up the Dividend
Try These In Your Head 372  6 = 496  4 = 576  8 = 380  5 = 438  6= 2880  9 =
How could you separate the dividend to make it easier to solve?
Created by Tania Colson (2010)

264. Strategy Breaking Up the Dividend
Break up the dividend into two parts. Both parts should be easy to multiplies of the divisor. Complete both new divisions. Find the total. Think: 256  4
240 is the closest multiple 4 to 256. Break it up : ( )  4
240 divded by 4 is 60.
16 divided by 4 is 4.
= 64
Created by Tania Colson (2010)

265. PB 1: Breaking Up the Dividend
192  3 =
108  4 =
375  5 =
285  3 =
207 3 =
156  2 =
444  6 =
264  8 =
2910  7 =
2880  9 =
Created by Tania Colson (2010)

266. PB 1: Breaking Up the Dividend
192  3 = Think ( ) = 62
108  4 = Think ( ) = 27
375  5 = Think ( ) = 75
285  3 = Think ( ) = 95
207 3 = Think ( ) = 69
156  2 = Think ( ) = 78
444  6 = Think ( ) = 74
264  8 = Think ( ) = 33
2910  7 = Think ( ) = 330
2880  9 = Think ( ) = 320
Created by Tania Colson (2010)

267. PB 2: Breaking Up the Dividend
192  3 =
228  4 =
340  5 =
492  6 =
371  7 =
336  8 =
175 5 =
1960  4 =
7440  8 =
3450  3 =
Created by Tania Colson (2010)

268. PB 2: Breaking Up the Dividend
192  3 = Think ( ) = 52
228  4 = Think ( ) = 57
340  5 = Think ( ) = 68
492  6 = Think ( ) = 82
371  7 = Think ( ) = 53
336  8 = Think ( ) = 42
175 5 = Think ( ) = 35
1960  4 = Think ( ) = 490
7440  8 = Think ( ) = 930
3450  3 = Think ( ) = 1150
Created by Tania Colson (2010)

269. PB 3: Breaking Up the Dividend
282  3 =
292  4 =
365  5 =
438  6 =
644  7 =
896  8 =
585 5 =
4960  4 =
3520  8 =
2580  3 =
Created by Tania Colson (2010)

270. PB 3: Breaking Up the Dividend
282  3 = Think ( ) = 82
292  4 = Think ( ) = 72
365  5 = Think ( ) = 73
438  6 = Think ( ) = 73
644  7 = Think ( ) = 92
896  8 = Think ( ) = 112
585 5 = Think ( ) = 117
4960  4 = Think ( ) = 1220
3520  8 = Think ( ) = 440
2580  3 = Think ( ) = 830
Created by Tania Colson (2010)

271. Strategy Intro Compensation (Division)
Try These In Your Head 304  8 = 295  5 = 261  5 = 228  6 = 352  4 = 1393  7 =
How could you separate the dividend to make it easier to solve?
Created by Tania Colson (2010)

272. Strategy Intro Compensation (Division)
Check Your Answers 304  8 =  5 =  9 =  6 =  4 =  7 = 199
How could you separate the dividend to make it easier to solve?
Created by Tania Colson (2010)

273. Strategy Compensation (Division)
Increase the dividend to an easy multiple of 10, 100, or Find the quotient for the new dividend and then adjust to compensate for the change you made. Think: 348  6
348 is about 360.
360 divided by 6 is 60.
That’s 12 too much or 2 extra groups of 6.
60 minus 2 is 58.
Created by Tania Colson (2010)

274. PB 1: Compensation (Division)
234  3 =
268  4 =
335  5 =
291  3 =
114  3 =
132  2 =
408  6 =
624  8 =
2086  7 =
7992  4 =
Created by Tania Colson (2010)

275. PB 1: Compensation (Division)
234  3 = 78
268  4 = 67
335  5 = 67
291  3 = 97
114  3 = 38
132  2 = 66
408  6 = 68
624  8 = 78
2086  7 = 298
7992  4 = 1998
Created by Tania Colson (2010)

276. PB 2: Compensation (Division)
267  3 =
152  4 =
445  5 =
354  3 =
891  3 =
176  2 =
534  6 =
224  8 =
7188  6 =
2792  4 =
Created by Tania Colson (2010)

277. PB 2: Compensation (Division)
267  3 = 89
152  4 = 38
445  5 = 89
354  3 = 118
891  3 = 297
176  2 = 88
534  6 = 89
224  8 = 28
7188  6 = 1198
2792  4 = 698
Created by Tania Colson (2010)

278. PB 3: Compensation (Division)
197  3 =
232  4 =
540  5 =
264 3 =
245  5 =
214  2 =
234  6 =
544  8 =
1798  2 =
3582  6 =
Created by Tania Colson (2010)

279. PB 3: Compensation (Division)
297  3 = 99
232  4 = 58
540  5 = 108
264 3 = 88
245  5 = 49
214  2 = 107
234  6 = 39
544  8 = 68
1798  2 = 899
3582  6 = 597
Created by Tania Colson (2010)

280. Strategy Intro Balancing for a Constant Quotient
Try These In Your Head 125  5 = 120  2.5 = 23.5  0.5 = 140  5 = 135  0.5 =
How could changing the equation make it easier to solve ?
Created by Tania Colson (2010)

281. Strategy Intro Balancing for a Constant Quotient
Check Your Answers 125  5 =  2.5 =  0.5 =  5 =  2.5 =  0.5 = 270
How could changing the equation make it easier to solve ?
Created by Tania Colson (2010)

282. Strategy Balancing for a Constant Quotient
Multiply both the dividend and the divisor by the same number to make an equation that is easier to solve. Try multiplying by a number that will make the divisor a multiple of 10 Think: 120  5
Double both numbers to get
240  10.
240  10 = 24
Created by Tania Colson (2010)

283. PB 1: Balancing for a Constant Quotient
230  5 =
150  2.5 =
42.5  0.5 =
115  5 =
300  2.5 =
20.5  0.5 =
250  25 =
520  5 =
30.5  0.5 =
50  2.5 =
Created by Tania Colson (2010)

284. PB 1: Balancing for a Constant Quotient
230  5 = 46
150  2.5 = 60
42.5  0.5 = 85
115  5 = 23
300  2.5 = 120
20.5  0.5 = 41
1200  25 = 48
520  5 = 104
30.5  0.5 = 61
50  2.5 = 20
Created by Tania Colson (2010)

285. PB 2: Balancing for a Constant Quotient
140  5 =
125  2.5 =
22.5  0.5 =
320  5 =
400  2.5 =
40.5  0.5 =
500  25 =
420  5 =
43  0.5 =
50  2.5 =
Created by Tania Colson (2010)

286. PB 2: Balancing for a Constant Quotient
140  5 = 28
125  2.5 = 50
22.5  0.5 = 45
320  5 = 64
40  2.5 = 16
40.5  0.5 = 81
500  25 = 20
420  5 = 84
43  0.5 = 86
50  2.5 = 20
Created by Tania Colson (2010)

287. PB 3: Balancing for a Constant Quotient
130  5 = 26
200  2.5 = 80
14.5  0.5 = 29
340  5 = 68
100  2.5 = 40
20.5  0.5 = 41
250  25 = 10
900  5 = 180
42.5  0.5 = 85
60  2.5 = 24
Created by Tania Colson (2010)

288. PB 3: Balancing for a Constant Quotient
130  5 = 26
200  2.5 = 80
14.5  0.5 = 29
340  5 = 68
100  2.5 = 40
20.5  0.5 = 41
250  25 = 10
900  5 = 180
42.5  0.5 = 85
60  2.5 = 24
Created by Tania Colson (2010)

289. Created by Tania Colson (2010)
ESTIMATION
Created by Tania Colson (2010)

290. Estimation Words and Symbols
Some of the common words and phrases are that
also mean estimate are:
about  
just about
between
a little more than
a little less than
close
close to
near
Symbol  ~
When estimating, one wavy bar can be used instead of an equal sign in an equation to show an approximate answer.
Created by Tania Colson (2010)

291. Strategy Intro Quick Estimates (Addition and Subtraction)
Try Estimating These In Your Head is about ___ is about ___ is about ___ is about ___ is about ___ is about ___
How can you use the digits in the highest place value to get a “ball park” or quick estimate?
Created by Tania Colson (2010)

292. Strategy Intro Quick Estimates (Addition and Subtraction)
Check Your Estimates is about is about is about is about is about is about 2000
To get a “ball park” or quick estimate use only the digits at the front end!
Created by Tania Colson (2010)

293. Strategy Quick Estimates (Addition & Subtraction)
Solve the problem by adding or subtracting the numbers at the front end only. This is the fastest way to estimate. It does not always provide the most accurate estimate. Think:
Focusing on the front end changes the problem to
100 plus 500,
that’s about 600
Created by Tania Colson (2010)

294. PB 1: Quick Estimates (Addition & Subtraction)~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Created by Tania Colson (2010)

295. PB 1: Quick Estimates (Addition & Subtraction)
~ 120
~ 1100
~ 700
~ 900
~ 8000
~ 10
~ 500
~ 200
~ 1000
~ 2000
Created by Tania Colson (2010)

296. PB 2: Quick Estimates (Addition & Subtraction)~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Created by Tania Colson (2010)

297. PB 2: Quick Estimates (Addition & Subtraction)
~ 70
~ 700
~ 600
~ 5000 ~
~ 30
~ 100
~ 400
~ 3000
~ 3000
Created by Tania Colson (2010)

298. PB 3: Quick Estimates (Addition & Subtraction)~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Created by Tania Colson (2010)

299. PB 3: Quick Estimates (Addition & Subtraction)
~ 130
~ 1000
~ 900 ~ ~
~ 50
~ 200
~ 800
~ 3000
~ 1000
Created by Tania Colson (2010)

300. Strategy Intro Quick Estimates (Multiplication)
Try Estimating These In Your Head 56 x 4 is about ___ 33 x 5 is about ___ 43 x 72 is about ___ 808 x 24 is about ___ 459 x 26 is about ___ 358 x 86 is about ___
To get a “ball park” or quick estimate use only the digits at the front end!
Created by Tania Colson (2010)

301. Strategy Intro Quick Estimates (Multiplication)
Check Your Estimates 56 x 4 is about x 5 is about x 72 is about x 24 is about x 26 is about x 86 is about
To get a “ball park” or quick estimate use only the digits at the front end!
Created by Tania Colson (2010)

302. Strategy Quick Estimates (Multiplication)
Solve the problem by multiplying the numbers at the front end only. This is the fastest way to estimate. It does not always provide the most accurate estimate. Think: 287 x 49
Focusing on the front end changes the problem to
200 multiplied 40,
that’s about 8000.
Created by Tania Colson (2010)

303. PB 1: Quick Estimates (Multiplication)
69 x 32 ~
25 x 70 ~
57 x 34 ~
46 x 48 ~
235 x 34 ~
874 x 72 ~
685 x 12 ~
498 x 280 ~
234 x 138 ~
956 x 743 ~
Created by Tania Colson (2010)

304. PB 1: Quick Estimates (Multiplication)
69 x 32 ~ 1800
25 x 70 ~ 1400
57 x 34 ~ 1500
46 x 48 ~ 1600
235 x 34 ~ 6 000
874 x 72 ~
685 x 12 ~ 6 000
498 x 280 ~
234 x 138 ~
956 x 743 ~
Created by Tania Colson (2010)

305. PB 2: Quick Estimates (Multiplication)
34 x 53 ~
46 x 37 ~
55 x 25 ~
86 x 49 ~
231 x 47 ~
854 x 55 ~
653 x 25 ~
732 x 584 ~
254 x 558 ~
836 x 653 ~
Created by Tania Colson (2010)

306. PB 2: Quick Estimates (Multiplication)
34 x 53 ~ 1500
46 x 37 ~ 1200
55 x 25 ~ 1000
86 x 49 ~ 2400
231 x 47 ~ 8 000
854 x 55 ~
653 x 25 ~
732 x 584 ~
254 x 558 ~
836 x 653 ~
Created by Tania Colson (2010)

307. PB 3: Quick Estimates (Multiplication)
35 x 56 ~
47 x 87 ~
85 x 45 ~
48 x 59 ~
345 x 51 ~
451 x 65 ~
354 x 85 ~
485 x 932 ~
858 x 358 ~
826 x 458 ~
Created by Tania Colson (2010)

308. PB 3: Quick Estimates (Multiplication)
35 x 56 ~ 1500
47 x 87 ~ 2400
85 x 45 ~ 2400
48 x 59 ~ 2000
345 x 51 ~
451 x 65 ~
354 x 85 ~
485 x 932 ~
858 x 358 ~
826 x 458 ~
Created by Tania Colson (2010)

309. Strategy Intro Rounding (Addition & Subtraction)
Try Estimating These In Your Head is about ___ is about ___ is about ___ is about ___ is about ___ is about ___
How can you round to get a better estimate?
Created by Tania Colson (2010)

310. Strategy Intro Rounding (Addition & Subtraction)
Check Your Estimates is about is about is about is about is about is about 2000
There are 2 rounding different strategies to get better estimates...What are they?
Created by Tania Colson (2010)

311. Strategy Rounding (Addition & Subtraction)
There are 2 basic ways to round numbers to
estimate an answer. This works for addition,
subtraction, multiplication and division.
Round both numbers using rounding rules.
Rounding Rhyme:
0 - 4 Stay on the floor (round off) Example: 429  400
5 - 9 Climb the vine (round up) Example: 489  500
Round one up and one down.
This works when both numbers in the problem have a about half-way between rounding down and rounding up.
Example: 456 x 359  500 x 300 = , this is a closer to the actual answer of Using the rounding rules the estimate would be 500 x 400 
Think: 150  5
Created by Tania Colson (2010)

312. Strategy Rounding (Addition & Subtraction)
Estimate the answer by choosing a rounding strategy that will help you get a closer estimate than using the front end strategy which gave only a “ball park”. Think:
If we round both numbers, this changes the problem to
200 plus 600,
that’s about 800.
(Our front end estimate would be only 600)
Created by Tania Colson (2010)

313. PB 1: Rounding (Addition & Subtraction)~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Created by Tania Colson (2010)

314. PB 1: Rounding(Addition & Subtraction)
~ ~ 100
~ ~ 1300
~ ~ 800
~ ~ 1000
~ ~ 9000
~ 90 – 70 ~ 20
~ 700 – 100 ~ 600
~ 500 – 300 ~ 200
~ 2000 – 1000 ~ 1000
~ – 7000 ~ 3000
Created by Tania Colson (2010)

315. PB 2: Rounding(Addition & Subtraction)~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Created by Tania Colson (2010)

316. PB 2: Rounding(Addition & Subtraction)
~ ~ 80
~ ~ 900
~ ~ 700
~ ~ 5000
~ ~
~ 50 – 20 ~ 30
~ 300 – 100 ~ 200
~ 800 – 300 ~ 500
~ 6000 – 2000 ~ 4000
~ – 6000 ~ 4000
Created by Tania Colson (2010)

317. PB 3: Rounding (Addition & Subtraction)~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Created by Tania Colson (2010)

318. PB 3: Rounding(Addition & Subtraction)
~ ~ 150
~ ~ 1200
~ ~ 1100
~ ~
~ ~
~ ~ 50
~ 500 – 300 ~ 200
~ 1000 – 400 ~ 800
~ 6000 – 2000 ~ 4000
~ 8000 – 7000 ~ 1000
Created by Tania Colson (2010)

319. Strategy Intro Rounding (Multiplication)
Try Estimating These In Your Head 56 x 4 is about ___ 33 x 5 is about ___ 45 x 75 is about ___ 808 x 24 is about ___ 459 x 25 is about ___ 358 x 85 is about ___
The same 2 rounding strategies used to get better estimates when adding and subtraction can be used for multiplying!
Created by Tania Colson (2010)

320. Strategy Intro Rounding (Multiplication)
Check Your Estimates 56 x 4 is about 60 x 4 ~ x 5 is about 30 x 5 ~ x 75 is about 50 x 70 ~ x 24 is about 800 x 20 ~ x 25 is about 500 x 20 ~ x 85 is about 400 x 80 ~
Created by Tania Colson (2010)

321. Strategy Rounding (Multiplication)
Estimate the answer by choosing a rounding strategy that will help you get a closer estimate than using the front end strategy which gave only a “ball park”. Think: 287 x 49
By rounding the problem
becomes 300 times 50, so
the rounded estimate is
*A quick estimate would have
been only
Created by Tania Colson (2010)

322. PB 1: Rounding (Multiplication)
69 x 32 ~
25 x 70 ~
57 x 34 ~
46 x 48 ~
235 x 34 ~
874 x 72 ~
685 x 12 ~
498 x 280 ~
234 x 138 ~
956 x 743 ~
Created by Tania Colson (2010)

323. PB 1: Rounding (Multiplication)
69 x 32 ~ 70 x 30 ~ 2100
25 x 70 ~ 30 x 70 ~ 2100
57 x 34 ~ 60 x 30 ~ 1800
46 x 48 ~ 50 x 50 ~ 2500
235 x 34 ~ 200 x 30 ~ 6000
874 x 72 ~ 900 x 70 ~
685 x 12 ~ 700 x 10 ~ 7 000
498 x 280 ~ 500 x 300 ~
234 x 138 ~ 200 x 100 ~
956 x 743 ~ 1000 x 700 ~
Created by Tania Colson (2010)

324. PB 2: Rounding (Multiplication)
34 x 53 ~
46 x 37 ~
55 x 25 ~
86 x 49 ~
231 x 47 ~
854 x 55 ~
653 x 25 ~
732 x 584 ~
254 x 558 ~
836 x 653 ~
Created by Tania Colson (2010)

325. PB 2: Rounding (Multiplication)
34 x 53 ~ 30 x 50 ~ 1500
46 x 37 ~ 50 x 40 ~ 2000
55 x 25 ~ 60 x 20 ~ 1200
86 x 49 ~ 90 x 50 ~ 4500
231 x 47 ~ 200 x 50 ~
854 x 55 ~ 900 x 50 ~
653 x 25 ~ 700 x 20 ~
732 x 584 ~ 700 x 600 ~
254 x 558 ~ 300 x 500 ~
836 x 653 ~ 800 x 700 ~
Created by Tania Colson (2010)

326. PB 3: Rounding (Multiplication)
35 x 56 ~
47 x 87 ~
85 x 45 ~
48 x 59 ~
345 x 51 ~
451 x 65 ~
354 x 85 ~
485 x 932 ~
858 x 358 ~
826 x 458 ~
Created by Tania Colson (2010)

327. PB 3: Rounding (Multiplication)
35 x 56 ~ 40 x 50 ~ 2000
47 x 87 ~ 50 x 90 ~ 4500
85 x 45 ~ 90 x 40 ~ 3600
48 x 59 ~ 50 x 60 ~ 3000
345 x 51 ~ 300 x 50 ~
451 x 65 ~ 500 x 60 ~
354 x 85 ~ 400 x 80 ~
485 x 932 ~ 500 x 900 ~
858 x 358 ~ 900 x 300 ~
826 x 458 ~ 800 x 500 ~
Created by Tania Colson (2010)

328. Strategy Intro Adjusted Front End (Division)
Try Estimating These In Your Head 56  4 is about ___ 33  5 is about ___ 629  70 is about ___ 358  54 is about ___ 4692  86 is about ___ 3582  96 is about ___
How could you change the digits at the front end to make an easier equation and then get a quick estimate?
Created by Tania Colson (2010)

329. Strategy Intro Adjusted Front End (Division)
Check Your Estimates 56  4 is about 60  4 ~  5 is about 30  5 ~  70 is about 630  70 ~  54 is about 350  50 ~  86 is about 4800   96 is about ___
Created by Tania Colson (2010)

330. Strategy Adjusted Front End(Division)
Estimate the answer by adjusting the front end of the dividend to the closest multiple of the divisor. This is the fastest way to estimate. It does not always provide the most accurate estimate. Think: 317  4
317 is close to 320 which is a multiple of the divisor (4).
So, 320 divided by 4 is 80.
Created by Tania Colson (2010)

331. PB 1: Adjusted Front End (Division)
46  4 ~ 48  4 ~ 12
57  6 ~ 60  6 ~ 10
209  3 ~ 210  30 ~ 7
269  7 ~ 280  7 ~ 40
235  3 ~ 240  3 ~ 80
874  7 ~ 840  7 ~ 120
585  12 ~ 600  12 ~ 50
498  28 ~ 480  20 ~ 24
234  64 ~ 240  60 ~ 4
956  47 ~ 800  4 ~ 200
Created by Tania Colson (2010)

332. PB 1: Adjusted Front End (Division)
46  4 ~ 48  4 ~ 12
57  6 ~ 60  6 ~ 10
209  3 ~ 210  30 ~ 7
269  7 ~ 280  7 ~ 40
235  3 ~ 240  3 ~ 80
874  7 ~ 840  7 ~ 120
585  12 ~ 600  10 ~ 60
498  28 ~ 480  20 ~ 24
234  64 ~ 240  60 ~ 4
956  47 ~ 800  4 ~ 200
Created by Tania Colson (2010)

333. PB 2: Adjusted Front End (Division)
53  6 ~ 54  6 ~ 9  4 ~ 12
47  2 ~ 48  2 ~ 24
317  3 ~ 330  3 ~  30 ~ 7
269  5 ~ 250  5 ~  7 ~ 40
273  4 ~ 280  4 ~ 70  3 ~ 80
874  8 ~ 880  8 ~ 110  7 ~ 120
427  12 ~ 400  10 ~ 40  12 ~ 50
498  59 ~ 480  20 ~ 24
234  64 ~ 240  60 ~ 4
956  87 ~ 800  4 ~ 200
Created by Tania Colson (2010)