Beginning the Journey into Algebra

1
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 2005
• www.mmp.uwm.edu

This material is based upon work supported by the
National Science Foundation Grant No.
EHR-0314898.
2
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.

3
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, PresidentNational Council of
  Teachers of Mathematics

4
Why Algebra?

• About 1/5 (1520) 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.

5
WKCE-CRT Mathematics Assessment Blueprint
6
(No Transcript)
7
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.

8
skill
memory
topic
Algebra
task
topic
memory
skill
task
9
Algebraic Relationships
Expressions, Equations, and Inequalities
Generalized Properties
Sub-skill Areas
a x b b x a
Patterns, Relations, and Functions
??? 25? 37
10
Does this figure remind you anything?
11

• Bridge of length 2

Bridge of length 3
Make a bridge of length 4. Build it with
toothpicks or draw it.
12
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.
13
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?
14
How do each of these generalized observations
relate to the bridge?

• n 2n (n 1) n number of rods
• 3n (n 1)
• 4n 1
• 3 4(n 1)
• 4(n 1) 3
• Next Now 4

15
NCTM Presidents MessageA Journey Into
Algebraic Thinking

• Individually Read and Note
• What are characteristics of algebraic thinking to
  develop throughout grades PK12?
• Small Group
• Create a group list of 35 key
• characteristics of algebraic thinking.
• Discuss In what ways were you engaged in
  algebraic thinking today?

16
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.

17
Big Idea Equivalence

• Any expression, equation or function can be
  expressed in equivalent ways.

18
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.