**National curriculum content**

- Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
- Compare and order fractions, including fractions > 1
- Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
- Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, ¼ x ½ = 1/8]
- Divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]
- Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8]

**Lesson objectives**

- Multiply fractions by integers
- Multiply fractions by fractions
- Divide a fraction by an integer
- Divide any fraction by an integer
- Mixed questions with fractions
- Fraction of an amount
- Fraction of an amount- find the whole

**What we want children to know**

- Simplify fractions, building on their knowledge of equivalent fractions in earlier years
- Apply their understanding when calculating with fractions and simplifying their answers
- Count forward and backwards in fractions
- Compare and order fractions with the same denominator or denominators that are multiples of the same number
- Place fractions on a number line and find the difference between fractions using a number line to support
- Use knowledge of equivalent fractions to compare fractions where the denominators are not multiples of the same number
- Find the lowest common multiple of the denominators in order to find equivalent fractions with the same denominators
- Compare numerators to find the larger or smaller fractions
- Compare fractions by finding a common numerator – when the numerators are the same, the larger the denominator, the smaller the fraction
- Decide whether the most efficient method when comparing fractions is to find common numerators or denominators
- Add and subtract fractions within 1 where the denominators are multiples of the same number
- Find the lowest common multiple in order to find a common denominator
- Add and subtract fractions where the denominators are not multiples of the same number
- When denominators are not multiples of the same number, we need to multiply the denominators together in order to find the LCM
- Add two fractions where one or both are mixed numbers or improper fractions
- Add mixed number using different methods depending on whether the fractions total more than one
- Subtract mixed numbers by exchanging wholes for fractions and subtracting the wholes and fractions separately and converting the mixed number to an improper fraction
- Solve problems involving adding and subtracting fractions and mixed numbers
- Multiply fractions and mixed numbers by integers
- Use concrete and pictorial representations to support them multiplying fractions by fractions
- Divide fractions by integers where the numerator is a multiple of the integer
- Divide fractions where the numerator is not a multiple of the integer they are dividing by
- How to combine the four operations when calculating with fractions
- Calculate fractions of an amount
- Find the whole amount from the unknown value of a fraction

**What skills we want children to develop**

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

**True or false?**

You can only divide a fraction by an integer if the numerator is a multiple of the divisor. Explain why.

**Spot the mistake**

Identify and explain mistakes when counting in more complex fractional steps.

**Make up an example**

Give an example of a **fraction** that is greater than 1.1 and less than 1.5.

Now give another example that no one will think of. Explain how you know.

**Odd one out**.

Which is the odd one out in each of these collections of 4 fractions?

5¾ 9/12 26/36 18/24

4/20 1/5 6/25 6/30

Why?

**Continue the pattern**

1/3 ÷ 2 = 1/6

1/6 ÷ 2 = 1/12

1/12 ÷ 2 = 1/24

**Vocabulary/Mathematical Talk**

- Can you make a list of the factors for each number?
- Which numbers appear in both lists? What do we call these (common factors)?
- What is the highest common factor of the numerator and denominator?
- Is a simplified fraction always equivalent to the original fraction? Why?
- Which numbers do I say when I count in eighths and when I count in quarters?
- Can you estimate where the fractions will be on the number line?
- Can you divide the number line into more intervals to place the fractions more accurately?
- How can you decide whether to find a common numerator or denominator?
- Do you need to change one or both numerators? Why?
- How does finding the lowest common multiple help to find a common denominator?
- Which of the subtractions has the biggest difference? Explain how you know. Can you order the differences in ascending order?
- How do we find the LCM of three numbers? Do we multiply them together? Is 120 the LCM of 4, 5 and 6?
- How many eighths can we exchange for one whole?
- Look at Amir’s calculation. What do you notice about the relationship between 3 2/5 and 1 7/10? (3 2/5 is double 1 7/10)
- Can you draw a bar model to represent the problem? Do we need to add or subtract the fractions?
- How do I know if my answer is simplified fully?
- Does multiplying two numbers always give you a larger product? Explain why.
- Can you write the worded problem as a number sentence?
- What is the value of the whole?
- How many equal parts are there altogether?
- How many equal parts do we need?
- What is the value of each equal part?
- Can you estimate what the answer is? Can you check the answer using a bar model?

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