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Beginning the Journey into Algebra & Algebraic Thinking

Launch your algebra journey, link with Wisconsin Standards, develop algebraic thinking from prekindergarten through high school. Explore big ideas, patterns, equivalence, variables, and algebraic relationships.

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Beginning the Journey into Algebra & Algebraic Thinking

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  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 (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.

  5. Process Number Geometry Measurement Statistics & Probability Algebra 3 4 5 6 7 8 10 • WKCE-CRT • Mathematics Assessment Blueprint

  6. 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.

  7. skill memory topic Algebra task topic memory skill task

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

  9. Does this figure remind you anything?

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

  11. 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.

  12. 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?

  13. 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

  14. 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?

  15. 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.

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

  17. 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.

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