created by tania colson (2010). mental math routine focus on 1-2 strategies each week practiced 3 to...

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.


Mental Math 6: Part 1Mental Calculation

A. Addition Basic Addition Facts Applied to Multiples of Powers of 10Front End FocusQuick Addition- No RegroupingFinding CompatiblesBreak Up and BridgeCompensation (Addition)Make Multiples of Powers of 10 B. Subtraction Basic Subtraction Facts Applied to Multiples of Powers of

10Quick SubtractionBack Through a Multiple of a Power of 10Up Through a Multiple of a Power of 10Break Up and BridgeCompensation (Subtraction)Balancing for a Constant Difference

C. Multiplication and DivisionQuick Multiplication — No RegroupingQuick Division — No RegroupingMultiplying by 10, 100, and 1000Dividing by tenths (0.1), hundredths (0.01) and thousandths (0.001)Dividing by Ten, Hundred and ThousandMultiplication of tenths, hundredths and thousandths Division when the divisor is a multiple of 10 and the dividend is a multiple of the divisorDivision using the Think Multiplication strategyCompensation(Multiplication)Halving and DoublingFront End Multiplication or the Distributive Principle in 10s, 100s, and 1000sFinding Compatible FactorsUsing Division Facts for Tens, Hundreds and ThousandsBreaking Up the DividendCompensation (Division)Balancing For a Constant Quotient

D. Computational EstimationQuick 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


Mental Math 6: Part 2 Measurement Estimation

LengthArea and PerimeterVolume and CapacityAngles

The Development of Spatial Sense

Mental Math 6: Part 3 Measurement Estimation


Strategy IntroUsing Basic Addition Facts

Try These In Your Head90 + 40 = 80 + 50 =600 + 600 = 4 000 + 5 00010 000, 40 000, 70 000, _________ 0.2 s + 0.6 s = 0.04 cm plus 0.03 cm=


Strategy Using Basic Addition Facts

Check you Answers90 + 40 = 13080 + 50 = 130600 + 600 = 1 200 4 000 + 5 000 = 9 00010 000, 40 000, 70 000, 100 000 0.2 s + 0.6 s = 0.8 s0.04 cm plus 0.03 cm= 0.07 cm

How many strategies can you think of to solve addition

problems?



Doubles Facts Examples: 2 + 2 or 5 + 5

Plus-One Facts Examples: 6 +1 or 8 +1

Near-Doubles (1-Aparts) FactsExamples: 6 + 5 or 2 + 3

Plus-Two FactsExamples: 3 + 2 or 7 + 2

Plus Zero Facts Examples 10 + 0 or 4 +0

Make-10 FactsExamples: 7 + 3, 2 + 8

These 6 strategies can be applied for 88 of the 100 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


PB 1 : Using Basic Addition Facts

1) 90 + 80 = 2) 100 more than 400 = 3) 7 000 plus 4 000 = 4) $6 000 + $9 000 = 5) 0.03 cm increased by 0.09cm = 6) 20 million and 30 million =7) The sum of 8 kg and 9 kg = 8) 0.6 mm + 0.9 mm = 9) $0.80 plus $0.90 = 10)0.8 billion and 0. 6 billion=


PB 1: Using Basic Addition Facts

1) 90 + 80 = 1702) 100 more than 400 = 5003) 7 000 plus 4 000 = 11 0004) $6 000 + $9 000 = $15 0005) 0.03 cm increased by 0.09cm =

0.12cm6) 20 million and 30 million = 50 million7) The sum of 8 kg and 9 kg = 17 kg8) 0.6 mm + 0.9 mm = 1.5 mm9) $0.80 plus $0.90 = $1.70 10)0.8 billion and 0. 6 billion= 1.4 billion



1) 60 + 70 = 2) 200 more than 900 = 3) 4 000 plus 8 000 = 4) $1 000 + $3 000 = 5) 0.05 cm increased by 0.05cm = 6) 30 million and 80 million =7) The sum of 2 kg and 6 kg = 8) 0.7 mm + 0.7 mm = 9) $0.60 plus $0.50 = 10)0.7 billion and 0. 9 billion=



1) 60 + 70 = 1302) 200 more than 900 = 1 1003) 4 000 plus 8 000 = 12 0004) $1 000 + $3 000 = 4 0005) 0.05 cm increased by 0.05cm =

0.10cm6) 30 million and 80 million = 110 million7) The sum of 2 kg and 6 kg = 8) 0.7 mm + 0.7 mm = 1.4 mm9) $0.60 plus $0.50 = $1.1010)0.7 billion and 0. 9 billion= 1.6 billion



1) 20 + 50 = 2) 600 more than 800 = 3) 3 000 plus 9 000 = 4) $4 000 + $7 000 = 5) 0.09 cm increased by 0.09cm = 6) 30 million and 70 million =7) The sum of 4 kg and 9 kg = 8) 0.8 mg + 0.8 mg = 9) $0.30 plus $0.40 = 10)0.2 billion and 0. 5 billion=



1) 20 + 50 = 702) 600 more than 800 = 14003) 3 000 plus 9 000 = 12 0004) $4 000 + $7 000 = 11 0005) 0.09 cm increased by 0.09cm =

0.18cm6) 30 million and 70 million = 100 million7) The sum of 4 kg and 9 kg = 13 kg8) 0.8 mg + 0.8 mg = 1.6 mg9) $0.30 plus $0.40 = $0.7010)0.2 billion and 0. 5 billion= 0.7 billion



1) 80 + 20 = 2) 400 more than 900 = 3) 1 000 plus 7 000 = 4) $5 000 + $8 000 = 5) 0.02 cm increased by 0.06cm = 6) 50 million and 80 million =7) The sum of 3g and 6g = 8) 0.4 mL + 0.6 mL = 9) $0.40 plus $0.70 = 10)0.2 s and 0. 5 s =



1) 80 + 20 = 1002) 400 more than 900 = 13003) 1 000 plus 7 000 = 8 0004) $5 000 + $8 000 = 13 0005) 0.02 cm increased by 0.06cm = 0.08

cm6) 50 million and 80 million =130 million7) The sum of 3g and 6g = 9g8) 0.4 mL + 0.6 mL = 1.0mL9) $0.40 plus $0.70 = $1.1010)0.2 s and 0. 5 s = 0.7s



1) 90 + 90 = 2) 300 more than 300 = 3) 4 000 plus 7 000 = 4) $4 000 + $5 000 = 5) 0.04 cm increased by 0.03cm = 6) 40 million and 20 million =7) The sum of 7g and 8g = 8) 0.2 L + 0.3 L = 9) $0.60 plus $0.70 = 10)0.4 + 0. 8 =



1) 90 + 90 = 1802) 300 more than 300 = 6003) 4 000 plus 7 000 = 11 0004) $4 000 + $5 000 = $9 0005) 0.04 cm increased by 0.03cm =

0.07cm6) 40 million and 20 million = 60 million7) The sum of 7g and 8g = 15 g8) 0.2 L + 0.3 L = 0.5L9) $0.60 plus $0.70 = 1.3010)0.4 + 0. 8 = 1.2


Strategy IntroFront End Focus Addition

Try These In Your Head37 + 28 = 307 and 206 =3600 + 2500 = 5.06 more than 3.05 = 7.2cm + 2.6cm = 5.8 million plus 2.5 million=


Strategy Front End Focus Addition

Check Your Answers37 + 28 = 65307 and 206 = 5133 600 + 2 500 = 6100 5.06 more than 3.05 = 8.11 7.2cm + 2.6cm = 56.97cm5.8 million plus 2.5 million= 8.3 million

Did you use the same strategy to solve all of these

problems?



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.



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.


PB 1: Front End Focus Addition

1) 45 +36 = 2) 18 kg more than 56 kg = 3) 102 plus 569 = 4) $660 + $270 = 5) 102 cm and 150cm more = 6) 3 400 + 5 800 =7) The sum of 2 040 and 5 060 = 8) 4.5 km + 2.7 km = 9) $3.12 plus $1.09 = 10)5.4 million + 1. 8 million =



1) 45 +36= 812) 18 kg more than 56 kg= 743) 102 plus 569= 6714) $660 + $270= $9305) 102 cm and 150cm more = 252cm6) 3 400 + 5 800 =9 2007) The sum of 2 040 and 5 060= 7 1008) 4.5 km + 2.7 km = 7.2 km9) $3.12 plus $1.09 = $4.21 10)5.4 million + 1. 8 million= 7.2

million



1) 19 + 24 = 2) 35 km more than 29 km = 3) 209 plus 403 = 4) $580 + $340 = 5) 309 cm and 268cm more = 6) 23 000 + 38 000 =7) The sum of 5 080 and 3 080 = 8) 2.6 cm + 3.9 cm = 9) $3.12 plus $1.09 = 10)4.8 billion and 3. 6 billion=



1) 19 + 24 = 432) 35 km more than 29 km = 64km3) 209 plus 403 = 612 4) $580 + $340 = 9205) 309 cm and 268cm more = 577 6) 23 000 + 38 000 = 61 0007) The sum of 5 080 and 3 080 = 8

1608) 2.6 cm + 3.9 cm = 6.5 cm9) $3.12 plus $1.09 = $4.2110)4.8 billion and 3. 6 billion = 8.4

billion Created by Tania Colson (2010)


1) 54 + 19 = 2) 67 m + 28 m = 3) 320 plus 490 = 4) $330 + $280 = 5) 208 cm more than 409cm = 6) 10 060 + 32 070 =7) The sum of 4 160 and 3 080 = 8) 4.5 cm + 7.9 cm = 9) $6.19 plus $1.05 = 10)1.8 billion and 2.6 billion =



1) 54 + 19 = 732) 67 m + 28 m = 95m3) 320 plus 490 = 8194) $330 + $280 = $6205) 208 cm more than 409cm = 617cm6) 10 060 + 32 070 = 42 1307) The sum of 4 160 and 3 080 = 7

2408) 4.5 cm + 7.9 cm = 12.4 cm9) $6.19 plus $1.05 = $7.2410)1.8 billion and 2.6 billion = 4.4

billion Created by Tania Colson (2010)


1) 65 + 28 = 2) 62 m + 59 m = 3) 240 plus 690 = 4) $460 + $280 = 5) 409 cm more than 601cm = 6) 20 040 + 12 070 =7) The sum of 6 030 and 1 080 = 8) 3.9 mm + 4.2 mm = 9) $7.09 plus $2.05 = 10)50.3 million and 2.8 million =



1) 65 + 28 = 932) 62 m + 59 m = 121m3) 240 plus 690 = 9304) $460 + $280 = $7405) 409 cm more than 601cm = 1010 cm6) 20 040 + 12 070 =32 1107) The sum of 6 030 and 1 080 = 7 1208) 3.9 mm + 4.2 mm = 8.1 mm9) $7.09 plus $2.05 = $9.1410)50.3 million and 2.8 million =

53.1millionCreated by Tania Colson (2010)


1) 15 + 58 = 2) 42 m + 39 m = 3) 210 plus 390 = 4) $480 + $180 = 5) 307 cm more than 409cm = 6) 10 050 + 54 060 =7) The sum of 7 030 and 2 080 = 8) 5.8 mm + 1.7 mm = 9) $12.08 plus $3.04 = 10)10.5 million and 3.7 million =



1) 15 + 58 = 73 2) 42 m + 39 m = 81 m3) 210 plus 390 = 6004) $480 + $180 = $6605) 307 cm more than 409cm = 716 cm6) 10 050 + 54 060 = 64 1107) The sum of 7 030 and 2 080 = 9 1108) 5.8 mm + 1.7 mm = 7.15mm9) $12.08 plus $3.04 = $15.1210)10.5 million and 3.7 million = 14.2

millionCreated by Tania Colson (2010)

Strategy Intro Quick Addition

Try These In Your Head54 + 32 =87 + 21 = 421 + 432 = 734 + 122 = 4.13 + 2.84 = 14.36 + 32.11 =

How are all these problems

alike?


Strategy Intro Quick Addition

Check your Answers54 + 32 = 8687 + 21 = 108421 + 432 = 853734 + 122 = 856 4.13 + 2.84 = 6.9714.36 + 32.11 = 46.47


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

1) 31 + 17 = 2) The sum of 43 and 12 3) 541 more than 126 4) 543 + 321= 5) 129 plus 230 =6) 734 + 153 =7) 231.2 increased by 152.3 8) The total of $4.12 and $3.36 9) 0.341 + 1.245 =10)1.2 m + 2.7 m =



1) 31 + 17 = 482) The sum of 43 and 12 = 553) 541 more than 126 = 6674) 543 + 321= 8645) 129 plus 230 = 3596) 734 + 153 = 8877) 231.2 increased by 152.3 = 383.58) The total of $4.12 and $3.36 =

$7.489) 0.341 + 1.245 = 1.58610)1.2 m + 2.7 m = 3.9m



1) 21 + 45 = 2) The sum of 13 and 64 3) 123 more than 810 4) 5230 + 3260= 5) 34 681 plus 54 104 =6) 73.4 + 15.3 =7) 72.2 increased by 14.6 8) The total of $0.66 and $0.33 9) 0.21 + 1.70 =10)2.2 m + 5.7 m =



1) 21 + 45 = 662) The sum of 13 and 64 = 77 3) 123 more than 810 = 9334) 5230 + 3260 = 84905) 34 681 plus 54 104 = 88 7856) 73.4 + 15.3 = 88.77) 72.2 increased by 14.6 = 86.88) The total of $0.66 and $0.33 =

$0.999) 0.21 + 1.70 = 1.9110)2.2 m + 5.7 m = 7.9m



1) 43 + 23 = 2) The sum of 54 and 33 3) 154 more than 712 4) 2210 + 2734= 5) 41 081 plus 33 905=6) 55.4 + 12.5 =7) 71.36 increased by 23.60 8) The total of $3.29and $4.509) 0.72 + 4.27 =10)8.4 cm + 1.5 cm =



1) 43 + 23 = 662) The sum of 54 and 33 = 873) 154 more than 712 = 8664) 2210 + 2734 = 49445) 41 081 plus 33 905= 74 9856) 55.4 + 12.5 = 67.97) 71.36 increased by 23.60 = 94.96 8) The total of $3.29and $4.50 =

$7.799) 0.72 + 4.27 = 4.9910)8.4 cm + 1.5 cm = 9.9 cm


Strategy IntroFinding Compatibles

Try These In Your Head1 + 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?


Strategy IntroFinding Compatibles

Check Your Answers1 + 7 + 9 + 8 + 3 = 2830 + 75 + 70 + 25 = 200300 + 800 + 700 + 600 + 200 = 2600 4 000 + 5 000 + 6000= 15 0009 500 + 2 200 + 500 = 12 2000.4 + 0.3 + 0.6= 1.3


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 + 38 plus 2 is 10.7 plus 3 is 10.

And…10 plus 10 is 20.


PB 1: Finding Compatibles

1) 30 + 60 + 40 +70 = 2) The total of $75, $95, and $425 =3) The sum of 200, 700, 500, 800 = 4) 5 000 + 3 000 + 5 000 + 7 000 = 5) 2 500 and 3 500 + 7 500 =6) 0.2 + 0.4 + 0.3 + 0.8 + 0.6 = 7) 6 –tenths + 9=tenths + 4 tenths = 8) $0.50 more than $0.75 plus $0.259) The sum of three lengths: 0.09m,

0.13m, 0.01m 10)2.0 + 7.0 + 8.0+ 3.0 + 4.0 =



1) 30 + 60 + 40 +70 = 2002) The total of $75, $95, and $425 = $5953) The sum of 200, 700, 500, 800 = 2200 4) 5 000 + 3 000 + 5 000 + 7 000 = 20 0005) 2 500 and 3 500 + 7 500 = 13 5006) 0.2 + 0.4 + 0.3 + 0.8 + 0.6 = 2.37) 6 –tenths + 9=tenths + 4 tenths = 1.98) $0.50 more than $0.75 plus $0.25 =

$1.259) The sum of three lengths: 0.09m,

0.13m, 0.01m = 0.2310)2.0 + 7.0 + 8.0+ 3.0 + 4.0 = 24.0



1) 20 + 30 + 80 +70 = 2) The total of $50, $25, and $350 =3) The sum of 600, 600, 400, 400 = 4) 2000 + 8 000 + 5 000 + 5 000 = 5) 3 500 and 5 500 + 7 500 =6) 0.5 + 0.2 + 0.3 + 0.5 + 0.7 = 7) 4 –tenths + 1=tenths + 9 tenths = 8) $0.75 more than $0.50 plus $0.259) The sum of three lengths: 0.04m,

0.01m, 0.06m 10)3.0 + 2.0 + 7.0+ 3.0 + 5.0 =



1) 20 + 30 + 80 +70 = 2002) The total of $50, $25, and $350 = $4253) The sum of 600, 600, 400, 400 = 20004) 2000 + 8 000 + 5 000 + 5 000 = 20 0005) 3 500 and 5 500 + 7 500 = 16 5006) 0.5 + 0.2 + 0.3 + 0.5 + 0.7 = 2.27) 4 –tenths + 1=tenths + 9 tenths = 1.48) $0.75 more than $0.50 plus $0.25 =

$1.509) The sum of three lengths: 0.04m,

0.01m, 0.06m = 0.11m10)3.0 + 2.0 + 7.0+ 3.0 + 5.0 = 20.0



1) 60 + 50 + 40 +50 = 2) The total of $50, $50, and $425 =3) The sum of 300, 200, 700, 800 + 100 = 4) 2 000 + 6 000 + 4 000 + 8 000 = 5) 1 500 and 2 000 + 9 500 =6) 0.1 + 0.2 + 0.8 + 0.9 + 0.4 = 7) 3 –tenths + 7=tenths + 2 tenths = 8) 0.30 more than $0.70 plus $0.509) The sum of three lengths: 0.3 m,

0.8m, 0.2m 10)1.0 + 6.0 + 9.0+ 3.0 + 4.0 =



1) 75 + 40 + 25 +60 = 2002) The total of $50, $50, and $425 = $5253) The sum of 300, 200, 700, 800 + 100 =

21004) 2 000 + 6 000 + 4 000 + 8 000 = 20 0005) 1 500 and 2 000 + 9 500 = 13 0006) 0.1 + 0.2 + 0.8 + 0.9 + 0.4 = 2.47) 3 –tenths + 7=tenths + 2 tenths = 1.28) 0.30 more than $0.70 plus $0.50 = $1.509) The sum of three lengths: 0.3 m, 0.8m,

0.2m = 1.3m10)1.0 + 6.0 + 9.0+ 3.0 + 4.0 = 2.3


Strategy IntroBreak Up and Bridge

Try These In Your Head45 + 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?



Check your answers45 + 36= 8117 more than 64= 81537 + 208 = 745 5 300 + 2 800 = 8 10034 000 + 27 000 = 61 0003.60 + 5.70 = 9.30


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 842842 plus 9 more is

851.


PB 1: Break Up and Bridge

1) 54 + 37= 2) 15 more than 76=3) The sum of $340 and $440 = 4) 365 increased by 109 = 5) 2 500 + 3 700=6) The total of 4070 girls and 3080

boys= 7) 46 000 + 37 000 = 8) $66 000 and $15 000 = 9) 4.7 m + 3.5 m = 10)4.56 kg more than 4.40 kg =



1) 54 + 37 = 91 2) 15 more than 76 = 913) The sum of $340 and $440 = $7804) 365 increased by 109 = 4745) 2 500 + 3 700= 6 2006) The total of 4070 girls and 3080

boys= 71507) 46 000 + 37 000 = 83 0008) $66 000 and $15 000 = $81 0009) 4.7 m + 3.5 m = 8.2 m10)4.56 kg more than 4.40 kg = 8.96 kg



1) 45 + 57 = 2) 19 more than 82 =3) The sum of $340 and $440 = 4) 215 increased by 467 = 5) 1 500 + 4 800 =6) The total of 5060 L and 2080 L = 7) 56 000 + 27 000 = 8) $63 000 and $45 000 = 9) 2.7 m + 3.4 m = 10)3.56 kg more than 4.90 kg =



1) 45 + 57 = 1022) 19 more than 82 = 1013) The sum of $340 and $440 = $7804) 215 increased by 467 = 6825) 1 500 + 4 800 = 6 3006) The total of 5060 L and 2080 L = 7) 56 000 + 27 000 = 8) $63 000 and $45 000 = 9) 2.7 m + 3.4 m = 10)3.56 kg more than 4.90 kg =



1) 28 + 65= 2) 53 more than 27=3) The sum of $760 and $260 = 4) 653 increased by 109 = 5) 2 900 + 3 200=6) The total of 2312 and 1748= 7) 36 000 + 38 000 = 8) $66 000 and $25 000 = 9) 4.9 million + 2.5 million = 10)3.50 L more than 4.80 L =



1) 28 + 65= 932) 53 more than 27= 803) The sum of $760 and $260 = 1 0204) 653 increased by 109 = 7625) 2 900 + 3 200= 6 1006) The total of 2302 and 1700= 40027) 3.6 + 3.8 = 7.48) $66 000 and $25 000 = 91 0009) 4.9 million + 2.5 million = 7.4

million10)3.50 L more than 4.80 L = 8.3 L


Strategy IntroCompensation (Addition)

Try These In Your Head52 + 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?


Strategy IntroCompensation (Addition)

Check Your Answers52 + 39 = 91345 + 198 = 5434 500 + 1 900 = 6 400 34 000 + 9 900 = 43 000 59 000 + 25 000 = 84 0004.6 + 1.8 = 6.40.54 + 0.29 = 0.83

One of the addends has a 8,

or 9 which makes is easy to

round off.


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


PB 1: Compensation (Addition)

1) 58 + 39 = 2) 49 + 38 =3) $198 more than $465 = 4) 3 456mm added to 999 mm= 5) 16 000 + 39 000 =6) The total of $38 000 and $9 900 = 7) 3.9 + 2.5 = 8) 3.5 km more than 4.8 km = 9) $0.36 + 0.39 = 10)2.47s more than 4.99s=



1) 58 + 39 = 972) 49 + 38 = 873) $198 more than $465 = $6634) 3 456mm added to 999 mm= 4455mm5) 16 000 + 39 000 = 55 0006) The total of $38 000 and $9 900 =

$47 0007) 3.9 + 2.5 = 6.48) 3.5 km more than 4.8 km = 8.3km9) $0.36 + $0.39 = $0.7510)2.47 s more than 4.99s = 7.46 s



1) 32 + 49 = 2) 67 + 28 =3) $198 more than $250 = 4) 4 500 mL added to 900 mL= 5) 26 000 + 59 000 =6) The total of $78 000 and $9 000 = 7) 2.9 + 2.4 = 8) 1.5 km more than 3.8 km = 9) $0.45+ $0.49 = 10)3.35 more than $2.99=



1) 32 + 49 = 812) 67 + 28 = 953) $198 more than $250 = $4484) 4 500 mL added to 900 mL= 5 400 mL5) 26 000 + 59 000 = 85 0006) The total of $78 000 and $9 000 =

$87 0007) 2.9 + 2.4 = 5.38) 1.5 km more than 3.8 km = 5.3 km9) $0.45+ $0.49 = $0.9410)$3.35 more than $2.99 = $6.34



1) 52 + 29 = 2) 60 + 38 =3) $498 more than $300 = 4) 4 500 L added to 900 L= 5) 10 000 + 29 000 =6) The sum of 25 000 and 8 000 = 7) 2.8 cm + 2.0 cm = 8) 2.3 more than 4.9 m = 9) $0.50+ $1.99 = 10)$4.99 more than $4.99=



1) 52 + 29 = 812) 60 + 38 = 983) $498 more than $300 = $6984) 4 500 L added to 900 L= 5 400L5) 10 000 + 29 000 = 39 0006) The sum of 25 000 and 8 000 = 33

0007) 2.8 cm + 2.0 cm = 3.8 cm8) 2.3 more than 4.9 m = 7.2 m9) $0.50+ $1.99 = $2.4910)$4.99 more than $4.99= $9.98


Strategy IntroMake Multiples of Powers

of 10Try These In Your Head92 + 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?


Strategy IntroMake Multiples of Powers

of 10Check Your Answers92 + 69= 161298 + 345 = 643650 + 190 = 840 34 000 + 28 000 = 62 0001.3 + 0.9 = 2.2 1.4 + 2.9 = 4.3 3.98 + 4.24= 8.22


Strategy Make Multiples of Powers

of 10Take 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.


PB 1: Make Multiples of Powers of 10

1) 51 + 39 =2) 42 + 38 = 3) $198 more than $402 = 4) 3 556 mL added to 999 mL= 5) 18 000 + 46 000 = 6) The sum of 38 000 and 9 000 = 7) 1.9 m + 2.6 m = 8) 5.8 cm more than 4.5 cm = 9) $0.25 + $0.59 = 10) 1.46 km more than 2.99km =



1) 51 + 39 = 902) 42 + 38 = 803) $198 more than $402 = $6004) 3 556 mL added to 999 mL= 4 5555) 18 000 + 46 000 = 64 0006) The sum of 38 000 and 9 000 = 47 0007) 1.9 m + 2.6 m = 4.5m8) 5.8 cm more than 4.5 cm = 10.3cm9) $0.25 + $0.59 = $0.8410) 1.46 km more than 2.99km = 4.45 km



1) 62 + 29 = 2) 73 + 18 =3) $498 more than $345 = 4) 2 600 L added to 900 L = 5) 16 000 + 29 000 =6) The sum of 35 000 and 9 000 = 7) 10.9 m + 2.4 m = 8) 3.9 cm more than 4.6 cm = 9) $0.29 + $0.76 = 10) 1.27 more than 2.99 =



1) 62 + 29 = 912) 72 + 28 = 1003) $498 more than $302 = $8004) 2 600 L added to 900 L = 3 500 L5) 16 000 + 29 000 = 45 0006) The sum of 35 000 and 9 000 = 44

0007) 10.9 m + 2.4 m = 13.3 m8) 3.9 cm more than 4.6 cm = 8.5 cm9) $0.29 + $0.76 = $1.0510) 1.27 more than 2.99 = 4.26



1) 42 + 29 = 2) 27 + 13 =3) $199 more than $150 = 4) 2 600 L added to 900 L = 5) 13 000 + 39 000 =6) The sum of 25 000 and 8 000 = 7) 1.9 m + 2.5 m = 8) 3.3 cm more than 1.9 cm = 9) $0.17 + $0.28 = 10) 2.07 more than 0.99 =



1) 42 + 29 = 712) 27 + 13 = 403) $199 more than $150 = $3494) 1 600 L added to 900 L = 2 500 L5) 13 000 + 39 000 = 52 0006) The sum of 25 000 and 8 000 = 33

0007) 1.9 m + 2.5 m = 4.4 m8) 3.3 cm more than 1.9 cm = 5.2 cm9) $0.17 + $0.28 = $0.4510) 2.07 more than 0.99 = 3.06


Strategy IntroUsing Basic Subtraction

FactsTry These In Your Head80 - 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?


Strategy IntroUsing Basic Subtraction

FactsCheck Your Answers80 - 30 = 50400 - 200 =2001 500 – 600 = 900 6 000 – 2 000= 4 0000.8 – 0.5 = 0.31.4 – 0.7 = 0.70.17 – 0.09= 0.08


Strategy Using Basic Subtraction

FactsKnowing 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!


PB 1: Using Basic Subtraction Facts

1) 120 – 70 =2) $20 less than $90 = 3) 700 kg decreased by 300 kg = 4) The difference between 1100 km

and 400 km = 5) 6000 minus 1000 = 6) 40 000 – 20 000 = 7) 0.7 kg – 0.2 kg = 8) 1.6 less 0.9 = 9) $0.16 - $0.08 = 10) 0.10 – 0.01 =



1) 120 – 70 = 502) $20 less than $90 = $703) 700 kg decreased by 300 kg = 400 kg4) The difference between 1100 km and

400 km = 700 km5) 6 000 minus 1 000 = 5 0006) 40 000 – 20 000 = 20 0007) 0.7 kg – 0.2 kg = 0.5 kg8) 1.6 less 0.9 = 0.79) $0.16 - $0.08= $0.0810) 0.10 – 0.01 = 0.09



1) 180 – 30 =2) $40 less than $60 = 3) 500 g decreased by 200 kg = 4) The difference between 1200 m and

600 m = 5) 8000 minus 3000 = 6) 60 000 – 40 000 = 7) 0.8 kg – 0.1 kg = 8) 1.2 less 1.0 = 9) $0.15 - $0.05 =10) 0.10 – 0.02 =



1) 180 – 30 = 1502) $40 less than $60 = $203) 500 g decreased by 200 kg = 300 kg4) The difference between 1200 m and

600 m = 600 5) 8 000 minus 3 000 = 5 0006) 60 000 – 40 000 = 20 0007) 0.8 kg – 0.1 kg = 0.07 kg8) 1.2 less 1.0 = 0.2 9) $0.15 - $0.05 = $0.1010) 0.10 cm – 0.02 cm = 0.08 cm



1) 120 – 40 =2) $160 less than $180 = 3) 300 g decreased by 100 g = 4) The difference between 1300 m and

400 m = 5) 9 000 minus 6 000 = 6) 60 000 – 50 000 = 7) 0.7 kg – 0.2 kg = 8) 1.5 less 1.3 = 9) $0.20 - $0.05 =10) 0.10 km – 0.03 km =



1) 120 – 40 = 80 2) $160 less than $180 = $203) 300 g decreased by 100 g = 200 g 4) The difference between 1 300 m and

400 m = 900 m5) 9 000 minus 6 000 = 3 0006) 60 000 – 50 000 = 10 0007) 0.7 kg – 0.2 kg = 0.5 kg8) 1.5 less 1.3 = 0.29) $0.20 - $0.05 = $0.15 10) 0.10 km – 0.03 km = 0.07 km


Strategy IntroQuick Subtraction

Try These In Your Head56- 32 = 268 – 124 =765 – 602 = 4070 – 3030 = 87 000 – 32 000 = 345.85 – 112.45 = 0.27 – 0.13 =


alike?


Strategy IntroQuick Subtraction

Try These In Your Head56- 32 = 24268 – 124 =144765 – 602 = 163 4070 – 3030 = 104087 000 – 32 000 = 55 000345.85 – 112.45 = 233.400.27 – 0.13 = 0.14

There’s no regrouping!


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 279 – 57 = 22


PB 1: Quick Subtraction

1) 56 – 21 =2) $604 less than $203 = 3) $245 less than $605 = 4) The difference between 1225 km

and 3575 km = 5) Subtract 575 from 3889 = 6) 45 678 – 21 543 = 7) 213.7 kg decreased by 101.2 kg = 8) 45.12 m less than 57.75 = 9) $300.26 - $200.01 = 10) 0.29 – 0.15 =



1) 56 – 21 = 35 2) $604 less than $203 = $4013) $245 less than $605 = $4404) The difference between 1225 km and

3575 km = 1350 km5) Subtract 575 from 3889 = 33146) 45 678 – 21 543 = 24 1357) 213.7 kg decreased by 101.2 kg =

112.5kg8) 45.12 m less than 57.75 = 12.63 m9) $300.26 - $200.01 = $100.2510) 0.29 – 0.15 = 0.14



1) 48 – 35 =2) $235 less than $115 = 3) 340 less than 220 = 4) 1304 fewer than 1509= 5) Subtract 625 from 855 = 6) 25 608 – 20 103 = 7) 12.2 kg decreased by 10.1 kg = 8) 67.15 m less than 89.25 = 9) $401.06 - $100.05 = 10) 0.39 – 0.13 =



1) 48 – 35 = 132) $235 less than $115 = $1203) 340 less than 220 = 1204) 1304 fewer than 1509= 2055) Subtract 625 from 855 = 230 6) 25 608 – 20 103 = 5 5057) 12.2 kg decreased by 10.1 kg = 2.1

kg8) 67.15 m less than 89.25 = 22.109) $401.06 - $100.05 = $300.0110) 0.39 – 0.13 = 0.26



1) 82 – 21 =2) $103 less than $205 = 3) $425 minus $315 = 4) 2040 km fewer than and 5050 km = 5) Subtract 6505 from 9999 = 6) 40 409 – 20 208 = 7) 27.9 g decreased by 15.4 g = 8) 26.2 m less than 56.7m = 9) $300.26 - $200.01 = 10) 0.67 – 0.42 =



1) 82 – 21 = 612) $103 less than $205 = $1023) $425 minus $315 = $1104) 2040 km fewer than and 5050 km =

3010km5) Subtract 6505 from 9999 = 34946) 40 409 – 20 208 = 20 2017) 27.9 g decreased by 15.4 g = 12.5g8) 26.2 m less than 56.7m = 30.5m9) $300.26 - $200.01 = $100.2510) 0.67 – 0.42 = 0.25


Strategy IntroBack Through a Multiple of

10 Try These In Your Head35 - 8 = 530 - 70=8 600 – 800 = 74 000 – 9 000 = 4.5 – 0.9 = 1.63 – 0.07=

Which strategy did you use?


Strategy IntroBack Through a Multiple of

10 Check Your Answers35 - 8 = 27530 – 70 = 4608 600 – 800 = 7 800 74 000 – 9 000 = 65 0004.5 – 0.9 = 3.61.63 – 0.07= 1.56


Strategy Back Through a Multiple of

10Start 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.


PB 1: Back Through a Multiple of 10

1) 9 fewer people than 92 =2) $40 less than $210 = 3) $340 - $70 = 4) The difference between 630 and 80 = 5) Subtract 600 from 2 300 = 6) 45 000 – 8 000 = 7) 23.5 L decreased by 0.8 L = 8) 13.2kg – 0.7kg = 9) 0.06 m less than 1.21 m= 10) $2.53 – $0.07=



1) 9 fewer people than 92 = 832) $40 less than $210 = $1703) $340 - $70 = $2704) The difference between 630 and 80 =

5505) Subtract 600 from 2 300 = 1 7006) 45 000 – 8 000 = 37 0007) 23.5 L decreased by 0.8 L = 22.7 L8) 13.2 kg – 0.7 kg = 12.5 kg9) 0.06 m less than 1.21 m= 1.15 m10) $2.53 – $0.07= $2.46



1) 8 fewer people than 76 =2) $50 less than $130 = 3) $280 - $90 = 4) The difference between 730 and 70 = 5) Subtract 500 from 3 200 = 6) 35 000 – 7 000 = 7) 31.5 L decreased by 0.6 L = 8) 1.2kg – 0.7kg = 9) 0.07 m less than 2.34 m = 10) $1.56 – $0.08 =



1) 8 fewer people than 76 = 682) $50 less than $130 = $1803) $280 - $90 = $1704) The difference between 730 and 70 =

6605) Subtract 500 from 3 200 = 2 7006) 35 000 – 7 000 = 28 0007) 31.5 L decreased by 0.6 L = 30.9 L8) 1.2kg – 0.7kg = 0.5 kg 9) 0.07 m less than 2.34 m = 2.2710) $1.56 – $0.08 = $1.48



1) 68% - 9% =2) $60 less than $240 = 3) $220 - $70 = 4) 440 minus 60 = 5) Subtract 300 from 1 100 = 6) 25 000 – 8 000 = 7) 20.5 L decreased by 0.8 L = 8) 2.3 g – 0.4 g = 9) 0.06 s less than 1.61 s = 10) $1.03 – $0.04 =



1) 68% - 9% = 59%2) $60 less than $240 = $1803) $220 - $70 = $1504) 440 minus 60 = 3805) Subtract 300 from 1 100 = 8006) 25 000 – 8 000 = 17 0007) 20.5 L decreased by 0.8 L = 19.7 L8) 2.3 g – 0.4 g = 1.9 g9) 0.06 s less than 1.61 s = 1.55 s10) $1.03 – $0.04 = $0.99


Strategy IntroUp Through a Multiple of 10

Try These In Your Head84 – 77 = 613 – 594 =2 310 – 1800 = 57 000 – 49 000 = 12.4 – 11. 8 = 6.12 – 5.99 = 12.54 – 12.48 =


similar?


Strategy IntroUp Through a Multiple of 10

Check Your Answers84 – 77 = 7613 – 594 = 192 310 – 1800 = 51057 000 – 49 000 = 8 00012.4 – 11. 8 = 0.66.12 – 5.99 = 0.1312.54 – 12.48 = 0.06

The two amounts are

relatively close together.


Strategy Up Through a Multiple of 10This 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.


PB 1: Up Through a Multiple of 10

1) 92 – 86 =2) $140 less than $210 = 3) 196 - 189 = 4) The difference between 630 and 580

= 5) 2 400 minus 1 700 = 6) 45 000 – 38 000 = 7) 83 000 m decreased by 79 000 m = 8) 13.2 kg – 12.7 kg = 9) 1.99 m less than 2.21 m= 10) $2.53 – $2.45 =



1) 92 – 86 = 62) $140 less than $210 = 703) 196 – 189 = 74) The difference between 630 and 580 =

50 5) 2 400 minus 1 700 = 7006) 45 000 – 38 000 = 7 0007) 83 000 m decreased by 79 000 m = 4 000

m8) 13.2 kg – 12.7 kg = 0.5 kg9) 1.99 m less than 2.21 m= 0.22 m10) $2.53 – $2.45 = $0.08



1) 52 – 48 =2) $190 less than $230 = 3) $183 - $179 = 4) The difference between 560 and 620

= 5) 2 200 minus 1 600 = 6) 55 000 – 48 000 = 7) 91 000 m decreased by 89 000 m = 8) 10.3 kg – 9.7 kg = 9) 1.99 m less than 2.33 m= 10) $3.54 – $3.49 =



1) 52 – 48 = 4 2) $190 less than $230 = 403) $183 - $179 = 44) The difference between 560 and 620 =

605) 2 200 minus 1 600 = 6006) 55 000 – 48 000 = 7 0007) 91 000 m decreased by 89 000 m = 3 000

m8) 10.3 kg – 9.7 kg = 0.6 kg 9) 1.99 m less than 2.33 m = 0.34 m 10) $3.54 – $3.49 = $0.05



1) 76 – 68 =2) $240 less than $170 = 3) $172 - $167 = 4) The difference between 430 and 390

= 5) 1 100 minus 800 = 6) 52 000 – 47 000 = 7) 32 000 m decreased by 27 000 m = 8) 22.2 kg – 21.9 kg = 9) 2.98 m less than 3.33 m= 10) $5.09 – $4.99 =



1) 76 – 68 = 82) $240 less than $170 = $703) $172 - $167 = $54) The difference between 430 and 390 =

405) 1 100 minus 800 = 3006) 52 000 – 47 000 = 5 0007) 32 000 m decreased by 27 000 m = 5 000

m8) 22.2 kg – 21.9 kg = 0.3 kg9) 2.98 m less than 3.33 m = 0.35 m 10) $5.09 – $4.99 = $0.10



Try These In Your Head92 – 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?



Check Your Answers92 – 26 = 66745 – 207 = 548860 – 370 = 4908 300 – 2 400 = 5 9005 700 – 680 = 507047 000 – 28 000 = 19 00024 500 – 2 700 = 21 800

How might you use a number line to solve

these problems?


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.



1) 53 – 25 =2) $306 less than $870 = 3) 750 km - 260 = 4) The difference between 640 and 170

= 5) 5 400 minus 1 500 = 6) 71 00 – 2 600 = 7) $8020 minus $3050 = 8) 63 000 – 25 000 = 9) 66 500 km – 18 000 km= 10) 10 600 less than 32 100 =



1) 53 – 25 = 28 2) $306 less than $870 = $5643) 750 km - 260 = 4904) The difference between 640 and 170

= 4705) 5 400 minus 1 500 = 3 9006) 7 100 – 2 600 = 4 5007) $8020 minus $3050 = $50308) 63 000 – 25 000 = 38 0009) 66 500 km – 18 000 km = 48 500 km10) 10 600 less than 32 100 = 21 500



1) 48 – 29 =2) $410 less than $780 = 3) 820 km - 330 = 4) The difference between 530 and 170




1) 48 – 29 = 19 2) $410 less than $780 = $3703) 820 km – 330 km = 490 km 4) The difference between 530 and 170

= 3605) 6 200 minus 2 500 = 3 7006) 4 100 – 1 700 = 2 400 7) $5020 minus $1050 = 3070 8) 83 000 – 24 000 = 59 0009) 12 500 km – 9 600 km = 2 900 km10) 15 000 less than 21 000 = 6 000



1) 78 – 19 =2) $380 less than $540 = 3) 920 km – 230 km = 4) The difference between 450 and 180




1) 78 – 19 = 592) $380 less than $540 = $1603) 920 km – 230 km = 690 km 4) The difference between 450 and 180

= 270 5) 3 400 minus 1 700 = 1 7006) 8 200 – 1 400 = 6 8007) $4030 minus $2050 = 19808) 76 000 – 28 000 = 48 0009) 13 500 km – 8 000 km= 5 500 km10) 24 000 less than 43 000 = 19 000


Strategy IntroCompensation (Subtraction)

Try These In Your Head36 – 8 = 85 – 29 =145 -99 = 750 - 190 = 5 700 – 999= 24 000 – 995 = 47 000 – 19 000 =

How can you tackle eights

and nine?


Strategy IntroCompensation (Subtraction)

Check Your Answers36 – 8 = 2885 – 29 = 56 145 -99 = 46 750 - 190 = 5605 700 – 999= 4 70124 000 – 995 = 23 00547 000 – 19 000 = 28 000


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.


PB 1: Compensation (Subtraction)

1) 92 – 38 = 2) $399 less than $875=3) 298 km fewer than 630 km = 4) 450 – 190 = 5) 5 700 – 997 =6) 4 500 less 1 990 = 7) The difference between $23 000

and $1 997 = 8) 33 000 km – 2980 km = 9) 64 000 minus 9 900= 10)Subtract 29 000 from 92 000 =



1) 92 – 38 = 542) $399 less than $875 = $4763) 298 km fewer than 630 km = 332 km4) 450 – 190 = 3605) 5 700 – 997 = 4 7036) 4 500 less 1 990 = 2 5107) The difference between $23 000

and $1 997 = $21 0038) 33 000 km – 2980 km = 30 020 km9) 64 000 minus 9 900 = 45 10010)Subtract 29 000 from 92 000 = 63 000



1) 72 – 28 = 2) $499 less than $775 =3) 198 km fewer than 540 km = 4) 340 – 180 = 5) 6 500 – 999 =6) 3 500 less 1 998 = 7) The difference between $43 000

and $2 997 = 8) 67 000 km – 5990 km = 9) 86 000 minus 9 000= 10)Subtract 19 000 from 72 000 =


PB 2: Compensation

1) 72 – 28 = 442) $499 less than $775 = $2763) 198 km fewer than 540 km = 341 km4) 340 – 180 = 1605) 6 500 – 999 = 55016) 3 500 less 1 998 = 1 5027) The difference between $43 000

and $2 997 = $40 0038) 67 000 km – 5990 km = 61 0109) 86 000 minus 9 000 = 77 000 10)Subtract 19 000 from 72 000 = 53 000


PB 3: Compensation

1) 58 – 29 = 2) $298 less than $560=3) 498 cm fewer than 940 cm = 4) 240 – 199 = 5) 3 200 – 997 =6) 6 600 less 3 999 = 7) The difference between $41 000

and $9 990 = 8) 99 000 m – 6980 m = 9) 68 000 minus 9 000= 10)Subtract 59 000 from 87 000 =



1) 58 – 29 = 292) $298 less than $560= $2623) 498 cm fewer than 940 cm = 442 cm4) 240 – 199 = 415) 3 200 – 997 = 22036) 6 600 less 3 999 = 2 6017) The difference between $41 000

and $9 990 = $31 0108) 99 000 m – 69980 m = 92 020 9) 68 000 minus 9 000 = 59 00010)Subtract 59 000 from 87 000 = 28 000


Strategy IntroBalancing for a Constant

DifferenceTry These In Your Head87 – 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?



DifferenceCheck Your Answers87 – 19 = 68345 – 198 = 1475 600 – 1 990 = 3 610 7 800 – 3 998 = 3 80445 000 – 19 000 = 46 000 67 000 – 29 999= 37 00152 000 – 9 800 = 42 200


Strategy Balancing for a Constant

DifferenceChanging 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


PB 1: Balancing for a Constant Difference

1) 77 – 39 = 2) $53 – $28 =3) $875 minus $399 = 4) 750 less 290 = 5) 830 decreased by 380 =6) 5 400 – 997 = 7) The difference between $8 500

and $3 900 = 8) 43 000 – 2997 = 9) 66 000 km – 4980 = 10)Subtract 38 000 from 92 000 =



1) 77 – 39 = 382) $53 – $28 = $253) $875 minus $399 = $4744) 750 less 290 = 4605) 830 decreased by 380 = 4506) 5 400 – 997 = 4 4037) The difference between $8 500

and $3 900 = $4 6008) 43 000 – 2997 = 40 0039) 66 000 km – 4980 = 61 02010)Subtract 38 000 from 92 000 = 54 000



1) 54 – 29 = 2) $68 – $49 =3) $540 minus $299 = 4) 870 less 190 = 5) 630 decreased by 270 =6) 6 900 – 998 = 7) The difference between $5 500

and $2 800 = 8) 32 000 – 1997 = 9) 58 000 km – 5980 = 10)Subtract 28 000 from 82 000 =



1) 54 – 29 = 252) $68 – $49 =193) $540 minus $299 = $2414) 870 less 190 = 6805) 630 decreased by 270 = 3606) 6 900 – 998 = 5 902 7) The difference between $5 500

and $2 800 = $2 7008) 32 000 – 1997 = 30 0039) 58 000 km – 5980 = 52 02010)Subtract 28 000 from 82 000 = 54 000



1) 82 – 59 = 2) 48% – 29% =3) $360 minus $299 = 4) 820 less 160 = 5) 500 decreased by 290 =6) 3 900 – 998 = 7) The difference between 7 500 km

and 3 900 km = 8) 23 000 – 1998 = 9) 48 000 km – 2900 = 10)Subtract 17 000 from 65 000 =



1) 82 – 59 = 232) 48% – 29% = 19%3) $360 minus $299 = $614) 820 less 160 = 6605) 500 decreased by 290 = 2106) 3 900 – 998 = 2 9027) The difference between 7 500 km

and 3 900 km = 3 600 km8) 23 000 – 1998 = 21 0029) 48 000 km – 2900 = 45 10010)Subtract 17 000 from 65 000 = 48 000


Strategy IntroQuick Multiplication

Try These In Your Head43 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 than4 x 9.5 ?


Strategy IntroQuick Multiplication

Check Your Answers43 x 2 = 861.42 x 2 = 2.844.2 x 4 = 8.43 x 12.3 = 36.97.2 x 3 = 21.641 x 2 = 8223 x 3 = 66

There is no regrouping to think about.


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.


PB 1: Quick Multiplication

1) 123 x 3 = 2) $3 x $41 =3) 54 times 2= 4) The perimeter of a square with a

side of 3.1 cm = 5) 4 groups of 22 =6) 211 x 3= 7) 4 sets of 121= 8) 2 x 432= 9) 3 times 4324 = 10)The product of 9 times 111=



1) 123 x 3 = 3692) $3 x $41 = 1233) 54 times 2 = 1084) The perimeter of a square with a

side of 3.1 cm = 12.4 cm5) 4 groups of 22 =886) 211 x 3= 6337) 4 sets of 121= 4848) 2 x 432= 8649) 3 times 4321 = 12 96310)The product of 9 times 111= 999



1) 343 x 2 = 2) $2 x $32 =3) 51 times 2= 4) The perimeter of a square with a

side of 1.2 m = 5) 3 groups of 130 =6) 201 x 3= 7) 4 sets of 212= 8) 3 x 132= 9) 2 times 1324 = 10)The product of 5 times 111=



1) 343 x 2 = 6862) $2 x $32 = $643) 51 times 2= 1024) The perimeter of a square with a

side of 1.2 m = 4.8 m5) 3 groups of 130 =3906) 201 x 3= 6037) 4 sets of 212= 8488) 3 x 132= 3969) 2 times 1324 = 264810)The product of 5 times 111= 555



1) 321 x 3 = 2) $3 x $32 =3) 41 times 2 = 4) The perimeter of a square with a

side of 2.11 cm = 5) 3 groups of 23 =6) 423 x 2= 7) 4 sets of 11.2= 8) 2 x 2.33= 9) 2 times 1232 = 10)The product of 7 times 101=



1) 321 x 3 = 3632) $3 x $32 = $963) 41 times 2 = 82 4) The perimeter of a square with a

side of 2.11 cm = 8.44 cm5) 3 groups of 23 = 696) 423 x 2= 8467) 4 sets of 11.2= 44.88) 2 x 2.33= 4.669) 2 times 1232 = 246410)The product of 7 times 101 = 707


Strategy IntroQuick Division

Try These In Your Head640 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 ?


Strategy IntroQuick Division

Check Your Answers640 2 = 3201290 3 = 430360 3 = 1204802 2 = 24017280 8 = 91032.8 4 = 8.224.18 6 = 4.03

They can be solved without regrouping.


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 = 1So… 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


PB 1: Quick Division

1) 68 2 = 2) 5010 5 =3) 186 divided by 6= 4) How many groups of 8 in 1680 = 5) 6036 kg 3 kg = 6) 6309 9= 7) The quotient of 328 cm 4 cm= 8) 153 m 3 m = 9) 4050 5= 10)The length of a side of a square

with a perimeter of 28.4 cm= Created by Tania Colson (2010)


1) 68 2 = 342) 5010 5 =10023) 186 divided by 6 = 314) How many groups of 8 in 1680 = 2105) 6036 kg 3 kg = 2012 kg6) 6309 9= 7017) The quotient of 328 cm 4 cm= 82 cm8) 153 m 3 m = 51 m9) 4050 5 = 81010)The length of a side of a square with a

perimeter of 28.4 cm= 7.1 cm



1) 147 7 = 2) 4040 2 =3) 246 divided by 3= 4) How many groups of 9 in 279 = 5) 8040 kg 4 kg = 6) 729 9 = 7) The quotient of 126 cm 3 cm= 8) 4907 m 7 m = 9) 355 5= 10)The length of a side of a square

with a perimeter of 36.8 cm= Created by Tania Colson (2010)


1) 147 7 = 212) 4040 2 = 20203) 246 divided by 3= 824) How many groups of 9 in 279 = 315) 8040 kg 4 kg = 2010 kg6) 729 9 = 817) The quotient of 126 cm 3 cm= 42 cm8) 4907 m 7 m = 701 m9) 355 5= 71 10)The length of a side of a square with a

perimeter of 36.8 cm= 9.2 cm



1) 287 7 = 2) 164 2 =3) 364 divided by 4= 4) How many groups of 6 in 546 = 5) 2480 kg 8 kg = 6) 5490 9 = 7) The quotient of 1869 cm 3 cm = 8) 2170 km 7 km = 9) 2005 5= 10)The length of a side of a equilateral

triangle with a perimeter of 27.9 m= Created by Tania Colson (2010)


1) 287 7 = 41 2) 164 2 = 82 3) 364 divided by 4= 914) How many groups of 6 in 546 = 915) 2480 kg 8 kg = 310 kg6) 5490 9 = 617) The quotient of 1869 cm 3 cm = 623 cm8) 2170 km 7 km = 310 km9) 2005 5= 40110)The length of a side of a equilateral

triangle with a perimeter of 27.9 m= 9.3 m


Strategy IntroMultiplying by 10, 100 and 1000

Try These In Your Head53 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?


Strategy IntroMultiplying by 10, 100 and 1000

Check Your Answers53 x 10 = 530 10 x 2.5 = 2560 x 100 = 6000 0.6 x 100 = 60120 x 1000 = 120 0008.36 x 1000 = 83600.03 x 1000 = 30

Each digit shifts 1, 2, or 3 places

to the left to have a higher place

value.


Strategy Multiplying by 10, 100 and

1000This 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


PB 1: Multiplying by 10, 100, and 1000

1) 10 x 53 = 2) 92 x 10 =3) 0.3 x 10 = 4) 5 cm = ______ mm 5) $50 x 100 = 6) 100 x 15 = 7) 0.12 m = ______ cm8) 1000 x $73= 9) 9.9 x 1000= 10)234 km = _______m

10 mm = 1 cm100 cm = 1 m1000 m = 1km



1) 10 x 53 = 5302) 92 x 10 =9203) 0.3 x 10 = 34) 5 cm = 50 mm 5) $50 x 100 = $50006) 100 x 15 = 1500 7) 0.12 m = 12cm8) 1000 x $73 = $73 0009) 9.9 x 1000 = 9 90010)234 km = 234 000m

10 mm = 1 cm100 cm = 1 m1000 m = 1km



1) 10 x $56 = 2) 239 x 10 =3) 0.5 x 10 = 4) _____ mg = 16 cg 5) $49 x 100 = 6) 100 x 654 = 7) _____ cm = 0.16 g8) 1000 x $68=9) 5.8 x 1000= 10)471 kg = _____g

10 mg = 1 cg100 cg = 1 g1000 g = 1kg



1) 10 x $56 = $5602) 239 x 10 =23903) 0.5 x 10 = 54) 160 mg = 16 cg 5) $49 x 100 = $4900 6) 100 x 654 = 65 4007) 16 cg = 0.16 g8) 1000 x $68= $68 0009) 5.8 x 1000= 5 80010)471 kg = 471 000 g

10 mg = 1 cg100 cg = 1 g1000 g = 1kg



1) 10 x $48 = 2) 583 x 10 =3) 0.31 x 10 = 4) _____ mm = 39 cm 5) $74 x 100 = 6) 100 x 398 = 7) _____ cm = 0.92 m8) 1000 x $432=9) 4.6 x 1000= 10) 85 km = _____ m

10 mm = 1 cm100 cm = 1 m1000 m = 1km



1) 10 x $48 = $4802) 583 x 10 =58303) 0.31 x 10 = 3.14) 390 mm = 39 cm 5) $74 x 100 = $7400 6) 100 x 398 = 39 8007) 92 cm = 0.92 m8) 1000 x $432 = $432 0009) 4.6 x 1000 = 460010) 85 km = 85 000 m

10 mm = 1 cm100 cm = 1 m1000 m = 1km


Strategy IntroDividing by 0.1, 0.01 and 0.001

Try These In Your Head53 0.1 = 25 0.1 =60 0.01 = 0.6 0.01 = 120 0.001 = 8.36 0.001 = 0.03 0.001 =

How does multiply by 0.1, 0.01 and 0.001


digit?

Warning! Model with Base 10 blocks!


Strategy IntroDividing by 0.1, 0.01 and 0.001

Check Your Answers53 0.1 = 53025 0.1 = 25060 0.01 = 6000 0.6 0.01 = 60120 0.001 = 120 0008.36 0.001 = 83600.03 0.001 = 30

Where have you seen this pattern

before?Click Here!



Strategy Dividing by 0.1, 0.01, and

0.001This 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 ofeach digit by three places to the left. Tack on 3 zeros OR hop the decimal 3 spaces to the right


PB 1: Dividing by 0.1, 0.01, and 0.001

1) 5 0.1 = 2) 23 0.1 =3) How many tenths in two tenths

(0.2)? 4) 5 0.01 =5) How many hundredth in 12? 6) 15 0.01 = 7) How many thousandths in 24? 8) 1000 0.001 =9) 9.7 0.001=10)6.5 0.001 =



1) 5 0.1 = 502) 23 0.1 = 2303) How many tenths in two tenths (0.2)?

24) 5 0.01 = 5005) How many hundredth in 12? 1200 6) 15 0.01 = 15007) How many thousandths in 24? 24 0008) 1000 0.001= 1 000 0009) 9.7 0.001= 970010)6.5 0.001 = 6500



1) 7 0.1 = 2) 34 0.1 =3) How many tenths in five tenths? 4) 7 0.01 =5) How many hundredths in 0.03? 6) 28 0.01 = 7) How many thousandths in 3? 8) 2500 0.001 = 9) 5.4 0.001=10)0.6 0.001 =



1) 7 0.1 = 702) 34 0.1 = 3403) How many tenths in five tenths? 54) 7 0.01 = 7005) How many hundredths in 0.03? 3 6) 28 0.01 = 28007) How many thousandths in 3? 3000 8) 2500 0.001 = 2 500 0009) 5.4 0.001= 5 40010)0.6 0.001 = 600



1) 60 0.1 = 2) 82 0.1 = 3) How many tenths in nine tenths? 4) 40 0.01 =5) How many hundredths in 0.05? 6) 93 0.01 = 7) How many thousandths in 4? 8) 4800 0.001 = 9) 3.7 0.001= 10)0.51 0.001 =



1) 60 0.1 = 6002) 82 0.1 = 8203) How many tenths in nine tenths? 94) 40 0.01 =40005) How many hundredths in 0.05? 56) 93 0.01 = 93007) How many thousandths in 4? 40008) 4800 0.001 = 4 800 0009) 3.7 0.001= 370010)0.51 0.001 = 510


Strategy IntroDividing by 10, 100 and 1000

Try These In Your Head50 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


digit?


Strategy IntroDividing by 10, 100 and 1000

Check Your Answers50 10 = 5640 10 = 64720 10 = 724 500 100 = 452 700 100 = 2771 000 1000 = 71840 000 1000 = 840


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.


PB 1: Dividing by 10, 100, and 1000

1) 53 10 = 2) 290 10 =3) 360 10 = 4) ______ cm = 50 mm 5) 3 00 100 = 6) 4 000 100 = 7) 3 200 cm = _____ m8) 34 000 1000 = 9) 13 000 1000 = 10)_____ km = 4 500 m

10 mm = 1 cm100 cm = 1 m1000 m = 1km



1) 53 10 = 5.32) 290 10 = 293) 360 10 = 364) 5 cm = 50 mm 5) 3 00 100 = 36) 40 000 100 = 407) 3 200 cm = 32 m8) 34 000 1000 = 349) 13 000 1000 = 1310)4.5 km = 4 500 m

10 mm = 1 cm100 cm = 1 m1000 m = 1km



1) 20 10 = 2) 340 10 =3) 760 10 = 4) ______ cL = 980 mL 5) 6 00 100 = 6) 9 000 100 = 7) 4 500 cL = _____ L8) 84 000 1000 = 9) 92 000 1000 = 10)_____ kL = 2 500 L

10 mL = 1 cL100 cL = 1 L1000 L = 1kL



1) 20 10 = 22) 340 10 = 34 3) 760 10 = 76 4) 98 cL = 980 mL 5) 6 00 100 = 66) 9 000 100 = 907) 4 500 cL = 45 L8) 84 000 1000 = 84 9) 92 000 1000 = 9210)2.5 kL = 2 500 L

10 mL = 1 cL100 cL = 1 L1000 L = 1kL



1) 50 10 = 2) 480 10 =3) 950 10 = 4) ______ cg = 920 mg 5) 7 00 100 = 6) 4 000 100 = 7) 8 000 cg = _____ g8) 76 000 1000 = 9) 29 000 1000 = 10)_____ kg = 3 000 g

10 mg = 1 cg100 cg = 1 g1000 g = 1kg



1) 50 10 = 52) 480 10 = 483) 950 10 = 954) 92 cg = 920 mg 5) 7 00 100 = 7 6) 4 000 100 = 407) 8 000 cg = 80 g8) 76 000 1000 = 769) 29 000 1000 = 2910)3 kg = 3 000 g

10 mg = 1 cg100 cg = 1 g1000 g = 1kg


Strategy IntroMultiplying by 0.1, 0.01 and

0.001Try These In Your Head50 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 =



digit?



Strategy IntroMultiplying by 0.1, 0.01 and

0.001Check Your Answers50 x 0.1 = 50.1 x 130 = 1339 x 0.01 = 0.3910 x 0.01 = 0.10900 x 0.001 = 0.93000 x 0.001 = 30.001 x 46 000 = 46



digit?



Strategy Multiplying by 0.1, 0.01 and

0.001This 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.


PB 1: Multiplying by 0.1, 0.01, and 0.01

1) 0.1 x 12 = 2) 5.5 x 0.1 =3) 0.3 x 0.1= 4) 0.1 x 48 =5) 500 x 0.01 = 6) 150 pennies = $______7) 1200 x 0.01 =8) 0.001 x 34 = 9) 990 x 0.001= 10) 3400 x 0.001 =

How many pennies in $1? in $10?



1) 0.1 x 12 = 1.22) 5.5 x 0.1 = 0.553) 0.3 x 0.1= 0.034) 0.1 x 48 = 4.85) 500 x 0.01 = 56) 150 pennies = $1.507) 1200 x 0.01 = 128) 0.001 x 34 = 0.0349) 990 x 0.001= 0.99010) 3400 x 0.001 = 3.4

There are 100 pennies in $1 and 1000 pennies in

$10



1) 0.1 x 8 = 2) 40 x 0.1 =3) 136 x 0.1= 4) 0.1 x 3.2 =5) 600 x 0.01 = 6) 300 pennies = $______7) 1500 x 0.01 =8) 0.001 x 26 = 9) 870 x 0.001= 10) 45 000 x 0.001 =




1) 0.1 x 8 = 0.82) 40 x 0.1 = 43) 136 x 0.1= 13.64) 0.1 x 3.2 =0.325) 600 x 0.01 = 66) 300 pennies = $37) 1500 x 0.01 = 158) 0.001 x 26 = 0.0269) 870 x 0.001= 0.87010) 45 000 x 0.001 = 45




1) 0.1 x 5 = 2) 70 x 0.1 =3) 180 x 0.1= 4) 0.1 x 6.2 =5) 900 x 0.01 = 6) 200 pennies = $______7) 2500 x 0.01 =8) 0.001 x 99 = 9) 720 x 0.001= 10) 84 000 x 0.001 =




1) 0.1 x 5 = 0.52) 70 x 0.1 = 7.03) 180 x 0.1= 18.04) 0.1 x 6.2 = 0.625) 900 x 0.01 = 9.006) 200 pennies = $27) 2500 x 0.01 = 25.008) 0.001 x 99 = 0.0999) 720 x 0.001= 0.72010) 84 000 x 0.001 = 84



Strategy IntroCancelling Common Zeros

Try These In Your Head500 10 = 900 30 = 8000 40 = 12 000 20 = 2000 50 = 18 000 600 = 24 000 300 =

How do you deal with all those

trailing zeros?

Warning! Model Shrinking with Base 10

blocks!


Strategy IntroCancelling Common Zeros

Try These In Your Head500 10 = 50 900 30 = 30 8000 40 = 200 12 000 20 = 6002000 50 = 40018 000 600 = 3024 000 300 = 80

You can cancel common zeros.

Warning! Model Shrinking with Base 10

blocks!


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


PB 1: Cancelling Common Zeros

1) 600 20 = 2) 800 divided by 40 =3) 9000 30 = 4) 9000 300 =5) The quotient of 6900 divided by 30

= 6) 1200 60 =7) 1500 divided by 500 =8) 1800 200 =9) Divide 90 000 by 3000 = 10) 48 000 12 000 =



1) 600 20 = 302) 800 divided by 40 = 203) 9000 30 = 3004) 9000 300 = 305) The quotient of 6900 divided by 30

= 2306) 1200 60 = 207) 1500 divided by 500 = 38) 1800 200 = 99) Divide 90 000 by 3000 = 3010) 48 000 12 000 = 4


Strategy IntroThink Multiplication

Try These In Your Head240 12 = 880 40 = 1470 70 = 3600 12 = 1260 60 = 6000 12 = 6500 50 =

How can knowing your

multiplication facts help you

divide?


Strategy IntroThink Multiplication

Check Your Answers240 12 = 20880 40 = 221470 70 = 213600 12 = 3001260 60 = 216000 12 = 5006500 50 = 130

How can knowing your

multiplication facts help you

divide?


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 40What 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!


PB 1: Think Multiplication

1) 880 40 = 2) How many groups of 70 in 1470?3) 660 60 = 4) 540 90 =5) The quotient of 840 divided by 12 = 6) 450 15 =7) 5400 divided by 30 =8) 2870 70 =9) Divide 49 700 by 700 = 10) 60 000 15 000 =



1) 880 40 = 222) How many groups of 70 in 1470? 213) 660 60 = 114) 540 90 = 65) The quotient of 840 divided by 12 =

706) 450 15 = 307) 5400 divided by 30 =1808) 2870 70 = 219) Divide 49 700 by 700 = 7110) 60 000 15 000 = 4



1) 880 80 = 2) How many groups of 40 in 320?3) 420 20 = 4) 9090 90 =5) The quotient of 480 divided by 12 = 6) 3600 12 =7) 5500 divided by 50 = 8) 2800 70 = 9) Divide 42 700 by 700 = 10) 90 000 15 000 =



1) 880 80 = 222) How many groups of 40 in 320? 83) 420 20 = 214) 9090 90 = 3035) The quotient of 480 divided by 12 =

406) 3600 12 = 3007) 5500 divided by 50 = 1108) 2800 70 = 409) Divide 42 700 by 700 = 6110) 90 000 15 000 = 6



1) 840 40 = 2) How many groups of 70 in 420?3) 420 60 = 4) 450 30 =5) The quotient of 960 divided by 12 = 6) 2400 20 =7) 5400 divided by 60 =8) 2800 70 =9) Divide 21 500 by 500 = 10) 355 000 5 000 =



1) 840 40 = 212) How many groups of 70 in 420? 63) 420 60 = 74) 450 30 =155) The quotient of 960 divided by 12 =

806) 2400 20 = 1207) 5400 divided by 60 = 908) 2800 70 = 409) Divide 21 500 by 500 = 4310) 355 000 5 000 = 71


Strategy IntroCompensation (Multiplication)

Try These In Your Head4.98 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?


Strategy IntroCompensation (Multiplication)

Check Your Answers4.98 X 2 = 9.969.99 x 8 = 79.926.99 x 9 = 62.915.98 x 4 =23.9219.99 x 5 = 99.9549.98 x 6 = 299.88

When buying more that one of

something!


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 9.009 is too much!

3 groups of 0.01 is 0.03

9.00 -0.03 = 8.97


PB 1: Compensation (Multiplication)

1) $1.99 x 2 = 2) $4.98 x 3=3) 5 CDs at $11.99 each totals $_______4) $14.98 x 3 = 5) 6 groups of $24.99 =6) The perimeter of a square with a side

length of 49.99 cm is _______ cm 7) $99.98 x 3 = 8) 5 times $199.98 = 9) $499.99 x 4 = 10)599.98 x 3 =



1) $1.99 x 2 = $3.982) $4.98 x 3= $14.943) 5 CDs at $11.99 each totals $59.954) $14.98 x 3 = $44.945) 6 groups of $24.99 = $149.946) The perimeter of a square with a side

length of 49.99 cm is 199.96 cm 7) $99.98 x 3 = $299.948) 5 times $199.98 = $999.909) $499.99 x 4 = 1999.9610)599.98 x 3 = 1799.94



1) $1.99 x 3 = 2) $3.98 x 2=3) 4 movie passes at $8.99 each totals

$______4) $11.98 x 3 = 5) 8 groups of $19.99 =6) The perimeter of a square with a side




1) $1.99 x 3 = $5.972) $3.98 x 2= $7.963) 4 movie passes at $8.99 each totals

$35.964) $11.98 x 3 = $35.945) 8 groups of $19.99 = $159.926) The perimeter of a square with a side

length of 29.99 cm is 119.96 cm 7) $99.98 x 3 = $299.948) 6 times $299.98 = $179.889) $499.99 x 5 = $2499.9510)599.98 x 2 = 1199.96Created by Tania Colson (2010)


1) $1.99 x 2 = 2) $1.98 x 4=3) 5 value meals at $3.99 each totals $______4) $9.98 x 4 = 5) 5 groups of $19.98 =6) The perimeter of a square with a side




1) $1.99 x 2 = $3.982) $1.98 x 4= $7.923) 5 value meals at $3.99 each totals $19.954) $9.98 x 4 = $39.925) 5 groups of $19.98 = $99.906) The perimeter of a square with a side

length of 8.99 cm is 35.96 cm 7) $99.98 x 2 = $199.968) 7 times $299.98 = $2099.869) $399.99 x 9 = $3599.91 10)999.98 x 2 = 1999.96


Strategy IntroHalving and Doubling

Try These In Your Head42 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?


Strategy IntroHalving and Doubling

Check Your Answers42 x 50 = 2100500 x 88 = 44 00012 x 2.5 = 304.5 x 2.2 = 9.9140 x 35 = 4900200 x 4.5 = 900

Halve the evens, double the odds!


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 10017 times 100 is 1700.


PB 1: Halving and Doubling

1) 86 x 50 = 2) 50 x 28 =3) 64 times 50 = 4) 70 x 500 = 5) 18 x 2.5=6) The area of a garden with

dimensions of 2.5m and 2.2m = 7) 1.5 x 6.6 = 8) The product of 60 and 2.5 = 9) 180 x 45 = 10)160 x 35 =



1) 86 x 50 = 43002) 50 x 28 = 1400 3) 64 times 50 = 32004) 70 x 500 = 35005) 18 x 2.5 = 456) The area of a garden with dimensions

of 2.5m and 2.2m = 5.5m2

7) 1.5 x 6.6 = 9.98) The product of 60 and 2.5 = 1509) 180 x 45 = 810010)160 x 35 = 5600



1) 44 x 50 = 2) 50 x 14 =3) 4 x 13 = 4) 14 x 2.5 = 5) 16 x 2.5 =6) The area of a room with dimensions

of 4.5m and 6 m = 7) 125 x 8 = 8) The product of 6 and 65 = 9) 8 x 225= 10)45 x 4=



1) 44 x 50 = 22002) 50 x 14 = 7003) 4 x 13 = 524) 14 x 2.5 = 355) 16 x 2.5 = 40 6) The area of a room with dimensions

of 4.5m and 6 m = 27m2

7) 125 x 8 = 10008) The product of 6 and 65 = 3909) 8 x 225= 180010)45 x 4= 180



1) 4 x 75= 2) 24 x 5 =3) 12 x 50= 4) 14 x 4.5 = 5) 16 x 3.5 =6) The area of a pool with dimensions

of 3.5m and 6 m = 7) 18 x 35 = 8) The product of 6 and 500 = 9) 8.8 x 500= 10)75 x 6 =



1) 4 x 75 = 3002) 24 x 5 =1203) 12 x 50 = 6004) 14 x 4.5 = 635) 16 x 3.5 = 566) The area of a pool with dimensions

of 3.5m and 6 m = 21m2

7) 18 x 35 = 6308) The product of 6 and 500 = 30009) 8.8 x 500 = 440010)75 x 6 = 450


Strategy IntroFront End Distributative

PrincipleTry These In Your Head62 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!


Strategy IntroFront End Distributative

PrincipleCheck Your Answers62 x 3 = 1864 x 64 = 2562 x 706 = 1412804 x 6 = 48245 x 6 100 = 30 5003 x 3 200 = 9 600


Strategy Front End Distributive

PrincipleFind 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 33 times 50 is 150.

3 times 3 is 9.150 plus 9 is 159.


PB 1: Front End Distributive Principle

1) 62 x 4 = 2) 53 x 3 = 3) 3 x 29 =4) 4 glasses of milk with 250 mL = 5) 503 x 3 = 6) 606 x 6 = 7) 7 groups of 309 = 8) 3 x 4 200 = 9) 5 x 5 100 = 10)4 300 x 2 =



1) 62 x 4 = 2482) 53 x 3 = 1593) 3 x 29 = 874) 4 glasses of milk with 250 mL =

1000 mL5) 503 x 3 = 15156) 606 x 6 = 36367) 7 groups of 309 = 21638) 3 x 4 200 = 12 6009) 5 x 5 100 = 25 50010)4 300 x 2 = 8 600



1) 32 x 4 = 2) 83 x 3 = 3) 92 x 5 = 4) The area of a tile 75mm by 8 mm = 5) 209 x 9 =6) 503 x 2 =7) 122 x 4 = 8) The product of 4 and 2 100 = 9) 4 300 x 2 = 10)2 100 x 7 =



1) 32 x 4 = 1282) 83 x 3 = 2493) 92 x 5 = 45104) The area of a tile 75mm by 8 mm =

600 5) 209 x 9 =18816) 503 x 2 = 10067) 122 x 4 = 4888) The product of 4 and 2 100 = 8 4009) 4 300 x 2 = 8 60010)2 100 x 7 = 14 700



1) 41 x 6 =2) 75 x 3 = 3) 35 x 4 = 4) 703 x 8 = 5) 804 x 6 = 6) 320 x 3 = 7) 3 100 x 6 = 8) 3 x 3 200 = 9) 4 x 4 200 = 10)2 100 x 8 =



1) 41 x 6 = 2462) 75 x 3 = 2253) 35 x 4 = 1404) 703 x 8 = 56245) 804 x 6 = 48246) 320 x 3 = 9607) 3 100 x 6 = 18 6008) 3 x 3 200 = 9 6009) 4 x 4 200 = 16 80010)2 100 x 8 = 16 800


Strategy IntroFinding Compatible Factors

Check Your Answers25 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?


Strategy IntroFinding Compatible Factors

Check Your Answers25 x 63 x 4 = 63002 x 78 x 500 = 78 0005 x 450 x 2 = 450025 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)


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.



1) 5 x 19 x 2 = 2) 2 x 43 x 50 = 3) 4 x 38 x 25 =4) 40 x 25 x 33 = 5) 250 x 56 x 4 = 6) 500 x 86 x 2 = 7) 25 x 32 = 8) 24 x 500 = 9) 250 x 8 = 10)36 x 25 =



1) 5 x 19 x 2 = 1902) 2 x 43 x 50 = 43003) 4 x 38 x 25 = 38004) 40 x 25 x 33 = 33 0005) 250 x 56 x 4 = 56 0006) 500 x 86 x 2 = 86 0007) 25 x 32 = 8008) 24 x 500 = 12 0009) 250 x 8 = 2000 10)36 x 25 = 900



1) 5 x 31 x 2 = 2) 2 x 62 x 50 = 3) 4 x 15 x 25 =4) 40 x 25 x 42 = 5) 250 x 92 x 4 = 6) 500 x 54 x 2 = 7) 25 x 16 = 8) 62 x 500 = 9) 250 x 32 = 10)48 x 25 =



1) 5 x 31 x 2 = 31002) 2 x 62 x 50 = 62003) 4 x 15 x 25 = 15004) 40 x 25 x 42 = 42 0005) 250 x 92 x 4 = 92 0006) 500 x 54 x 2 = 54 0007) 25 x 16 = 4008) 62 x 500 = 31 0009) 250 x 32 = 800010)48 x 25 = 1200



1) 5 x 70 x 2 = 2) 2 x 41 x 50 = 3) 4 x 55 x 25 =4) 40 x 37 x 25= 5) 4 x 38 x 25= 6) 5000 x 9 x 2 = 7) 250 x 24 = 8) 34 x 500 = 9) 250 x 28 = 10)48 x 50 =



1) 5 x 70 x 2 = 7002) 2 x 41 x 50 = 41003) 4 x 55 x 25 = 55004) 40 x 37 x 25= 37 0005) 4 x 38 x 25= 38006) 5000 x 9 x 2 = 90 0007) 250 x 24 = 60008) 34 x 500 = 17 000 9) 250 x 28 = 700010)48 x 50 = 2400


Strategy IntroUsing Division Facts

Try These In Your Head60 3 = 80 4 = 90 3 = 120 6 = 180 9 =250 5 =

How can division facts help you solve these?


Strategy IntroUsing Division Facts

Check Your Answers60 3 = 2080 4 = 40900 3 = 3001200 6 = 20018 000 9 = 2 00025 000 5 = 5 000


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.


PB 1: Using Division Facts

1) 60 2 =

2) 210 7 = 3) 450 9 = 4) 240 6 = 5) 800 4 = 6) 3 500 7 = 7) 1600 4 = 8) 72 000 8 = 9) 24 000 3 = 10)40 000 8 =



1) 60 2 = 30

2) 210 7 = 30

3) 450 9 = 50 4) 240 6 = 405) 800 4 = 2006) 3 500 7 = 5007) 1600 4 = 4008) 72 000 8 = 9 0009) 24 000 3 = 8 00010)40 000 8 = 5 000



1) 80 2 =

2) 210 3 = 3) 450 5 = 4) 240 4 = 5) 800 2 = 6) 3 600 6 = 7) 2800 7 = 8) 54 000 6 = 9) 24 000 8 = 10)42 000 7 =



1) 80 2 = 402) 210 3 = 703) 450 5 = 90 4) 240 4 = 605) 800 2 = 4006) 3 600 6 = 6007) 2800 7 = 4008) 54 000 6 = 9 0009) 24 000 8 = 3 00010)42 000 7 = 6 000



1) 60 2 =

2) 280 4 = 3) 630 9 = 4) 300 6 = 5) 1200 4 = 6) 4900 7 = 7) 2000 4 = 8) 81 000 9 = 9) 56 000 7 = 10)48 000 12 =



1) 60 2 = 302) 280 4 = 703) 630 9 = 704) 300 6 = 505) 1200 4 = 3006) 4900 7 = 7007) 2000 4 = 5008) 81 000 9 = 9 0009) 56 000 7 = 8 00010)48 000 12 = 4 000


Strategy IntroBreaking Up the Dividend


How could you separate the dividend to make it

easier to solve?


Strategy IntroBreaking Up the Dividend

Try These In Your Head372 6 = 496 4 = 576 8 = 380 5 = 438 6=2880 9 =


easier to solve?


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


PB 1: Breaking Up the Dividend

1) 192 3 =

2) 108 4 =

3) 375 5 =4) 285 3 =5) 207 3 =6) 156 2 = 7) 444 6 =8) 264 8 =9) 2910 7 =10)2880 9 =



1) 192 3 = Think (180 +12) = 62

2) 108 4 = Think (100 + 8) = 27

3) 375 5 = Think (350 + 25) = 75

4) 285 3 = Think (270 + 15) = 95

5) 207 3 = Think (180 + 27) = 69

6) 156 2 = Think (140 + 16) = 78

7) 444 6 = Think (420 + 24) = 74

8) 264 8 = Think (240 + 24) = 33

9) 2910 7 = Think (2100 + 210) = 330

10)2880 9 = Think (2700 + 180) = 320



1) 192 3 =2) 228 4 =3) 340 5 =4) 492 6 =5) 371 7 =6) 336 8 =7) 175 5 =8) 1960 4 =9) 7440 8 =10)3450 3 =



1) 192 3 = Think (180 + 12) = 522) 228 4 = Think (200 + 28) = 573) 340 5 = Think (300 + 40) = 684) 492 6 = Think (480 + 12) = 825) 371 7 = Think (350 + 21) = 536) 336 8 = Think (320 + 16) = 427) 175 5 = Think (150 + 25) = 358) 1960 4 = Think (1600 + 360) = 4909) 7440 8 = Think (7200 + 240) = 93010)3450 3 = Think (3300 + 150) =

1150Created by Tania Colson (2010)


1) 282 3 =2) 292 4 =3) 365 5 =4) 438 6 =5) 644 7 =6) 896 8 =7) 585 5 =8) 4960 4 =9) 3520 8 =10)2580 3 =



1) 282 3 = Think (270 + 12) = 822) 292 4 = Think (280 + 12) = 723) 365 5 = Think (350 + 15) = 734) 438 6 = Think (420 + 18) = 735) 644 7 = Think (630 + 14) = 926) 896 8 = Think (880 + 16) = 1127) 585 5 = Think (550 + 35) = 1178) 4960 4 = Think (4800 + 160) = 12209) 3520 8 = Think (3200+ 320) = 44010)2580 3 = Think (2400 + 180) = 830


Strategy IntroCompensation (Division)



easier to solve?


Strategy IntroCompensation (Division)

Check Your Answers304 8 = 38295 5 = 59261 9 = 29228 6 = 38352 4 = 881393 7 = 199


easier to solve?


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.


PB 1: Compensation (Division)

1) 234 3 =

2) 268 4 =

3) 335 5 =4) 291 3 =5) 114 3 =6) 132 2 = 7) 408 6 =8) 624 8 =9) 2086 7 =10)7992 4 =



1) 234 3 = 782) 268 4 = 673) 335 5 = 674) 291 3 = 975) 114 3 = 386) 132 2 = 667) 408 6 = 688) 624 8 = 789) 2086 7 = 29810)7992 4 = 1998



1) 267 3 =2) 152 4 =3) 445 5 =4) 354 3 =5) 891 3 =6) 176 2 = 7) 534 6 =8) 224 8 =9) 7188 6 =10)2792 4 =



1) 267 3 = 892) 152 4 = 383) 445 5 = 894) 354 3 = 1185) 891 3 = 2976) 176 2 = 887) 534 6 = 898) 224 8 = 289) 7188 6 = 119810)2792 4 = 698



1) 197 3 =2) 232 4 =3) 540 5 =4) 264 3 =5) 245 5 =6) 214 2 = 7) 234 6 =8) 544 8 =9) 1798 2 =10)3582 6 =



1) 297 3 = 992) 232 4 = 583) 540 5 = 1084) 264 3 = 885) 245 5 = 496) 214 2 = 1077) 234 6 = 398) 544 8 = 689) 1798 2 = 89910)3582 6 = 597



QuotientTry These In Your Head125 5 = 120 2.5 = 23.5 0.5 = 140 5 = 120 2.5 =135 0.5 =

How could changing the equation make it easier

to solve ?



QuotientCheck Your Answers125 5 = 25120 2.5 = 4823.5 0.5 = 47140 5 = 28300 2.5 = 120135 0.5 = 270

How could changing the equation make it easier

to solve ?


Strategy Balancing for a Constant

QuotientMultiply 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 get240 10.

240 10 = 24


PB 1: Balancing for a Constant Quotient

1) 230 5 =

2) 150 2.5 =

3) 42.5 0.5 =4) 115 5 =5) 300 2.5 =6) 20.5 0.5 = 7) 250 25 =8) 520 5 =9) 30.5 0.5 =10)50 2.5 =



1) 230 5 = 462) 150 2.5 = 603) 42.5 0.5 = 854) 115 5 = 235) 300 2.5 = 1206) 20.5 0.5 = 417) 1200 25 = 488) 520 5 = 1049) 30.5 0.5 = 6110)50 2.5 = 20



1) 140 5 =

2) 125 2.5 =

3) 22.5 0.5 =4) 320 5 =5) 400 2.5 =6) 40.5 0.5 = 7) 500 25 =8) 420 5 =9) 43 0.5 =10) 50 2.5 =



1) 140 5 = 282) 125 2.5 = 503) 22.5 0.5 = 454) 320 5 = 645) 40 2.5 = 166) 40.5 0.5 = 817) 500 25 = 208) 420 5 = 849) 43 0.5 = 8610) 50 2.5 = 20



1) 130 5 = 26 2) 200 2.5 = 803) 14.5 0.5 = 294) 340 5 = 685) 100 2.5 = 406) 20.5 0.5 = 417) 250 25 = 108) 900 5 = 1809) 42.5 0.5 = 85 10) 60 2.5 = 24


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.


Strategy IntroQuick Estimates (Addition and

Subtraction)Try Estimating These In Your Head56 + 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?


Strategy IntroQuick Estimates (Addition and

Subtraction)

Check Your Estimates56 + 42 is about 90 332 + 157 is about 400434 + 272 is about 60098 - 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!


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 + 589Focusing on the front end changes the problem to

100 plus 500, that’s about 600


PB 1: Quick Estimates (Addition & Subtraction)

1) 69 + 32 ~

2) 256 + 980 ~ 3) 457 + 304 ~

4) 545 + 478 ~

5) 5856 + 3437 ~

6) 87 - 72 ~

7) 685 - 129 ~

8) 498 - 280 ~

9) 2348 - 1385 ~

10)9564 - 7431 ~ Created by Tania Colson (2010)


1) 69 + 32 ~ 120

2) 256 + 980 ~ 1100 3) 457 + 304 ~ 700

4) 545 + 478 ~ 900

5) 5856 + 3437 ~ 8000

6) 87 - 72 ~ 10

7) 685 - 129 ~ 500

8) 498 - 280 ~ 200

9) 2348- 1385 ~ 1000

10)9564- 7431 ~ 2000Created by Tania Colson (2010)


1) 54 + 28 ~

2) 294 + 587 ~ 3) 576 + 120 ~

4) 3480 + 2054 ~

5) 2698 + 8371 ~

6) 49 - 16 ~

7) 284 - 107 ~

8) 783 - 330 ~

9) 5954 - 2278 ~



1) 54 + 28 ~ 70

2) 294 + 587 ~ 700 3) 576 + 120 ~ 600

4) 3480 + 2054 ~ 5000

5) 2698 + 8371 ~ 10 000

6) 49 - 16 ~ 30

7) 284 - 107 ~ 100

8) 783 - 330 ~ 400

9) 5954 - 2278 ~ 3000

10)9568 - 6431 ~ 3000Created by Tania Colson (2010)


1) 89 + 56 ~

2) 494 + 687 ~ 3) 576 + 489 ~

4) 8463 + 2948 ~

5) 6062 + 6872 ~

6) 67 - 18 ~

7) 484 - 290 ~

8) 1283 - 430 ~

9) 5760 - 2021 ~



1) 89 + 56 ~ 130

2) 494 + 687 ~ 1000 3) 576 + 489 ~ 900

4) 8463 + 2948 ~ 10 000

5) 6062 + 6872 ~ 12 000

6) 67 - 18 ~ 50

7) 484 - 290 ~ 200

8) 1283 - 430 ~ 800

9) 5760 - 2021 ~ 3000

10)8220 - 7401 ~ 1000Created by Tania Colson (2010)

Strategy IntroQuick Estimates (Multiplication)

Try Estimating These In Your Head56 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 ___


end!


Strategy IntroQuick Estimates (Multiplication)

Check Your Estimates56 x 4 is about 20033 x 5 is about 150 43 x 72 is about 2800 808 x 24 is about 16 000459 x 26 is about 8 000 358 x 86 is about 24 000


end!


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.


PB 1: Quick Estimates (Multiplication)

1) 69 x 32 ~

2) 25 x 70 ~ 3) 57 x 34 ~

4) 46 x 48 ~

5) 235 x 34 ~

6) 874 x 72 ~

7) 685 x 12 ~

8) 498 x 280 ~

9) 234 x 138 ~

10)956 x 743 ~ Created by Tania Colson (2010)


1) 69 x 32 ~ 1800

2) 25 x 70 ~ 1400 3) 57 x 34 ~ 1500

4) 46 x 48 ~ 1600

5) 235 x 34 ~ 6 000

6) 874 x 72 ~ 56 000

7) 685 x 12 ~ 6 000

8) 498 x 280 ~ 80 000

9) 234 x 138 ~ 20 000

10)956 x 743 ~ 630 000Created by Tania Colson (2010)


1) 34 x 53 ~

2) 46 x 37 ~ 3) 55 x 25 ~

4) 86 x 49 ~

5) 231 x 47 ~

6) 854 x 55 ~

7) 653 x 25 ~

8) 732 x 584 ~

9) 254 x 558 ~



1) 34 x 53 ~ 1500

2) 46 x 37 ~ 1200

3) 55 x 25 ~ 1000

4) 86 x 49 ~ 2400

5) 231 x 47 ~ 8 000

6) 854 x 55 ~ 45 000

7) 653 x 25 ~ 12 000

8) 732 x 584 ~ 350 000

9) 254 x 558 ~ 100 000



1) 35 x 56 ~

2) 47 x 87 ~ 3) 85 x 45 ~

4) 48 x 59 ~

5) 345 x 51 ~

6) 451 x 65 ~

7) 354 x 85 ~

8) 485 x 932 ~

9) 858 x 358 ~



1) 35 x 56 ~ 1500

2) 47 x 87 ~ 2400

3) 85 x 45 ~ 2400

4) 48 x 59 ~ 2000

5) 345 x 51 ~ 15 000

6) 451 x 65 ~ 24 000

7) 354 x 85 ~ 24 000

8) 485 x 932 ~ 360 000

9) 858 x 358 ~ 240 000


Strategy IntroRounding (Addition & Subtraction)

Try Estimating These In Your Head56 + 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?


Strategy IntroRounding (Addition & Subtraction)

Check Your Estimates56 + 42 is about 90 332 + 157 is about 400434 + 272 is about 60098 - 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?


Strategy Rounding (Addition &

Subtraction) There are 2 basic ways to round numbers to estimate an answer. This works for addition,subtraction, multiplication and division.

1.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

2.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


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)


PB 1: Rounding (Addition & Subtraction)

1) 69 + 32 ~

2) 256 + 980 ~ 3) 457 + 304 ~

4) 545 + 478 ~

5) 5856 + 3437 ~

6) 87 - 72 ~

7) 685 - 129 ~

8) 498 - 280 ~

9) 2348 - 1385 ~


PB 1: Rounding(Addition & Subtraction)

1) 69 + 32 ~ 70 + 30 ~ 100

2) 256 + 980 ~ 300 + 1000 ~ 1300

3) 457 + 304 ~ 500 + 300 ~ 800

4) 545 + 478 ~ 500 + 500 ~ 1000

5) 5856 + 3437 ~ 6000 + 3000 ~ 9000

6) 87 - 72 ~ 90 – 70 ~ 20

7) 685 - 129 ~ 700 – 100 ~ 600

8) 498 - 280 ~ 500 – 300 ~ 200

9) 2348- 1385 ~ 2000 – 1000 ~ 1000

10)9564- 7431 ~ 10 000 – 7000 ~ 3000Created by Tania Colson (2010)


1) 54 + 28 ~

2) 294 + 587 ~ 3) 576 + 120 ~

4) 3480 + 2054 ~

5) 2698 + 8371 ~

6) 49 - 16 ~

7) 284 - 107 ~

8) 783 - 330 ~

9) 5954 - 2278 ~



1) 54 + 28 ~ 50 + 30 ~ 80

2) 294 + 587 ~ 300 + 600 ~ 900 3) 576 + 120 ~ 600 + 100 ~ 700

4) 3480 + 2054 ~ 3000 + 2000 ~ 5000

5) 2698 + 8371 ~ 3000 + 8000 ~ 11 000

6) 49 - 16 ~ 50 – 20 ~ 30

7) 284 - 107 ~ 300 – 100 ~ 200

8) 783 - 330 ~ 800 – 300 ~ 500

9) 5954 - 2278 ~ 6000 – 2000 ~ 4000

10)9568 - 6431 ~ 10 000 – 6000 ~ 4000Created by Tania Colson (2010)

PB 3: Rounding (Addition & Subtraction)

1) 89 + 56 ~

2) 494 + 687 ~ 3) 576 + 489 ~

4) 8463 + 2948 ~

5) 6062 + 6872 ~

6) 67 - 18 ~

7) 484 - 290 ~

8) 1283 - 430 ~

9) 5760 - 2021 ~



1) 89 + 56 ~ 90 + 60 ~ 150

2) 494 + 687 ~ 500 + 700 ~ 1200 3) 576 + 489 ~ 600 + 500 ~ 1100

4) 8463 + 2948 ~ 8000 + 3000 ~ 11 000

5) 6062 + 6872 ~ 6000 + 7000 ~ 13 000

6) 67 - 18 ~ 70 - 20 ~ 50

7) 484 - 290 ~ 500 – 300 ~ 200

8) 1283 - 430 ~ 1000 – 400 ~ 800

9) 5760 - 2021 ~ 6000 – 2000 ~ 4000

10)8220 - 7401 ~ 8000 – 7000 ~ 1000 Created by Tania Colson (2010)

Strategy IntroRounding (Multiplication)

Try Estimating These In Your Head56 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!


Strategy IntroRounding (Multiplication)

Check Your Estimates56 x 4 is about 60 x 4 ~ 24033 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 000459 x 25 is about 500 x 20 ~ 10 000 358 x 85 is about 400 x 80 ~ 32 000


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.


PB 1: Rounding (Multiplication)

1) 69 x 32 ~

2) 25 x 70 ~ 3) 57 x 34 ~

4) 46 x 48 ~

5) 235 x 34 ~

6) 874 x 72 ~

7) 685 x 12 ~

8) 498 x 280 ~

9) 234 x 138 ~



1) 69 x 32 ~ 70 x 30 ~ 2100

2) 25 x 70 ~ 30 x 70 ~ 2100 3) 57 x 34 ~ 60 x 30 ~ 1800

4) 46 x 48 ~ 50 x 50 ~ 2500

5) 235 x 34 ~ 200 x 30 ~ 6000

6) 874 x 72 ~ 900 x 70 ~ 63 000

7) 685 x 12 ~ 700 x 10 ~ 7 000

8) 498 x 280 ~ 500 x 300 ~ 150 000

9) 234 x 138 ~ 200 x 100 ~ 20 000

10)956 x 743 ~ 1000 x 700 ~ 700 000 Created by Tania Colson (2010)


1) 34 x 53 ~

2) 46 x 37 ~ 3) 55 x 25 ~

4) 86 x 49 ~

5) 231 x 47 ~

6) 854 x 55 ~

7) 653 x 25 ~

8) 732 x 584 ~

9) 254 x 558 ~



1) 34 x 53 ~ 30 x 50 ~ 1500

2) 46 x 37 ~ 50 x 40 ~ 2000

3) 55 x 25 ~ 60 x 20 ~ 1200

4) 86 x 49 ~ 90 x 50 ~ 4500

5) 231 x 47 ~ 200 x 50 ~ 10 000

6) 854 x 55 ~ 900 x 50 ~ 45 000

7) 653 x 25 ~ 700 x 20 ~ 14 000

8) 732 x 584 ~ 700 x 600 ~ 420 000

9) 254 x 558 ~ 300 x 500 ~ 15 000

10)836 x 653 ~ 800 x 700 ~ 560 000 Created by Tania Colson (2010)


1) 35 x 56 ~

2) 47 x 87 ~ 3) 85 x 45 ~

4) 48 x 59 ~

5) 345 x 51 ~

6) 451 x 65 ~

7) 354 x 85 ~

8) 485 x 932 ~

9) 858 x 358 ~



1) 35 x 56 ~ 40 x 50 ~ 2000

2) 47 x 87 ~ 50 x 90 ~ 4500

3) 85 x 45 ~ 90 x 40 ~ 3600

4) 48 x 59 ~ 50 x 60 ~ 3000

5) 345 x 51 ~ 300 x 50 ~ 15 000

6) 451 x 65 ~ 500 x 60 ~ 30 000

7) 354 x 85 ~ 400 x 80 ~ 32 000

8) 485 x 932 ~ 500 x 900 ~ 450 000

9) 858 x 358 ~ 900 x 300 ~ 270 000

10)826 x 458 ~ 800 x 500 ~ 400 000Created by Tania Colson (2010)

Strategy IntroAdjusted Front End (Division)

Try Estimating These In Your Head56 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?


Strategy IntroAdjusted Front End (Division)

Check Your Estimates56 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 ~ 74692 86 is about 4800 80 3582 96 is about ___


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.

Itdoes 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.


PB 1: Adjusted Front End (Division)

1) 46 4 ~ 48 4 ~ 12

2) 57 6 ~ 60 6 ~ 10

3) 209 3 ~ 210 30 ~ 7

4) 269 7 ~ 280 7 ~ 40

5) 235 3 ~ 240 3 ~ 80

6) 874 7 ~ 840 7 ~ 120

7) 585 12 ~ 600 12 ~ 50

8) 498 28 ~ 480 20 ~ 24

9) 234 64 ~ 240 60 ~ 4

10)956 47 ~ 800 4 ~ 200Created by Tania Colson (2010)


1) 46 4 ~ 48 4 ~ 12

2) 57 6 ~ 60 6 ~ 10

3) 209 3 ~ 210 30 ~ 7

4) 269 7 ~ 280 7 ~ 40

5) 235 3 ~ 240 3 ~ 80

6) 874 7 ~ 840 7 ~ 120

7) 585 12 ~ 600 10 ~ 60

8) 498 28 ~ 480 20 ~ 24

9) 234 64 ~ 240 60 ~ 4



1) 53 6 ~ 54 6 ~ 9 4 ~ 12

2) 47 2 ~ 48 2 ~ 24

3) 317 3 ~ 330 3 ~ 110210 30 ~ 7

4) 269 5 ~ 250 5 ~ 50280 7 ~ 40

5) 273 4 ~ 280 4 ~ 70 3 ~ 80

6) 874 8 ~ 880 8 ~ 110 7 ~ 120

7) 427 12 ~ 400 10 ~ 40 12 ~ 50

8) 498 59 ~ 480 20 ~ 24

9) 234 64 ~ 240 60 ~ 4


created by tania colson (2010). mental math routine focus on 1-2 strategies each week practiced 3 to...

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