How did you see it? How can you write it? Is your expression as simplified as possible? CPM Materials modified by Mr. Deyo

Transcription

1 . Preparation for 8.EE.7a, 8.EE.7b in Lesson 2..8 How did you see it? How can you write it? Is your expression as simplified as possible? CPM Materials modified by Mr. Deyo

2 Title: IM8 Ch What Does Minus Mean? Date: Learning Target By the end of the period, I will construct and simplify algebraic expressions using algebra les. 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 Pg. Problems 2 29 to 2 33

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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 ) Combining Like Terms 2) Variable 3) Coefficient 4) Additive Inverse

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9 2..3 Expressions In this section, you will look at algebraic expressions and see how they can be interpreted using an Expression Mat. To achieve this goal, you first need to understand the different meanings of the minus symbol, which is found in expressions such as 5 2, x, and ( 3). While working today, ask yourself and your teammates these focus questions: How did you see it? How can you write it? Is your expression as simplified as possible?

10 2 22. LEARNING LOG Meanings of Minus Date In your Learning Log, What does mean? Find as many ways as you can to describe this symbol and discuss how these descriptions differ from one another. Share your ideas with the class and record the different uses in your Learning Log.

11 2 23. USING AN EXPRESSION MAT Your introduction to algebra tiles in Lessons 2.. and 2..2 involved only positive values. Today you will look at how you can use algebra tiles to represent minus. Below are several tiles with their associated values. Note that the shaded tiles are positive and the un shaded tiles are negative. The diagram at right will appear throughout the text as a reminder. Minus can also be represented with a new tool called an Expression Mat, shown at right. An Expression Mat is an organizing tool that will be used to represent expressions. Notice that there is a positive region at the top and a negative (or opposite ) region at the bottom. Note that in these examples, the diagram on the left side uses negative tiles in the + region, while the diagram on the right side uses positive tiles in the region. If using the algebra tiles, be sure to select the gear icon and then the appropriate mat.

12 2 23 (Continued) Using the Expression Mat, the value 3 can be shown in several ways, two of which are shown below. Note that in these examples, the diagram on the left side uses negative tiles in the + region, while the diagram on the right side uses positive tiles in the region. If using the algebra tiles, be sure to select the gear icon and then the appropriate mat. Can you make another example?

13 2 23a Build two different representations for 2x using an Expression Mat. + + x y x y x 2 xy x 2 y 2 y 2 xy

14 2 23b Similarly, build 3x ( 4). How many different ways can you build 3x ( 4)? Draw vertical lines to separate each version you built. + x y x y x 2 xy x 2 y 2 y 2 xy

15 2 24. As you solved problem 2 23, did you see all of the different ways to represent minus that you listed in problem 2 22? Discuss, write down, and illustrate how you could use an Expression Mat to represent the different meanings discussed in class.

16 2 25a Use the Expression Mat to create the expression, 3x + 4, with algebra tiles. Find at least two different representations for the expression. Be prepared to share your different representations with the class. + x y x y x 2 xy x 2 y 2 y 2 xy

17 2 25b Use the Expression Mat to create the expression, (y 2), with algebra tiles. Find at least two different representations for the expression. Be prepared to share your different representations with the class. + x y x y x 2 xy x 2 y 2 y 2 xy

18 2 25c Use the Expression Mat to create the expression, y 3, with algebra tiles. Find at least two different representations for the expression. Be prepared to share your different representations with the class. + x y x y x 2 xy x 2 y 2 y 2 xy

19 2 25d Use the Expression Mat to create the expression, 5x (3 2x), with algebra tiles. Find at least two different representations for the expression. Be prepared to share your different representations with the class. + x y x y x 2 xy x 2 y 2 y 2 xy

20 2 26a In problem 2 25, you represented algebraic expressions with algebra tiles. In this problem, you will need to reverse your thinking to write an expression from a diagram of algebra tiles. Write algebraic expressions for each representation. Start by building each problem using your algebra tiles. + Algebraic Expression x y x y x 2 xy x 2 y 2 y 2 xy

21 2 26b In problem 2 25, you represented algebraic expressions with algebra tiles. In this problem, you will need to reverse your thinking to write an expression from a diagram of algebra tiles. Write algebraic expressions for each representation. Start by building each problem using your algebra tiles. + Algebraic Expression x y x y x 2 xy x 2 y 2 y 2 xy

22 2 26c In problem 2 25, you represented algebraic expressions with algebra tiles. In this problem, you will need to reverse your thinking to write an expression from a diagram of algebra tiles. Write algebraic expressions for each representation. Start by building each problem using your algebra tiles. + Algebraic Expression x y x y x 2 xy x 2 y 2 y 2 xy

23 2 26d In problem 2 25, you represented algebraic expressions with algebra tiles. In this problem, you will need to reverse your thinking to write an expression from a diagram of algebra tiles. Write algebraic expressions for each representation. Start by building each problem using your algebra tiles. + Algebraic Expression x y x y x 2 xy x 2 y 2 y 2 xy

24 2 27. Patti, Emilie, and Carla are debating the answer to part (d) of problem Patti wrote 2 + 2x 3. Carla thinks that the answer is 2x Emilie is convinced that the answer is 2x 2. Discuss with your team how each person might have arrived at her answer. Who do you think is correct? When you decide, write an explanation and justify your answer.

25 2 28. LEARNING LOG Representing Expressions on an Expression Mat Date Using an Expression Mat, find two different ways to represent x (2x 3). Sketch the different representations and write a few sentences to describe the differences between your representations.

26 P 2 29a ch2_files/cc3_2_29m.html Simplify the following expression by combining like terms. Using or drawing sketches of algebra tiles may be helpful. 2x + 3x x x x y Simplified expression x 2 y 2 xy

27 P 2 29b ch2_files/cc3_2_29m.html Simplify the following expression by combining like terms. Using or drawing sketches of algebra tiles may be helpful. 4x + 4y 2 + y x + 3x x y Simplified expression x 2 y 2 xy

28 P 2 29c ch2_files/cc3_2_29m.html Simplify the following expression by combining like terms. Using or drawing sketches of algebra tiles may be helpful. 2x x 2 + 4x x x y Simplified expression x 2 y 2 xy

29 P 2 29d ch2_files/cc3_2_29m.html Simplify the following expression by combining like terms. Using or drawing sketches of algebra tiles may be helpful xy + 4y y 2 + xy x y Simplified expression x 2 y 2 xy

30 tiledata=a2x boy ZaayamanCC3%202 30a%20HW %20eTool avbodaavcbcmaacwdbabfjccaxedb8aveng8ave8gw IM 8 Ch2..3 What Does Minus Mean 2 30a ch2_files/cc3_2_30m.html Find a simplified algebraic expression for the Expression Mat below. + Algebraic Expression x y x y x 2 xy x 2 y 2 y 2 xy

31 tiledata=a2x boy ZaayaraoCC3%202 30b%20HW%20eTool avbac +avcvckaveddmacb2daaadtbmaxdygk IM 8 Ch2..3 What Does Minus Mean 2 30b ch2_files/cc3_2_30m.html Find a simplified algebraic expression for the Expression Mat below. + Algebraic Expression x y x y x 2 xy x 2 y 2 y 2 xy

32 tiledata=a2x boy ZaayaranCC3%202 30c%20HW %20eTool afclchaxejcbaxfcbxajcsf+avdbgwavd7hj IM 8 Ch2..3 What Does Minus Mean 2 30c ch2_files/cc3_2_30m.html Find a simplified algebraic expression for the Expression Mat below. + Algebraic Expression x y x y x 2 xy x 2 y 2 y 2 xy

33 P 2 3 Define a variable and then write and solve an equation for the problem below. Remember that you can use the 5 D Process (described in the Lesson..3 Math Notes box) to help you get started. State your solution in a sentence. Susan is buying three different colors of tiles for her kitchen floor. She is buying 25 more red tiles than beige tiles, and three times as many navyblue tiles as beige tiles. If Susan buys 435 tiles altogether, how many tiles of each color does she buy? ch2_files/cc3_2_3m.html

34 P ch2_files/cc3_2_32m.html COMPUTATION Without a calculator, compute the value of each expression below.

35 P 2 33 To bake 00 of his favorite cookies, Mr. Wallis needs 350 grams of sugar. How many grams of sugar would he need to bake 0 cookies? What about 20 cookies? Show all work. ch2_files/cc3_2_33m.html What is the unit rate? That is, how many grams of sugar are needed for cookie? To help him know how much sugar to use when baking cookies, Mr. Wallis started to make a table, as shown above. Complete his table.