Beginning the Journey into Algebra & Algebraic Thinking Dr. DeAnn Huinker, Dr. Kevin McLeod, Dr. Henry Kepner University of Wisconsin-Milwaukee Milwaukee Mathematics Partnership (MMP) Math Teacher Leader (MTL) Kickoff, August This material is based upon work supported by the National Science Foundation Grant No. EHR

Session Goals To launch our journey into algebra. To link our algebra journey with the Wisconsin Standards and Assessment Framework. To begin examining the “big ideas” of algebra.

Why Algebra? A key to success “in algebra” is the development of algebraic thinking as a cohesive thread in the mathematics curriculum from prekindergarten through high school. Cathy Seeley, President National Council of Teachers of Mathematics

Why Algebra? About 1/5 (15%–20%) of the WKCE points in all grades assess algebra. MPS students score low in this area. Need more focus in math programs and in math instruction.

WKCE-CRT Mathematics Assessment Blueprint Process Number Geometry Measurement Statistics & Probability Algebra

What is algebra? What are your memories of learning it? Individually, reflect silently for a moment. Small group graffiti.  Write algebra in the middle of the paper.  Everyone grabs a marker and records phrases or draws pictures/diagrams.  Take turns summarizing.

skill memory skill topic task

Generalized Properties Patterns, Relations, and Functions Expressions, Equations, and Inequalities Sub-skill Areas    – 25  = 37 a x b = b x a Algebraic Relationships

Does this figure remind you anything?

Bridge of length 2 Bridge of length 3 Make a bridge of length 4. Build it with toothpicks or draw it.

Investigate: How many rods are needed for a bridge of length 2? Length 3? Length 4? And so on. Note: All rods are the same length.

What are you noticing? How many rods would be needed for a bridge of length 20? Length 100? Describe your reasoning. How does your reasoning relate to the bridge?

How do each of these generalized observations relate to the bridge? n + 2n + (n – 1) n = number of rods 3n + (n – 1) 4n – (n – 1) 4(n – 1) + 3 Next = Now + 4

NCTM President’s Message “A Journey Into Algebraic Thinking” Individually: Read and Note… What are characteristics of algebraic thinking to develop throughout grades PK–12? Small Group  Create a group list of “3–5” key characteristics of algebraic thinking.  Discuss: In what ways were you engaged in algebraic thinking today?

Big Idea: Patterns Mathematical situations often have numbers or objects that repeat in predictable ways called patterns. Patterns can often be generalized using algebraic expressions, equations or functions.

Big Idea: Equivalence Any expression, equation or function can be expressed in equivalent ways.

Big Idea: Variable Numbers or other mathematical objects can be represented abstractly using variables. Relationships between mathematical objects can often be represented abstractly by combining variables in expressions, equations or functions.