WHAT IS A FRACTION?

1. WHAT IS A FRACTION?

2. A fraction can be thought of as: • The result of dividing a whole number into equal parts and taking one or more of those parts (the part/whole aspect), or • How many times one number can be divided by another

3. Level 3 • Use simple fractions that are several parts of a whole and recognise when two simple fractions are equivalent. E.g. - understand and use unit fractions such as ½, ¼, 1/3, 1/5, 1/10 and find those fractions of shapes and sets of objects - recognise and record fractions that are several parts of the whole such as ¾, 2/5 - recognise some fractions that are equivalent to ½ • Level 4 • Recognise approximate proportions of a whole and use simple fractions and percentages to describe these: - recognise simple equivalence between fractions, decimals and percentages - convert mixed numbers to improper fractions and vice versa

6. 6 Big ideas • Fractions of shapes • Fractions of numbers • Fractional numbers on a number line • Fractions as divisions • Equivalence • Links with Decimal Place Value

7. To Explore the Models and Images of Fractions

8. Part of a whole that is divided into equal parts Comparing the size of two measurements Comparison between a subset and the whole set FRACTIONS Comparing two sets of objects A point on a number line The result of a division

9. Part of a whole which is divided into equal parts 4 0 3/4

10. Comparison between a subset and the whole set

11. A point on a number line • For example: count in halves from 0 to 2 together and model the variety of symbols. • For example: count in thirds together and model the variety of symbols.

12. The result of division • Fractions of shapes • For example: 3 x ¼ = ¾ = 3 ÷ 4 • This can be seen as sharing 3 ‘pizzas’ between 4 people. • Each person has a quarter from each pizza, thus three-quarters altogether.

13. The result of division

14. Comparing two sets of objects

15. Comparing the size of 2 cylinders Cylinder B

16. Links with Decimal Place Value This really helps to get children to correctly order decimals..(common misconception) 1.23 1.3 1.29 1.32 Turn all numbers into mixed fractions: 1 23/100 1 3/10=1 30/100 1 29/100 1 32/100 (equivalent fraction)

17. Understanding and Using the Terms Numerator and Denominator Show a shape cut into pieces with several shaded - what’s the numerator/denominator? Show several identical shapes cut into pieces and one piece on each shaded - what’s the numerator/denominator?

18. Fraction wall

19. Multiplication table

20. To identify and discuss the errors and misconceptions children make with fractions Which fraction is bigger: 1/3 or 1/6? How many pupils will say 1/6?

21. Some learners may identify this diagram as representing 1/3 because they see it as one shaded over three unshaded.

22. 1 3

23. Draw your own mind map of what is involved in teaching fractions and what route you will take to help students to fully understand fractions so they can use them confidently in any situation and to answer any question.

24. Resources Mini-whiteboards and whiteboard pens These enable learners to easily jot down responses, and work out ideas, freeing them from worry about crossing out mistakes. • Sets of fraction cards with fractions in numbers, area • diagrams ,number lines, percentages and decimals These can be cut up and laminated if appropriate, or they can simply be printed out for each session and cut up by the learners themselves. > Number lines, both numbered and blank A useful way of modelling fractions. Blank number lines which learners can annotate themselves are useful. > Counting sticks, metre sticks, rulers, tape measures > Fraction wall (see BBC Skillswise www.bbc.co.uk/skillswise/) > Fraction dice (use ordinary dice with fraction stickers)

25. Calculators 2D and 3D fraction sets OHP resources including transparent coloured fraction blocks, number lines, clock faces, calculators Fraction dominoes These can be custom-made, using a basic template, for matching fractions in various representations. Sets of cubes, both separate and interlocking A range of measuring equipment, e.g. scales, balances, weights, Measuring jugs and beakers of different capacities, calibrated in different ways Digital clocks with moveable hands, blank clock faces 1 cm and 2 cm squared paper Tangrams Coloured counters, Post-It notes, index cards, tracing paper, scissors, card, glue sticks, string.

26. Assessment Some possible questions about fractions • Using mini whiteboards • “Show me a fraction (encourage naming in words, using numbers and diagrams). Show me a harder fraction.” • “Show me a question where the answer is 6. Now use 1/2 in the question. Now use 1/4. Now make a really hard question. Show me a question where the answer is 21/2” • “Here is half a shape (drawn on board), what could the whole shape look like? Similarly for 1/4, or 1/3 as appropriate.” (When collecting answers on the board, ask learners to describe shapes as a way of reinforcing idea of equal pieces) • “Show me a fraction bigger than 1/4. Show me a fraction between 1/2 and 1, between 3/4 and 1, bigger than 1…” (Encourage learners to draw diagrams and represent on number lines) • “Which is the odd one out: 1/2, 1/4, 2/4? or 1/4, 2/5, 0.4? Can you make each of them the odd one out?”

27. Assessment • 2. To understand reasoning • “Why are 1/3 and 2/6 the same?” • “Why did you change 3/4 to 9/12? Suppose you were comparing 3/4 and 5/8: • What would you do then?” • “How did you work out that 2/3 of 60 million was the same as 40 million? How would you explain your method to someone who hadn’t done this kind of thing before?”

28. To summarise: • p means p ÷ q q • q is called the denominator , because it gives the name of the fraction • p is called the numerator, because it gives either the number which is divided or the number of fractional parts • Fractions less than 1 p < q and are called proper fractions • Fractions greater than 1 p > q are called improper fractions • Improper fractions can also be written as mixed numbers, that is, a whole number with a proper fraction.