DIG INTO LINEAR FUNCTIONS: THE ROPE PROBLEM Presented by MathLinks - - PowerPoint PPT Presentation

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DIG INTO LINEAR FUNCTIONS: THE ROPE PROBLEM Presented by MathLinks - - PowerPoint PPT Presentation

Mar 25, 2024 202 likes •335 views

DIG INTO LINEAR FUNCTIONS: THE ROPE 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:

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DIG INTO LINEAR FUNCTIONS: THE ROPE 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

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In this session, we will explore a context that helps students:

— Use mathematical representations to solve a

problem.

— Interpret slope and y-intercept in a meaningful

way.

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The Rope Problem

What relationships could we explore?

layer 1 1 cut layer 2 bend layer 3

Suppose a rope is “bent” back and forth. When cut, it may look something like this.

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3 layers 2 cuts 7 pieces Figure B

Exploring layers, cuts, and pieces

3 layers 1 cut 4 pieces Figure A Incorrect way to cut! Cuts should be vertical. Figure C Incorrect way to cut! Cuts should go through all layers. Figure D

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Collect Data

  • 1. # of layers (q) = 1

# of cuts (c) # of pieces (p) 1 1 2 2 3 3 4 Rule for any number of cuts: p = c + 1

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Collect Data

  • 2. # of layers (q) = 2

# of cuts (c) # of pieces (p) 1 1 3 2 5 3 7 Rule for any number of cuts: p = 2c + 1

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Collect Data

  • 3. # of layers (q) = 3

# of cuts (c) # of pieces (p) 1 1 4 2 7 3 10 Rule for any number of cuts: p = 3c + 1

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Connect and Extend

# of pieces

How are the expressions and graphs related?

p = q⋅c +1

Number

  • f Layers

(q) Number

  • f Pieces

(p) 1 1c + 1 2 2c + 1 3 3c + 1 4 4c + 1 # of cuts

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In this session, students generalized relationships in the rope problem by:

— Using mathematical representations to solve the

problem

— Interpreting slope and y-intercept in a

meaningful way

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Handout

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www.mathandteaching.org/webinars

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OUR PROGRAMS:

— Comprehensive 6-8 curriculum — Customized intervention grades 6-9 — Special Education programs — Supplemental programs

For more information, please visit our website at www.mathandteaching.org

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THANK YOU!

Shelley Kriegler (shelley@mathandteaching.org) Mark Goldstein (mark@mathandteaching.org) To download handouts or view webinars go to

www.mathandteaching.org/webinars