1. Carole Saundry-Fullerton Math 9 - Implementation Adventures in re-thinking

2. revisiting the IRP

3. statements from the IRP

4. revisiting the IRP What are the implications?

6. good questions... addressing the big math ideas in the pattern and algebra strand...

7. Increasing patterns

8. How can you make an increasing pattern with your materials? How does your pattern change? Use words and numbers to describe it. Record the change in a T-Chart. What expression can you write? Graph the relation. How can you?

12. # of blocks=4(years) + 2

17. Popcorn stories...

18. student samples... Student 2 A- the tub is filled up and the movie just started. B-commercials; no popcorn was eaten C&D- they ate some popcorn E-they continued to enjoy the popcorn F- the movie got drastically exciting and they ate popcorn like crazy F&G&H-they ran out; Hayley went to get more I- the tub is full again J- they are eating it K-they are eating it slower L- the movie and the popcorn is over

19. Student 9 Between A-B Hayley bought a tub of popcorn. Between B-C They ate popcorn gradually, not in handfuls but in rapid amounts like trains leading to a tunnel. Between C-D They took a break of not eating popcorn after they realized they had eaten way too much and they to save it for later. Between D-E Hayley started eating secretly very little then felt a bit guilty and stopped. Between E-F Ariel started eating secretly very little then felt a bit guilty and stopped. Between F-G They started laughing really hard and then they accidentally dropped the popcorn. Between H-I They refilled the tub at a slight discount. Between I-J They grabbed a huge clump at a time but eating it one at a time from their hands though. Between J-K They continued grabbed a huge clump at a time but eating it one at a time from their hands though. Then they ate it the way a normal person does. Between K-L They ate it gradually and then ate the rest all at once during the credits

20. Student 9 Between A-B Hayley bought a tub of popcorn. Between B-C They ate popcorn gradually, not in handfuls but in rapid amounts like trains leading to a tunnel. Between C-D They took a break of not eating popcorn after they realized they had eaten way too much and they to save it for later. Between D-E Hayley started eating secretly very little then felt a bit guilty and stopped. Between E-F Ariel started eating secretly very little then felt a bit guilty and stopped. Between F-G They started laughing really hard and then they accidentally dropped the popcorn. Between H-I They refilled the tub at a slight discount. Between I-J They grabbed a huge clump at a time but eating it one at a time from their hands though. Between J-K They continued grabbed a huge clump at a time but eating it one at a time from their hands though. Then they ate it the way a normal person does. Between K-L They ate it gradually and then ate the rest all at once during the credits

21. What’s my point? y=x+2 y= 1/2 x-2 y=-4x-11 (-3,1) I have 2 points. They are on the line y=-4x-11. (-4, 5) (-2,-3) Is one of your points (-2, -3)? (-2,-3) is on the line, but below my points. Is one of your points (-4, 5)?

22. the curriculum says... G RADE 9 Patterns B1 generalize a pattern arising from a problem-solving context using linear equations and verify by substitution [C, CN, PS, R, V] B2 graph linear relations, analyse the graph, and interpolate or extrapolate to solve problems [C, CN, PS, R, T, V]

23. the curriculum says...

24. consider... The manipulatives to get them there...

25. algebra tiles... Assumed prior knowledge... Addition, subtraction of integers. Area models for multiplication.

26. equation persuasion Choose a secret n, between -9 and +9. Record your number privately. Remove the face cards, then deal 3 cards to each player. Follow the instructions in the chart, and re-write your equation.

27. equation persuasion

28. 5(4n + 4) = 5(1 + 3n) n = -3 n+4 = 1 4n + 4 = 1 + 3n

29. equation persuasion Trade equations with a partner. Use algebra tiles. Solve your partner’s equation, & find “n”. Correct answers score 5 points. First one to 50 points wins.

31. the curriculum says... B5 demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2) [C, CN, R, V]

32. consider... Take a handful of algebra tiles. Place them on the table in front of you. What polynomial name can you give to the group? Write it down. Are there other names? How do you know? Record the new name.

34. consider... Use your set of algebra tiles (arranged to show a polynomial expression) from before. Work with a partner. ADD your polynomial expressions together. What’s your sum?

35. consider... Use your set of algebra tiles (arranged to show a polynomial expression). Work with a NEW partner. Subtract one polynomial expression from the other. What’s the difference?

36. tasks Shade a T on a hundreds chart. What’s the sum of the 5 numbers? What polynomial can you write to describe the sum and locate any T on a hundreds chart??

37. the curriculum says... B6 model, record, and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially, and symbolically (limited to polynomials of degree less than or equal to 2) [C, CN, PS, R, V]

38. the curriculum says... B7 model, record, and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials, concretely, pictorially, and symbolically [C, CN, R, V]

40. performance tasks What do you notice about the sum of the diagonals in any 3x3 square? Determine a relationship between the number at the centre of a 3x3 square and the sum of the numbers in the diagonal.

41. performance tasks Let x be the number at the centre of the square. Write a polynomial in terms of x, for the numbers at the 4 corners of the square. Add the polynomials in each diagonal. What’s the sum? How does this explain what you found earlier? ?? x ??

42. performance tasks What can you find out about the diagonals in a 5x5 square? A 7x7 square?

44. so? what have you heard so far? what connections are you making?

45. planning Meet in school groups - or better yet, meet in mixed school groupings. Discuss/make plans for the next few weeks. How will manipulatives figure in?

46. resources

48. reflect What did you come away with? What was helpful/useful about the structure of the day? What questions do you still have?

49. carole fullerton mindfull.consulting@gmail.com blog: http://mindfull.wordpress.com mindfull.consulting@gmail.com