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DIG INTO REPRESENTATIONS: A BAGEL PROBLEM Presented by MathLinks - PowerPoint PPT Presentation

Oct 17, 2023 •601 likes •729 views

DIG INTO REPRESENTATIONS: A BAGEL PROBLEM Presented by MathLinks Authors Mark Goldstein and Shelley Kriegler For more information about our core programs for middle school and intervention programs for grades 6-9, please visit:

  1. DIG INTO REPRESENTATIONS: A BAGEL PROBLEM Presented by MathLinks Authors Mark Goldstein and Shelley Kriegler For more information about our core programs for middle school and intervention programs for grades 6-9, please visit: www.mathandteaching.org

  2. In this session, we will: — examine multiple representations for displaying which is a better buy among two items — make connections among representations 2

  3. A Context What do you know? What do you wonder? 3

  4. A Straightforward Question and Answer Which is the better buy? ⎛ ⎞ 3.00 ⎛ ⎞ 4.00 = 0.75 = ⎜ ⎟ 0.80 ⎜ ⎟ 4 ⎝ ⎠ 5 ⎝ ⎠ At Smear ‘n Things, each bagel costs $.75. At Hole-y Bread, each bagel costs $.80. Therefore Smear ‘N Things is the better buy. 4

  5. But there is so much more to learn from this context… 5

  6. Tables Shmear ‘n Shmear ‘n Shmear ‘n Shmear ‘n Shmear ‘n Shmear ‘n Shmear ‘n Things Things Things Things Things Things Things Hole-y Bread Hole-y Bread Hole-y Bread # of bagels # of bagels # of bagels # of bagels # of bagels # of bagels Cost in $ Cost in $ Cost in $ Cost in $ Cost in $ Cost in $ # of bagels # of bagels # of bagels Cost in $ Cost in $ Cost in $ ( x ) ( x ) ( x ) ( x ) ( x ) ( x ) ( y ) ( y ) ( y ) ( y ) ( y ) ( y ) ( x ) ( x ) ( x ) ( y ) ( y ) ( y ) 4 4 4 4 4 3 3 3 3 3 5 5 4 10 8 8 8 8 8 6 6 6 6 10 10 8 16 12 15 12 16 16 16 12 12 12 15 15 12 2 2 1.50 1.50 20 20 16 10 7.50 10 7.50 25 25 20 6

  7. Graphs 0 2 4 6 8 10 12 Holey Bread Smear ‘n Things Cost More bagels for the same money at Smear ‘n Things 0 2 4 6 8 10 12 # of bagels 7

  8. Equations Shmear ‘n Things Hole-y Bread # of bagels Cost in $ # of bagels Cost in $ ( x ) ( y ) ( x ) ( y ) 4 3 5 4 8 6 10 8 16 12 15 12 y = 0.75 x y = 0.80 x unit rate! 8

  9. In this session, we — created tables, graphs, and equations to determine the better buy in a “best buy” context. — explored connections among representations. 9

  10. OUR PROGRAMS: — Comprehensive 6-8 curriculum — Customized intervention grades 6-9 — Special Education programs — Supplemental programs — Professional development For more information, please visit our website at www.mathandteaching.org 10

  11. THANK YOU! Shelley Kriegler (shelley@mathandteaching.org) Mark Goldstein (mark@mathandteaching.org) To download handouts or view webinars go to www.mathandteaching.org/webinars

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