1. Calculate with Fractions
Grade 5
Calculate with Fractions
Calculate with fractions including problem solving
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Calculate with fractions including problem solving
Grade 5
Prior Knowledge
Simplifying fractions
Converting between mixed numbers and improper fractions Basic operations for integers without a calculator
Duration
Suggested time to cover the content of objective with practice time is 60 minutes.
Resources
Print slides: 4, 6, 8, 11, 16, 19
Equipment
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Fraction basics (should be prior knowledge). Write fractions, simplifying, basic operations
Give students slide 4 printed as starter. It is an assortment of questions related to the prior knowledge needed for this lesson. Review the answers using slide 5. 10
Converting mixed number to improper fraction and vice versa
Give students slide 6 printed. Students are to calculate the conversions and write an explanation using their own words the method used for these conversions.
Adding and subtracting fractions
Give students slide 8 printed. Demonstrate one addition and one subtraction using slide 9. Allow students to complete 4 practice questions. Then show example on slide 10 where numbers are mixed. Students to complete 2 further questions on slide 4 with mixed numbers. 15
Multiplying and dividing fractions
Give students slide 11. Demonstrate one multiplication using slide 12 and then a further example where can cross multiply before (but not necessary) on slide 13 and one division using slide 14 and one division with a mixed number on slide 15. Allow students to complete 6 practice questions.
Give students slide 16 printed. Further mixed practice.
Calculating with fractions including problem solving in OCR exam questions (from specimen papers)
Give students slide 19. This includes 4 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 to show how the marks are allocated.
Next Steps
Algebraic fractions
Assessment
PLC/Reformed Specification/Target 5/Number/Calculating with Fractions

3. Key Vocabulary
Numerator Denominator Equivalent Improper Fraction Mixed Number Simplify

4. Fractions - Intro Student Sheet 1
Which fraction is not equivalent to ¼
There are only black and green pens in a box. The ratio of the number of black to green is 2 : 5. What fraction of the pens are black?
What fraction of the students in the class 11A are girls?
ABCD is a square drawn accurately. What fraction of the square is shaded?
Write as a fraction in its simplest form.
There are 35 pens in a box. 15 are green and the rest are red. What fraction of the pens in the box are red?
Student Sheet 1

5. Fractions - Intro + + = = = = + + = × × 2 7 15 29 1 64 3 4 1 16 75
Which fraction is not equivalent to ¼
There are only black and green pens in a box. The ratio of the number of black to green is 2 : 5. What fraction of the pens are black?
What fraction of the students in the class 11A are girls? 2 7 15 29
ABCD is a square drawn accurately. What fraction of the square is shaded? + + 1 64
Write as a fraction in its simplest form. 3 4 1 16 = 75
1000 3 40 = 1 4 × 1 4 1 16
There are 35 pens in a box. 15 are green and the rest are red. What fraction of the pens in the box are red? = 1 16 1 4 1 64 = + + × 20 35 4 7 = 48 64 4 64 1 64 53 64

6. Describe the method for converting (use an example to demonstrate)
Convert Mixed Number / Improper
1 4
9 4 2
Describe the method for converting (use an example to demonstrate)
3 7 3
9 5
2 9 5
13 4
Student Sheet 2

7. Convert Mixed Number / Improper
1 4
9 4 2
3 7
24 7 3
4 5
9 5 1
2 9
47 9 5
1 4
13 4 3

8. How to add/subtract fractions
2 5 − 1 8
4 7 − 1 3
7 9 − 2 5
−3 2 7
Student Sheet 3

9. How to add/subtract fractions
Denominators must be the same!
(b) − 2 5 =
x 5
x 7
= 7 9 − 2 5
x 5
x 9
Make each fraction an equivalent fraction with a common denominator
x 7
x 5
x 5
x 9
= =
= − = 35−18 45
Only add the numerators
Only subtract the numerators =
= =1 6 35
Leave in simplest form

10. How to add/ subtract mixed numbers...=
Convert to improper fractions
= − 23 7
= − 23 7 =
x 3
x 5
Denominators must be the same!
x 7
x 3
x 5
x 7
x 3
x 3
= =
= − =
Only add the numerators
Only subtract the numerators = =
Leave in simplest form

11. How to Multiply/Divide Fractions
4 7 x 3 5
1 4 x 5 6
2 5 ÷ 1 8
3 5 x 1 3
4 7 ÷ 1 3
7 9 ÷ 2 5 x
÷3 2 7
Student Sheet 4

12. How to multiply by a fraction
We can just multiply the numerators and multiply the denominators
4 7
3 5 ×
12 35 =

13. How to multiply by a fraction
We can cross cancel to make things easier but you do not have to!
(We can just multiply the numerators and multiply the denominators)
21 5 ÷7
10 7 ×
Look diagonally to spot common factors! ÷7
3 5
10 1 × = 2
6 1
3 5
10 1 × = ÷5 =
= 6 1 ÷5

14. How to divide by a fraction
We can just multiply the numerators and multiply the denominators
7 9
2 5 ÷
Keep the 1st
Flip the 2nd
Change to X
7 9
5 2 ×
35 18
17 18 = = 1

15. Divide by a mixed number
4 7
2 5
Firstly change the mixed number to an improper fraction! 2 ÷
18 7 ×
5 2
KEEP
CHANGE
FLIP
90 14
6 14
3 7 = 6 = 6

16. Practice Student Sheet 5
Austin has gone shopping. He spends 4 ¾ minutes walking from the bus into the town. He then spends minutes in ‘supersaves’, minutes in ‘station fun’ and then another 18 ½ minutes walking back to the bus stop.
What is the total time he spent in town?
Student Sheet 5

17. Calculating with fractions now you try..

18. Problem solving and reasoning
Austin has gone shopping. He spends 4 ¾ minutes walking from the bus into the town. He then spends minutes in ‘supersaves’, minutes in ‘station fun’ and then another 18 ½ minutes walking back to the bus stop.
What is the total time he spent in town?
4 ¾ ½
= = around 45 minutes

19. Exam Questions – Specimen Papers
Student Sheet 6

20. Exam Questions – Specimen Papers

21. Exam Questions – Specimen Papers

22. Exam Questions – Specimen Papers

23. Exam Questions – Specimen Papers