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Constructing Algebra Pamela Weber Harris @pwharris pamelawharris.com pharris@byu.net

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Math is figure-out- able!

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Cathy Fosnot - Young Mathematicians at Work Big, rich problems Class congress: specific groups share toward targeted goal More directed, focused mini-lessons

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Landscape of Learning

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The New TEKS A.b.3 Students will study linear, quadratic, and exponential functions and their related transformations, equations, and associated solutions.

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The New TEKS A.b.3 Students will use technology to collect and explore data and analyze statistical relationships.

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The New TEKS A.b.3 Students will study polynomials of degree one and two, radical expressions, sequences, and laws of exponents. Students will generate and solve linear systems with two equations and two variables and will create new functions through transformations.

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The New TEKS A.c.3 Linear Functions, Equations, Inequalities The student will determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d

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Motion Sensor TI CBR2

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What Other Scenarios?

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How Can I Walk? a line that goes up? a line that is steep? a curve that opens up? a curve that opens down? a graph that starts at 6? a horizontal line?

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Watch the Bird Fly

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What Did We Learn?

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Birds Fly

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What Did We Learn?

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Compare Birds Flights

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What Did We Learn?

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Proble m Strings 2 x 274 x 278 x 2710 x 279 x 275 x 27100 x 2799 x 27

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Proble m Strings 49 + 287 x 7 + 4 x 777 + 6311 x 7 + 9 x 7 56 + 247 x 8 + 3 x 8 88 + 72 11a + 9a

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Counting Additive Multiplicative Proportional Reasoning Algebraic Reasoning

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Proble m Strings Start at 2, walk away 1 ft/s Start at 10, walk toward 2 ft/s Start at 5 and stand still Saw at 2 ft at 1 s, 3 ft at 2 s Saw at 16 ft at 3s, 15 ft at 2 s Saw at 4 ft at 3 s, 8 ft at 6 s

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Wait Time...

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Piaget Social Knowledge Logico-Mathematical Knowledge

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Do you go up first or over? (2, -3) Which axis is called x? y? Who is the 8 th president of the US? Whose variable notation do we use?

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Math is Figure-out- able Give kids a chance to build intuition Its about relationships: - Between what you know and the new, build to the new - Between teachers and students to build young mathematicians

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Constructing Algebra Pamela Weber Harris @pwharris pamelawharris.com pharris@byu.net

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