1. Teaching Proportions and Ratios Kapiti Inquiry Group

2. The day…. 9-12:30pm Teaching proportions and ratios – leading this. 1- 2:30pmInquiry group meetings.

3. Outcomes  Leading the teaching of Fractions, Proportions and Ratios  Helping teachers identifying strategies on Number Framework  Exploring key ideas and involved in understanding fractions, decimals, ratios and proportions

4. Let’s start with the Best Evidence …What works? Using the ‘Understanding Fractions’ booklet. What does the research say is best practice? What are the key findings from this for you and the teachers at your school? What will you take back?

5. Sharing current practice Sit with someone from another school. Share any equipment or activities you have brought along. Any you think should be shared as a whole group?

6. Representations for 3/4 … Using the materials show six representations for ¾ Can you see any similarities and differences between all your representations (materials and grid)? 3/4

7. Fraction Concepts - Discrete Wiremu had six lollies. He gave his friend two- thirds. How many did he give away? Whole to Part Toni got two-thirds of the lollies. How many lollies were there? Part to Whole

8. Fraction Concepts - Continuous This is one-quarter of a shape. What is the shape? Part to Whole How many ways can you find to cut this shape into quarters? Whole to Part

9. Whole to part vs Part to whole Book 7 page 14 What’s the difference?

10. What does ¾ mean? A part of a whole eg. “3 parts out of 4 equal parts” A comparison between a set of objects and part of the set eg. ¾ of the dots are shaded.    

11. What does ¾ mean? Measure eg. “3 measures of ¼’’ A number on a number line 0 ¾ 1 ¼ cup

12. What does ¾ mean? The result of a division “3 divided by 4”. eg. How much chocolate does each person get if three bars are divided amongst four people?

13. What does ¾ mean? A comparison between sizes of 2 sets of objects or 2 measurements Ashley has ¾ as many stars as Ani Line A is ¾ the length of Line B   

14. Ways to show ¾. Number box assessment idea. Consider how you could use/adapt this to suit your class level for an activity and/or assessment. ¾

15. Luke’s fraction display What does Luke understand? What is a possible next step?

16. We are learning about fractions

18. What are the implications of using this language?

20. References CA-AC Fair Shares p.11 AC-EA Wafers p.16 EA-AA Seed Packets p. 30 AA-AM Hot Shots p.47

21. ICT Link – Fraction Fiddle http://www.tki.org.nz/r/digistore/protected/objects/?id=2802&vers=1.0

22. Key understandings for Fractions A fraction is defined by it’s relationship to a ‘whole’. The ‘whole’ or the one is constantly changing. (Back to whole – important!!) It’s not about counting – there is no obvious sequence. Fractions have an infinite number of names ie equivalent fractions Fractions as an extension of the whole number system Fractions exist both as numbers and operators. Students need opportunities to split up (partition) and repackage (re-unitise) to assist in understanding the relationship between numerator and denominator.