1. K-8 Mathematics Standards Content Training Rate of Change Grades 6-12

2.  Cathey Bolson, Math Coordinator, ESD 123  Debi DePaul, Math Coordinator, ESD 123 2

3.  Develop participant’s conceptual understanding of rate of change.  Experience activities that help students develop these concepts.  Determine the level of understanding for these concepts at your grade level based on the state standards. 3

4.  Allow ourselves and others to be seen as learners.  Monitor own airtime and sidebar conversations.  Allow for opportunities for equitable sharing.  Presume positive intentions.  Be respectful when giving and receiving opinions, ideas and approaches. 4

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6. For all students to learn significant mathematics, content should be taught and assessed in meaningful situations. 6

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8.  Conceptual Understanding ◦ Making sense of mathematics  Procedural Proficiency ◦ Skills, facts, and procedures  Mathematical Processes ◦ Using mathematics to reason and think 8

9.  At each grade level: ◦ 3-4 Core Content areas ◦ Additional Key Content ◦ Core Processes (reasoning, problem solving, communication)  For each of these: ◦ Overview paragraph ◦ Performance Expectation ◦ Comments/Examples 9

10.  Use either your Standards Document or Strands Document to find all K-8 references to measurement.  Go back and carefully read the Performance Expectations and Explanatory Comments and Examples for your grade level.  Note the expectations for the grade level above and below yours. 10 What should your students already know? What do you need to teach this year? What do they need to know for next year? What should your students already know? What do you need to teach this year? What do they need to know for next year?

11.  Study the pattern below. How many tiles would be in the next step?  Predict what type of equation this pattern will produce.  Write an equation for the number of tiles in the n th step. 11

12. Context Find the number of tiles in the n th step. Table GraphEquation t = 12n - 3 t = total number of tiles n = step number 12

13.  Work through the investigation with a partner  What standard(s) does this activity address?  Which representation was the easiest to use to answer questions 7-10? 13 Adapted from Discovering Algebra: An Investigative Approach (Key Curriculum Press)

14. 30 minutes

15.  Complete the Painted-Cube Patterns activity with a partner  How hard would it have been to find the equations without a sketch of the cubes? What about for students?  Were your predictions correct?  What standard(s) does this activity address? 15 Adapted from Frogs, Fleas, and Painted Cubes (Connected Mathematics 2002)

16.  What type of equation would you expect from the problem?  How do you know if it is a growth or decay problem? 16

17.  Complete the activity as a table  What prior knowledge would students need to complete this task?  How could this task be scaffold up or down to meet the needs of your students?  What standard(s) does this task address? 17 Adapted from Discovering Algebra: An Investigative Approach (Key Curriculum Press)

18.  Frogs, Fleas, and Painted Cubes, Connected Mathematics  Teaching Student-Centered Mathematics Grades 5-8, John A. Van de Walle  Discovering Algebra an Investigative Approach, Key Curriculum Press 18

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