Beyond X's and Y's: Making Algebraic Thinking Happen

Columbus Regional Mathematics Collaborative

October 2013

Welcome

• http://www.youtube.com/watch?v=yQej8AOjEHc

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 topicsWhet your mathematical appetite Contact us for help/clarificationResources will be located at

http://crmc.columbusstate.edu/

Algebra Tiles

Modeling & Solving Equations with Algebra Tiles

http://illuminations.nctm.org/ActivityDetail.aspx?ID=216

x + 5 = -8

3x = -12

- x – 3 = 8

3x – 2 = 4x + 5

-2x + 7 = 3x – 3

3x – 5 – 4x = 6 – 2x + 1

Equations with Fractional Coefficients

• Making fractional coefficients have meaning

• Using…• Pattern Blocks• Two-color counters

x = 6

x = 9

x = 20

Proportional Reasoning

• Making the relationships explicit

• Using… • Square tiles• Tables

• Introduce a pictorial representation before introducing

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 = 5x – y = 5

2x + y = 52x + 3y = 11

2x + y = 7x – 2y = 6

Systems of Equations Mat for Elimination

Solving by Substitution

y = 2x + 33x + 2y = 20

x = -y + 52x + 4y = -6

x = y + 3-2x – 3y = 4

Systems of Equations Mat for Substitution

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Gizmos: Exciting & New

• http://www.explorelearning.com/

• 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• First, pick the number of times a week that you would like to have

chocolate (more than once but less than 10….. 1)

• Multiply this number by 2 • Add 5• Multiply by 50 • If you have already had your birthday this year, add 1763. If you

haven't, add 1762.• Now subtract the four-digit year that you were born.• You should have a three-digit number.• The first digit of this is your original number (how many times you

want to have chocolate each week).• The next two numbers are…YOUR AGE!

How does this work?