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Circle-Square

19
skips
81
questions

Act One

• Dan Meyer

March 03, 2014

What's happening here anyway? How are the square and the circle changing? What controls their change?

• Teacher note
Host a brief argument. Some students may claim the area is held constant. Some may go for the perimeter. Have students restate each other's ideas. Don't settle the question just yet.

Act Two

• VideoCircle-Square w/ Numbers
• 1.

Guess where the circle and the square have equal area.

• 2.

What's a number you know is too high?

• 3.

What's a number you know is too low?

• Teacher note
Share out.

Make sure everyone is on the same page. We're talking about the point where the circle is tangent to the square.

Once everyone has their three numbers guessed. Have everybody share out. Locate the highest answer in the class. Locate the lowest answer.
• Teacher note
Check.

Now ask them to take their guess and calculate the area of the circle and the square at their guess and find out if they were right.

If students finish quickly, tell them they should pick a different guess and see if that one is right.
• Teacher note
Generalize.

Now have them put an x wherever they previously had their guess and put them in the following Desmos graph.

Act Three

Sequel

• 4.

How would the point change for Circle-Triangle, Circle-Octagon, and Circle-Circle? How do you know?

• 5.

Rephrase our original question using words only.

### show 81 more questions

• jeremiah L

March 03, 2014

is there a time when the areas are equivilant?

• Karri Schlegel

March 03, 2014

When are they the same size?

• Anne Figge

March 03, 2014

When is the sum of the area of the circle and of the square maximized?

• Candace Matthews

March 03, 2014

When do the circle and square have the same area?

• Linda Sweeney

March 03, 2014

What's the relationship of the size of the two shapes?

• Michael Williams

March 03, 2014

Is the area of square and circle equal when the intersection of the two shapes is at the midpoint of the line segment?

• abeek

March 04, 2014

WHat is the relationship between the side length of the square and the chord?

• Heather Moore

March 04, 2014

At what point is the total area the largest?

• jose Pizarro

March 04, 2014

is the length of the line the same of the perimeter of the square plus the perimeter of the circle?

• Jean Hamabe

March 04, 2014

when are they equal

• Larry Ellam

March 04, 2014

Are we comparing the areas?

• March 04, 2014

At what point is the area of the square equal to the area of the circle?

• Gail

March 04, 2014

What is the length of line and size of circle and square?

• gary bacco

March 05, 2014

is the circumference of the circle the length of the square?

• Frank Cardwell

March 05, 2014

when are the perimeters the same

• • Bindu Sunil

March 05, 2014

How is the area of square and circle related?

• Carolyn Droll

March 06, 2014

How do the perimeter of the full-sized square and the circumference of the full-sized circle compare?

• Anna Cederfjord

March 06, 2014

when are they the same sice

• David Kamishlian

March 07, 2014

when will the areas be equal?

• Rich Cometta

March 07, 2014

Is the relationship of the perimeters proportional?

• courtney lewis

March 07, 2014

whats the relationship between the perimeter of a square and circumference of a circle?

• Louise Aston

March 07, 2014

when is the perimeter of the square the same as the circumference of the circle

• Catherine Hill

March 08, 2014

Are the square and circle proportional

• Brian Dean

March 09, 2014

Does the amount of line left represent the perimeter of the object?

• Ann Sandine

March 09, 2014

What is the relationship

• Emily Triffault

March 10, 2014

Is the total area the same ?

• Benita von Bahr

March 10, 2014

is the square equal to the circle?

• vtierney

March 11, 2014

when are they the same size

• Jennifer B Smith

March 11, 2014

When will the square and the circle have the same area?

• Glenn McIntyre

March 12, 2014

How does the width of the square relate to the area of the circle?

• Barb Smalley

March 12, 2014

What is the maximum possible area between the two figures.

• Eduardo Arteaga

March 12, 2014

At what point, do the circle and the square are equal in area?

• Manas Kulkarni

March 12, 2014

At what point is the diameter of the circle equal to a side of the square?

• Gavin Wuthrich

March 12, 2014

When is the area of the square and the circle the same?

• Lynn Sytsma

March 13, 2014

When will the square and circle have the same perimeter?

• Elizabeth

March 13, 2014

what are we trying to do

• Carol Neilson

March 13, 2014

when is the perimeter of the square equal to the circumference of the circle?

• Joe Concialdi

March 13, 2014

How are the areas changing?

• JOE ARNOLD

March 13, 2014

At what point on the line will the area of the circle and square be the same

• Leeanna Boe

March 14, 2014

area of square and circle

• Retta Reser

March 14, 2014

Why does the circle go partially below the line, whereas the square does not go above?

• Greg Janzen

March 16, 2014

Are the perimeters of the shapes equal to the length of the line?

• Rachel Prather

March 17, 2014

How long is the line?

• Heidi Rhodes

March 17, 2014

When are the areas the same?

• Ann Allison

March 18, 2014

Why is the square larger than the circle

• Cheryl Hall

March 19, 2014

What's that circle doing next to that square?

• Anne O'Shea

March 20, 2014

When do the square and circle have the same area?

• • Karen McGrail

March 20, 2014

When do the circle and square have the same area?

• Matt Richardson

March 20, 2014

How do the areas compare?

• Maggie Chapa

March 20, 2014

what is the box and the red circle?

• Jen Sorbara

March 20, 2014

What's the difference between circumference and perimeter?

• James White

March 20, 2014

when are the areas equal?

• Nicola Coles

March 20, 2014

How long is the initial line?

• Zach Freistat

March 20, 2014

When are they the same size?

• Mollie

March 21, 2014

Why is it getting bigger and smaller?

• Jennie Ebeling

March 21, 2014

Is the square's perimeter the same as the circumference of the circle?

• • Geneva Hinchliffe

March 22, 2014

what is the relationship between the circumference/area of circle/square?

• wevoltaire

March 23, 2014

when are the shapes the same size

• Heather Welsh

March 24, 2014

When will the circle and square have (approximately) the same area?

• sarah Caban

March 24, 2014

why is the square below the line?

• matthew thorogood

March 24, 2014

Can they ever share the same area? Can they share the same perimeter?

• mark Richards

March 24, 2014

what is the question?

• Robert Parrilla

March 24, 2014

When will the areas be equal?

• Natalie Holm

March 24, 2014

Where along the line will they have the same area?

• Mark Dittmer

March 24, 2014

Which shape has the bigger area?

• Simon Walton

March 25, 2014

When are the ares the same

• Nate Bracy

March 25, 2014

WHen will the areas be equal?

• Joe Illichman

March 25, 2014

At which point will both the square and circle have the same area?

• • Ramona Weigel

March 25, 2014

when are the areas the same

• Katie Muhtaris

March 26, 2014

What is the length of the original line?

• Amber Cordell

March 27, 2014

Are they ever the same size?

• abel soto

March 27, 2014

when will the two shapes have the same area?

• Brandi Merrick

March 28, 2014

What is the point of this?

• Jacob Culver

March 28, 2014

what is going on here

• Cydelia ChÃ¡vez

March 28, 2014

When will the areas be equal?

• michael lohmann

March 28, 2014

Why is square blue?

• Elizabeth R. Simpson

March 28, 2014

For what value of x or r will the areas be approximately the same?