how did you see it? how can you write it? simplified as possible? -...

IM 8 Ch2.1.4 What Makes Zero

CPM Materials modified by Mr. Deyo

How did you see it?

How can you write it?

Is your expression as simplified as possible?

.

Preparation for 8.EE.7a, 8.EE.7b in Lesson 2.1.8


By the end of the period, I will represent zero in mulple ways 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.

Learning TargetTitle: IM8 ‐ Ch. 2.1.4 ‐ What Makes Zero? Date:


Home Work: Sec. 2.1.4Desc. Date Due

Review & Preview Pg.

Problems 2‐41 to 2‐45


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


Team RolesResource 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?”


Vocabulary1) Combining Like Terms

2) Variable

3) Coefficient

4) Additive Inverse


2.1.4 Simplifying Expressions What Makes Zero?Today you will continue your work with rewriting algebraic expressions.

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?


Imagine the following situations:234. LIKELY STORY!Julie babysits for her neighbor’s baby and stuffs the $15 she earned into her purse. When she gets home, the $15 is nowhere to be found. It must have fallen out of her purse.The Burton Pumas football team completes a pass and gains 12 yards. But on the very next play, the quarterback holds onto the ball too long and gets sacked, losing 12 yards.

Rolando is at the beach. He digs a hole in the sand and places the sand he removes in a pile next to his hole. Someone comes along and pushes the pile back into the hole.

What do each of these situations have in common?

Can you represent each of them using symbols? How?


235. How can you represent zero with tiles on an Expression Mat? With your team, try to find at least two different ways to do this (and more if you can). Be ready to share your ideas with the class.

1

xy

y yx x

y2y2x2xy

1

x2

+


236a Gretchen used seven algebra tiles to build the expression shown below. Build this collection of tiles on your own Expression Mat and write its value.

1

xy

y yx x

y2y2x2xy

1

x2

+

Algebraic Expression

http://www.cpm.org/technology/general/tiles/?tiledata=a2x__buy__daaaf5c+aafwb.achqbzavihcAavfwfOavgGg3avhTfCayfqaECC3%20236__

http://www.cpm.org/technology/general/tiles/?tiledata=a2x__buy__daaaf5c+aafwb.achqbzavihcAavfwfOavgGg3avhTfCayfqaECC3%202-36__


236b Represent this same value from 236a three different ways, each time using a different number of tiles. Be ready to share your representations with the class.

1

xy

y yx x

y2y2x2xy

1

x2

+

236a Expression:


237a Build the expression below so that your representation does not match those of your teammates. Once your team is convinced that together you have found four different, valid representations, sketch your representation on your paper and be ready to share your answer with the class.

1

xy

y yx x

y2y2x2xy

1

x2

+

Expression: −3x + 5 + y


237b Build the expression below so that your representation does not match those of your teammates. Once your team is convinced that together you have found four different, valid representations, sketch your representation on your paper and be ready to share your answer with the class.

1

xy

y yx x

y2y2x2xy

1

x2

+

Expression: −(−2y + 1)


237c Build the expression below so that your representation does not match those of your teammates. Once your team is convinced that together you have found four different, valid representations, sketch your representation on your paper and be ready to share your answer with the class.

1

xy

y yx x

y2y2x2xy

1

x2

+

Expression: 2x − (x − 4)


238a Write the algebraic expression shown on the Expression Mat below. Build the model and then simplify the expression by removing as many tiles as you can without changing the value of the expression. Finally, write the simplified algebraic expression.

1

xy

y yx x

y2y2x2xy

1

x2

+

Original ExpressionSimplified Expression:

+

Original Expression


238b Write the algebraic expression shown on the Expression Mat below. Build the model and then simplify the expression by removing as many tiles as you can without changing the value of the expression. Finally, write the simplified algebraic expression.

1

xy

y yx x

y2y2x2xy

1

x2

+


+

Original Expression


239a Simplify the following expression by building it on your Expression Mat and removing zeros.

1

xy

y yx x

y2y2x2xy

1

x2

+

+

simplifiedoriginal 3x − (2x + 4)


239b Simplify the following expression by building it on your Expression Mat and removing zeros.

1

xy

y yx x

y2y2x2xy

1

x2

+

+

simplifiedoriginal 7 − (4y − 3) + 2y − 4


In your Learning Log, describe the different ways you can represent zero using your Expression Mat. Include an example and be sure to draw the tiles.

240. LEARNING LOG Using Zeros to Simplify” Date ________


Can zero be represented by any number of tiles? Using only the unit tiles (in other words, only the 1 and –1 tiles), determine whether you can represent zero on an Expression Mat with the number of tiles below. If you can, draw an Expression Mat demonstrating that it is possible. If it is not possible, explain why not.

11

+

http://www.cpm.org/technology/general/tiles/?tiledata=a2x__boy__ZaayamakCC3%20241%20HW%20eTool__

http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch2_Answers/ch2_files/CC3_2_41m.html241

a) 2 tiles b) 6 tiles c) 3 tiles+

+

http://www.cpm.org/technology/general/tiles/?tiledata=a2x__boy__ZaayamakCC3%202-41%20HW%20eTool__

http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch2_Answers/ch2_files/CC3_2_41m.html


242a

1

xy

y yx x

y2y2x2xy

1

x2

+


+

Original Expression

http://www.cpm.org/technology/general/tiles/?tiledata=a2x__boy__ZaayamakCC3%20242a%20HW%20eTool__aab+bSabffblaxcic4axdZcjaxggbwavfBgQabdmgl

Write and simplify the algebraic expression shown in the Expression Mat below.


http://www.cpm.org/technology/general/tiles/?tiledata=a2x__boy__ZaayamakCC3%202-42a%20HW%20eTool__aab+bSabffblaxcic4axdZcjaxggbwavfBgQabdmgl



242b

1

xy

y yx x

y2y2x2xy

1

x2

+


+

Original Expression

Write and simplify the algebraic expression shown in the Expression Mat below.


http://www.cpm.org/technology/general/tiles/?tiledata=a2x__boy__ZaayalamCC3%20242b%20HW%20eTool__avbOc.avcRbjaxeJaWavggbyakdDcoaid_df


http://www.cpm.org/technology/general/tiles/?tiledata=a2x__boy__ZaayalamCC3%202-42b%20HW%20eTool__avbOc.avcRbjaxeJaWavggbyakdDcoaid_df


P 243ac Read the Math Notes box in this lesson. Then evaluate each expression below.




P 243de Read the Math Notes box in this lesson. Then evaluate each expression below.




P 244Complete each of the Diamond Problems below. The pattern used in the Diamond Problems is shown.

DIAMOND PROBLEMShttp://www.cpm.org/students/homework/CC3_Problems/CC3_Ch2_Answers/ch2_files/CC3_2_44m.html



P 245 Find the perimeter of the entire rectangle shown here (that is, the length of the outside boundary of the figure). Notice that the areas of two of the parts have been labeled inside the rectangle. Also find the total area. Remember to show all work leading to your solution.


(Drawing NOT to Scale)

Perimeter =

Area =


how did you see it? how can you write it? simplified as possible? -...

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