Have a Math weekend

MENTAL MATH

MENTAL MATH

A. Addition — Fact Learning 

It is important to note here that by grade 6, students should have mastered their addition, 

subtraction, multiplication and division number facts. If there are students who have not done this, it 

is necessary to go back to where the fact learning strategies are introduced and to work from those 

students are comfortable. 

See grade 5 for the grade 6 review. 

 

B. Addition and Subtraction — Mental Calculation 

Quick Addition and Subtraction – No Regrouping: 

This pencil-and-paper strategy is used when there are more than two combinations in the 

calculations, but no regrouping is needed and the questions are presented visually instead of orally. It 

is included here as a mental math strategy because students will do all the combinations in their heads 

starting at the front end. It is important to present these addition questions both horizontally and 

vertically. 

Examples 

For example: For 2.327 + 1.441, simply record, starting at the front end, 3.768. 

For example: For 7.593 – 2.381, simply record, starting at the front end, 5.212. 

Some examples of practice items 

Some practice items for numbers in the thousandths are: 

 7.406 + 2.592 = 4.234 + 2.755 = 12.295 + 7.703 

 6.234 + 2.604 = 32.107 + 10.882 = 100.236 + 300.543 = 

 8.947 – 2.231 = 7.076 – 3.055 = 12.479 – 1.236 = 

 0.735 – 0.214 = 96.983 – 12.281 = 125.443 – 25.123 = 

 

C. Multiplication and Division — Mental Calculation 

Some of the following material is review from grade 5, but it is necessary to include it here to 

consolidate the understanding of multiplying by tenths, hundredths and thousandths; the related 

division by tens, hundreds and thousands; the reverse of multiplying by tens, hundreds and 

thousands; the related division by tenths, hundredths and thousandths. 

Quick Multiplication – No Regrouping 

Note: This pencil-and-paper strategy is used when there is no regrouping and the questions are 

presented visually instead of orally. It is included here as a mental math strategy because students will 

do all the combinations in their heads starting at the front end. 

Examples 

For example: For 52 × 3, simply record, starting at the front end, 150 + 6 = 156. 

For example: Foe 423 × 2, simply record, starting at the front end, 800 + 40 + 6 = 846. 

 

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 MENTAL MATH 

 

 

Some examples of practice items 

Here are some practice items. 

 43 × 2 = 72 × 3= 84 × 2 = 

 142 × 2 = 803 × 3 = 342 × 2 = 

 12.3 × 3 = 14 3 × 2 = 63 000 × 2 = 

 1 220 × 3 = 42 000 × 4 = 43.42 × 2 = 

Quick Division – No Regrouping 

Note: This pencil-and-paper strategy is used when there is no regrouping and the questions are 

presented visually instead of orally. It is included here as a mental math strategy because students will 

do all of the combinations in their heads starting at the front end. 

Examples 

For 640 ÷ 2, simply record, starting at the front end, 300 + 20 = 320. 

For 1 290 ÷ 3, simply record, starting at the front end, 400 + 30 = 430. 

Some examples of practice items 

Here are some practice items. 

 360 ÷ 3 = 420 ÷ 2 = 707 ÷ 7 = 

 105 ÷ 5 = 426 ÷ 6 = 320 ÷ 8 = 

 490 ÷ 7 = 505 ÷ 5 = 819 ÷ 9 = 

 328 ÷ 4 = 103 ÷2 = 455 ÷ 5 = 

 2 107 ÷ 7 = 7 280 ÷ 8 = 3 570 ÷ 7 = 

 3 612 ÷ 6 = 248 000 ÷ 8 = 279 000 ÷ 9 = 

Multiplying & Dividing by 10, 100 and 1000 

Multiplication: This strategy involves keeping track of how the place values have changed. 

Multiplying by 10 increases all the place values of a number by one place . For 10 × 67, think: the 6 

tens will increase to 6 hundreds and the 7 ones will increase to 7 tens; therefore, the answer is 670. 

Multiplying by 100 increases all the place values of a number by two places. For 100 × 86, think: the 

8 tens will increase to 8 thousands and the 6 ones will increase to 6 hundreds; therefore, the answer is 

8 600. It is necessary that students use the correct language when orally answering questions where 

they multiply by 100. For example, the answer to 100 × 86 should be read as 86 hundred and not 8 

thousand 6 hundred. 

Multiplying by1000 increases all the place values of a number by three places. For 1000 × 45, think: 

the 4 tens will increase to 40 thousands and the 5 ones will increase to 5 thousands; therefore, the 

answer is 45 000. It is necessary that students use the correct language when orally answering 

questions where they multiply by 1000. For example the answer to 1000 × 45 should be read as 45 

thousand and not 4 ten thousands and 5 thousand. 

 

6 MENTAL COMPUTATION GRADE 6 — DRAFT SEPTEMBER 2006 

 

  

 MENTAL MATH

 

Some examples of practice items 

Some mixed practice items are: 

 10 × 53 = 10 × 34 = 87 × 10 = 

 10 × 20 = 47 × 10 = 78 × 10 = 

 92 × 10 = 10 × 66 = 40 × 10 = 

 100 × 7 = 100 × 2 = 100 × 15 = 

 100 × 74 = 100 × 39 = 37 × 100 = 

 10 × 10 = 55 × 100 = 100 × 83 = 

 100 × 70 = 90 × 90 = 40 × 100 = 

 1 000 × 6 = 1 000 × 14 = 83 × 1 000 = 

 $73 × 1 000 = $20 × 1 000 = 16 × $1 000 = 

 5m = ___ cm 8m = ___cm 3m =___cm 

 $3 × 10 = $7 × 10 = $50 × 10 = 

 3 m = _____mm 7m = ____ 4.2m = ___m 

 6.2m = ____mm 6cm = ___mm 9km = ____m 

 7.7km = ____m 3dm = ____mm 3dm = ____ cm 

 10 × 3.3 = 4.5 × 10 = 0.7 × 10 = 

 8.3 × 10 = 7.2 × 10 = 10 × 4.9 = 

 100 × 2.2 = 100 × 8.3 = 100 × 9.9 = 

 7.54 × 10 = 8.36 x10 = 10 × 0.3 = 

 100 × 0.12 = 100 × 0.41 = 100 × 0.07 = 

 3.78 × 100 = 1 000 × 2.2 = 1 000 × 43.8 = 

 1 000 × 5.66 = 8.02 × 1 000 = 0.04 × 1 000 = 

Dividing by tenths (0.1), hundredths (0.01) and thousandths (0.001) 

When students fully understand decimal tenths and hundredths, they will be able to use this 

knowledge in understanding multiplication and division by tenths and hundredths in mental math 

situations. 

Multiplying by 10s, 100s and 1 000s, is similar to dividing by tenths, hundredths and thousandths. 

1) Dividing by tenths increases all the place values of a number by one place. 

2) Dividing by hundredths increases all the place values of a number by two places. 

Examples 

1) For 3 ÷ 0.1, think: the 3 ones will increase to 3 tens, therefore the answer is 30. 

For 0.4 ÷ 0.1, think: the 4 tenths will increase to 4 ones, therefore the answer is 4. 

2) For 3 × 0.01, think: the 3 ones will increase to 3 hundreds, therefore the answer is 300. 

For 0.4 ÷ 0.01, think: the 4 tenths will increase to 4 tens, therefore the answer is 40. 

For 3.7 ÷ 0.01, think: the 3 ones will increase to 3 hundreds and the 7 tenths will increase 

to 7 tens, therefore, the answer is 37. 

 

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 MENTAL MATH 

 

 

Some examples of practice items 

1) Here are some practice items: 

 5 ÷ 0.1 = 7 ÷ 0.1 = 23 ÷ 0.1 = 

 46 ÷ 0.1 = 0.1 ÷ 0.1 = 2.2 ÷ 0.1 = 

 0.5 ÷ 0.1 = 1.8 ÷ 0.1 = 425 ÷ 0.1 = 

 0.02 ÷ 0.1 = 0.06 ÷ 0.1 = 0.15 ÷ 0.1 = 

 14.5 ÷ 0.1 = 1.09 ÷ 0.1 = 253.1 ÷ 0.1 = 

2) Here are some practice items: 

 4 ÷ 0.01 = 7 ÷ 0.01 = 4 ÷ 0.01 = 

 1 ÷ 0.01 = 9 ÷ 0.01 = 0.5 ÷ 0.01 = 

 0.2 ÷ 0.01 = 0.3 ÷ 0.01 = 0.1 ÷ 0.01 = 

 0.8 ÷ 0.01 = 5.2 ÷ 0.01 = 6.5 ÷ 0.01 = 

 8.2 ÷ 0.01 = 9.7 ÷ 0.01 = *17.5 ÷ 0.01 = 

Dividing by Ten, Hundred and Thousand 

Division: This strategy involves keeping track of how the place values have changed. 

Dividing by10 decreases all the place values of a number by one place. 

Dividing by 100 decreases all the place values of a number by two places. 

Dividing by 1000 decreases all the place values of a number by three places. 

Examples 

For 340 ÷ 10, think: the 3 hundreds will decrease to 3 tens and the 4 tens will decrease to 4 

ones; therefore, the answer is 34. 

For, 7 500 ÷ 100; think: the 7 thousands will decrease to 7 tens and the 5 hundreds will 

decrease to 5 ones; therefore, the answer is 75. 

For, 63 000 ÷ 1000; think: the 6 ten thousands will decrease to 6 tens and the 3 thousands 

will decrease to 3 ones; therefore, the answer is 63. 

Some examples of practice items 

Here are some mixed practice items: 

 80 ÷ 10 = 60 ÷ 10 = 100 ÷ 10 = 

 420 ÷ 10 = 790 ÷ 10 = 360 ÷ 10 = 

 1 200 ÷ 10 = 4 400 ÷ 10 = 900 ÷ 100 = 

 700 ÷ 100 = 3 000 ÷ 100 = 4 000 ÷ 100 = 

 2 400 ÷ 100 = 3 800 ÷ 100 = 37 000 ÷ 100 = 

 7 000 ÷ 1 000 = 34 000 ÷ 1 000 = 29 000 ÷ 1 000 = 

 80 000 ÷ 1 000 = 96 000 ÷ 1 000 = 100 000 ÷ 1 000 = 

 2 000 ÷ 1 000 = 13 000 ÷ 1 000 = 750 000 ÷ 1 000 = 

 

8 MENTAL COMPUTATION GRADE 6 — DRAFT SEPTEMBER 2006 

 

  

 MENTAL MATH

 

Division when the divisor is a multiple of 10 and the dividend is a 

multiple of the divisor. 

Division by a power of ten should be understood to result in a uniform “shrinking” of hundreds, tens 

and units which could be demonstrated and visualized with base -10 blocks. 

Example 

For 400 ÷ 20, think: 400 shrinks to 40 and 40 divided by 2 is 20. 

Some examples of practice items 

Here are some practice items: 

 500 ÷ 10= 700 ÷ 10 = 900 ÷ 10 = 

 900 ÷ 30 = 600 ÷ 20 = 4 000 ÷ 10 = 

 8 000 ÷ 40 = 120 ÷ 10 = 240 ÷ 40 = 

 12 000 ÷ 20 = 2 000 ÷ 50 = 18 000 ÷ 600 = 

Division using the Think Multiplication strategy. 

This is a convenient strategy to use when dividing mentally. For example, when dividing 60 by 12, 

think: “What times 12 is 60?” 

This could be used in combination with other strategies. 

Example 

For 920 ÷ 40, think: “20 groups of 40 would be 800, leaving 120, which is 3 more groups 

of 40 for a total of 23 groups. 

Some examples of practice items 

Some practice items are: 

 240 ÷ 12 = 3 600 ÷ 12 = 660 ÷ 30 = 

 880 ÷ 40 = 1 260 ÷ 60 = 690 ÷ 30 = 

 1 470 ÷ 70 = 6 000 ÷ 12 = 650 ÷ 50 = 

Multiplication and Division of tenths, hundredths and thousandths. 

Multiplying by tenths, hundredths and thousandths is similar to dividing by tens, hundreds and 

thousands. 

This strategy involves keeping track of how the place values have changed. 

1) Multiplying by 0.1 decreases all the place values of a number by one place. 

2) Multiplying by 0.01 decreases all the place values of a number by two places. 

3) Dividing by 100 decreases all the place values of a number by two places. 

4) Multiplying by 0.001 decreases all the place values of a number by three places. 

5) Dividing by 1000 decreases all the place values of a number by three places . 

 

 

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 MENTAL MATH 

 

 

Example 

1) For 5 × 0.1, think: the 5 ones will decrease to 5 tenths; therefore, the answer is 0.5. 

For, 0.4 × 0.1, Think: the 4 tenths will decrease to 4 hundredths, therefore the answer is 

0.04. 

2) For 5 × 0.01, think: the 5 ones will decrease to 5 hundredths, therefore the answer is 0.05. 

For, 0.4 × 0.01, think: the 4 tenths will decrease to 4 thousandths, therefore the answer is 

0.004. 

3) For, 7 500 ÷ 100; think: the 7 thousands will decrease to 7 tens and the 5 hundreds will 

decrease to 5 ones; therefore, the answer is 75. This is an opportunity to show the 

relationship between multiplying by one hundredth and dividing by 100. 

4) For 5 × 0.001, think: the 5 ones will decrease to 5 thousandths; therefore, the answer is 

0.005. 

For, 8 × 0.001, think: the 8 ones will decrease to 8 thousandths; therefore, the answer is 

0.008. 

5) For, 75 000 ÷ 1000; think: the 7 ten thousands will decrease to 7 tens and the 5 thousands 

will decrease to 5 ones; therefore, the answer is 75. This is an opportunity to show the 

relationship between multiplying by one thousandth and dividing by 1000. 

Some examples of practice items 

1) Tenths 

 6 × 0.1 = 8 × 0.1 = 3 × 0.1 = 

 9 × 0.1 = 1 × 0.1 = 12 × 0.1 = 

 72 × 0.1 = 136 × 0.1 = 406 × 0.1 = 

 0.7 × 0.1 = 0.5 × 0.1 = 0.1 × 10 = 

 1.6 × 0.1 = 0.1 × 84 = 0.1 × 3.2 = 

2) Hundredths: 

 6 × 0.01 = 8 × 0.01 = 1.2 × 0.01 = 

 0.5 × 0.01 = 0.4 × 0.01 = 0.7 × 0.01 = 

 2.3 × 0.01 = 3.9 × 0.01 = 10 × 0.01 = 

 100 × 0.01 = 330 × 0.01 = 46 × 0.01 = 

3) Here are some practice items: 

 400 ÷ 100 = 900 ÷ 100 = 6 000 ÷ 100 = 

 4 200 ÷ 100 = 7 600 ÷ 100 = 8 500 ÷ 100 = 

 9 700 ÷ 100 = 4 400 ÷ 100 = 10 000 ÷ 100 = 

 600 pennies = $_____ 1 800 pennies =$_____ 56 000 pennies = $____ 

4) Her are some practice items: 

3 × 0.001 = 7 × 0.001 = 80 × 0.001 = 

21 × 0.001 = 45 × 0.001 = 12 × 0.001 = 

600 × 0.001 = 325 × 0.001 = 4 261 × 0.001 = 

4mm = ____m 9mm = _____m 6m = ____km 

 

10 MENTAL COMPUTATION GRADE 6 — DRAFT SEPTEMBER 2006 

 

  

 MENTAL MATH

 

5) Here are some practice items: 

82 000 ÷ 1 000 = 98 000 ÷ 1 000 = 12 000 ÷ 1 000 = 

66 000 ÷ 1 000 = 70 000 ÷ 1 000 = 100 000 ÷ 1 000 = 

430 000 ÷ 1 000 = 104 000 ÷ 1 000 = 4 500 ÷ 1 000 = 

77 000m = _____km 84 000m = ____km 7 700m = _____km