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?