Penny Circle CLASS CODE Checklist My Learning Targets: Penny Circle 30-45 minutes Application In...

Activity Checklist

My Learning Targets:

Penny Circle30-45 minutes Application

In this activity, students gather data, build a model, and then use that model to answer the question, "How many pennies fit in a large circle?"

CLASS CODE

Complete the activity using student preview.

Identify your learning targets for the activity.

Determine the screens where you’ll bring the class together using Teacher Pacing and PauseClass. What will you discuss on those screens?

Anticipate screens where students will struggle, then plan your response.

Plan a challenge for students who finish the activity quickly and successfully.

Make yourself available during the activity to students for individual help and questions whenappropriate.

Write out your summary of the activity's main ideas. How will you pull student work into thatsummary? Which parts of the activity can you skip to ensure that summary receives sufficienttime?

Penny Circle • Teacher Guide https://teacher.desmos.com/activitybuilder/teacherguide/586ab1...

1 of 10 6/2/17, 10:55 AM

Activity Screens: Teacher Pacing and Pause Class

Use this page to plan your use of Teacher Pacing and Pause Class. Teacher Pacing lets yourestrict students to a single screen or a range of screens. Pause Class keeps students frominteracting with whatever screens they are currently viewing. Use these two tools to createconversations in your classroom.

Consider these questions as you plan:

Which screen(s) should everyone work on at the same time? Why?

Which screen(s) do you want to keep students from seeing until you're ready for the class tosee them together? (Perhaps because they reveal answers or require a whole classconversation for introduction.)

Are there any points in the lesson where you will want to make sure students aren’t playingwith the screens while you discuss something as a class?

!!!!!!!!!Watch the video, then predict:

"

111111111 Make a predictiMake a predictiMake a predictiMake a predictiMake a predictiMake a predictiMake a predictiMake a predictiMake a predicti………………………Let's look at SMALLER circles to help us

222222222 StrategyStrategyStrategyStrategyStrategyStrategyStrategyStrategyStrategyDrag some virtual pennies #

333333333 Collect some dCollect some dCollect some dCollect some dCollect some dCollect some dCollect some dCollect some dCollect some d………………………The graph here shows

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444444444 Build a model.Build a model.Build a model.Build a model.Build a model.Build a model.Build a model.Build a model.Build a model.

%

Why do you think the model

555555555 Explain your thiExplain your thiExplain your thiExplain your thiExplain your thiExplain your thiExplain your thiExplain your thiExplain your thi………………………The model you built on Screen

"

666666666 Use your model.Use your model.Use your model.Use your model.Use your model.Use your model.Use your model.Use your model.Use your model.

!!!!!!!!!Your original estimate: 200 pennies

777777777 RevealRevealRevealRevealRevealRevealRevealRevealRevealWhat is the diameter of the

"

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Would you rather have all the

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2 of 10 6/2/17, 10:55 AM

Watch the video, then predict:

How many pennies will fit in the large circle?

Teacher Tip:

Emphasize the range of student responses on this screen. It's okay—even desirable—to lack consensus at this stage. The activity will build toward consensus later on.

My Notes:

Let's look at SMALLER circles to help us make a prediction about the LARGER circle.

When you're ready, continue to the next screen.

My Notes:

!!!!!!!!!

Watch the video, then predict:

"

111111111 Make a prediction.Make a prediction.Make a prediction.Make a prediction.Make a prediction.Make a prediction.Make a prediction.Make a prediction.Make a prediction.

Let's look at SMALLER circles to help us make a prediction about the

222222222 StrategyStrategyStrategyStrategyStrategyStrategyStrategyStrategyStrategy


3 of 10 6/2/17, 10:55 AM

Drag some virtual pennies into the virtual circle. Pack in as many as you can, then record your data in the table.

Do this for at least three different circles.

Each time you fill the circle, enter your data in the table.

Teacher Tip:

Students should enter at least three ordered pairs, though they can contribute up to nine. (Anything beyond that will be ignored on future screens.)

Be on the lookout for students who reverse the numbers in the table (entering "pennies" under "diameter," and vice-versa). When that occurs, rather than point out the error directly, casually ask students to explain the meaning of the points in the table. If they don't see their mistake, ask what the headers in the table indicate.

My Notes:

Drag some virtual pennies into the virtual

#

333333333 Collect some data.Collect some data.Collect some data.Collect some data.Collect some data.Collect some data.Collect some data.Collect some data.Collect some data.


4 of 10 6/2/17, 10:55 AM

The graph here shows your data (orange) and your classmates' data (blue) from the previous screen.

What kind of function do you think will best fit the data?

After you make your selection, drag the red points to fit the curve to the data.

Then continue to the next screen.

Teacher Tip:

Wait until Screen 5 to discuss students' choices (and rationale) for their models.

My Notes:

The graph here shows your data

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444444444 Build a model.Build a model.Build a model.Build a model.Build a model.Build a model.Build a model.Build a model.Build a model.


5 of 10 6/2/17, 10:55 AM

Why do you think the model you chose makes sense here?

Teacher Tip:

Highlight unique answers for the class. Ask students to justify their responses and critique each others' reasoning.

Sample Answer: "I chose a quadratic model because the data increases in a nonlinear manner (ruling out linear as a good fit). I decided against an exponential model because that would grow too quickly in the long run. Also, quadratic makes sense given that the number of pennies we can fit in a circle is related to the area of the circle, and circle area formula is quadratic."

My Notes:

%

Why do you think the model you

555555555 Explain your thinking.Explain your thinking.Explain your thinking.Explain your thinking.Explain your thinking.Explain your thinking.Explain your thinking.Explain your thinking.Explain your thinking.


6 of 10 6/2/17, 10:55 AM

The model you built on Screen 4 is shown in red.

The equation of your model is EQUATION.

Based on everything you know now, make a final calculation: How many pennies will fit in the 22-inch circle?

Teacher Tip:

Invite students to notice that the range of calculations is narrower than the range of estimates from earlier in the activity, if that's true. Math is power, not punishment!

My Notes:

The model you built on Screen 4 is shown in

"

666666666 Use your model.Use your model.Use your model.Use your model.Use your model.Use your model.Use your model.Use your model.Use your model.


7 of 10 6/2/17, 10:55 AM

Your original estimate: 200 penniesYour final calculation: 643 pennies

Teacher Tip:

Consider asking one or more follow up questions:

(1) How did your predictions compare to the actual answer?(2) Which model proved most accurate? Why do you think that's the case?

My Notes:

What is the diameter of the smallest circle that would enclose 2,000 pennies? How do you know?

Teacher Tip:

Sample Answer: About 38.2 inches. I plotted the data from earlier in this activity, built a quadratic model, graphed the line y= 2000 , and found the intersection. https://www.desmos.com/calculator/nihn64i09z

My Notes:

!!!!!!!!!

Your original estimate: 200 penniesYour final calculation: 643 pennies

777777777 RevealRevealRevealRevealRevealRevealRevealRevealReveal

What is the diameter of the smallest

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8 of 10 6/2/17, 10:55 AM

Would you rather have all the PENNIES that fill a 40-inch diameter circle, or all the NICKELS that fill a 20-inch diameter circle?

Teacher Tip:

Encourage students to support their choice with mathematical reasoning (ideally, more sophisticated than "nickels are worth more, so I'll choose them!").

Here are two potential approaches:

1. BUILD A MODEL FOR NICKELSStudents use their existing penny model to find the value of the coins in the 40-inch circle. Then they use real nickels, paper with circles of various sizes to gather data, desmos.com/calculator to build and use a model. (For building the model, they might use regression.)

2. REASON ABOUT RATIOSStudents use a search engine (or Wikipedia) to find the diameters of each coin type. Then they consider the ratio of coin size (i.e., area), coin value, and circle size (again, area). Here's what this second approach might look like:

"A nickel takes up slightly more space (about 1.24x), but is worth considerably more (5x). So filling a same-size circle with

nickels would be worth 1.245

= 4.032 as much. But these

circles are not the same size. The half-size radius means the area will be one-quarter the size, meaning that the values will be very, very close (with a slightly higher value for the nickels)."

My Notes:

Would you rather have all the PENNIES

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9 of 10 6/2/17, 10:55 AM

Summary Notes:


10 of 10 6/2/17, 10:55 AM

Penny Circle CLASS CODE Checklist My Learning Targets: Penny Circle 30-45 minutes Application In...

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