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1 Gear Ratios, Resistance and Recipe Yields Galore: Leveraging CT for Math Understanding Greetings from Kathleen Southern Regional Education Board Leveraging CTE tasks for a “productive struggle” Fun thought challenge: Two sheets of 8.5X11 “ paper… roll one into a short cylinder and the other into a tall cylinder…does one hold more popcorn than the other?

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2 The Mathematical Mind How many students in a mathematics class answered these questions as follows?

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3 Study: Mild Shocks to Brain Improve Math Skills Huffington Post, 5/17/13

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4 Essential Questions: Why is it everyone’s job to help students understand math? What does math teaching look like in the non-math classroom? How should math and CTE teachers collaborate to support student understanding of mathematics? Southern Regional Education Board

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5 “just in time” mathematics…

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6 Security Cameras…

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10 Source: CTE and Innovation Opportunity The Power of Problems 2012 Skydive from Space!

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12 SDW

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13 Venn Diagram Approach to Thinking… Your job is to brainstorm where in your CTE tasks, projects, LIFE….you can see and “supersize” mathematics…

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14 Areas Enhanced via CTE High School CCSSM Numbers and Quantity Algebra Geometry Functions Modeling Statistics and Probability Middle School CCSSM Number Sense Expressions and Equations Functions Geometry Statistics and Probability

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15 Proportional reasoning Rates of change Spatial relationships: lengths, areas, volumes Measurement: time, money, resources—precision and accuracy Fixed and variable costs Data analysis

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16 From the Common Core State Standard-minds …

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21 Richness: Go Larry!

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22 Richness: Go Eric!

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24 How does a “mathematical expert” think?

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25 Standards for Mathematical Practice 1.Make sense of problems and persevere in solving them 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

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26 Mathematics Design Collaborative

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27 The Gates’ BIG IDEA of Formative Assessment Students and teachers Using evidence of learning To adapt teaching and learning To meet immediate learning needs Minute-to-minute and day-by-day What resonate s? ~ Marnie Thompson and Dylan Wiliam (2008)

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28 What is a Formative Assessment Lesson? The common core standards make clear that students must be able to use mathematics with precision—to get the numbers right, and also to solve problems that are not routine, to gain a conceptual understanding of the math and apply it. Formative assessment lessons are designed to help teachers uncover student misconceptions and find a path to help students progress.

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29 Why Formative Assessment Lessons?

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30 vs.

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31 Keep the momentum! Where do we go now?

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32 Google: “Mathematics Assessment Project” Shell Centre for Mathematics Education ~ University of Nottingham & U.C. Berkeley

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33 Keep “super-sizing” that Numeracy! Kathleen McNally Kathleen.mcnally@sreb.org Thank you for the awesome opportunities you provide across The USA! Keep the mathematics momentum going!

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