1. Developing Conceptual Understanding of Fractions in Years 3 and 4

2. Aims
To review and further develop personal subject knowledge relating to teaching fractions and consider progression from KS1 to Y3 and Y4
To consider how children learn about fractions and misconceptions that may arise.
To explore effective pedagogies - models and images to support conceptual understanding of fractions

3. Task
Look at the progression in fractions. What do you think are the prerequisite skills pupils learn in Y1 & Y2 that are key to pupils understanding fractions in Y3 and Y4?

4. Multiple Representations
Sort the cards into families so that each family shows the same fraction in different ways

5. Can you locate a fraction in between them?
Exploring Misconceptions: ‘Fractions are part of shapes, not numbers in their own right’
Provide regular opportunities to count forwards and backwards in fractions
Locate fractions on a number line, e.g and
Can you locate a fraction in between them?

6. Use structured apparatus to support understanding of Fractions and the link with decimals1 10
This highlights relationship between tenths and dividing by ten
0.5

7. Comparing, ordering and equivalence

8. Paper Folding: Equivalence
Compare and order fractions whose denominators are all multiples of the same number
Paper activity 1 – A4 paper
Paper activity 2 – strips paper **link to fractions of amounts***
Folding fractions

10. Fraction Wall

11. Fractions ITP FRACTIONS ITP
Need to secure understanding around equivalent fractions
Build on the work undertaken in Y3 and Y4 using diagrams (fraction walls and Fractions ITP paper folding and numicon shapes)
Seeing the images is improtant in pupils understanding of the concept adding fractions

12. Equivalent Fractions
What do you notice about the equivalent fractions?

13. Exploring the tangram http://nrich.maths.org/1
Determine the fractional
value of each piece if the square is 1?
each large triangle =
each small triangle =
medium triangle =
square =
parallelogram = 1 4 16 8
Pose the question “If the whole area is 1, what is the area of different bits?”

14. Comparing and ordering Fractions with the same denominator

15. To order fractions, learners also need to see them as points on a number line and convert to decimals..
Use bead bar or bead strings to locate decimals, fractions and percentages and highlight relationships between them:
If you get 50% put it over 100 as this is 100%
This is the type of activities you would be doing in your basic skills sessions
If you have 17/25 as a comparison fractions – easily converted into 68/100 (scaling)
This is fluency in making connections between numbers – seeing we can use knowledeg of equivalence and scaling up of and 20th s 25ths to 100ths helping to make comparisions of fractions

16. Using measuring equipment:
Y3 Count up and down in tenths Y4 hundredths, Y4 recognise hundredths arise when dividing an object by one hundred Y3 and dividing tenths by ten
Using measuring equipment:
Talk about ml in terms of medicine spoon – small amounts
CLICK for ARROW TO APPEAR
Convert 600ml to litres =
600ml children feel like they need to x by 1000 – but the proportion we have is smaller than the whole so the answer will be 0.6 litres

17. Use structured apparatus on a place value chart to highlight relationships…
If children struggling with the concept of fractions and decimals take them back to place value …..
This links perfectly to all the work you have already done on place value – (x and dividing by and 1000)
REPRESENTATION HEALTH WARNING
When the representation becomes 1 (but shows 100 – base 10 flat)
Use the multiplicative language 10 times bigger 100 times smaller etc

18. Use money on a place value chart to highlight relationships…

19. Introduce ‘pixie deines’ to highlight the relationship between each of the decimal places:

20. Calculating with Fractions

21. Raised Expectations Year 3
add and subtract fractions with the same denominator within one whole
Year 4
add and subtract fractions with the same denominator

22. Calculating Fractions with Structured Apparatus=
Missing Number Box: =
Bridging through 1: = 1

23. Adding and Subtracting Fractions
Potential misconception: When adding (or subtracting) fractions, pupils add (or subtract) both the numerators and the denominators
0.2 & 20% & 50% & 70%
Using a range of representations can support understanding

24. :

25. The picture should now look like this:
Simplify the fraction
Look for the greatest common factor of both 3 and 6 = 3

26. Application
In this question we have the missing box and application of the skills
Equivalence
5/15 is orange
6/15 apple juice
Answer 3/15 is lime
or simplified 1/5

28. Always, sometimes, never

29. KS2 Sample Arithmetic paper 2016

30. Sample KS2 Reasoning Papers 2016