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## Mental Math 6

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**Mental Math 6**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 1Mental Calculation**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 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 Break Up and Bridge Compensation (Subtraction) Balancing for a Constant Difference 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)**ADDITION**Created by Tania Colson (2010)**Strategy IntroUsing 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)**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 IntroFront 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)**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)**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)**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)**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)**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)**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)**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 IntroFinding 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 IntroFinding 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)