TURN ALGEBRA EXERCISES into COMMON CORE PRACTICE TASKS

 Make Sense and Persevere.  Reason Abstractly.  Construct Viable Arguments.  Model with Mathematics.  Look for and Use Structure.  Look for and Express Regularity. CORE PRACTICES

 Rewrite Equivalent Expressions; Justify.  Create and Reconcile Algebraic Representations.  Decide on a Strategy for Solving  Solve a Really Hard Problem PROBLEM MAKING STRATEGIES

 Identify/Explain Errors.  Work Backwards  Have Students Create the Problem  Give an Example of………  Reverse Your Class Routine  Play a Game

Rewriting Equivalent Expressions and Equations : Rewrite each of the following expressions in at least two different ways. Verify using tables, graphs, or algebra that each new expression is equivalent to the original.

a. b. c.

Ramon’s group was trying to rewrite in simpler form. They came up with four different results:,,, Which are equivalent? Use graphs, tables, and algebra to explain.

Create and Reconcile Algebraic Representations

Create and Reconcile Algebraic Representations Work with a partner and use the one xy piece and one y piece to form a figure. Record the area and perimeter for your figure. How many different results are there for the perimeter? For the area?

Using exactly these three pieces build an arrangement for each of the following perimeters. a. 4y + 4 b. 2x + 4y c. 2x + 6y

With your group, solve 8(x – 5) = 64 for x in at least two different ways. Explain how you found x in each case and be prepared to share your explanations with the class. Decide on a Strategy to Solve:

For each equation below, with your group decide whether it would be best to rewrite, look inside, or undo. Then solve the equation, showing your work and writing down the name of the approach you used.

a. b. c. d. e.

a. Solve this equation using all three approaches studied in this lesson. b. Did you get the same solution using all three strategies? If not, why not? c. Discuss with your group which method is most efficient. What did you decide? Why?

a. d. b. e. c.

Think before solving! a.Read the equation and list the operations on the variable. b.List the ‘undo’ operations. c.Write the steps of your solution.

Now that you have the skills necessary to solve many interesting equations and inequalities, work with your team to solve the equation below. Solve a Really Hard Problem

Identifying & Correcting Errors: 4 Solution is complete and is essentially correct. 3 Solution would be correct except for a small error or solution is not complete. 2 Solution is partially correct. There is a major error or omission. 1 Solution attempted.

Work with a partner, and the simple equation x = –4. When you and your partner have agreed on a complicated equation, trade your equation with your team-partners and see if they solve it and get –4. Now start with 5 + i. Work Backwards: Have Students Create the Problems

Write two linear equations whose graphs a.Intersect at (-3, 1). b.Are parallel. c.Are the same. Work Backwards: Have Students Create the Problems

 Instead of a set of review problems try a summary. Start with a brainstorming session on the big ideas of the chapter. As a class reach agreement on 2-5 ideas.  Assignment: Find N problems that to represent each big idea. Write each problem and show its solution. Work Backwards: Give an Example of……….

You have seen that graphs of equations in three variables can lead to inconclusive results. What other strategies can you use to find the intersection? Consider the following problem and discuss this with your group. Work Backwards: Start with the Problems

a.Elisa noticed she could combine the first two and get and equation with only x and y. b.Can you combine a different pair and get only x and y? c.If you solve for x and y you can get z.

Matching representations: Linear equations: graph, table, situation, equation. Parabolas: Graph, standard, form, vertex form, and factored form of the equation. Equivalent expressions: (2 to 4) Expressions with exponents Rational expressions Play a Game

A taxi charges $1 to begin with, and $3 for each mile traveled. y is the amount charged for traveling x miles. y = 3x + 1 TABLEGRAPH

GAME FORMS: Group formation in class. Concentration. Old Maid. Go Fish or Authors.

 Identify/Explain Errors.  Rewrite Equivalent Expressions; Justify.  Create and Reconcile Algebraic Representations.  Decide on a Strategy for Solving PROBLEM MAKING STRATEGIES

 Solve a Really Hard Problem  Work Backwards  Have students create the problem  Give an Example of………  Reverse Your Class Routine  Play a Game

 Judy Kysh, San Francisco State University and CPM Educational Program Enjoy making algebra exercises more problematic!