Algebraic Thinking Chapter 12

Algebra Study of patterns and relationships Way of thinking An art—characterized by order and internal consistency Language that uses carefully defined terms and symbols Tool

Algebra Traditionally students don’t begin Algebra until they have a solid foundation in arithmetic, unfortunately students who didn’t do well in math were not offered the opportunity to study Algebra NCTM standards infused Algebra into all elementary grades in an effort to produce better problem solvers

NCTM standards for Algebra K-5 (see pg 311) Algebra Instructional programs from prekindergarten through grade 12 should enable all students to— Understand patterns, relations, and functions Understand patterns Represent and analyze mathematical situations and structures using algebraic symbols Represent and analyze Use mathematical models to represent and understand quantitative relationships Use mathematical models Analyze change in various contexts Analyze change Understand patterns, relations, and functions Pre-K–2 Expectations: In pre-K through grade 2 all students should– sort, classify, and order objects by size, number, and other properties; recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another; analyze how both repeating and growing patterns are generated. Grades 3–5 Expectations: In grades 3–5 all students should– describe, extend, and make generalizations about geometric and numeric patterns; represent and analyze patterns and functions, using words, tables, and graphs.

Algebra –complete this math puzzle why (how) does it work? Game #1 a. pick a number b. add 4 c. double it d. subtract 6 e. divide by 2 f. subtract 1 g. What did you get? Why does it work?

Patterns- Remember that your students see things differently than you do—Have them explain their reasoning as they complete these patterns Try These (grade 4) Pattern A 1,2,4,… give the next three numbers Three numbers in the pattern

Patterns Pattern A 1,2,4,… give the next three numbers Three numbers in the pattern Student 1 5,7,8 what is he thinking? Student 2 8,16,32 what is he thinking? Student 3 6,9,12 what is he/she thinking? Make sure students always explain and communicate their thinking.

Patterns This one is given to second grade students Patten B 1,4,9,16,…find the next three numbers in the pattern Student1 25,36,49 by following pattern +3, +5, +7… is this correct? Student 2 11,13,15 why? Student 3 1,4,9,16,1,4,9, what is he/she thinking?

Relation/ Functions Boys (x) Hands (y) Use a rule to describe this relation Y= ______x

Function/ Relations Input x36720 Output y As the students get older the function table becomes more complicated can you describe the pattern?(rule) Y= _____x + _____

Language/ vocabulary Variable Equality = Inequality Expressions 4x +3 Equations 4x+4 =8 Relation (x,y) Function –rule y= 2x+4