dis3-8.docx

Discussion Questions 3-8mathematical Inquiry

Dis#3, For the following prompts, use the WileyPlus Interactive Resources in Chapter 4. These are found online in the Wiley Course Resources:

1) Platonic Solids: Work with this interactive resource to show the plane intersected through these platonic solids. Can you make a three-sided intersection? Four-sided? Five-sided? Six-sided?Seven-sided? Is eight-sided possible? Have some fun with this, bring the text to life, and post your results.

2) Proving that Pythagoras was right: Can you use the interactive pictures to demonstrate that the old Greek mathematician was correct? Explain how the image proves the theorem. Can you do this for both widgets?

Dis4Rubber sheet geometry says two objects are equivalent by distortion if we can stretch, shrink, bend, or twist one without cutting or gluing and deform it into the other. Review the shapes below. Are these two shapes equivalent by distortion or not and why?

Möbius strips are fascinating.  Try this at home.  Get a piece of paper, scissors, and tape.  Cut a strip of paper, maybe an inch wide.  How many edges does this piece of paper have? How many surfaces?  Now twist one end and tape it onto the other end, making a Möbius strip.  Now, trace the sides; how many sides?  How many surfaces?  How can you tell?  Post a few photos of your Möbius strip!

Dis5, For the following prompts, use the WileyPlus Interactive Resources in Chapter 7: 1) Koch Snowflake – Can you show and determine how many sides a Koch Snowflake has after one iteration? Can you do the same for two iterations? Three? Four? Five? The widget will verify these. How many sides does a Koch Snowflake have after eight iterations? Can you write an equation for the number of sides for a Koch Snowflake after n iterations? 2) Sierpinski Carpet – Can you show and determine how many squares a Sierpinski Carpet has after one iteration? Can you do the same for two iterations? Three? Four? Five? What about eight iterations? Can you determine a formula for n iterations?

Dis6)What are the odds you will win the lottery? Pick your favorite lottery and the current payout, and figure out your odds of winning with one ticket. Is this a good investment?  What if you bought many tickets? Can you purchase enough tickets to make it a good investment?  Why or why not?  How high would the payout have to be to make it a good investment?

Consider the section that discusses Bayesian Analysis, how the example of a disease in the book is diagnosed using different bits of information, and how this changes the odds of diagnoses.  The COVID-19 global pandemic has touched many lives. Have you seen evidence of this type of Bayesian Analysis in how the world is diagnosing and treating the disease?  Do you see evidence of this in how governments are attempting to protect the public?

Dis7)First, use the Interactive Explorations in WileyPlus Chapter 9: Histogram and Box Plot.  In the interaction, enter the ages of your family, immediate, then extended.  Enter at least 20 data points.  Then, post what the Histogram and Box Plot looks like. What can you deduce from each of these?

Second, can you find a recent biased display of data in the media? If the display has already been used in the discussion, find an alternative. Don't post the same bias display as a peer. Finally, in the discussion, describe how the data display is biased and how to fix it.

Dis8)This module's Discussion Board is centered on the public policy response to the COVID-19 Pandemic.  Respond to the following questions following the discussion rubric:

1.) What untended consequences did the U.S. experience due to the policy response to Covid?  Can we quantify any of these consequences? Explain.  

2.) Can we make a cost estimate of the cost per life saved during the pandemic? Is it possible to estimate the lives saved?  How much did it cost?  How do these estimations stack up against the leading causes of death in the U.S., such as heart disease and cancer?

Discussion Q

uestions

3

–

8

mathematical

I

nquiry

Dis#

3

, For

the following prompts, use the WileyPlus Interactive Resources in Chapter 4.

These are found online in the Wiley Course Resources:

1) Platonic Solids: Work with this interactive resource to show the plane intersected

through these platonic solids. Can you make a three

–

sided intersection? Four

–

sided?

Five

–

sided? Six

–

sided?Seven

–

sided? Is eight

–

sided possible? Have some fun with this,

b

ring the text to life, and post your results.

2) Proving that Pythagoras was right: Can you use the interactive pictures to

demonstrate that the old Greek mathematician was correct? Explain how the image

proves the theorem. Can you do this for both widgets

?

Dis

4

Rubber sheet geometry says two objects are equivalent by distortion if we can

stretch, shrink, bend, or twist one without cutting or gluing and deform it into the other.

Review the shapes below. Are these two shapes equivalent by distortion or not and

why?

Möbius strips are fascinating.

Try this at home.

Get a piece of paper, scissors, and

tape.

Cut a strip of paper, maybe an inch wide.

How many edges does this piece of paper

have? How many surfaces?

Now twist one end and tape it onto the other end, mak

ing a

Möbius strip.

Now, trace the sides; how many sides?

How many surfaces?

How can you

tell?

Post a few photos of your Möbius strip!

Dis

5

, For

the following prompts, use the WileyPlus Interactive Resources in Chapter 7:

1) Koch Snowflake

–

Can you sho

w and determine how many sides a Koch Snowflake has

after one iteration? Can you do the same for two iterations? Three? Four? Five? The

widget will verify these. How many sides does a Koch Snowflake have after eight

iterations? Can you write an equation fo

r the number of sides for a Koch Snowflake after

n iterations?

2) Sierpinski Carpet

–

Can you show and determine how many squares a Sierpinski

Carpet has after one iteration? Can you do the same for two iterations? Three? Four?

Five? What about eight ite

rations? Can you determine a formula for n iterations?

Discussion Questions 3-8mathematical Inquiry

Dis#3, For the following prompts, use the WileyPlus Interactive Resources in Chapter 4.

These are found online in the Wiley Course Resources:

1) Platonic Solids: Work with this interactive resource to show the plane intersected

through these platonic solids. Can you make a three-sided intersection? Four-sided?

Five-sided? Six-sided?Seven-sided? Is eight-sided possible? Have some fun with this,

bring the text to life, and post your results.

2) Proving that Pythagoras was right: Can you use the interactive pictures to

demonstrate that the old Greek mathematician was correct? Explain how the image

proves the theorem. Can you do this for both widgets?

Dis4Rubber sheet geometry says two objects are equivalent by distortion if we can

stretch, shrink, bend, or twist one without cutting or gluing and deform it into the other.

Review the shapes below. Are these two shapes equivalent by distortion or not and why?

Möbius strips are fascinating. Try this at home. Get a piece of paper, scissors, and

tape. Cut a strip of paper, maybe an inch wide. How many edges does this piece of paper

have? How many surfaces? Now twist one end and tape it onto the other end, making a

Möbius strip. Now, trace the sides; how many sides? How many surfaces? How can you

tell? Post a few photos of your Möbius strip!

Dis5, For the following prompts, use the WileyPlus Interactive Resources in Chapter 7:

1) Koch Snowflake – Can you show and determine how many sides a Koch Snowflake has

after one iteration? Can you do the same for two iterations? Three? Four? Five? The

widget will verify these. How many sides does a Koch Snowflake have after eight

iterations? Can you write an equation for the number of sides for a Koch Snowflake after

n iterations?

2) Sierpinski Carpet – Can you show and determine how many squares a Sierpinski

Carpet has after one iteration? Can you do the same for two iterations? Three? Four?

Five? What about eight iterations? Can you determine a formula for n iterations?

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