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IM 8 Ch 4.1.5 What Are The Connections

CPM Materials modified by Mr. Deyo

What is the connection?

Is there a pattern?

How does the pattern grow?

How does the pattern show up in the table, graph, and

rule?

Common Core Standard: 8.F.2, 8.F.4


By the end of the period, I will create multiple representations of linear equations and show the connections between pattern growth, Figure Zero, a data table, a rule, and a graph.

I will demonstrate this by completing Four‑Square notes and by solving problems in a pair/group activity.

Learning TargetTitle: IM8 ‑ Ch. 4.1.5 What Are The Connections? Date:


Home Work: Sec. 4.1.5Desc. Date Due

Review & Preview

Day 1: 3 Problems: 4‑43, 4‑44, 4‑46

Day 2: 3 Problems: 4‑50, 4‑51, 4‑52


Vocabulary1) growth factor

2) Figure Zero

3) rule

4) graph


4.1.5 What Are The Connections?In the last several lessons, you have been finding connections and relationships between different representations of patterns. You have worked backward and forward. You have also used information about Figure 0 (or the starting point) and the pattern of growth to write rules. In today’s activity, you will use pieces of information from various parts of the web to generate a complete pattern.By the end of this lesson, you should be able to answer the following target questions:

How is growth shown in a graph?

How is growth shown in a rule?

How can you determine the number of tiles in Figure 0 from a graph?

How can you determine which tile pattern grows faster from a graph?


442. CHECKING THE CONNECTIONS: TEAM CHALLENGEToday you are going to apply what you know about the starting point (Figure 0), the pattern of growth, and the connections between representations to answer some challenging questions. The information in each question, parts (a) through (d), describes a different pattern. The graph of each pattern is a line. From this information, generate the rule, x → y table, graph, and tile pattern (Figures 0 through 3) that follow the pattern. You may answer these questions in any order, but make sure you answer each one completely before starting another problem.

Three students working together at a table.Work together as a team. The more you listen to how other people see the connections and the more you share your own ideas, the more you will know at the end of the lesson. Stick together and be sure to talk through every idea.

Each person will turn in his or her own paper at the end of this activity, showing four complete representations for each pattern. Your work does not need to be identical to your teammates’ work, but you should have talked and agreed that all explanations are correct.


442a Create/complete four connected representations (a pattern, a table, a rule, and a graph) for the following:

What is the rule? y = ( )x + ( )

TableFigure 0 Figure 1 Figure 2

Graph


442b Create/complete four connected representations (a pattern, a table, a rule, and a graph) for the following:



Graph


442c Create/complete four connected representations (a pattern, a table, a rule, and a graph) for the following:



Graph


442d Create/complete four connected representations (a pattern, a table, a rule, and a graph) for the following:

What is the rule? y = (3)x + (7)


Graph


443 "Representations of Patterns Web” Date: _________Update your Representations of Pattern Web from problem 4‑16 with any new connections that you can make between representations following today’s work. Pay attention to the direction of any arrows that you draw. Explain the connections you made and why you made them.


444 Complete a table for the rule y = 3x − 2. Draw a complete graph for this rule. Is (−50, −152) a

point on the graph? Explain how you know.

https://www.desmos.com/calculator/0d6s0g9vkj http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch4/lesson/4.1.5/problem/444

x y

https://www.desmos.com/calculator/0d6s0g9vkj

http://homework.cpm.org/cpm-homework/homework/category/CC/textbook/CC3/chapter/Ch4/lesson/4.1.5/problem/4-44


445 Look at the table. Write down everything you know about the tile pattern represented by the x → y table at right. Be as specific as possible.

y = ( )x + ( )

https://www.desmos.com/calculator/5w6j6xw9sx http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch4/lesson/4.1.5/problem/445

How many tiles are in Figure 0? In Figure 4?

What is the pattern of growth?

What is the rule for the pattern?

https://www.desmos.com/calculator/5w6j6xw9sx



446 Find the area and circumference of a circle that has a diameter of 17 mm. Write your answers in terms of and as a decimal approximation.

Area CircumferenceCircumference = 2 r

http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch4/lesson/4.1.5/problem/446

17mm



447 Complete each of the Diamond Problems below. The pattern used in the Diamond Problems is shown at right.




a)

c)

448 Simplify each expression.

−(5x + 1) b)

d)

6x − (−5x + 1)

−5x + (x − 1) −(1 − 5x)




Draw the 0 figure.

Draw the 1st figure.

449

Draw the 2nd & 3rd figures.

Invent a tile pattern that grows by 4 each time. Draw Figures 0, 1, 2, and 3. Use color or shading to show the growth.




450 Complete a table for the rule y = 3 − x. Draw a complete graph for this rule. Is (32, 29) a point

on the graph? Explain how you know.

x y

https://www.desmos.com/calculator/wkuhqb6sqy http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch4/lesson/4.1.5/problem/450

https://www.desmos.com/calculator/wkuhqb6sqy



451a

Explanation

• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative InverseSolve for the variable. Record

your work & check the solution.

3p −7 +9 − 2p = p + 2




451b

Explanation



−2x +5 +(−x) −5 = 0




451c

Explanation



12 = r + 6 − 2r




451d

Explanation



−(y2 − 2) = y2 − 5 − 2y2




a)

c)

352 Solve each equation for x. Then, check your solutions.b)

d)

2 x5 40

x 38 4

x 1210 15

1 x8 12




Luis rides his skateboard at the same speed all the way home. It takes him ten minutes to get there.

453a Sketch a graph to match the story below using appropriately labeled axes. http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch4/lesson/4.1.5/problem/453

Speed

Time



Corinna jogs along at the same speed until she reaches a hill, and then she slows down until she finally stops to rest.

453b Sketch a graph to match the story below using appropriately labeled axes. http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch4/lesson/4.1.5/problem/453

Speed

Time



Sergei is talking with his friends at the donut shop when he realizes that it is almost time for math class. He runs toward school, but he slows to a walk when he hears the bell ring and realizes that he is already late. He sits down in class four minutes after he left the donut shop.

453c Sketch a graph to match the story below using appropriately labeled axes. http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch4/lesson/4.1.5/problem/453

Speed

Time


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