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Teaching Proportions and Ratios Kapiti Inquiry Group

Teaching Proportions and Ratios Kapiti Inquiry Group. The day…. 9-12:30pm Teaching proportions and ratios – leading this. 1- 2:30pm Inquiry group meetings. Outcomes. Leading the teaching of Fractions, Proportions and Ratios

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Teaching Proportions and Ratios Kapiti Inquiry Group

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  1. Teaching Proportions and RatiosKapiti Inquiry Group

  2. The day…. 9-12:30pm Teaching proportions and ratios – leading this. 1- 2:30pm Inquiry 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. What’s the difference? Whole to part vs Part to whole Book 7 page 14

  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 ¼ cup 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

  17. What are the implications of using this language?

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

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

  20. 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.

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