year 6 spring term block 1- percentages fluency reviewed · 2020-06-16 · fluency teaching slides...
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6Fluency Teaching Slides
Number: Percentages
6Fluency Teaching Slides
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6Fluency Teaching Slides
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Fractions to Percentages
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Activity 1 Fractions to Percentages
What fraction of each hundred square is shaded?
Write the fractions as percentages.
? What does the word ‘percent’ mean?
Percentages - 6
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Activity 1 Fractions to Percentages
What fraction of each hundred square is shaded?
Write the fractions as percentages.
= 20%___20100
= 74%___74100
Percentages - 6
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Activity 2 Fractions to Percentages
What fraction of each hundred square is shaded?
Write the fractions as percentages.
? What does the word ‘percent’ mean?
Percentages - 6
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Activity 2 Fractions to Percentages
What fraction of each hundred square is shaded?
Write the fractions as percentages.
= 32%___32100
= 30%___30100
Percentages - 6
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Activity 2 Fractions to Percentages
Fraction Percentage
1__
2
1__
4
1__
10
1__
5
Complete the table.
Percentages - 6
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Activity 2 Fractions to Percentages
Fraction Percentage
1__
2
1__
4
1__
10
1__
5
50%
Complete the table.
25%
10%
20%
Percentages - 6
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Activity 3 Fractions to Percentages
15___
100= %
___25
50= % = ___
100
___
100= % 57
___100
= % 39 ___78
Fill in the missing numbers.
? How do you convert the fraction to get the percentage?
Percentages - 6
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Activity 3 Fractions to Percentages
15___
100= %
___25
50= % = ___
100
___
100= % 57
___100
= % 39 ___78
Fill in the missing numbers.
15
5050
57
50
Percentages - 6
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Discuss
What does the word ‘percent’ mean?
How can you convert tenths to hundredths?
Why is it easy to convert fiftieths to hundredths? What other fractions are easy to convert to percentages?
12
Fractions to Percentages
% % % % % %Percentages - 6
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Equivalent FDP
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Activity 1 Equivalent FDP
Decimal Fraction Percentage
0.25 25%
0.48
0.5
0.01
___25
100
Complete the table.
Percentages - 6
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Activity 1 Equivalent FDP
Decimal Fraction Percentage
0.25 25%
0.48
0.5
0.01
___25
100
Complete the table.
48%
50%
1%
___48
100
___50
100
___1
100
Percentages - 6
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Activity 2 Equivalent FDP
Use <, > or = to complete the statements.
? Which is easiest to convert? Decimals to fraction or decimals to percentage?
0.74 30%
0.50 80%
0.31__
6
0.281__
5
Percentages - 6
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Activity 2 Equivalent FDP
0.74 30%
0.50 80%
0.31__
6
0.281__
5
Use <, > or = to complete the statements.
>
<
>
<
Percentages - 6
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Activity 3 Equivalent FDP
___40
100
___4
1000.04
___8
500.4
Which of these are equivalent to 40%?
Percentages - 6
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Activity 3 Equivalent FDP
___40
100
___4
1000.04
___8
500.4
Which of these are equivalent to 40%?
ü
ü4% 4%
16%
Percentages - 6
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Discuss
How does converting a decimal to a fraction help you to convert it to a percentage?
How do you convert a percentage to a decimal?
Can you use a hundred square to represent your conversions?
20
Equivalent FDP
% % % % % %Percentages - 6
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Order FDP
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Activity 1 Order FDP
62% 0.627__
8
0.38 74%4__
5
49.5 30%__5
25
Use <, > or = to complete the statements.
? Can you answer the calculations mentally?
Percentages - 6
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Activity 1 Order FDP
62% 0.627__
8
0.38 74%4__
5
49.5 30%__5
25
Use <, > or = to complete the statements.
>
= <
< <
<
Percentages - 6
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Activity 2 Order FDP
___5
10
___75
1000.43
___3
500.22
Order from smallest to largest:
Percentages - 6
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Activity 2 Order FDP
___5
10
___75
1000.43
___3
500.22
Order from smallest to largest:
6% 22% 43% 50% 75%
Percentages - 6
26
Order FDP
20% 0.25 10%0.3?
Activity 3
Five friends share a cake. Esin eats 20% of the cake, Zach eats 0.25 of the cake, Tia eats 10% of the cake,
and Leanna eats 0.3 of the cake.
Write the amount each child eats as a fraction.
? Who eats the most? Who eats the least? Is there any left for their friend Malachi?
Percentages - 6
27
Order FDP
20% 0.25 10%0.3?
Activity 3
Five friends share a cake. Esin eats 20% of the cake, Zach eats 0.25 of the cake, Tia eats 10% of the cake,
and Leanna eats 0.3 of the cake.
Write the amount each child eats as a fraction.
___20100
___25100
___10100
___30100
There is left for Malachi.
Leanna eats the most, and Tia eats least.
___15
100
Percentages - 6
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Discuss
What do you notice about the fractions, decimals or percentages? Can you compare any straight away?
What is the most efficient way to order them?
Do you prefer to convert your numbers to decimals, fractions, or percentages? Why?
If you put them in ascending order, what will it look like? If you put them in descending order, what will it look like?
28
Order FDP
% % % % % %Percentages - 6
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Percentage of an Amount (1)
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Activity 1 Percentage of an Amount (1)
50% is equivalent to ½.To find 50% of an amount, you can
divide by 2.
__1
__1
__1
Complete the sentences.
25% is equivalent to . To find 25% of an amount, divide by ____.
10% is equivalent to . To find 10% of an amount, divide by ____.
1% is equivalent to . To find 1% of an amount, divide by ____.
Percentages - 6
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Activity 1 Percentage of an Amount (1)
25% is equivalent to . To find 25% of an amount, divide by ____.
10% is equivalent to . To find 10% of an amount, divide by ____.
1% is equivalent to . To find 1% of an amount, divide by ____.
50% is equivalent to ½.To find 50% of an amount, you can
divide by 2.
__1
__1
__1
Complete the sentences.
4
10
100
4
10
100
Percentages - 6
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Activity 2 Percentage of an Amount (1)
10% 20%0% 30% 40% 50% 60% 70% 80% 90% 100%
?
10% 20%0% 30% 40% 50% 60% 70% 80% 90% 100%
?
408 124
Use the bar models to help you complete the calculations.
? What method do you use to solve the calculations faster? Do you use the bar models?
50% of 408 = 25% of 124 =
Percentages - 6
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Activity 2 Percentage of an Amount (1)
10% 20%0% 30% 40% 50% 60% 70% 80% 90% 100% 10% 20%0% 30% 40% 50% 60% 70% 80% 90% 100%
50% of 408 = 204 25% of 124 = 31
408 124
Use the bar models to help you complete the calculations.
408 ÷ 2 124 ÷ 4
Percentages - 6
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Activity 3 Percentage of an Amount (1)
50% of 300 =
50% of 30 =
50% of 60 =
Solve the following:
25% of 300 =
25% of 30 =
25% of 60 =
10% of 300 =
10% of 30 =
10% of 60 =
1% of 300 =
1% of 30 =
1% of 60 =
Percentages - 6
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Activity 3 Percentage of an Amount (1)
50% of 300 =
50% of 30 =
50% of 60 =
Solve the following:
25% of 300 =
25% of 30 =
25% of 60 =
10% of 300 =
10% of 30 =
10% of 60 =
1% of 300 =
1% of 30 =
1% of 60 =
150
15
30
75
7.5
15
30
3
6
3
0.3
0.6
Percentages - 6
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Discuss
Why do you divide a quantity by 2 in order to find 50%?
How do you calculate 10% of a number mentally?
What’s the same and what’s different about 10% of 300 and 10% of 30?
36
Percentage of an Amount (1)
% % % % % %Percentages - 6
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Percentage of an Amount (2)
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Activity 1 Percentage of an Amount (2)
10% 20%0% 30% 40% 50% 60% 70% 80% 90% 100%
?
10% of 90 = 9 .
So 40% of 90 = 4 x 9 = 36.
38
Zach uses a bar model to find 40% of 90.
? Use Zachʻs method to calculate:
20% of 140 30% of 890 70% of 70 90% of 660
Percentages - 6
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Activity 1 Percentage of an Amount (2)
10% 20%0% 30% 40% 50% 60% 70% 80% 90% 100%
?
39
Zach uses a bar model to find 40% of 90.
20% of 140
30% of 890
70% of 70
90% of 660
10% of 140 = 14, so 20% of 140 = 2 x 14 = 28.
10% of 890 = 89, so 30% of 890 = 3 x 89 = 267.
10% of 70 = 7, so 70% of 70 = 7 x 7 = 49.
10% of 660 = 66, so 90% of 660 = 9 x 66 = 594.
Percentages - 6
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Activity 2 Percentage of an Amount (2)
40
To find 5% of a number, divide by 10 and then divide by 2.
Use this method to work out:
5% of 160 5% of 280 5% of 1m 60cm
? How else could we work 5%?
Percentages - 6
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Activity 2 Percentage of an Amount (2)
41
To find 5% of a number, divide by 10 and then divide by 2.
Use this method to work out:
5% of 160
5% of 280
5% of 1m 60cm
160 ÷ 10 = 16 and then 16 ÷ 2 = 8.
280 ÷ 10 = 28 and then 28 ÷ 2 = 14.
160cm ÷ 10 = 16cm and then 16cm ÷ 2 = 8 cm.
We can also directly divide by 20.
Percentages - 6
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Activity 3 Percentage of an Amount (2)
42
Calculate:
65% of 30m 35% of 170g 15% of £50
Percentages - 6
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Activity 3 Percentage of an Amount (2)
43
Calculate:
65% of 30m 35% of 170g 15% of £50
19.5m 59.5g £7.5
Percentages - 6
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Discuss
Is dividing by 10 and multiplying by 5 the most efficient way to find 50%? Explain why.
Is dividing by 10 and multiplying by 9 the most efficient way to find 90%? Explain why.
How many ways can you think of to calculate 60% of a number?
44
Percentage of an Amount (2)
% % % % % %Percentages - 6
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Percentages –Missing Values
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Activity 1
15% of the people visited in the first week.40% of the people visited on the second week.
Percentages – Missing Values
Percentages - 6
350,000 tourists visited Buckingham Palace last month.
? How many tourists visited Buckingham Palace during the rest of the month?
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Activity 1
Remaining values =
100% - 15% - 40% = 45%
Therefore, during the rest of the month =
350,000 x 45% = 157,500 tourists
Percentages – Missing Values
Percentages - 6
350,000 tourists visited Buckingham Palace last month.
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Activity 2 Percentages – Missing Values
10% 20%0% 30% 40% 50% 60% 70% 80% 90% 100%
?
8
Percentages - 6
? What method did you use to solve for the missing value?
If 8 is 10% of a number, what is the number?Use the bar model to help you.
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Activity 2 Percentages – Missing Values
10% 20%0% 30% 40% 50% 60% 70% 80% 90% 100%
80
8
Percentages - 6
8 x 10 = 80
If 8 is 10% of a number, what is the number?Use the bar model to help you.
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Activity 3 Percentages – Missing Values
Complete the following:
Percentages - 6
? Can you see a link between the questions?
10% of 250 =
30% of 100 =
30% of = 75
30% of = 300
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Activity 3 Percentages – Missing Values
Complete the following:
10% of 250 =
30% of 100 =
25
Percentages - 6
30% of = 75
30% of = 30030
250
1000
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Discuss
If you know a percentage, can you work out the whole?
If you know the whole and the amount, can you find what percentage has been calculated?
What diagrams could help you visualise this problem? Is there more than one way to solve the problem?
What is the most efficient way to find a missing value?
52
Percentages – Missing Values
Percentages - 6
% % % % % %
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