Fractions Workshop Marie Hirst

1. Fractions WorkshopMarie Hirst Have a go at the Fraction Hunt on your table while you are waiting!

2. Objectives • Understand the progressive strategy stages of proportions and ratios • Understand common misconceptions and key ideas when teaching fractions and decimals. • Explore equipment and activities used to teach fraction knowledge and strategy

3. 4 Stages of the PD Journey Organisation Orgnising routines, resources etc. Focus on Content Familiarisation with books, teaching model etc. Focus on the Student Move away from what you are doing to noticing what the student is doing Reacting to the Student Interpret and respond to what the student is doing

4. Knowledge Strategies Number Identification Number Sequence and Order Grouping and Place Value Basic Facts Written Recording Addition & Subtraction Multiplication & Division Fractions and Proportions The Number Frameworks

5. Assess Your Fraction Strategies and Fraction Knowledge

6. Assigning a strategy stage for proportions and ratios

7. Fraction Snapshots Here are 12 jelly beans to spread on the cake. If you ate one third of the cake how many jelly beans will you eat?

8. Fraction Snapshots (cont’d) Stage 6 (AA) Using multiplication What is 3/4 of 80? 16 is four ninths of what number? Stage 7 (AM) Using division To make 8 aprons it takes 6 metres of cloth. How many metres would you need to make 20 aprons? Stage 8 (AP)

9. What misconceptions may young children have when beginning fractions? • Misconceptions about finding one half when beginning fractions: • Share without any attention to equality • Share appropriate to their perception of size, age etc. • Measure once halved but ignore any remainder • So what do we need to teach to move to equal sharing? • Introduce the vocabulary of equal / fair shares with both regions and sets for halves and then quarters.

10. Draw two pictures of one quarter

11. Discrete and continuous models One Quarter: Continuous Discrete (regions/lengths) (sets) Label your drawings as discrete or continuous models. Children need experience with both models from the very start.

12. Key Idea 1 Work with both shapes and sets of fractions from early on.

13. Linking regions/shapes and sets Find one quarter

14. Existing Knowledge & Strategies Using Imaging Using Number Properties Using Materials Using Materials New Knowledge & Strategies The Strategy Teaching Model

15. Using Materials - fraction regions Find one quarter

16. Using Materials - fraction regions Find one quarter of 12

17. Existing Knowledge & Strategies Using Imaging Using Number Properties Using Materials Using Materials New Knowledge & Strategies The Strategy Teaching Model

18. Using Imaging Find one quarter of 12 Key idea: quarters means you need 4 equal groups. One quarter is the number in one of those groups.

19. Existing Knowledge & Strategies Using Imaging Using Number Properties Using Materials Using Materials New Knowledge & Strategies The Strategy Teaching Model

20. Using Number Properties Find one quarter of 40, 400, 4000

21. 3 3 3 3 Develop early additive thinking by using addition facts Find one quarter of 12 ? ? ? ?

22. Using Materials - cubes Four birds found a worm in the ground 20 smarties long. What proportion of the worm do they each get? How many smarties will each bird get?

23. Key Idea 2 3 sevenths 3 out of 7 7/3 7 thirds

24. 5 views of fractions 3 over 7 3 ÷ 7 3 out of 7 3 : 7 3 sevenths

25. x 24 = 1 2 2 3 3 5 2 3 2 out of 3 multiplied by 24 !!!!! + = The problem with “out of” “I ate 1 out of the 2 sandwiches in my lunchbox, Kate ate 2 out of the 3 sandwiches in her lunchbox, so together we ate 3 out of the 5 sandwiches”

26. Fraction Language Use words before and use symbols with care. e.g. ‘one fifth’ not 1/5 How do you explain the top and bottom numbers? 1 2 The number of parts chosen The number of parts the whole has been divided into

27. Fractional vocabulary One half One third One quarter Don’t know

28. Emphasise the ‘ths’ code 1 dog + 2 dogs = 3 dogs 1 fifth + 2 fifths = 3 fifths 1/5 + 2/5 =3/5 3 fifths+ ?/5 =1 1 - ?/5 = 3/5 17 1 - ?/20 = 3/20

29. Key Idea 2 Fraction language is confusing. Emphasise the ‘ths’ code. Use words before symbols. Introduce symbols with care. The bottom number tells how many parts the whole has been split into,the top number tells how many of those parts have been chosen.

30. Key Idea 3 6 is one third of what number? This is one quarter of a shape. What does the whole look like?

31. 18

32. Key Idea 3 Go from part-to-whole as well as whole-to-part with both shapes and sets. Children need experience in both reconstructing the whole as well as dividing a whole.

33. Perception check on two key ideas Where in the table does this question fit? Hemi got two thirds of the lollies. How many were there altogether?

34. Write 3 more questions to fit the other parts of the table.

35. Extending the idea of going from part-to-whole with non-unit fractions Hemi got three fifths of the lollies and got 12. How many lollies were there altogether? i.e. 12 is three fifths of what number? Draw a diagram/use equipment to help your thinking.

36. 4 4 4 12 is three fifths of what number? 20 12 8 4 4

37. Key Idea 4 5 children share three chocolate bars evenly. How much chocolate does each child receive? 3 ÷ 5 Discuss in groups what you think children would do and then how you would solve this problem.

38. Division 3 ÷ 5 1/5+1/5+1/5 =3/5

39. Key Idea 4 Division is the most common context for fractions when units of one are not accurate enough for measuring and sharing problems. e.g. 5 ÷ 3

40. A B C D E F 0 1 2 3 Which letter shows 5 halves as a number?

41. 5 halves 5 21/2 1 Key Idea 5Fractions are not always less than 1.Push over 1 early to consolidate the understanding of the top and bottom numbers.

42. 0 1 half 2 halves 3 halves 4 halves Using fraction number lines to consolidate understanding of denominator and numerator Push over 1 0 1/2 2/2 3/2 4/2 0 1/2 111/2 2

43. Fraction Circles Play the fraction circle game. Put the circle pieces in the “bank”. Take turns to roll the die and collect what ever you roll from the bank. You may need to swap and exchange as necessary. The winner is the person who has made the most ‘wholes’ when the bank has run out of fraction pieces.

44. X X e.g. Roll a 3 and a 5 Mark a cross on either 3 fifths or 5 thirds. The winner is the first person to get three crosses in a row. Three in a row (use two dice or numeral cards)A game to practice using improper fractions as numbers 0 1 2 3 4 5 6

45. Key Idea 6Fractions are numbers as well as operators 1/2 is a number between 0 and 1 (number) Find one half of 12 (operator)

46. 20 60 3 5 100 0 1 5 1 0 Using Double Number Lines Put a peg on where you think 3/5 will be. (Fractions as a number). How will you work it out? Use a bead string and double number line to find 3/5 of 100. (Fractions as an operator). How will you work it out?

47. Key Idea 7 Sam had one half of a cake, Julie had one quarter of a cake, so Sam had most. True or False or Maybe

48. Key Idea 7 Fractions are always relative to the whole. Halves are not always bigger than quarters, it depends on what the whole is.

49. What is the whole?

50. Key Idea 8 - Ratios! 1:1 Write 1/2 as a ratio 3: 4 is the ratio of red to blue beans. What fraction of the beans are red? 3/7 Think of some real life contexts when ratios are used.