reasoning & problem solving · multiply by 10, 100 and 1,000 fluency & precision 6 lesson 2...
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Fluency & PrecisionMultiply by 10, 100 and 1,000 6
Lesson 2 – Number Decimals - Multiply by 10, 100 and 1,000
NC Objective:Identify the value of each digit in numbers given to 3 decimal places and multiply numbers by 10, 100 and 1,000 giving answers up to 3 decimal places.Multiply 1-digit numbers with up to 2 decimal places by whole numbers.
Resources needed:Differentiated SheetsTeaching Slides
Vocabulary:Decimals, Place Value, Tenths, Hundredths, Thousandths, Multiply, Multiples, Gattengno
Children multiply numbers with up to three decimal places by 10, 100 and 1,000.They discover that digits move to the left when they are multiplying and use zero as a place value holder. The decimal point does not move. Once children are confident in multiplying by 10, 100 and 1,000, they use these skills to investigate multiplying by multiples of these numbers e.g. 2.4 × 20.
Key Questions:What number is represented on the place value chart? Why is 0 important when multiplying by 10, 100 and 1,000? What patterns do you notice? What is the same and what is different when multiplying by 10, 100, 1,000 on the place value chart compared with the Gattegno chart?
Children on this sheet have a place value grid with spaces to write the number to help them understand the number. They can use a place value chart with counters alongside the worksheet. Children do not have missing numbers and explore multiples of the same calculation.
Children on this sheet have a place value grid and can use one with counters if needed. Children have missing numbers and explore multiplying a number with decimals by multiples of 10,100 and 1,000.
Children on this sheet are confident multiplying by 10, 100 and 1,000. They multiply multiples of these numbers.
Reasoning & Problem Solving
Working Towards Working Within Greater Depth
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Fluency & Precision 6Multiply by 10, 100 and 1,000
The number represented on the place value chart is: ____________________
Tens Ones Tenths Hundredths Thousandths
___________ multiplied by ten equals ___________ ___________ multiplied by one hundred equals __________
___________ multiplied by one thousand equals __________
The number represented on the place value chart is: ____________________
___________ x 10 = ___________ ___________ x 100 = __________ ___________ x 1,000 = __________
2.442 x 100 =
Identify the number represented and multiply it correctly.
The number represented on the place value chart is: ____________________
Hundreds Tens Ones Tenths Hundredths
___________ x 10 = ___________ ___________ x 100 = __________ ___________ x 1,000 = __________
Tens Ones Tenths Hundredths Thousandths
2.442 x 200 =
1.53 x 10 =
1.53 x 20 =
3.2 x 1000 =
3.2 x 2000 =
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Fluency & Precision 6AnswersMultiply by 10, 100 and 1,000
The number represented on the place value chart is: ____________________
Tens Ones Tenths Hundredths Thousandths
___________ multiplied by ten equals ___________ ___________ multiplied by one hundred equals __________
___________ multiplied by one thousand equals __________
The number represented on the place value chart is: ____________________
___________ x 10 = ___________ ___________ x 100 = __________ ___________ x 1,000 = __________
2.442 x 100 =
Identify the number represented and multiply it correctly.
1.213
1.213 12.13 1.213 121.3
12131.213
10.431
10.431 104.31 10.431 1,043.1 10.431 10,431
The number represented on the place value chart is: ____________________
Hundreds Tens Ones Tenths Hundredths
___________ x 10 = ___________ ___________ x 100 = __________ ___________ x 1,000 = __________
322.45
322.45 3,224.5 322.45 32,245 322.45 322,450
Tens Ones Tenths Hundredths Thousandths
1 2 1 3
1 0 4 3 1
3 2 2 4 5
2.442 x 200 =
1.53 x 10 =
1.53 x 20 =
3.2 x 1000 =
3.2 x 2000 =
244.2
488.4
15.3
30.6
3200
6400
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Fluency & Precision 6Multiply by 10, 100 and 1,000
The number represented on the place value chart is: ____________________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
___________ multiplied by ten equals ___________ ___________ multiplied by one hundred equals __________
___________ multiplied by one thousand equals __________
The number represented on the place value chart is: ____________________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
___________ x 10 = ___________ ___________ x 100 = __________ ___________ x 1,000 = __________
x 26.96 = 26,960 x 0.234 = 2.34 x 33.02 = 3302
1,000 x = 2050 42.603 x = 426.03 10 x = 4562.3
2.2 x = 44 x 200 = 644 x 2.001 = 8004
Identify the number represented and multiply it correctly.
The number represented on the place value chart is: ____________________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
___________ x 10 = ___________ ___________ x 100 = __________ ___________ x 1,000 = __________
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Fluency & Precision 6AnswersMultiply by 10, 100 and 1,000
The number represented on the place value chart is: ____________________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
___________ multiplied by ten equals ___________ ___________ multiplied by one hundred equals __________
___________ multiplied by one thousand equals __________
The number represented on the place value chart is: ____________________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
___________ x 10 = ___________ ___________ x 100 = __________ ___________ x 1,000 = __________
x 26.96 = 26,960 x 0.234 = 2.34 x 33.02 = 3,302
1,000 x = 2,050 42.603 x = 426.03 10 x = 4,562.3
2.2 x = 44 x 200 = 644 x 2.001 = 8,004
Identify the number represented and multiply it correctly.
1.132
1.132 11.32 1.132 113.2
1,1321.132
20.071
20.071 200.71 20.071 2,007.1 20.071 20,071
The number represented on the place value chart is: ____________________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
___________ x 10 = ___________ ___________ x 100 = __________ ___________ x 1,000 = __________
115.404
115.404 1,154.04 115.404 11,540.4 115.404 115,404
1,000 10 100
2.05 10 456.23
20 3.22 4,000
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Fluency & Precision 6Multiply by 10, 100 and 1,000
The number represented on the place value chart is: ____________________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
___________ multiplied by two tens equals ___________ ___________ multiplied by two hundreds equals __________
___________ multiplied by two thousands equals __________
x 26.96 = 53,920 x 0.234 = 7.02 x 33.02 = 6,604
4,000 x = 8,200 42.603 x = 1,278.09 50 x = 610
2.2 x = 660 x 400 = 1,288 x 2.001 = 16,008
Exchange the counters correctly and show this in the place value chart below. Then multiply the given number.
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
The number represented on the place value chart is: ____________________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
___________ multiplied by two tens equals ___________ ___________ multiplied by two hundreds equals __________
___________ multiplied by two thousands equals __________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
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Fluency & Precision 6AnswersMultiply by 10, 100 and 1,000
The number represented on the place value chart is: ____________________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
___________ multiplied by two tens equals ___________ ___________ multiplied by two hundreds equals __________
___________ multiplied by two thousands equals __________
x 26.96 = 53,920 x 0.234 = 7.02 x 33.02 = 6,604
4,000 x = 8,200 42.603 x = 1,278.09 50 x = 610
2.2 x = 660 x 400 = 1,288 x 2.001 = 16,008
Exchange the counters correctly and show this in the place value chart below. Then multiply the given number.
23.49
23.49 469.8 23.49 4,698
46,98023.49
2,000 30 200
2.05 30 12.2
300 3.22 8,000
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
The number represented on the place value chart is: ____________________
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
___________ multiplied by two tens equals ______________________ multiplied by two hundreds equals __________
___________ multiplied by two thousands equals __________
636.593
636.593 12,731.86 636.593 127,318.6
1,273,186636.593
Thousands Hundreds Tens Ones Tenths Hundredths Thousandths
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Reasoning & Problem Solving
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Reasoning & Problem Solving
6Multiply by 10, 100 and 1,000
Multiply by 10, 100 and 1,000 6
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 2.134.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 100.What patterns do you notice?
Do you agree? Explain your thinking.
Rosie says,
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 2.134.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 100.What patterns do you notice?
Do you agree? Explain your thinking.
Rosie says,
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
When you
multiply by 10, you should add
one zero.
When you
multiply by 10, you should add
one zero.
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Reasoning & Problem Solving
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Reasoning & Problem Solving
6Answers
Answers
Multiply by 10, 100 and 1,000
Multiply by 10, 100 and 1,000 6
Children will be able to see how the counter will move two rows for multiplying by 100. They can see that this happens to each
digit regardless of the value. For example, 2.134 × 100 becomes 213.4.
Each counter moves up a row but stays in the same column.
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 2.134.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 100.What patterns do you notice?
Children should explain that when you multiply by 10 the digits move
one place to the left.For example:
0.25 × 10 = 0.250 is incorrect as 0.25 is the same as 0.250.
Also: 0.25 + 0 = 0.25.Children show 0.25 × 10 = 2.5.
Do you agree? Explain your thinking.
Rosie says,
When you
multiply by 10, you should add
one zero.
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
Children will be able to see how the counter will move two rows for multiplying by 100. They can see that this happens to each
digit regardless of the value. For example, 2.134 × 100 becomes 213.4.
Each counter moves up a row but stays in the same column.
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 2.134.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 100.What patterns do you notice?
Children should explain that when you multiply by 10 the digits move
one place to the left.For example:
0.25 × 10 = 0.250 is incorrect as 0.25 is the same as 0.250.
Also: 0.25 + 0 = 0.25.Children show 0.25 × 10 = 2.5.
Do you agree? Explain your thinking.
Rosie says,
When you
multiply by 10, you should add
one zero.
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
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Reasoning & Problem Solving
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Reasoning & Problem Solving
6Multiply by 10, 100 and 1,000
Multiply by 10, 100 and 1,000 6
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 4.521.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 100, by 1,000.
What patterns do you notice?
Do you agree? Explain your thinking.
Rosie says,
When you multiply by 100, you should add
two zeros.10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 4.521.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 100, by 1,000.
What patterns do you notice?
Do you agree? Explain your thinking.
Rosie says,
When you multiply by 100, you should add
two zeros.10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
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Reasoning & Problem Solving
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Reasoning & Problem Solving
6Answers
Answers
Multiply by 10, 100 and 1,000
Multiply by 10, 100 and 1,000 6
Children will be able to see how the counter will move three rows for multiplying by 1,000. They can see that this happens to each
digit regardless of the value. For example, 4.521 × 100 = 452.1 and 4.521 × 1,000 = 4,521.
Each counter moves up a row but stays in the same column.
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 4.521.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 100, by 1,000.
What patterns do you notice?
Children should explain that when you multiply by 100 the digits move
two places to the left.For example:
0.93 × 100 = 0.9300 is incorrect as 0.93 is the same as 0.93000.
Also: 0.93 + 0 + 0 = 0.93.Children show 0.93 × 100 = 93.
Do you agree? Explain your thinking.
Rosie says,
When you
multiply by 100, you should add
two zeros.
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
Children will be able to see how the counter will move three rows for multiplying by 1,000. They can see that this happens to each digit
regardless of the value. For example, 4.521 × 100 = 452.1 and 4.521 × 1,000 = 4,521.
Each counter moves up a row but stays in the same column.
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 4.521.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 100, by 1,000.
What patterns do you notice?
Children should explain that when you multiply by 100 the digits move
two places to the left.For example:
0.93 × 100 = 0.9300 is incorrect as 0.93 is the same as 0.93000.
Also: 0.93 + 0 + 0 = 0.93.Children show 0.93 × 100 = 93.
Do you agree? Explain your thinking.
Rosie says,
When you
multiply by 100, you should add
two zeros.
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
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Reasoning & Problem Solving
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Reasoning & Problem Solving
6Multiply by 10, 100 and 1,000
Multiply by 10, 100 and 1,000 6
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 52.734.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 10, by 100, by 1,000.
What patterns do you notice?
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 52.734.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 10, by 100, by 1,000.
What patterns do you notice?
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
Do you agree? Explain your thinking.
Rosie says,
When you multiply by 1,000,
you should add three zeros.
Do you agree? Explain your thinking.
Rosie says,
When you multiply by 1,000,
you should add three zeros.
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Reasoning & Problem Solving
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Reasoning & Problem Solving
6Answers
Answers
Multiply by 10, 100 and 1,000
Multiply by 10, 100 and 1,000 6
Children will be able to see how the counter will move up a row for multiplying by 10. They can see that this happens to each digit regardless
of the value. For example, 52.734 × 10 = 527.34, 52.734 × 100 = 5,273.4,
52.734 × 1,000 = 52,734. Each counter moves up a row but stays in the same column.
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 52.734.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 10, by 100, by 1,000.
What patterns do you notice?
Children should explain that when you multiply by 1,000 the digits
move three places to the left.For example:
0.56 × 1,000 = 0.56000 is incorrect as 0.56 is the same as 0.56000.Also: 0.56 + 0 + 0 + 0 = 0.56.
Children show 0.56 × 1,000 = 560.
Do you agree? Explain your thinking.
Rosie says,
When you multiply by 1,000,
you should add three zeros.
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
Children will be able to see how the counter will move up a row for multiplying by 10. They can see that this happens to each digit regardless
of the value. For example, 52.734 × 10 = 527.34, 52.734 × 100 = 5,273.4,
52.734 × 1,000 = 52,734. Each counter moves up a row but stays in the same column.
Using the digit cards 0-9 create a number with up to 3 decimal places e.g. 52.734.
Cover the number using counters on your Gattegno chart.
Explore what happens when you multiply your number by 10, by 100, by 1,000.
What patterns do you notice?
Children should explain that when you multiply by 1,000 the digits
move three places to the left.For example:
0.56 × 1,000 = 0.56000 is incorrect as 0.56 is the same as 0.56000.Also: 0.56 + 0 + 0 + 0 = 0.56.
Children show 0.56 × 1,000 = 560.
Do you agree? Explain your thinking.
Rosie says,
When you multiply by 1,000,
you should add three zeros.
10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
100 200 300 400 500 600 700 800 900
10 20 30 40 50 60 70 80 90
1 2 3 4 5 6 7 8 9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009