Constructing Algebra Pamela Weber Harris @pwharris pamelawharris.com [email protected].

Constructing Algebra

Pamela Weber Harris@pwharris

[email protected]

Math is figure-out-

able!

Cathy Fosnot - Young

Mathematicians at Work• Big, rich problems

•Class congress: specific groups share toward targeted goal•More directed, focused mini-lessons

Landscape of Learning

The New TEKS

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

The New TEKS

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

The New TEKS

A.b.3Students 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.

The New TEKS

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

Motion Sensor

TI CBR2

What Other Scenarios?

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?

Watch the Bird Fly

What Did We Learn?

Birds Fly

What Did We Learn?

Compare Birds’ Flights

What Did We Learn?

Problem

Strings

2 x 274 x 278 x 2710 x 279 x 275 x 27100 x

2799 x 27

Problem

Strings

49 + 287 x 7 + 4 x 777 + 6311 x 7 + 9 x

756 + 247 x 8 + 3 x 8

88 + 7211a + 9a

Counting

Additive

Multiplicative

Proportional Reasoning

Algebraic Reasoning

Problem

Strings

Start at 2, walk away 1 ft/s

Start at 10, walk toward 2 ft/s

Start at 5 and stand stillSaw at 2 ft at 1 s, 3 ft at

2 sSaw at 16 ft at 3s, 15 ft

at 2 sSaw at 4 ft at 3 s, 8 ft at

6 s

Wait Time ...

Piaget

•Social Knowledge

•Logico-Mathematical Knowledge

Do you go up first or over? (2, -3)

Which axis is called x? y?Who is the 8th president of the

US?Whose variable notation do

we use?

Math is Figure-out-able

•Give kids a chance to build intuition

•It’s about relationships:

- Between what you know and the new, build to the new

- Between teachers and students to build young mathematicians

Constructing Algebra

Pamela Weber Harris@pwharris

[email protected]