CircleSquare
by Dan Meyer
skips
questions
Act One

March 03, 2014
What's happening here anyway? How are the square and the circle changing? What controls their change?
 Teacher noteHost 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
 VideoCircleSquare 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 noteShare 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 noteCheck.
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 noteGeneralize.
Now have them put an x wherever they previously had their guess and put them in the following Desmos graph.  LinkCircleSquare Graph
Act Three
 VideoAnswer Graph
Sequel
 4.
How would the point change for CircleTriangle, CircleOctagon, and CircleCircle? How do you know?
 5.
Rephrase our original question using words only.
show 81 more questions






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



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



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






How do the perimeter of the fullsized square and the circumference of the fullsized circle compare?




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

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











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




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


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


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
















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


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




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

















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