Beyond X's and Y's: Making Algebraic Thinking Happen Columbus Regional Mathematics Collaborative October 2013

Welcome

Can your students solve for a variable? Balance equations? Solve a proportion? That's only part of the story! Students who can "do" algebra do not, necessarily, think algebraically. Yet, algebraic reasoning forms the core of the middle grades CCGPS standards. Learn ways to improve students’ algebraic thinking without relying on a procedural approach, while engaging them in meaningful problem solving and discourse. Help students discover that mathematics involves creativity and non-routine thinking.

“Speed Dating” Approach to Algebraic Thinking  Introduce a variety of topics  Whet your mathematical appetite  Contact us for help/clarification  Resources will be located at

Algebra Tiles

Modeling & Solving Equations with Algebra Tiles x + 5 = -8 3x = x – 3 = 8 3x – 2 = 4x x + 7 = 3x – 3 3x – 5 – 4x = 6 – 2x + 1

Equations with Fractional Coefficients Making fractional coefficients have meaning Using… Pattern Blocks Two-color counters

Proportional Reasoning

We have observed that the M&M’s company seems to make 3 blue candies for every 5 non-blue candies. How many non-blue candies would you expect to find in a bag with 27 blue candies?

A family bought 12-pack Cokes to serve at their football party. There were 18 people at the party. They used 4 ½ packs of the 12-pack drinks. Next year the party will be expanded, and there will be 24 people. How many 12-pack Cokes should the family buy?

Percent Problems A tool to make symbolic relationships visual Using… Dot paper 1. The PTA reported that 75% of the total number of families were represented at the meeting. If students from 320 families go to the school, how many were represented at the meeting? 2. Zane bought his new computer at a 37½% discount. He paid $700. How many dollars did he save by buying it at a discount? 3. The hardware store bought widgets at 80 cents each and sold them for $1 each. What percent did the store mark up the price of each widget?

Systems of Equations Using algebra tiles to model the mathematics Making relationships explicit Solving by Substitution Elimination

Solving by Elimination x + y = 5 x – y = 5 2x + y = 5 2x + 3y = 11 2x + y = 7 x – 2y = 6

Systems of Equations Mat for Elimination

Solving by Substitution y = 2x + 3 3x + 2y = 20 x = -y + 5 2x + 4y = -6 x = y x – 3y = 4

Systems of Equations Mat for Substitution

Gizmos: Exciting & New The world's largest library of interactive online simulations for math and science education in grades 3-12 Simulations called Gizmos Subscription required

Farewell on a Light Note