What is this problem about? What is it asking you to do? What …maestrodeyo.weebly.com/uploads/1/7/1/0/17102056/im_8... · 2018. 10. 13. · IM 8 Ch1.1.4 How Can I Use Data to Solve

IM 8 Ch1.1.4 How Can I Use Data to Solve a Problem

CPM Materials modified by Mr. Deyo

What is this problem about?

What is it asking you to do?

What information can help you answer this question?

How can you get the information you need?


By the end of two periods, I will collect data, graph data, create a scaer plot, and analyze the collected data.

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

Learning TargetTitle: IM8 ‐ Ch. 1.1.4 ‐ Can I Graph Myself? Date:


Home Work: Secon 1.1.4Descripon Date Due

Review & Preview Pg.

Day 1 ‐ Problems 1‐30 to 1‐34

Day 2 ‐ Problems 1‐35 to 1‐40


Team Roles

1) Resource Manager

2) Facilitator

3) Recorder/Reporter

4) Task Manager


Vocabulary

1) Scatter Plot

2) x axis

3) independent variable

4) y axis

5) dependent variable


Newton's RevengeP 124Have you heard about Newton’s Revenge, the new roller coaster? It is so big, fast, and scary that rumors about it are already spreading. Some people are worried about the tunnel that thrills riders with its low ceiling.

The closest the ceiling of the tunnel ever comes to the seat of the rollercoaster car is 200 cm. Although no accidents have been reported yet, it is said that very tall riders have stopped riding the roller coaster.

Your Task: Consider how you could determine whether the tunnel is actually safe for any rider, no matter how tall. Discuss the questions below with your team. Be ready to share your responses with the rest of the class.

DISCUSSION POINTSWhat is this problem about?What is it asking you to do?




Newton's Revenge DiscussionP 124

Have you heard about Newton’s Revenge, the new roller coaster? It is so big, fast, and scary that rumors about it are already spreading. Some people are worried about the tunnel that thrills riders with its low ceiling.

The closest the ceiling of the tunnel ever comes to the seat of the rollercoaster car is 200 cm. Although no accidents have been reported yet, it is said that very tall riders have stopped riding the roller coaster.

Your Task: Consider how you could determine whether the tunnel is actually safe for any rider, no matter how tall. Discuss the questions below with your team. Be ready to share your responses with the rest of the class.

DISCUSSION POINTSWhat is this problem about?

What is it asking you to do?




Newton's Revenge Data CollectionP 125a&bCollect data from each member of your team. Each member of the team needs to be measured twice. First, have one team member stand and have another team member measure his or her height. Second, have the same student sit in a chair or desk, raise his or her arms so that they are stretched as far as possible above his or her head, and measure the distance from the seat of the chair to his or her fingertips (called “the reach”). All measurements should be in centimeters. Each person should record the team’s data in the table. b) Send one person to record your team's data on the class table. Then, add the rest of the class data to your own table. (For the names, just put initials.)

https://www.desmos.com/calculator/lltn8qraov



Newton's Revenge Data CollectionP 125cEach person should put his or her own height and reach coordinate as dot on the Class Height vs. Reach graph. The team should agree on the graph's title, labels, and scale.




Newton's Revenge Data AnalysisP 126a&ba) Are there any dots that you think show human error? That is, are there any dots that appear to be graphed incorrectly or that someone may have measured incorrectly? Explain why or why not.

b) Is a person’s reach related to his or her height? That is, what seems to be true about the reach of taller people? Explain.


Newton's Revenge Data AnalysisP 126c&dc) Since a person’s reach depends on his or her height, the reach is called the dependent quantity (or variable) and the height the independent quantity (or variable). Examine the class graph of the data from problem 125.

d) Is there a trend in the data?

On which axis was the dependent data represented?

On which axis was the independent data represented?

How can you generalize the trend?


Complaining about the graph!!P 127a&ba) Jorge is confused about how the teacher decided to set up the graph. “Why is it a 1stquadrant graph instead of a 4quadrant graph?” Answer Jorge’s question. In general, how should you decide what kind of graph to use?

b) Lauren is annoyed with the xaxis. “Why didn’t the teacher just use the numbers from the table?” she whined. “Why count by twenties?” What do you think?


Complaining about the graph!!P 127c&dc) Hosai thinks that the graph is TOO BIG. “The dots are all mashed together! Why did the teacher begin both the x and yaxes at zero? Anyone that short would never be allowed on the roller coaster. Why not just start closer to the smallest numbers on the table?” she asked. What do you think?

d) Sunita says the graph is TOO SMALL! “If we’re supposed to be using this data to check if the coaster is safe for really tall people, the graph has to have room to graph tall people’s dots too.” Do you agree? If so, how much room do you think is needed?


Graph & Draft of ExplanationP 128Using all of your ideas from problem 127, make your own graph that will help you determine whether the ride is safe for very tall people. An example of a “very tall” person is Yao Ming, who retired from the NBA in 2011. He was one of the tallest NBA players in history, measuring 7 feet 6 inches (about 228.6 cm) tall. Is the roller coaster safe for him? Explain.


Is the Roller Coaster SAFE for ALL Riders?P 129Is the roller coaster safe for all riders? Prepare a poster that shows and justifies your team’s answer to this question. Every team poster should include:

• A large, clear graph.• A complete, clear, and convincing explanation of why your team thinks the ride is or is not safe for all riders.


P 130 Kerin discovered that a human’s height is related to his or her reach. Kerin is curious if the same thing is true for foot size.

a) It was not practical for Kerin to measure her classmates' feet, so Kerin collected the following shoesize data from some of her classmates. Make a graph with appropriately scaled axes.

b) Is there a relationship between shoe size and height? Explain.

http://www.cpm.org/technology/general/stats/

http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_30m.html

http://www.cpm.org/technology/general/stats/http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_30m.html


P 131 One important statistical display is a box plot. If you need help remembering what a box plot is, refer to the glossary before you complete parts (a) through (d) below.

a) What is the median shoe size in problem 130? The minimum shoe size? The maximum?

b) What are the quartiles (the median of the upper half, and the median of the lower half)?

c) Above a number line, plot the five numbers you found in parts (a) and (b) and then create a box plot.

d) Where does your own shoe size fall in the distribution of Kerin's classmates?



http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_31m.htmlhttp://www.cpm.org/technology/general/stats/


P 132 Latisha is determined to do well in school this year. Her goal is to maintain at least an 85% average (mean) in all her courses.

a) Latisha started her history class with two scores on tests, 72% and 89%. Confirm that the mean of these two scores is 80.5%. Show your work!

b) Latisha's third score was 90%. Use her scores from part (a) to figure our her mean now. Be sure to show your work!!




P 133ah Use the pattern to complete each diamond problem. Some of them may be challenging!




P 134 Compute WITHOUT using a calculator!http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_34m.html



P 135 The area of each rectangle below is shown in the middle of the rectangle. For each figure, find the missing length or width.




P 136 Compute WITHOUT using a calculator!http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_36m.html



P 137 Latisha is determined to do well in school this year. Her goal is to maintain at least an 85% average (mean) in all her courses.

Latisha earned an 85% on her test today. Her previous scores were 72%, 89%, and 90%. Calculate her new average (mean).




P 138 Consider this data: 22, 15, 30, 51, 27, 33, 19

a) Arrange the data into a stemandleaf plot. b) Find the mean and median

c) If the value 51 was replace with 33, which measure(s) of central tendency would change and which would not? Explain.

(Refer to the glossary if you need a reminder of what a stemandleaf plot is.)



http://www.cpm.org/technology/general/stats/http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_38m.html


P 139 Estimate the areas of Montana and California using the grid below. Which state has the greater area? Compare the area of Montana to the area of California.

Explain how you estimated the area of each state.




P 140 The pattern below is composed of nested squares. Draw the next figure in the pattern.

Find the area of the shaded region for the figure you drew above.

http://www.cpm.org/technology/general/tiles/?tiledata=a2x__boy__XbayaHaDCC3%20140%20HW%20eTool__ayaIbcDirections%3A%20Draw%20the%20next%20figure%20(Figure%204)%20in%20the%20pattern.__ayaJbOFind%20the%20area%20of%20the%20shaded%20(black)%20region%20for%20the%20figure%20you%20drew%20in%20part%20(a).__bibVdNbabqdNbabqdibabVdibabqeebabVeebacmeebacmdNbacmdiaybsdN1__aya+dN2__aybBe.Figure%201__ayb4iKFigure%203__ayiGi0Figure%204__ayiwe+Figure%202__biitdNbiiYdNbiitdibiiYdibah_cRbaitcRbah_dibah_dNbah_eebaiteebaiYeebaiYcRbajpcRbajpdibajpdNbajpeeayh0dy2__ayhwdx3__bibVgBbibVg2bibVhxbicmhxbicRgBbicmg2bicmgBbicRg2bicRhxbabqf6babqgBbabVf6babqg2babqhxbacmf6bacRf6badif6babqh_babVh_bacmh_badigBbadig2badihxbacRh_badih_aybug13__aya+g24__


http://www.cpm.org/technology/general/tiles/?tiledata=a2x__boy__XbayaHaDCC3%201-40%20HW%20eTool__ayaIbcDirections%3A%20Draw%20the%20next%20figure%20(Figure%204)%20in%20the%20pattern.__ayaJbOFind%20the%20area%20of%20the%20shaded%20(black)%20region%20for%20the%20figure%20you%20drew%20in%20part%20(a).__bibVdNbabqdNbabqdibabVdibabqeebabVeebacmeebacmdNbacmdiaybsdN1__aya+dN2__aybBe.Figure%201__ayb4iKFigure%203__ayiGi0Figure%204__ayiwe+Figure%202__biitdNbiiYdNbiitdibiiYdibah_cRbaitcRbah_dibah_dNbah_eebaiteebaiYeebaiYcRbajpcRbajpdibajpdNbajpeeayh0dy2__ayhwdx3__bibVgBbibVg2bibVhxbicmhxbicRgBbicmg2bicmgBbicRg2bicRhxbabqf6babqgBbabVf6babqg2babqhxbacmf6bacRf6badif6babqh_babVh_bacmh_badigBbadig2badihxbacRh_badih_aybug13__aya+g24__http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_40m.html

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What is this problem about? What is it asking you to do? What …maestrodeyo.weebly.com/uploads/1/7/1/0/17102056/im_8... · 2018. 10. 13. · IM 8 Ch1.1.4 How Can I Use Data to Solve