1. Compare fractions, decimals and percentages
Grade 4
Compare fractions, decimals and percentages
Compare quantities by calculating equivalent fractions, decimals and percentages
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Compare quantities by calculating equivalent fractions, decimals and percentages
Grade 4
Prior Knowledge
Number line
Inequality signs
Common F, D, P conversions
Division
Duration
Allow at least 60 minutes for this lesson.
Resources
Print slides: 6, 10, 12, 16, 18, 24
Equipment
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Standard conversions fraction, decimal, percentage
Show students slide 4 and 5. These conversions should be familiar and all students should be able to easily convert by memory or process. 5
Method for conversion between fraction, decimal and percentage
Give students slide 6 printed. They need to complete the grid and make notes on the method for conversion. Using slides 7, 8 & 9 take one conversion at a time to review the method. Give students slide 10 printed to apply these conversion methods. 15
Method for conversion (more complex) between fraction, decimal and percentage
Give students slide 12 printed. Using slides 13, 14, & 15 review how to do more complex conversions. This includes fraction to decimal where you cannot make an equivalent fraction with denominator 100 and need to use the method of division.
Give students slide 16 printed – further practice
Comparing numbers in contextualised problems
Give students slide 18. Allow students to attempt the question on their own for 2 minutes. Review question together and model answer. Stress the importance of making a conclusion where asked to do so.
Comparing numbers in OCR exam questions (from specimen papers)
Give students slide 24. This is an exam questions related to objective. Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme. 10
Next Steps
Assessment
PLC/Reformed Specification/Target 4/Ratio, Proportion and Rates of Change/Comparing Fractions, Decimal and Percentages

3. Key Vocabulary
Fractions Decimals Percentages

4. Fractions, decimals and percentages
There are three different ways of writing exactly the same number; as a fraction, decimal or percentage.
Here are some examples:
1 2 = 0.50 = 50%
1 4 = 0.25 = 25%
= 0.18 = 18%

5. Fractions, decimals and percentages
Here are some common fractions, decimals and percentages you need to know
Fraction
Decimal
Percentage
1 2
0.5
50%
1 4
0.25
25%
1 3
…..
0. 3 %
3 4
0.75
75%
1 5
0.2
20%
1 10
0.1
10%

6. How to compare decimals, fractions and percentages
0.54
0.03
75% 8%
4 10
7 25
Student Sheet 1

7. How to compare decimals, fractions and percentages54
100 27 50
54%
0.54 =
out of 100
x 100 3_
100 3%
0.03
out of 100
x 100

8. How to compare decimals, fractions and percentages
75% 75
100 3 4
0.75 =
out of 100
÷ 100 8% 8
100 2 25
0.08 =
out of 100
÷ 100

9. How to compare decimals, fractions and percentages4 10 40
100
40%
0.4 =
numerator
÷ 100 7 25 28
100
28%
0.28 =
numerator
÷ 100

10. Compare decimals, fractions and percentages – Now you try …
1) Write
26% as fraction and decimal
0.56 as percentage and fraction in its simplest form
0.03 as percentage and fraction in its simplest form
2/5 as percentage and decimal
2) Order the following numbers, smallest first
0.23, ¼, 24%
Student Sheet 2

11. Compare decimals, fractions and percentages – Now you try …
1) Write
26% as fraction and decimal
0.56 as percentage and fraction in its simplest form
0.03 as percentage and fraction in its simplest form
2/5 as percentage and decimal
2) Order the following numbers, smallest first
0.23, ¼, 24%
26/100 = 13/
56% /100 = 14/25
3% /100
40%

12. Fractions, decimals and percentages
Change the fractions into decimals:
1) ) 5 6
Order the following numbers from lowest to highest:
40% %
Change the following decimals into fractions:
0.65 =
0.08 =
0.1 =
0.51 =
Student Sheet 3

13. Fractions, decimals and percentages
Change the following fractions into decimals:
1) ) 5 6
Is the same as 3÷8
Is the same as 5÷6
3 is a recurring decimal
=0.8 3 8)
- 0
3 0
6 0
4 0
8x3=24
8x7=56
8x5=40
….. 6)
- 0
5 0
2 0 2
6x8=48
6x3=18

14. Fractions, decimals and percentages
Change the following decimals into fractions:
0.65 =
0.08 =
0.1 =
0.51 =
𝟔𝟓 𝟏𝟎𝟎
𝟖 𝟏𝟎𝟎
𝟏𝟎 𝟏𝟎𝟎
𝟓𝟏 𝟏𝟎𝟎
= 𝟏𝟑 𝟓𝟎
= 𝟒 𝟓𝟎 = 𝟐 𝟐𝟓
= 𝟏 𝟏𝟎
The digits of the decimal make the numerator of a fraction
Two decimal places make a fraction over one hundred which is the denominator.
Fractions can then be simplified by dividing the numerator and denominator by the same factor

15. Fractions, decimals and percentages
Order the following numbers from lowest to highest:
40% %
Convert all numbers in to decimals:
Now you can order the numbers from lowest to highest:

16. Fractions, decimals and percentages
Convert in to a decimal.
Order the following numbers from lowest to highest:
% % 1 10
Insert either of the following symbols to make each statement correct: =, ≠, <, >, ≤, ≥
– (ii) 82% (ii) %
Order the following numbers from highest to lowest:
Convert the following fraction into a decimal
Student Sheet 4

17. Fractions, decimals and percentages
Convert in to a decimal.
Order the following numbers from lowest to highest:
% % 1 10
Insert either of the following symbols to make each statement correct: =, ≠, <, >, ≤, ≥
– (ii) 82% (ii) %
Order the following numbers from highest to lowest:
Convert the following fraction into a decimal
=2.75
𝟏 𝟏𝟎 % 𝟏 𝟑 %
< =
<
= 0. 4

18. Problem solving and reasoning
In a quiz, competitors get 6 points for answering a question correctly and lose 5 points if they answer incorrectly. In the first round Sam answered all three questions correctly, his score was 18.
In the same round Jay answered two questions correctly and one question incorrectly. What was his score?
If Carl answered one question incorrect and two questions correctly. What is his score?
Three students completed their end of term maths assessment.
Amy scored
Tom answered 62% of his test correctly.
Farah’s test score was equivalent to 0.58.
Out of the three students who achieved the highest score?
Circle each card that shows more than a half.
𝟔 𝟖
𝟑𝟔%
𝟑 4
0.34
0.55
𝟑 𝟔
𝟕𝟎%
Celine has £48 to spend on food and clothes. She wants to spend more on food. Should she spend 3/8 or 0.4 of her money on food?
Ben, Jake and Rachel have solved a problem. Ben’s answer is 0.33, Jake’s answer is 1/3 and Rachel’s answer is 6/20. The correct answer is Whose answer is closest to the correct answer?
Student Sheet 5

19. Problem solving and reasoning
In a quiz, competitors get 6 points for answering a question correctly and lose 5 points if they answer incorrectly.
In the first round Sam answered all three questions correctly, his score was 18.
In the same round Jay answered two questions correctly and one question incorrectly. What was his score?
If Carl answered one question incorrect and two questions correctly. What is his score?
As Jay answered 2 questions correctly he gets 6 points for every correct answer
6 + 6 =12
He then answers one questions incorrectly, so 5 points must be deducted
12 – 5 = 7
Jay has a total score of 7
As Carl answered 2 questions incorrectly he has to deduct five for each incorrect answer
points =
He answered one question correctly which is 6 points
= - 4
Carl has a total score of -4

20. Problem solving and reasoning
Three students completed their end of term maths assessment. Amy scored Tom answered 62% of his test correctly. Farah’s test score was equivalent to Out of the three students who achieved the highest score?
In order to compare their test results all numbers need to be converted into percentages.
Amy’s result
= = = 60% ÷6
x10
Farah’s result
0.58 = 58%
Tom achieved the highest percentage of 62% therefore he achieved the highest result.

21. Problem solving and reasoning
Circle each card that shows more than a half.
𝟔 𝟖
𝟑𝟔%
𝟑 4
0.34
0.55
𝟑 𝟔
𝟕𝟎%
More than a half is any value which is greater than 0.50
Which decimal values are greater than 0.50?
Start by changing fractions and percentages into decimals.
36% = 0.36
70% = 0.70
𝟔 𝟖 = 𝟑 𝟒 = 0.75
𝟑 𝟔 = 0.50

22. Problem Solving and Reasoning
Celine has £48 to spend on food and clothes. She wants to spend more on food. Should she spend 3/8 or 0.4 of her money on food?
If she spends 3/8 on food => 3/8 x £48 = £18
If she spends 0.4 on food => 0.4 x £48 = £19.20
She should spend 0.4 of her money on food

23. Problem Solving and Reasoning
Ben, Jake and Rachel have solved a problem. Ben’s answer is 0.33, Jake’s answer is 1/3 and Rachel’s answer is 6/20. The correct answer is Whose answer is closest to the correct answer?
Ben => 0.33
Jake => 1/3 = …
Rachel => 6/20 = 3/10 = 0.3
0.29 < 0.3 < 0.33 < ….
Rachel’s answer is closest.

24. Exam Question – Specimen Papers
Student Sheet 6

25. Exam Question – Specimen Papers