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

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)

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)

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)

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

Strategy Intro Using Basic Addition Facts Try These In Your Head 90 + 40 = 80 + 50 = 600 + 600 = 4 000 + 5 000 10 000, 40 000, 70 000, _________ 0.2 s + 0.6 s = 0.04 cm plus 0.03 cm= Created by Tania Colson (2010)

Strategy Using Basic Addition Facts Check you Answers 90 + 40 = 130 80 + 50 = 130 600 + 600 = 1 200 4 000 + 5 000 = 9 000 10 000, 40 000, 70 000, 100 000 0.2 s + 0.6 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)

Strategy Using Basic Addition Facts Doubles Facts Examples: 2 + 2 or 5 + 5 Plus-One Facts Examples: 6 +1 or 8 +1 Near-Doubles (1-Aparts) Facts Examples: 6 + 5 or 2 + 3 Plus-Two Facts Examples: 3 + 2 or 7 + 2 Plus Zero Facts Examples 10 + 0 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)

Strategy Using Basic Addition Facts Knowing your basic addition facts can help you add other problems in your head. Think: 70 + 60 … 7 tens plus 6 tens is 13 tens or 130. Think: 4 000 + 7 000 … 4 thousand plus 7 thousand is 11 thousand or 11 000 Think: 0.09 + 0.06 …9 hundredths plus 6 is 15 hundredths or 0.15 Created by Tania Colson (2010)

PB 1 : Using Basic Addition Facts 90 + 80 = 100 more than 400 = 7 000 plus 4 000 = $6 000 + $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 + 0.9 mm = $0.80 plus $0.90 = 0.8 billion and 0. 6 billion= Created by Tania Colson (2010)

PB 1: Using Basic Addition Facts 90 + 80 = 170 100 more than 400 = 500 7 000 plus 4 000 = 11 000 $6 000 + $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 + 0.9 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)

PB 2: Using Basic Addition Facts 60 + 70 = 200 more than 900 = 4 000 plus 8 000 = $1 000 + $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 + 0.7 mm = $0.60 plus $0.50 = 0.7 billion and 0. 9 billion= Created by Tania Colson (2010)

PB 2: Using Basic Addition Facts 60 + 70 = 130 200 more than 900 = 1 100 4 000 plus 8 000 = 12 000 $1 000 + $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 + 0.7 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)

PB 3: Using Basic Addition Facts 20 + 50 = 600 more than 800 = 3 000 plus 9 000 = $4 000 + $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 + 0.8 mg = $0.30 plus $0.40 = 0.2 billion and 0. 5 billion= Created by Tania Colson (2010)

PB 3: Using Basic Addition Facts 20 + 50 = 70 600 more than 800 = 1400 3 000 plus 9 000 = 12 000 $4 000 + $7 000 = 11 000 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 + 0.8 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)

PB 4: Using Basic Addition Facts 80 + 20 = 400 more than 900 = 1 000 plus 7 000 = $5 000 + $8 000 = 0.02 cm increased by 0.06cm = 50 million and 80 million = The sum of 3g and 6g = 0.4 mL + 0.6 mL = $0.40 plus $0.70 = 0.2 s and 0. 5 s = Created by Tania Colson (2010)

PB 4: Using Basic Addition Facts 80 + 20 = 100 400 more than 900 = 1300 1 000 plus 7 000 = 8 000 $5 000 + $8 000 = 13 000 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 + 0.6 mL = 1.0mL $0.40 plus $0.70 = $1.10 0.2 s and 0. 5 s = 0.7s Created by Tania Colson (2010)

PB 5: Using Basic Addition Facts 90 + 90 = 300 more than 300 = 4 000 plus 7 000 = $4 000 + $5 000 = 0.04 cm increased by 0.03cm = 40 million and 20 million = The sum of 7g and 8g = 0.2 L + 0.3 L = $0.60 plus $0.70 = 0.4 + 0. 8 = Created by Tania Colson (2010)

PB 5: Using Basic Addition Facts 90 + 90 = 180 300 more than 300 = 600 4 000 plus 7 000 = 11 000 $4 000 + $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 + 0.3 L = 0.5L $0.60 plus $0.70 = 1.30 0.4 + 0. 8 = 1.2 Created by Tania Colson (2010)

Strategy Intro Front End Focus Addition Try These In Your Head 37 + 28 = 307 and 206 = 3600 + 2500 = 5.06 more than 3.05 = 7.2cm + 2.6cm = 5.8 million plus 2.5 million= Created by Tania Colson (2010)

Strategy Front End Focus Addition Check Your Answers 37 + 28 = 65 307 and 206 = 513 3 600 + 2 500 = 6100 5.06 more than 3.05 = 8.11 7.2cm + 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)

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: 37 + 28 … 30 plus 20 is 50. 7 plus 8 is 15. Now add the totals… 50 + 15 = 65. Created by Tania Colson (2010)

Strategy Front End Focus Addition It works on really big numbers and really small numbers just the same. Try: 3 600 + 2 500…3 000 plus 2 000 is 5 000, 600 plus 500 is 1 100, and 5 000 and 1100 is 6 100. Try: 5.06 + 3.05…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)

PB 1: Front End Focus Addition 45 +36 = 18 kg more than 56 kg = 102 plus 569 = $660 + $270 = 102 cm and 150cm more = 3 400 + 5 800 = The sum of 2 040 and 5 060 = 4.5 km + 2.7 km = $3.12 plus $1.09 = 5.4 million + 1. 8 million = Created by Tania Colson (2010)

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 3 400 + 5 800 =9 200 The sum of 2 040 and 5 060= 7 100 4.5 km + 2.7 km = 7.2 km $3.12 plus $1.09 = $4.21 5.4 million + 1. 8 million= 7.2 million Created by Tania Colson (2010)

PB 2: Front End Focus Addition 19 + 24 = 35 km more than 29 km = 209 plus 403 = $580 + $340 = 309 cm and 268cm more = 23 000 + 38 000 = The sum of 5 080 and 3 080 = 2.6 cm + 3.9 cm = $3.12 plus $1.09 = 4.8 billion and 3. 6 billion= Created by Tania Colson (2010)

PB 2: Front End Focus Addition 19 + 24 = 43 35 km more than 29 km = 64km 209 plus 403 = 612 $580 + $340 = 920 309 cm and 268cm more = 577 23 000 + 38 000 = 61 000 The sum of 5 080 and 3 080 = 8 160 2.6 cm + 3.9 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)

PB 3: Front End Focus Addition 54 + 19 = 67 m + 28 m = 320 plus 490 = $330 + $280 = 208 cm more than 409cm = 10 060 + 32 070 = The sum of 4 160 and 3 080 = 4.5 cm + 7.9 cm = $6.19 plus $1.05 = 1.8 billion and 2.6 billion = Created by Tania Colson (2010)

PB 3: Front End Focus Addition 54 + 19 = 73 67 m + 28 m = 95m 320 plus 490 = 819 $330 + $280 = $620 208 cm more than 409cm = 617cm 10 060 + 32 070 = 42 130 The sum of 4 160 and 3 080 = 7 240 4.5 cm + 7.9 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)

PB 4: Front End Focus Addition 65 + 28 = 62 m + 59 m = 240 plus 690 = $460 + $280 = 409 cm more than 601cm = 20 040 + 12 070 = The sum of 6 030 and 1 080 = 3.9 mm + 4.2 mm = $7.09 plus $2.05 = 50.3 million and 2.8 million = Created by Tania Colson (2010)

PB 4: Front End Focus Addition 65 + 28 = 93 62 m + 59 m = 121m 240 plus 690 = 930 $460 + $280 = $740 409 cm more than 601cm = 1010 cm 20 040 + 12 070 =32 110 The sum of 6 030 and 1 080 = 7 120 3.9 mm + 4.2 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)

PB 5: Front End Focus Addition 15 + 58 = 42 m + 39 m = 210 plus 390 = $480 + $180 = 307 cm more than 409cm = 10 050 + 54 060 = The sum of 7 030 and 2 080 = 5.8 mm + 1.7 mm = $12.08 plus $3.04 = 10.5 million and 3.7 million = Created by Tania Colson (2010)

PB 5: Front End Focus Addition 15 + 58 = 73 42 m + 39 m = 81 m 210 plus 390 = 600 $480 + $180 = $660 307 cm more than 409cm = 716 cm 10 050 + 54 060 = 64 110 The sum of 7 030 and 2 080 = 9 110 5.8 mm + 1.7 mm = 7.15mm $12.08 plus $3.04 = $15.12 10.5 million and 3.7 million = 14.2 million Created by Tania Colson (2010)

Strategy Intro Quick Addition Try These In Your Head 54 + 32 = 87 + 21 = 421 + 432 = 734 + 122 = 4.13 + 2.84 = 14.36 + 32.11 = How are all these problems alike? Created by Tania Colson (2010)

Strategy Intro Quick Addition Check your Answers 54 + 32 = 86 87 + 21 = 108 421 + 432 = 853 734 + 122 = 856 4.13 + 2.84 = 6.97 14.36 + 32.11 = 46.47 Created by Tania Colson (2010)

Strategy Quick Addition Adding can be done quickly when there is no regrouping. You can start at the front end. Think: 47 + 21 … 4 tens plus 2 tens is 6 tens or 60 . 7 plus 1 is 8. So… 47 + 21 = 68 . Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 1: Quick Addition 31 + 17 = The sum of 43 and 12 541 more than 126 543 + 321= 129 plus 230 = 734 + 153 = 231.2 increased by 152.3 The total of $4.12 and $3.36 0.341 + 1.245 = 1.2 m + 2.7 m = Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 1: Quick Addition 31 + 17 = 48 The sum of 43 and 12 = 55 541 more than 126 = 667 543 + 321= 864 129 plus 230 = 359 734 + 153 = 887 231.2 increased by 152.3 = 383.5 The total of $4.12 and $3.36 = $7.48 0.341 + 1.245 = 1.586 1.2 m + 2.7 m = 3.9m Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 2: Quick Addition 21 + 45 = The sum of 13 and 64 123 more than 810 5230 + 3260= 34 681 plus 54 104 = 73.4 + 15.3 = 72.2 increased by 14.6 The total of $0.66 and $0.33 0.21 + 1.70 = 2.2 m + 5.7 m = Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 2: Quick Addition 21 + 45 = 66 The sum of 13 and 64 = 77 123 more than 810 = 933 5230 + 3260 = 8490 34 681 plus 54 104 = 88 785 73.4 + 15.3 = 88.7 72.2 increased by 14.6 = 86.8 The total of $0.66 and $0.33 = $0.99 0.21 + 1.70 = 1.91 2.2 m + 5.7 m = 7.9m Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 3: Quick Addition 43 + 23 = The sum of 54 and 33 154 more than 712 2210 + 2734= 41 081 plus 33 905= 55.4 + 12.5 = 71.36 increased by 23.60 The total of $3.29and $4.50 0.72 + 4.27 = 8.4 cm + 1.5 cm = Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 3: Quick Addition 43 + 23 = 66 The sum of 54 and 33 = 87 154 more than 712 = 866 2210 + 2734 = 4944 41 081 plus 33 905= 74 985 55.4 + 12.5 = 67.9 71.36 increased by 23.60 = 94.96 The total of $3.29and $4.50 = $7.79 0.72 + 4.27 = 4.99 8.4 cm + 1.5 cm = 9.9 cm Created by Tania Colson (2010)

Strategy Intro Finding Compatibles Try These In Your Head 1 + 7 + 9 + 8 + 3 = 30 + 75 + 70 + 25= 300 + 800 + 700 + 600 + 200 = 4 000 + 5 000 + 6000= 9 500 + 2 200 + 500 = 0.4 + 0.3 + 0.6= Did you add each number in order? Created by Tania Colson (2010)

Strategy Intro Finding Compatibles Check Your Answers 1 + 7 + 9 + 8 + 3 = 28 30 + 75 + 70 + 25 = 200 300 + 800 + 700 + 600 + 200 = 2600 4 000 + 5 000 + 6000= 15 000 9 500 + 2 200 + 500 = 12 200 0.4 + 0.3 + 0.6= 1.3 Created by Tania Colson (2010)

Strategy Finding Compatibles Search for pairs of numbers that add to 10, 100, 1000 or 10 000. For small numbers find pairs that add to 1 or 0.1. Think: 2 + 7 + 8 + 3 8 plus 2 is 10. 7 plus 3 is 10. And…10 plus 10 is 20. Created by Tania Colson (2010)

PB 1: Finding Compatibles 30 + 60 + 40 +70 = The total of $75, $95, and $425 = The sum of 200, 700, 500, 800 = 5 000 + 3 000 + 5 000 + 7 000 = 2 500 and 3 500 + 7 500 = 0.2 + 0.4 + 0.3 + 0.8 + 0.6 = 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 2.0 + 7.0 + 8.0+ 3.0 + 4.0 = Created by Tania Colson (2010)

PB 1: Finding Compatibles 30 + 60 + 40 +70 = 200 The total of $75, $95, and $425 = $595 The sum of 200, 700, 500, 800 = 2200 5 000 + 3 000 + 5 000 + 7 000 = 20 000 2 500 and 3 500 + 7 500 = 13 500 0.2 + 0.4 + 0.3 + 0.8 + 0.6 = 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 2.0 + 7.0 + 8.0+ 3.0 + 4.0 = 24.0 Created by Tania Colson (2010)

PB 2: Finding Compatibles 20 + 30 + 80 +70 = The total of $50, $25, and $350 = The sum of 600, 600, 400, 400 = 2000 + 8 000 + 5 000 + 5 000 = 3 500 and 5 500 + 7 500 = 0.5 + 0.2 + 0.3 + 0.5 + 0.7 = 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 3.0 + 2.0 + 7.0+ 3.0 + 5.0 = Created by Tania Colson (2010)

PB 2: Finding Compatibles 20 + 30 + 80 +70 = 200 The total of $50, $25, and $350 = $425 The sum of 600, 600, 400, 400 = 2000 2000 + 8 000 + 5 000 + 5 000 = 20 000 3 500 and 5 500 + 7 500 = 16 500 0.5 + 0.2 + 0.3 + 0.5 + 0.7 = 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 3.0 + 2.0 + 7.0+ 3.0 + 5.0 = 20.0 Created by Tania Colson (2010)

PB 3: Finding Compatibles 60 + 50 + 40 +50 = The total of $50, $50, and $425 = The sum of 300, 200, 700, 800 + 100 = 2 000 + 6 000 + 4 000 + 8 000 = 1 500 and 2 000 + 9 500 = 0.1 + 0.2 + 0.8 + 0.9 + 0.4 = 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 1.0 + 6.0 + 9.0+ 3.0 + 4.0 = Created by Tania Colson (2010)

PB 3: Finding Compatibles 75 + 40 + 25 +60 = 200 The total of $50, $50, and $425 = $525 The sum of 300, 200, 700, 800 + 100 = 2100 2 000 + 6 000 + 4 000 + 8 000 = 20 000 1 500 and 2 000 + 9 500 = 13 000 0.1 + 0.2 + 0.8 + 0.9 + 0.4 = 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 1.0 + 6.0 + 9.0+ 3.0 + 4.0 = 2.3 Created by Tania Colson (2010)

Strategy Intro Break Up and Bridge Try These In Your Head 45 + 36= 17 more than 64= 537 + 208 = 5 300 + 2 800 = 34 000 + 27 000 = 3.60 + 5.70 = How did you break up the numbers to solve? Created by Tania Colson (2010)

Strategy Intro Break Up and Bridge Check your answers 45 + 36= 81 17 more than 64= 81 537 + 208 = 745 5 300 + 2 800 = 8 100 34 000 + 27 000 = 61 000 3.60 + 5.70 = 9.30 Created by Tania Colson (2010)

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 + 309 542 plus 300 is 842 842 plus 9 more is 851. Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 1: Break Up and Bridge 54 + 37= 15 more than 76= The sum of $340 and $440 = 365 increased by 109 = 2 500 + 3 700= The total of 4070 girls and 3080 boys= 46 000 + 37 000 = $66 000 and $15 000 = 4.7 m + 3.5 m = 4.56 kg more than 4.40 kg = Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 1: Break Up and Bridge 54 + 37 = 91 15 more than 76 = 91 The sum of $340 and $440 = $780 365 increased by 109 = 474 2 500 + 3 700= 6 200 The total of 4070 girls and 3080 boys= 7150 46 000 + 37 000 = 83 000 $66 000 and $15 000 = $81 000 4.7 m + 3.5 m = 8.2 m 4.56 kg more than 4.40 kg = 8.96 kg Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 2: Break Up and Bridge 45 + 57 = 19 more than 82 = The sum of $340 and $440 = 215 increased by 467 = 1 500 + 4 800 = The total of 5060 L and 2080 L = 56 000 + 27 000 = $63 000 and $45 000 = 2.7 m + 3.4 m = 3.56 kg more than 4.90 kg = Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 2: Break Up and Bridge 45 + 57 = 102 19 more than 82 = 101 The sum of $340 and $440 = $780 215 increased by 467 = 682 1 500 + 4 800 = 6 300 The total of 5060 L and 2080 L = 56 000 + 27 000 = $63 000 and $45 000 = 2.7 m + 3.4 m = 3.56 kg more than 4.90 kg = Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 3: Break Up and Bridge 28 + 65= 53 more than 27= The sum of $760 and $260 = 653 increased by 109 = 2 900 + 3 200= The total of 2312 and 1748= 36 000 + 38 000 = $66 000 and $25 000 = 4.9 million + 2.5 million = 3.50 L more than 4.80 L = Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 3: Break Up and Bridge 28 + 65= 93 53 more than 27= 80 The sum of $760 and $260 = 1 020 653 increased by 109 = 762 2 900 + 3 200= 6 100 The total of 2302 and 1700= 4002 3.6 + 3.8 = 7.4 $66 000 and $25 000 = 91 000 4.9 million + 2.5 million = 7.4 million 3.50 L more than 4.80 L = 8.3 L Created by Tania Colson (2010)

Strategy Intro Compensation (Addition) Try These In Your Head 52 + 39 = 345 + 198 = 4 500 + 1 900 = 34 000 + 9 900 = 59 000 + 25 000 = 4.6 + 1.8 = 0.54 + 0.29 = Did you notice anything nifty about one of the addends? Created by Tania Colson (2010)

Strategy Intro Compensation (Addition) Check Your Answers 52 + 39 = 91 345 + 198 = 543 4 500 + 1 900 = 6 400 34 000 + 9 900 = 43 000 59 000 + 25 000 = 84 000 4.6 + 1.8 = 6.4 0.54 + 0.29 = 0.83 One of the addends has a 8, or 9 which makes is easy to round off. Created by Tania Colson (2010)

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: 330 + 390 390 rounds up to 400. 330 plus 400 is 730. 730 minus the extra 10 leaves 720 Created by Tania Colson (2010)

PB 1: Compensation (Addition) 58 + 39 = 49 + 38 = $198 more than $465 = 3 456mm added to 999 mm= 16 000 + 39 000 = The total of $38 000 and $9 900 = 3.9 + 2.5 = 3.5 km more than 4.8 km = $0.36 + 0.39 = 2.47s more than 4.99s= Created by Tania Colson (2010)

PB 1: Compensation (Addition) 58 + 39 = 97 49 + 38 = 87 $198 more than $465 = $663 3 456mm added to 999 mm= 4455mm 16 000 + 39 000 = 55 000 The total of $38 000 and $9 900 = $47 000 3.9 + 2.5 = 6.4 3.5 km more than 4.8 km = 8.3km $0.36 + $0.39 = $0.75 2.47 s more than 4.99s = 7.46 s Created by Tania Colson (2010)

PB 2: Compensation (Addition) 32 + 49 = 67 + 28 = $198 more than $250 = 4 500 mL added to 900 mL= 26 000 + 59 000 = The total of $78 000 and $9 000 = 2.9 + 2.4 = 1.5 km more than 3.8 km = $0.45+ $0.49 = 3.35 more than $2.99= Created by Tania Colson (2010)

PB 2: Compensation (Addition) 32 + 49 = 81 67 + 28 = 95 $198 more than $250 = $448 4 500 mL added to 900 mL= 5 400 mL 26 000 + 59 000 = 85 000 The total of $78 000 and $9 000 = $87 000 2.9 + 2.4 = 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)

PB 3: Compensation (Addition) 52 + 29 = 60 + 38 = $498 more than $300 = 4 500 L added to 900 L= 10 000 + 29 000 = The sum of 25 000 and 8 000 = 2.8 cm + 2.0 cm = 2.3 more than 4.9 m = $0.50+ $1.99 = $4.99 more than $4.99= Created by Tania Colson (2010)

PB 3: Compensation (Addition) 52 + 29 = 81 60 + 38 = 98 $498 more than $300 = $698 4 500 L added to 900 L= 5 400L 10 000 + 29 000 = 39 000 The sum of 25 000 and 8 000 = 33 000 2.8 cm + 2.0 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)

Strategy Intro Make Multiples of Powers of 10 Try These In Your Head 92 + 69= 298 + 345 = 650 + 190 = 34 000 + 28 000 = 1.3 + 0.9 = 1.4 + 2.9 = 3.98 + 4.24= Did you use a strategy other than compensation? Created by Tania Colson (2010)

Strategy Intro Make Multiples of Powers of 10 Check Your Answers 92 + 69= 161 298 + 345 = 643 650 + 190 = 840 34 000 + 28 000 = 62 000 1.3 + 0.9 = 2.2 1.4 + 2.9 = 4.3 3.98 + 4.24= 8.22 Created by Tania Colson (2010)

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: 237 + 394 Take 6 from 237 to make 400. 237 minus 6 is 231. Add 231 and 400. Created by Tania Colson (2010)

PB 1: Make Multiples of Powers of 10 51 + 39 = 42 + 38 = $198 more than $402 = 3 556 mL added to 999 mL= 18 000 + 46 000 = The sum of 38 000 and 9 000 = 1.9 m + 2.6 m = 5.8 cm more than 4.5 cm = $0.25 + $0.59 = 1.46 km more than 2.99km = Created by Tania Colson (2010)

PB 1: Make Multiples of Powers of 10 51 + 39 = 90 42 + 38 = 80 $198 more than $402 = $600 3 556 mL added to 999 mL= 4 555 18 000 + 46 000 = 64 000 The sum of 38 000 and 9 000 = 47 000 1.9 m + 2.6 m = 4.5m 5.8 cm more than 4.5 cm = 10.3cm $0.25 + $0.59 = $0.84 1.46 km more than 2.99km = 4.45 km Created by Tania Colson (2010)

PB 2: Make Multiples of Powers of 10 62 + 29 = 73 + 18 = $498 more than $345 = 2 600 L added to 900 L = 16 000 + 29 000 = The sum of 35 000 and 9 000 = 10.9 m + 2.4 m = 3.9 cm more than 4.6 cm = $0.29 + $0.76 = 1.27 more than 2.99 = Created by Tania Colson (2010)

PB 2: Make Multiples of Powers of 10 62 + 29 = 91 72 + 28 = 100 $498 more than $302 = $800 2 600 L added to 900 L = 3 500 L 16 000 + 29 000 = 45 000 The sum of 35 000 and 9 000 = 44 000 10.9 m + 2.4 m = 13.3 m 3.9 cm more than 4.6 cm = 8.5 cm $0.29 + $0.76 = $1.05 1.27 more than 2.99 = 4.26 Created by Tania Colson (2010)

PB 3: Make Multiples of Powers of 10 42 + 29 = 27 + 13 = $199 more than $150 = 2 600 L added to 900 L = 13 000 + 39 000 = The sum of 25 000 and 8 000 = 1.9 m + 2.5 m = 3.3 cm more than 1.9 cm = $0.17 + $0.28 = 2.07 more than 0.99 = Created by Tania Colson (2010)

PB 3: Make Multiples of Powers of 10 42 + 29 = 71 27 + 13 = 40 $199 more than $150 = $349 1 600 L added to 900 L = 2 500 L 13 000 + 39 000 = 52 000 The sum of 25 000 and 8 000 = 33 000 1.9 m + 2.5 m = 4.4 m 3.3 cm more than 1.9 cm = 5.2 cm $0.17 + $0.28 = $0.45 2.07 more than 0.99 = 3.06 Created by Tania Colson (2010)

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

Strategy Intro Using Basic Subtraction Facts Try These In Your Head 80 - 30 = 400 - 200 = 1 500 – 600 = 6 000 – 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)

Strategy Intro Using Basic Subtraction Facts Check Your Answers 80 - 30 = 50 400 - 200 =200 1 500 – 600 = 900 6 000 – 2 000= 4 000 0.8 – 0.5 = 0.3 1.4 – 0.7 = 0.7 0.17 – 0.09= 0.08 Created by Tania Colson (2010)

Strategy Using Basic Subtraction Facts Knowing your basic subtraction facts can help you solve other problems in your head. Think: 70 - 50 … 7 tens minus 5 tens is 2 tens or 20. Focus on the facts! Created by Tania Colson (2010)

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 = 40 000 – 20 000 = 0.7 kg – 0.2 kg = 1.6 less 0.9 = $0.16 - $0.08 = 0.10 – 0.01 = Created by Tania Colson (2010)

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 1 000 = 5 000 40 000 – 20 000 = 20 000 0.7 kg – 0.2 kg = 0.5 kg 1.6 less 0.9 = 0.7 $0.16 - $0.08= $0.08 0.10 – 0.01 = 0.09 Created by Tania Colson (2010)

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 = 60 000 – 40 000 = 0.8 kg – 0.1 kg = 1.2 less 1.0 = $0.15 - $0.05 = 0.10 – 0.02 = Created by Tania Colson (2010)

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 3 000 = 5 000 60 000 – 40 000 = 20 000 0.8 kg – 0.1 kg = 0.07 kg 1.2 less 1.0 = 0.2 $0.15 - $0.05 = $0.10 0.10 cm – 0.02 cm = 0.08 cm Created by Tania Colson (2010)

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 6 000 = 60 000 – 50 000 = 0.7 kg – 0.2 kg = 1.5 less 1.3 = $0.20 - $0.05 = 0.10 km – 0.03 km = Created by Tania Colson (2010)

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 1 300 m and 400 m = 900 m 9 000 minus 6 000 = 3 000 60 000 – 50 000 = 10 000 0.7 kg – 0.2 kg = 0.5 kg 1.5 less 1.3 = 0.2 $0.20 - $0.05 = $0.15 0.10 km – 0.03 km = 0.07 km Created by Tania Colson (2010)

Strategy Intro Quick Subtraction Try These In Your Head 56- 32 = 268 – 124 = 765 – 602 = 4070 – 3030 = 87 000 – 32 000 = 345.85 – 112.45 = 0.27 – 0.13 = How are all these problems alike? Created by Tania Colson (2010)

Strategy Intro Quick Subtraction Try These In Your Head 56- 32 = 24 268 – 124 =144 765 – 602 = 163 4070 – 3030 = 1040 87 000 – 32 000 = 55 000 345.85 – 112.45 = 233.40 0.27 – 0.13 = 0.14 There’s no regrouping! Created by Tania Colson (2010)

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

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 = 45 678 – 21 543 = 213.7 kg decreased by 101.2 kg = 45.12 m less than 57.75 = $300.26 - $200.01 = 0.29 – 0.15 = Created by Tania Colson (2010)

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 45 678 – 21 543 = 24 135 213.7 kg decreased by 101.2 kg = 112.5kg 45.12 m less than 57.75 = 12.63 m $300.26 - $200.01 = $100.25 0.29 – 0.15 = 0.14 Created by Tania Colson (2010)

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 = 25 608 – 20 103 = 12.2 kg decreased by 10.1 kg = 67.15 m less than 89.25 = $401.06 - $100.05 = 0.39 – 0.13 = Created by Tania Colson (2010)

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 25 608 – 20 103 = 5 505 12.2 kg decreased by 10.1 kg = 2.1 kg 67.15 m less than 89.25 = 22.10 $401.06 - $100.05 = $300.01 0.39 – 0.13 = 0.26 Created by Tania Colson (2010)

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 = 40 409 – 20 208 = 27.9 g decreased by 15.4 g = 26.2 m less than 56.7m = $300.26 - $200.01 = 0.67 – 0.42 = Created by Tania Colson (2010)

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 40 409 – 20 208 = 20 201 27.9 g decreased by 15.4 g = 12.5g 26.2 m less than 56.7m = 30.5m $300.26 - $200.01 = $100.25 0.67 – 0.42 = 0.25 Created by Tania Colson (2010)

Strategy Intro Back Through a Multiple of 10 Try These In Your Head 35 - 8 = 530 - 70= 8 600 – 800 = 74 000 – 9 000 = 4.5 – 0.9 = 1.63 – 0.07= Which strategy did you use? Created by Tania Colson (2010)

Strategy Intro Back Through a Multiple of 10 Check Your Answers 35 - 8 = 27 530 – 70 = 460 8 600 – 800 = 7 800 74 000 – 9 000 = 65 000 4.5 – 0.9 = 3.6 1.63 – 0.07= 1.56 Created by Tania Colson (2010)

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 - 80 … 250 minus 50 of the 80 leaves 200. Take away 30 more is 170. Created by Tania Colson (2010)

PB 1: Back Through a Multiple of 10 9 fewer people than 92 = $40 less than $210 = $340 - $70 = The difference between 630 and 80 = Subtract 600 from 2 300 = 45 000 – 8 000 = 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)

PB 1: Back Through a Multiple of 10 9 fewer people than 92 = 83 $40 less than $210 = $170 $340 - $70 = $270 The difference between 630 and 80 = 550 Subtract 600 from 2 300 = 1 700 45 000 – 8 000 = 37 000 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)

PB 2: Back Through a Multiple of 10 8 fewer people than 76 = $50 less than $130 = $280 - $90 = The difference between 730 and 70 = Subtract 500 from 3 200 = 35 000 – 7 000 = 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)

PB 2: Back Through a Multiple of 10 8 fewer people than 76 = 68 $50 less than $130 = $180 $280 - $90 = $170 The difference between 730 and 70 = 660 Subtract 500 from 3 200 = 2 700 35 000 – 7 000 = 28 000 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)

PB 3: Back Through a Multiple of 10 68% - 9% = $60 less than $240 = $220 - $70 = 440 minus 60 = Subtract 300 from 1 100 = 25 000 – 8 000 = 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)

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 1 100 = 800 25 000 – 8 000 = 17 000 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)

Strategy Intro Up Through a Multiple of 10 Try These In Your Head 84 – 77 = 613 – 594 = 2 310 – 1800 = 57 000 – 49 000 = 12.4 – 11. 8 = 6.12 – 5.99 = 12.54 – 12.48 = How are all these problems similar? Created by Tania Colson (2010)

Strategy Intro Up Through a Multiple of 10 Check Your Answers 84 – 77 = 7 613 – 594 = 19 2 310 – 1800 = 510 57 000 – 49 000 = 8 000 12.4 – 11. 8 = 0.6 6.12 – 5.99 = 0.13 12.54 – 12.48 = 0.06 The two amounts are relatively close together. Created by Tania Colson (2010)

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: 64 -57… 57 is 3 from 60. 60 is 4 more from 64. 3 plus 4 more is 7. The difference is 7. Created by Tania Colson (2010)

PB 1: Up Through a Multiple of 10 92 – 86 = $140 less than $210 = 196 - 189 = The difference between 630 and 580 = 2 400 minus 1 700 = 45 000 – 38 000 = 83 000 m decreased by 79 000 m = 13.2 kg – 12.7 kg = 1.99 m less than 2.21 m= $2.53 – $2.45 = Created by Tania Colson (2010)

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 1 700 = 700 45 000 – 38 000 = 7 000 83 000 m decreased by 79 000 m = 4 000 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)

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 1 600 = 55 000 – 48 000 = 91 000 m decreased by 89 000 m = 10.3 kg – 9.7 kg = 1.99 m less than 2.33 m= $3.54 – $3.49 = Created by Tania Colson (2010)

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 1 600 = 600 55 000 – 48 000 = 7 000 91 000 m decreased by 89 000 m = 3 000 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)

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 = 52 000 – 47 000 = 32 000 m decreased by 27 000 m = 22.2 kg – 21.9 kg = 2.98 m less than 3.33 m= $5.09 – $4.99 = Created by Tania Colson (2010)

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 52 000 – 47 000 = 5 000 32 000 m decreased by 27 000 m = 5 000 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)

Strategy Intro Break Up and Bridge Try These In Your Head 92 – 26 = 745 – 207 = 860 – 370 = 8 300 – 2 400 = 5 700 – 680 = 47 000 – 28 000 = 24 500 – 2 700 = How might you use a number line to solve these problems? Created by Tania Colson (2010)

Strategy Intro Break Up and Bridge Check Your Answers 92 – 26 = 66 745 – 207 = 548 860 – 370 = 490 8 300 – 2 400 = 5 900 5 700 – 680 = 5070 47 000 – 28 000 = 19 000 24 500 – 2 700 = 21 800 How might you use a number line to solve these problems? Created by Tania Colson (2010)

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 -37… 81 minus 30 is 51. 51 minus 7 is 44. The difference is 44. Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 1: Break Up and Bridge 53 – 25 = $306 less than $870 = 750 km - 260 = The difference between 640 and 170 = 5 400 minus 1 500 = 71 00 – 2 600 = $8020 minus $3050 = 63 000 – 25 000 = 66 500 km – 18 000 km= 10 600 less than 32 100 = Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 1: Break Up and Bridge 53 – 25 = 28 $306 less than $870 = $564 750 km - 260 = 490 The difference between 640 and 170 = 470 5 400 minus 1 500 = 3 900 7 100 – 2 600 = 4 500 $8020 minus $3050 = $5030 63 000 – 25 000 = 38 000 66 500 km – 18 000 km = 48 500 km 10 600 less than 32 100 = 21 500 Created by Tania Colson (2010)

Created by Tania Colson (2010) PB 2: Break Up and Bridge 48 – 29 = $410 less than $780 = 820 km - 330 = The difference between 530 and 170 = 6 200 minus 2 500 = 4 100 – 1 700 = $5020 minus $1050 = 83 000 – 24 000 = 12 500 km – 9 000 km= 15 000 less than 21 000 = Created by Tania Colson (2010)

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 2 500 = 3 700 4 100 – 1 700 = 2 400 $5020 minus $1050 = 3070 83 000 – 24 000 = 59 000 12 500 km – 9 600 km = 2 900 km 15 000 less than 21 000 = 6 000 Created by Tania Colson (2010)

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 1 700 = 8 200 – 1 400 = $4030 minus $2050 = 76 000 – 28 000 = 13 500 km – 8 000 km= 24 000 less than 43 000 = Created by Tania Colson (2010)

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 = 1 700 8 200 – 1 400 = 6 800 $4030 minus $2050 = 1980 76 000 – 28 000 = 48 000 13 500 km – 8 000 km= 5 500 km 24 000 less than 43 000 = 19 000 Created by Tania Colson (2010)

Strategy Intro Compensation (Subtraction) Try These In Your Head 36 – 8 = 85 – 29 = 145 -99 = 750 - 190 = 5 700 – 999= 24 000 – 995 = 47 000 – 19 000 = How can you tackle eights and nine? Created by Tania Colson (2010)

Strategy Intro Compensation (Subtraction) Check Your Answers 36 – 8 = 28 85 – 29 = 56 145 -99 = 46 750 - 190 = 560 5 700 – 999= 4 701 24 000 – 995 = 23 005 47 000 – 19 000 = 28 000 Created by Tania Colson (2010)

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: 850 - 290 290 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)

PB 1: Compensation (Subtraction) 92 – 38 = $399 less than $875= 298 km fewer than 630 km = 450 – 190 = 5 700 – 997 = 4 500 less 1 990 = The difference between $23 000 and $1 997 = 33 000 km – 2980 km = 64 000 minus 9 900= Subtract 29 000 from 92 000 = Created by Tania Colson (2010)

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 1 990 = 2 510 The difference between $23 000 and $1 997 = $21 003 33 000 km – 2980 km = 30 020 km 64 000 minus 9 900 = 45 100 Subtract 29 000 from 92 000 = 63 000 Created by Tania Colson (2010)

PB 2: Compensation (Subtraction) 72 – 28 = $499 less than $775 = 198 km fewer than 540 km = 340 – 180 = 6 500 – 999 = 3 500 less 1 998 = The difference between $43 000 and $2 997 = 67 000 km – 5990 km = 86 000 minus 9 000= Subtract 19 000 from 72 000 = Created by Tania Colson (2010)

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 1 998 = 1 502 The difference between $43 000 and $2 997 = $40 003 67 000 km – 5990 km = 61 010 86 000 minus 9 000 = 77 000 Subtract 19 000 from 72 000 = 53 000 Created by Tania Colson (2010)

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 3 999 = The difference between $41 000 and $9 990 = 99 000 m – 6980 m = 68 000 minus 9 000= Subtract 59 000 from 87 000 = Created by Tania Colson (2010)

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 3 999 = 2 601 The difference between $41 000 and $9 990 = $31 010 99 000 m – 69980 m = 92 020 68 000 minus 9 000 = 59 000 Subtract 59 000 from 87 000 = 28 000 Created by Tania Colson (2010)

Strategy Intro Balancing for a Constant Difference Try These In Your Head 87 – 19 = 345 – 198 = 5 600 – 1 990 = 7 800 – 3 998 = 45 000 – 19 000 = 67 000 – 29 999= 52 000 – 9 800 = How is 12 minus 2 like 14 minus 4? How are they different? Created by Tania Colson (2010)

Strategy Intro Balancing for a Constant Difference Check Your Answers 87 – 19 = 68 345 – 198 = 147 5 600 – 1 990 = 3 610 7 800 – 3 998 = 3 804 45 000 – 19 000 = 46 000 67 000 – 29 999= 37 001 52 000 – 9 800 = 42 200 Created by Tania Colson (2010)

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: 56 - 48 48 is 2 from 50. Add 2 to both numbers. 58 minus 50 is the new problem. 58 - 50 =8 Created by Tania Colson (2010)

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 $8 500 and $3 900 = 43 000 – 2997 = 66 000 km – 4980 = Subtract 38 000 from 92 000 = Created by Tania Colson (2010)

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 $8 500 and $3 900 = $4 600 43 000 – 2997 = 40 003 66 000 km – 4980 = 61 020 Subtract 38 000 from 92 000 = 54 000 Created by Tania Colson (2010)

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 $5 500 and $2 800 = 32 000 – 1997 = 58 000 km – 5980 = Subtract 28 000 from 82 000 = Created by Tania Colson (2010)

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 $5 500 and $2 800 = $2 700 32 000 – 1997 = 30 003 58 000 km – 5980 = 52 020 Subtract 28 000 from 82 000 = 54 000 Created by Tania Colson (2010)

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 7 500 km and 3 900 km = 23 000 – 1998 = 48 000 km – 2900 = Subtract 17 000 from 65 000 = Created by Tania Colson (2010)

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 7 500 km and 3 900 km = 3 600 km 23 000 – 1998 = 21 002 48 000 km – 2900 = 45 100 Subtract 17 000 from 65 000 = 48 000 Created by Tania Colson (2010)

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

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)

Strategy Intro Quick Multiplication Check Your Answers 43 x 2 = 86 1.42 x 2 = 2.84 4.2 x 4 = 8.4 3 x 12.3 = 36.9 7.2 x 3 = 21.6 41 x 2 = 82 23 x 3 = 66 There is no regrouping to think about. Created by Tania Colson (2010)

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)

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)

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 = 12 963 The product of 9 times 111= 999 Created by Tania Colson (2010)

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)

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)

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)

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)

Strategy Intro Quick Division Try These In Your Head 640  2 = 1290  3 = 360  3 = 4802  2 = 7280  8 = 32.8  4 = 24.18  6 = Why are these sentences easier to solve than 675 divided by 5 ? Created by Tania Colson (2010)

Strategy Intro Quick Division Check Your Answers 640  2 = 320 1290  3 = 430 360  3 = 120 4802  2 = 2401 7280  8 = 910 32.8  4 = 8.2 24.18  6 = 4.03 They can be solved without regrouping. Created by Tania Colson (2010)

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. 300 + 20 + 1 = 321 Created by Tania Colson (2010)

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)

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)

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)

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)

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)

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)

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)

Strategy Intro Multiplying by 10, 100 and 1000 Check Your Answers 53 x 10 = 530 10 x 2.5 = 25 60 x 100 = 6000 0.6 x 100 = 60 120 x 1000 = 120 000 8.36 x 1000 = 8360 0.03 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)

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)

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)

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 = 234 000m 10 mm = 1 cm 100 cm = 1 m 1000 m = 1km Created by Tania Colson (2010)

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)

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 = 65 400 16 cg = 0.16 g 1000 x $68= $68 000 5.8 x 1000= 5 800 471 kg = 471 000 g 10 mg = 1 cg 100 cg = 1 g 1000 g = 1kg Created by Tania Colson (2010)

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)

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 = 39 800 92 cm = 0.92 m 1000 x $432 = $432 000 4.6 x 1000 = 4600 85 km = 85 000 m 10 mm = 1 cm 100 cm = 1 m 1000 m = 1km Created by Tania Colson (2010)

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  0.001 = 8.36  0.001 = 0.03  0.001 = Warning! Model with Base 10 blocks! How does multiply by 0.1, 0.01 and 0.001 change the place value of each digit? Created by Tania Colson (2010)

Strategy Intro Dividing by 0.1, 0.01 and 0.001 Check Your Answers 53  0.1 = 530 25  0.1 = 250 60  0.01 = 6000 0.6  0.01 = 60 120  0.001 = 120 000 8.36  0.001 = 8360 0.03  0.001 = 30 Warning! Model with Base 10 blocks! Where have you seen this pattern before? Click Here! Created by Tania Colson (2010)

Strategy Intro Multiplying by 10, 100 and 1000 Check Your Answers 53 x 10 = 530 10 x 2.5 = 25 60 x 100 = 6000 0.6 x 100 = 60 120 x 1000 = 120 000 8.36 x 1000 = 8360 0.03 x 1000 = 30 It’s the same! Go Back to dividing by 0.1, 0.01 and 0.001 Created by Tania Colson (2010)

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 0.001 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)

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  0.01 = How many thousandths in 24? 1000  0.001 = 9.7  0.001= 6.5  0.001 = Created by Tania Colson (2010)

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  0.01 = 1500 How many thousandths in 24? 24 000 1000  0.001= 1 000 000 9.7  0.001= 9700 6.5  0.001 = 6500 Created by Tania Colson (2010)

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  0.01 = How many thousandths in 3? 2500  0.001 = 5.4  0.001= 0.6  0.001 = Created by Tania Colson (2010)

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  0.01 = 2800 How many thousandths in 3? 3000 2500  0.001 = 2 500 000 5.4  0.001= 5 400 0.6  0.001 = 600 Created by Tania Colson (2010)

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  0.01 = How many thousandths in 4? 4800  0.001 = 3.7  0.001= 0.51  0.001 = Created by Tania Colson (2010)

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  0.01 = 9300 How many thousandths in 4? 4000 4800  0.001 = 4 800 000 3.7  0.001= 3700 0.51  0.001 = 510 Created by Tania Colson (2010)

Strategy Intro Dividing by 10, 100 and 1000 Try These In Your Head 50  10 = 640  10 = 720  10 = 4 500  100 = 2 700  100 = 71 000  1000 = 840 000  1000 = How does dividing by 10, 100 and 1000 change the place value of each digit? Created by Tania Colson (2010)

Strategy Intro Dividing by 10, 100 and 1000 Check Your Answers 50  10 = 5 640  10 = 64 720  10 = 72 4 500  100 = 45 2 700  100 = 27 71 000  1000 = 71 840 000  1000 = 840 Created by Tania Colson (2010)

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)

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 34 000  1000 = 13 000  1000 = _____ km = 4 500 m 10 mm = 1 cm 100 cm = 1 m 1000 m = 1km Created by Tania Colson (2010)

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 40 000  100 = 40 3 200 cm = 32 m 34 000  1000 = 34 13 000  1000 = 13 4.5 km = 4 500 m 10 mm = 1 cm 100 cm = 1 m 1000 m = 1km Created by Tania Colson (2010)

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 84 000  1000 = 92 000  1000 = _____ kL = 2 500 L 10 mL = 1 cL 100 cL = 1 L 1000 L = 1kL Created by Tania Colson (2010)

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 84 000  1000 = 84 92 000  1000 = 92 2.5 kL = 2 500 L 10 mL = 1 cL 100 cL = 1 L 1000 L = 1kL Created by Tania Colson (2010)

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 76 000  1000 = 29 000  1000 = _____ kg = 3 000 g 10 mg = 1 cg 100 cg = 1 g 1000 g = 1kg Created by Tania Colson (2010)

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 76 000  1000 = 76 29 000  1000 = 29 3 kg = 3 000 g 10 mg = 1 cg 100 cg = 1 g 1000 g = 1kg Created by Tania Colson (2010)

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 0.001 = 3000 x 0.001 = 0.001 x 46 000 = Warning! Model with Base 10 blocks! How does multiply by 0.1, 0.01 and 0.001 change the place value of each digit? Created by Tania Colson (2010)

Strategy Intro Multiplying by 0.1, 0.01 and 0.001 Check Your Answers 50 x 0.1 = 5 0.1 x 130 = 13 39 x 0.01 = 0.39 10 x 0.01 = 0.10 900 x 0.001 = 0.9 3000 x 0.001 = 3 0.001 x 46 000 = 46 Warning! Model with Base 10 blocks! How does multiply by 0.1, 0.01 and 0.001 change the place value of each digit? Created by Tania Colson (2010)

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 0.001 is like dividing by 1000 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)

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 0.001 = How many pennies in $1? in $10? Created by Tania Colson (2010)

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 0.001 = 3.4 There are 100 pennies in $1 and 1000 pennies in $10 Created by Tania Colson (2010)

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= 45 000 x 0.001 = How many pennies in $1? in $10? Created by Tania Colson (2010)

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 45 000 x 0.001 = 45 How many pennies in $1? in $10? Created by Tania Colson (2010)

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= 84 000 x 0.001 = How many pennies in $1? in $10? Created by Tania Colson (2010)

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 84 000 x 0.001 = 84 How many pennies in $1? in $10? Created by Tania Colson (2010)

Strategy Intro Cancelling Common Zeros Try These In Your Head 500  10 = 900  30 = 8000  40 = 12 000  20 = 2000  50 = 18 000  600 = 24 000  300 = Warning! Model Shrinking with Base 10 blocks! How do you deal with all those trailing zeros? Created by Tania Colson (2010)

Strategy Intro Cancelling Common Zeros Try These In Your Head 500  10 = 50 900  30 = 30 8000  40 = 200 12 000  20 = 600 2000  50 = 400 18 000  600 = 30 24 000  300 = 80 Warning! Model Shrinking with Base 10 blocks! You can cancel common zeros. Created by Tania Colson (2010)

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)

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 90 000 by 3000 = 48 000  12 000 = Created by Tania Colson (2010)

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 90 000 by 3000 = 30 48 000  12 000 = 4 Created by Tania Colson (2010)

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 82 000 by 200 = 60 000  10 000 = Created by Tania Colson (2010)

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 82 000 by 200 = 410 60 000  10 000 = 6 Created by Tania Colson (2010)

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 40 000 by 5000 = 100 000  20 000 = Created by Tania Colson (2010)

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 40 000 by 5000 = 8 100 000  20 000 = 5 Created by Tania Colson (2010)

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)

Strategy Intro Think Multiplication Check Your Answers 240  12 = 20 880  40 = 22 1470  70 = 21 3600  12 = 300 1260  60 = 21 6000 12 = 500 6500  50 = 130 How can knowing your multiplication facts help you divide? Created by Tania Colson (2010)

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)

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 49 700 by 700 = 60 000  15 000 = Created by Tania Colson (2010)

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 49 700 by 700 = 71 60 000  15 000 = 4 Created by Tania Colson (2010)

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 42 700 by 700 = 90 000  15 000 = Created by Tania Colson (2010)

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 42 700 by 700 = 61 90 000  15 000 = 6 Created by Tania Colson (2010)

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 21 500 by 500 = 355 000  5 000 = Created by Tania Colson (2010)

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 21 500 by 500 = 43 355 000  5 000 = 71 Created by Tania Colson (2010)

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 = 19.99 x 5 = 49.98 x 6 = During what everyday activity might you have to do this kind of calculation? Created by Tania Colson (2010)

Strategy Intro Compensation (Multiplication) Check Your Answers 4.98 X 2 = 9.96 9.99 x 8 = 79.92 6.99 x 9 = 62.91 5.98 x 4 =23.92 19.99 x 5 = 99.95 49.98 x 6 = 299.88 When buying more that one of something! Created by Tania Colson (2010)

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 9.00 -0.03 = 8.97 Created by Tania Colson (2010)

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 49.99 cm is _______ cm $99.98 x 3 = 5 times $199.98 = $499.99 x 4 = 599.98 x 3 = Created by Tania Colson (2010)

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 49.99 cm is 199.96 cm $99.98 x 3 = $299.94 5 times $199.98 = $999.90 $499.99 x 4 = 1999.96 599.98 x 3 = 1799.94 Created by Tania Colson (2010)

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 29.99 cm is _______ cm $99.98 x 3 = 6 times $299.98 = $499.99 x 5 = 599.98 x 2 = Created by Tania Colson (2010)

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 29.99 cm is 119.96 cm $99.98 x 3 = $299.94 6 times $299.98 = $179.88 $499.99 x 5 = $2499.95 599.98 x 2 = 1199.96 Created by Tania Colson (2010)

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 $299.98 = $399.99 x 9 = 999.98 x 2 = Created by Tania Colson (2010)

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 35.96 cm $99.98 x 2 = $199.96 7 times $299.98 = $2099.86 $399.99 x 9 = $3599.91 999.98 x 2 = 1999.96 Created by Tania Colson (2010)

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)

Strategy Intro Halving and Doubling Check Your Answers 42 x 50 = 2100 500 x 88 = 44 000 12 x 2.5 = 30 4.5 x 2.2 = 9.9 140 x 35 = 4900 200 x 4.5 = 900 Halve the evens, double the odds! Created by Tania Colson (2010)

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)

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)

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)

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)

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)

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)

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)

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 6 100 = 3 x 3 200 = Take it one step at a time! Created by Tania Colson (2010)

Strategy Intro Front End Distributative Principle Check Your Answers 62 x 3 = 186 4 x 64 = 256 2 x 706 = 1412 804 x 6 = 4824 5 x 6 100 = 30 500 3 x 3 200 = 9 600 Created by Tania Colson (2010)

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)

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 4 200 = 5 x 5 100 = 4 300 x 2 = Created by Tania Colson (2010)

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 4 200 = 12 600 5 x 5 100 = 25 500 4 300 x 2 = 8 600 Created by Tania Colson (2010)

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 2 100 = 4 300 x 2 = 2 100 x 7 = Created by Tania Colson (2010)

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 2 100 = 8 400 4 300 x 2 = 8 600 2 100 x 7 = 14 700 Created by Tania Colson (2010)

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 3 200 = 4 x 4 200 = 2 100 x 8 = Created by Tania Colson (2010)

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 = 18 600 3 x 3 200 = 9 600 4 x 4 200 = 16 800 2 100 x 8 = 16 800 Created by Tania Colson (2010)

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)

Strategy Intro Finding Compatible Factors Check Your Answers 25 x 63 x 4 = 6300 2 x 78 x 500 = 78 000 5 x 450 x 2 = 4500 25 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)

Strategy Finding Compatibles Look for pairs of factors whose product will be 10, 100, or 1000. 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)

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)

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 = 33 000 250 x 56 x 4 = 56 000 500 x 86 x 2 = 86 000 25 x 32 = 800 24 x 500 = 12 000 250 x 8 = 2000 36 x 25 = 900 Created by Tania Colson (2010)

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)

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 = 42 000 250 x 92 x 4 = 92 000 500 x 54 x 2 = 54 000 25 x 16 = 400 62 x 500 = 31 000 250 x 32 = 8000 48 x 25 = 1200 Created by Tania Colson (2010)

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)

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= 37 000 4 x 38 x 25= 3800 5000 x 9 x 2 = 90 000 250 x 24 = 6000 34 x 500 = 17 000 250 x 28 = 7000 48 x 50 = 2400 Created by Tania Colson (2010)

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)

Strategy Intro Using Division Facts Check Your Answers 60  3 = 20 80  4 = 40 900  3 = 300 1200  6 = 200 18 000  9 = 2 000 25 000  5 = 5 000 Created by Tania Colson (2010)

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)

PB 1: Using Division Facts 60  2 = 210  7 = 450  9 = 240  6 = 800  4 = 3 500  7 = 1600  4 = 72 000  8 = 24 000  3 = 40 000  8 = Created by Tania Colson (2010)

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 72 000  8 = 9 000 24 000  3 = 8 000 40 000  8 = 5 000 Created by Tania Colson (2010)

PB 2: Using Division Facts 80  2 = 210  3 = 450  5 = 240  4 = 800  2 = 3 600  6 = 2800  7 = 54 000  6 = 24 000  8 = 42 000  7 = Created by Tania Colson (2010)

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 54 000  6 = 9 000 24 000  8 = 3 000 42 000  7 = 6 000 Created by Tania Colson (2010)

PB 3: Using Division Facts 60  2 = 280  4 = 630  9 = 300  6 = 1200  4 = 4900  7 = 2000  4 = 81 000  9 = 56 000  7 = 48 000  12 = Created by Tania Colson (2010)

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 81 000  9 = 9 000 56 000  7 = 8 000 48 000  12 = 4 000 Created by Tania Colson (2010)

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)

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)

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 : (240 +16)  4 240 divded by 4 is 60. 16 divided by 4 is 4. 60 + 4 = 64 Created by Tania Colson (2010)

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)

PB 1: Breaking Up the Dividend 192  3 = Think (180 +12) = 62 108  4 = Think (100 + 8) = 27 375  5 = Think (350 + 25) = 75 285  3 = Think (270 + 15) = 95 207 3 = Think (180 + 27) = 69 156  2 = Think (140 + 16) = 78 444  6 = Think (420 + 24) = 74 264  8 = Think (240 + 24) = 33 2910  7 = Think (2100 + 210) = 330 2880  9 = Think (2700 + 180) = 320 Created by Tania Colson (2010)

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)

PB 2: Breaking Up the Dividend 192  3 = Think (180 + 12) = 52 228  4 = Think (200 + 28) = 57 340  5 = Think (300 + 40) = 68 492  6 = Think (480 + 12) = 82 371  7 = Think (350 + 21) = 53 336  8 = Think (320 + 16) = 42 175 5 = Think (150 + 25) = 35 1960  4 = Think (1600 + 360) = 490 7440  8 = Think (7200 + 240) = 930 3450  3 = Think (3300 + 150) = 1150 Created by Tania Colson (2010)

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)

PB 3: Breaking Up the Dividend 282  3 = Think (270 + 12) = 82 292  4 = Think (280 + 12) = 72 365  5 = Think (350 + 15) = 73 438  6 = Think (420 + 18) = 73 644  7 = Think (630 + 14) = 92 896  8 = Think (880 + 16) = 112 585 5 = Think (550 + 35) = 117 4960  4 = Think (4800 + 160) = 1220 3520  8 = Think (3200+ 320) = 440 2580  3 = Think (2400 + 180) = 830 Created by Tania Colson (2010)

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)

Strategy Intro Compensation (Division) Check Your Answers 304  8 = 38 295  5 = 59 261  9 = 29 228  6 = 38 352  4 = 88 1393  7 = 199 How could you separate the dividend to make it easier to solve? Created by Tania Colson (2010)

Strategy Compensation (Division) Increase the dividend to an easy multiple of 10, 100, or 1000. 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)

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)

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)

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)

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)

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)

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)

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)

Strategy Intro Balancing for a Constant Quotient Check Your Answers 125  5 = 25 120  2.5 = 48 23.5  0.5 = 47 140  5 = 28 300  2.5 = 120 135  0.5 = 270 How could changing the equation make it easier to solve ? Created by Tania Colson (2010)

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)

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)

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)

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)

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)

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)

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)

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

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)

Strategy Intro Quick Estimates (Addition and Subtraction) Try Estimating These In Your Head 56 + 42 is about ___ 332 + 157 is about ___ 434 + 272 is about ___ 98 - 34 is about ___ 459 - 363 is about ___ 3578 - 1586 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)

Strategy Intro Quick Estimates (Addition and Subtraction) Check Your Estimates 56 + 42 is about 90 332 + 157 is about 400 434 + 272 is about 600 98 - 34 is about 40 459 - 363 is about 100 3578 - 1586 is about 2000 To get a “ball park” or quick estimate use only the digits at the front end! Created by Tania Colson (2010)

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: 199 + 589 Focusing on the front end changes the problem to 100 plus 500, that’s about 600 Created by Tania Colson (2010)

PB 1: Quick Estimates (Addition & Subtraction) 69 + 32 ~ 256 + 980 ~ 457 + 304 ~ 545 + 478 ~ 5856 + 3437 ~ 87 - 72 ~ 685 - 129 ~ 498 - 280 ~ 2348 - 1385 ~ 9564 - 7431 ~ Created by Tania Colson (2010)

PB 1: Quick Estimates (Addition & Subtraction) 69 + 32 ~ 120 256 + 980 ~ 1100 457 + 304 ~ 700 545 + 478 ~ 900 5856 + 3437 ~ 8000 87 - 72 ~ 10 685 - 129 ~ 500 498 - 280 ~ 200 2348- 1385 ~ 1000 9564- 7431 ~ 2000 Created by Tania Colson (2010)

PB 2: Quick Estimates (Addition & Subtraction) 54 + 28 ~ 294 + 587 ~ 576 + 120 ~ 3480 + 2054 ~ 2698 + 8371 ~ 49 - 16 ~ 284 - 107 ~ 783 - 330 ~ 5954 - 2278 ~ 9568 - 6431 ~ Created by Tania Colson (2010)

PB 2: Quick Estimates (Addition & Subtraction) 54 + 28 ~ 70 294 + 587 ~ 700 576 + 120 ~ 600 3480 + 2054 ~ 5000 2698 + 8371 ~ 10 000 49 - 16 ~ 30 284 - 107 ~ 100 783 - 330 ~ 400 5954 - 2278 ~ 3000 9568 - 6431 ~ 3000 Created by Tania Colson (2010)

PB 3: Quick Estimates (Addition & Subtraction) 89 + 56 ~ 494 + 687 ~ 576 + 489 ~ 8463 + 2948 ~ 6062 + 6872 ~ 67 - 18 ~ 484 - 290 ~ 1283 - 430 ~ 5760 - 2021 ~ 8220 - 7401 ~ Created by Tania Colson (2010)

PB 3: Quick Estimates (Addition & Subtraction) 89 + 56 ~ 130 494 + 687 ~ 1000 576 + 489 ~ 900 8463 + 2948 ~ 10 000 6062 + 6872 ~ 12 000 67 - 18 ~ 50 484 - 290 ~ 200 1283 - 430 ~ 800 5760 - 2021 ~ 3000 8220 - 7401 ~ 1000 Created by Tania Colson (2010)

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)

Strategy Intro Quick Estimates (Multiplication) Check Your Estimates 56 x 4 is about 200 33 x 5 is about 150 43 x 72 is about 2800 808 x 24 is about 16 000 459 x 26 is about 8 000 358 x 86 is about 24 000 To get a “ball park” or quick estimate use only the digits at the front end! Created by Tania Colson (2010)

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)

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)

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 ~ 56 000 685 x 12 ~ 6 000 498 x 280 ~ 80 000 234 x 138 ~ 20 000 956 x 743 ~ 630 000 Created by Tania Colson (2010)

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)

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 ~ 45 000 653 x 25 ~ 12 000 732 x 584 ~ 350 000 254 x 558 ~ 100 000 836 x 653 ~ 480 000 Created by Tania Colson (2010)

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)

PB 3: Quick Estimates (Multiplication) 35 x 56 ~ 1500 47 x 87 ~ 2400 85 x 45 ~ 2400 48 x 59 ~ 2000 345 x 51 ~ 15 000 451 x 65 ~ 24 000 354 x 85 ~ 24 000 485 x 932 ~ 360 000 858 x 358 ~ 240 000 826 x 458 ~ 320 000 Created by Tania Colson (2010)

Strategy Intro Rounding (Addition & Subtraction) Try Estimating These In Your Head 56 + 42 is about ___ 332 + 157 is about ___ 434 + 272 is about ___ 98 - 34 is about ___ 459 - 363 is about ___ 3578 - 1586 is about ___ How can you round to get a better estimate? Created by Tania Colson (2010)

Strategy Intro Rounding (Addition & Subtraction) Check Your Estimates 56 + 42 is about 90 332 + 157 is about 400 434 + 272 is about 600 98 - 34 is about 40 459 - 363 is about 100 3578 - 1586 is about 2000 There are 2 rounding different strategies to get better estimates...What are they? Created by Tania Colson (2010)

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 = 150 000, this is a closer to the actual answer of 159 144. Using the rounding rules the estimate would be 500 x 400  20 000. Think: 150  5 Created by Tania Colson (2010)

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: 199 + 589 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)

PB 1: Rounding (Addition & Subtraction) 69 + 32 ~ 256 + 980 ~ 457 + 304 ~ 545 + 478 ~ 5856 + 3437 ~ 87 - 72 ~ 685 - 129 ~ 498 - 280 ~ 2348 - 1385 ~ 9564 - 7431 ~ Created by Tania Colson (2010)

PB 1: Rounding(Addition & Subtraction) 69 + 32 ~ 70 + 30 ~ 100 256 + 980 ~ 300 + 1000 ~ 1300 457 + 304 ~ 500 + 300 ~ 800 545 + 478 ~ 500 + 500 ~ 1000 5856 + 3437 ~ 6000 + 3000 ~ 9000 87 - 72 ~ 90 – 70 ~ 20 685 - 129 ~ 700 – 100 ~ 600 498 - 280 ~ 500 – 300 ~ 200 2348- 1385 ~ 2000 – 1000 ~ 1000 9564- 7431 ~ 10 000 – 7000 ~ 3000 Created by Tania Colson (2010)

PB 2: Rounding(Addition & Subtraction) 54 + 28 ~ 294 + 587 ~ 576 + 120 ~ 3480 + 2054 ~ 2698 + 8371 ~ 49 - 16 ~ 284 - 107 ~ 783 - 330 ~ 5954 - 2278 ~ 9568 - 6431 ~ Created by Tania Colson (2010)

PB 2: Rounding(Addition & Subtraction) 54 + 28 ~ 50 + 30 ~ 80 294 + 587 ~ 300 + 600 ~ 900 576 + 120 ~ 600 + 100 ~ 700 3480 + 2054 ~ 3000 + 2000 ~ 5000 2698 + 8371 ~ 3000 + 8000 ~ 11 000 49 - 16 ~ 50 – 20 ~ 30 284 - 107 ~ 300 – 100 ~ 200 783 - 330 ~ 800 – 300 ~ 500 5954 - 2278 ~ 6000 – 2000 ~ 4000 9568 - 6431 ~ 10 000 – 6000 ~ 4000 Created by Tania Colson (2010)

PB 3: Rounding (Addition & Subtraction) 89 + 56 ~ 494 + 687 ~ 576 + 489 ~ 8463 + 2948 ~ 6062 + 6872 ~ 67 - 18 ~ 484 - 290 ~ 1283 - 430 ~ 5760 - 2021 ~ 8220 - 7401 ~ Created by Tania Colson (2010)

PB 3: Rounding(Addition & Subtraction) 89 + 56 ~ 90 + 60 ~ 150 494 + 687 ~ 500 + 700 ~ 1200 576 + 489 ~ 600 + 500 ~ 1100 8463 + 2948 ~ 8000 + 3000 ~ 11 000 6062 + 6872 ~ 6000 + 7000 ~ 13 000 67 - 18 ~ 70 - 20 ~ 50 484 - 290 ~ 500 – 300 ~ 200 1283 - 430 ~ 1000 – 400 ~ 800 5760 - 2021 ~ 6000 – 2000 ~ 4000 8220 - 7401 ~ 8000 – 7000 ~ 1000 Created by Tania Colson (2010)

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)

Strategy Intro Rounding (Multiplication) Check Your Estimates 56 x 4 is about 60 x 4 ~ 240 33 x 5 is about 30 x 5 ~ 150 45 x 75 is about 50 x 70 ~ 3500 808 x 24 is about 800 x 20 ~ 16 000 459 x 25 is about 500 x 20 ~ 10 000 358 x 85 is about 400 x 80 ~ 32 000 Created by Tania Colson (2010)

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 15 000. *A quick estimate would have been only 8000. Created by Tania Colson (2010)

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)

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 ~ 63 000 685 x 12 ~ 700 x 10 ~ 7 000 498 x 280 ~ 500 x 300 ~ 150 000 234 x 138 ~ 200 x 100 ~ 20 000 956 x 743 ~ 1000 x 700 ~ 700 000 Created by Tania Colson (2010)

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)

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 ~ 10 000 854 x 55 ~ 900 x 50 ~ 45 000 653 x 25 ~ 700 x 20 ~ 14 000 732 x 584 ~ 700 x 600 ~ 420 000 254 x 558 ~ 300 x 500 ~ 15 000 836 x 653 ~ 800 x 700 ~ 560 000 Created by Tania Colson (2010)

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)

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 ~ 15 000 451 x 65 ~ 500 x 60 ~ 30 000 354 x 85 ~ 400 x 80 ~ 32 000 485 x 932 ~ 500 x 900 ~ 450 000 858 x 358 ~ 900 x 300 ~ 270 000 826 x 458 ~ 800 x 500 ~ 400 000 Created by Tania Colson (2010)

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)

Strategy Intro Adjusted Front End (Division) Check Your Estimates 56  4 is about 60  4 ~ 12 33  5 is about 30  5 ~ 7 629  70 is about 630  70 ~ 9 358  54 is about 350  50 ~ 7 4692  86 is about 4800  80 3582  96 is about ___ Created by Tania Colson (2010)

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)

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)

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)

PB 2: Adjusted Front End (Division) 53  6 ~ 54  6 ~ 9  4 ~ 12 47  2 ~ 48  2 ~ 24 317  3 ~ 330  3 ~ 110210  30 ~ 7 269  5 ~ 250  5 ~ 50280  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)