How can you simplify? How can you get x alone? Is there more than one way to simplify? Is there always a solution? CPM Materials modified by Mr.
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1 Common Core Standard 8.EE.7a, 8.EE.7b How can you simplify? How can you get x alone? Is there more than one way to simplify? Is there always a solution? CPM Materials modified by Mr. Deyo
2 Title: IM8 Ch What If Both Sides Are Equal? Date: Learning Target By the end of the period, I will simplify algebraic expressions and solve each equaon for its variable. I will demonstrate this by compleng Four Square notes and by solving problems in a pair/group acvity.
3 Home Work: Sec Desc. Date Due Review & Preview 3 Problems: 2 76, 2 77, 2 80
4
5 Team Roles To help you and your team work together today, each member of your team has a specific job. Resource Manager Facilitator Recorder/Reporter Task Manager
6 Team Roles Resource Manager: If your name comes first alphabetically: Make sure that the team has tape. Ask the teacher when the entire team has a question. No one has an idea? Should I ask the teacher? Make sure your team cleans up by delegating tasks. You could say, I will put away the while you. Facilitator: If your name comes second alphabetically: Start the team s discussion of the graph by asking, What could this graph be about? What are some ideas? Help the team agree on a story: Do we agree on all of the parts of our story? Recorder/Reporter: If your name comes third alphabetically: Tape the graph pieces together on a piece of paper to form the graph. Take notes for the team. The notes should include phrases like, For part one and explanations like, Because part one is not so steep Task Manager: If your name comes fourth alphabetically: Remind the team to stay on task and not to talk to students in other teams. You can suggest, Let s move on to another part of the graph. Listen for reasons and challenge your teammates to justify their thinking. But why do you think that?
7 Vocabulary 1) Additive Inverse Property a is the opposite of a a (a) 0 For example, 3 (3) 0 or ) Multiplicative Inverse Property a ( 1 ) 1 a For example,
8
9 2.1.8 What If Both Sides Are Equal? Can you always tell whether one algebraic expression is greater than another? In this section, you will continue to practice the different simplification strategies you have learned so far to compare two expressions and see which one is greater. However, sometimes you do not have enough information about the expressions. When both sides of an equation are equal, you can learn even more about x. As you work today, focus on these questions: How can you simplify? How can you get x alone? Is there more than one way to simplify? Is there always a solution?
10 tiledataa2x boy N d1axcsdyavcaewaxd 72a 272a WHICH IS GREATER? Build each expression represented below with the tiles provided by your teacher or explore using 272a tiles (CPM). Left Right Expression for Left Side: 1 x y x Expression for Right Side: y 1 x 2 xy x 2 y 2 y 2 xy
11 tiledataa2x boy Naaxcia6avbRbBaxa9b5axa d1axcsdyavcaewaxddewavhpenavibexavgxck 72a 272a (continued). RECORDING YOUR WORK Left Expression Right Expression Explanation
12 272b Use algebra tiles to build the expressions below on an Expression Comparison Mat. Use legal simplification moves to determine which expression is greater, if possible. If it is not possible to tell which expression is greater, explain why. x 1 (1 2x) 3 x 1 (x 4) 1 x y x y 1 x 2 xy x 2 y 2 y 2 xy
13 273 WHAT IF BOTH SIDES ARE EQUAL? If the number 5 is compared to the number 7, then it is clear that 7 is greater. However, what if you compare x with 7? In this case, x could be smaller, larger, or equal to 7. Examine the Expression Comparison Mat: a) If the left expression is smaller than the right expression, what does that tell you about the value of x? b) If the left expression is greater than the right expression, what does that tell you about the value of x? c) What if the left expression is equal to the right expression? What does x have to be for the two expressions to be equal?
14 tiledataa ewavh4e 274a SOLVING FOR X Build the equation represented by the Equation Mat using algebra tiles. Simplify as much as possible and then solve for x. Be sure to record your work. Left Right Equation: 1 x y x y 1 x 2 xy x 2 y 2 y 2 xy
15 274b SOLVING FOR X Build the equation represented by using algebra tiles. Simplify as much as possible and then solve for x. Be sure to record your work. Left Right Equation: 2x 5 1 5x 2 1 x y x y 1 x 2 xy x 2 y 2 y 2 xy
16 274b RECORDING YOUR WORK Simplify as much as possible and then solve for x. Be sure to record your work. Left Expression Right Expression 2x 5 1 5x 2 Explanation Combine Like Terms Add/Subtract to Both Sides Divide Both Sides by
17 275a SOLVING FOR X Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Right Equation 3x x y x y 1 x 2 xy x 2 y 2 y 2 xy
18 275a RECORDING YOUR WORK Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Expression 3x 7 2 Right Expression Explanation Combine Like Terms Add/Subtract to Both Sides Divide Both Sides by
19 275b SOLVING FOR X Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Right Equation 1 2x x x 5 x 1 x y x y 1 x 2 xy x 2 y 2 y 2 xy
20 275b RECORDING YOUR WORK Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Expression Right Expression 1 2x x x 5 x Explanation Combine Like Terms Add/Subtract to Both Sides Divide Both Sides by
21 275c SOLVING FOR X Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Right Equation 3 2x 2x 5 1 x y x y 1 x 2 xy x 2 y 2 y 2 xy
22 275c RECORDING YOUR WORK Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Expression Right Expression 3 2x 2x 5 Explanation Combine Like Terms Add/Subtract to Both Sides Divide Both Sides by
23 275d SOLVING FOR X Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Right Equation 3 2x (x 1) 3x 6 1 x y x y 1 x 2 xy x 2 y 2 y 2 xy
24 275d RECORDING YOUR WORK Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Expression 3 2x (x 1) 3x 6 Right Expression Explanation Combine Like Terms Add/Subtract to Both Sides Divide Both Sides by
25 275e SOLVING FOR X Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Right Equation (x 3 x) 2x 7 1 x y x y 1 x 2 xy x 2 y 2 y 2 xy
26 275e RECORDING YOUR WORK Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Expression (x 3 x) 2x 7 Right Expression Explanation Combine Like Terms Add/Subtract to Both Sides Divide Both Sides by
27 275f SOLVING FOR X Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Right Equation 4 2x 2 x 1 x 1 x y x y 1 x 2 xy x 2 y 2 y 2 xy
28 275f RECORDING YOUR WORK Now apply the solving skill from problem 274 by building, simplifying, and solving each equation for x. Record your work. Left Expression Right Expression 4 2x 2 x 1 x Explanation Combine Like Terms Add/Subtract to Both Sides Divide Both Sides by
29 tiledataa2x bo axf8azaxgcbva d8axgee9aahser 276 SOLVING FOR X Translate the Equation Mat at right into an equation. Remember that the double line represents equals. Left Right chapter Equation: 1 x y x y 1 x 2 xy x 2 y 2 y 2 xy
30 277 Decide if each statement below is true or false. Explain how you know and name any properties you use. Refer to the Math Notes boxes in this lesson and in Lessons and to help you. chapter/ch2/lesso Associative Property Of Addition Associative Property of Multiplication Identity Property of Addition Identity Property of Multiplication Additive Inverse Property Multiplicative Inverse Property a) True or False? Why? Why not? b) True or False? Why? Why not? c) True or False? Why? Why not? d) True or False? Why? Why not?
31 278 Simplify each expression below as much as possible. chapter/ch2/lesson/2.1.8 a) b) c) d)
32 280 Evaluate the expressions below for the given values. chapter/ch2/lesson/2.1.8/p a) b) c) d)
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