1 / 31

Generalising from number properties to algebra

Generalising from number properties to algebra. A Adviser in Numeracy, Mathematics and NCEA. Teaching progression (adapted from Pierre – Kieren). Materials. Images. Knowledge. A Teaching Progression. Start by: Using materials, diagrams to illustrate and solve the problem Progress to:

pennie
Download Presentation

Generalising from number properties to algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Generalising from number properties to algebra A Adviser in Numeracy, Mathematics and NCEA

  2. Teaching progression (adapted from Pierre – Kieren) • Materials Images Knowledge

  3. A Teaching Progression Start by: • Using materials, diagrams to illustrate and solve the problem Progress to: • Developing mental images to help solve the problem Extend to: • Working abstractly with the number property

  4. To reinforce and consolidate Move back and forth between: • Using materials, diagrams to illustrate and solve the problem and: • Developing mental images to help solve the problem and: • Working abstractly with the number property

  5. Discovering algebraic ‘rules’ for expanding Based on an array model for multiplication • Ideas adapted from • Cyril Quinlan. Analysing teaching/learning strategies for algebra. P 459-464. MERGA 18 (Eighteenth annual conference of the mathematics education research group of Australasia Darwin 1995). • http://www.blackdouglas.com.au

  6. One bracket with addition • Start with 3 rows of 7 counters

  7. Discuss how this might be written Focus on

  8. Place a straw between two columns What does it now show?Record it as

  9. How else can you place the straw to show the same thing? Discuss what this shows:

  10. How else can you place the straw to show something different?

  11. How many different ways of placing the straw can you find? • How many different ways can you find of writing ? • Record them all. • Can you find a pattern?

  12. What about placing the straw along the row?

  13. Repeat using different numbers with one straw. • Progress to using grids to show the same thing.

  14. Generalise to number properties

  15. Generalise to number properties

  16. Numbers greater than 10…

  17. A suggested progression • Start with rows of counters in columns • Use a straw to generate different number properties • Repeat for different numbers • Generalise number properties with words • Extend from counters to grids or arrays • Generalise properties using symbols

  18. Investigate • Two brackets with addition • One bracket with subtraction • Two brackets with subtraction

  19. Two brackets with addition

  20. One bracket with subtraction

  21. What about these?

  22. Is the use of counters necessary? Do students need to cut out grids or is shading of rectangles sufficient? How important is recording? What is the best way of leading into the use of symbols? Questions to consider…

More Related