National curriculum content

• Compare and order fractions whose denominators are all multiples of the same number
• Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
• Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 5 2 + 5 4 = 5 6 = 1 5 1 ]
• Add and subtract fractions with the same denominator and denominators that are multiples of the same number
• Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

Lesson objectives

1. Recap What is a fraction?
2. Recap Equivalent fractions
3. Equivalent fractions
4. Recap Fractions greater than 1
5. Improper fractions to mixed numbers
6. Mixed numbers to improper fractions
7. Number sequences
8. Compare and order fractions less than 1
9. Compare and order fractions greater than 1
10. Add and subtract fractions
11. Add fractions within 1
12. Add 3 or more fractions
13. Add fractions
14. Add mixed numbers
15. Subtract fractions
16. Subtract mixed numbers
17. Subtraction – breaking the whole
18. Subtract 2 mixed numbers
19. Multiply unit fractions by an integer
20. Multiply non-unit fractions by an integer
21. Multiply mixed numbers by integers
22. Recap Calculate fractions of a quantity
23. Fractions of an amount
24. Using fractions as operators

What we want children to know

• Fractions, decimals and percentages are different ways of expressing proportions.
• They extend their knowledge of fractions to thousandths and connect to decimals and measures. Pupils connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions.
• Connect multiplication by a fraction to using fractions as operators (fractions of), and to division, building on work from previous years. This relates to scaling by simple fractions, including fractions > 1.
• Practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number.
• Continue to practise counting forwards and backwards in simple fractions.
• Continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities.

What skills we want children to develop

Use knowledge to solve reasoning and problem solving questions such as:

Equivalent fractions:

Chiz and Caroline each had two sandwiches of the same size.

Chiz ate 1 ½ of his sandwiches.

Caroline ate 5/4 of her sandwiches.

Draw diagrams to show how much Chiz and Caroline each ate.

Who ate more? How much more?

Fractions greater than 1:

3 friends share some pizzas.

Each pizza is cut into 8 equal slices.

Altogether, they eat 25 slices.

How many whole pizzas do they eat?

Fraction of an amount:

716  of a class are boys.

There are 18 girls in the class.

How many children are in the class?

Vocabulary/Mathematical Talk

• Can a fraction have more than one equivalent fraction?
• What do you notice about the numerator and denominator when a fraction is equivalent to a whole?
• How many parts are there in a whole?
• How many quarters/halves/eighths/fifths are there in a whole?
• Are the fractions increasing or decreasing?
• How does a bar model help us to visualise the fractions?
• Is it more efficient to compare using numerators or denominators?
• Can you find a common denominator? Do you need to convert both fractions or just one?
• Can you simplify your answer?
• What has happened to the numerator/denominator?