Ask, Don’t Tell (Part 4): The Equation of a Circle
By Jennifer Wilson, posted July 6, 2015 –
I used to tell my students how to write the equation of a
circle, given its center and radius. Then I would give them the center and
radius of a circle and ask for an equation. Now I provide my students an
opportunity to figure it out by practicing The Common Core’s Standard for
Mathematical Practice 8: Look for and express regularity in repeated reasoning.
Jill Gough and I have worked this year on
leveled learning progressions for giving students a path to using the Standards
for Mathematical Practice when they don’t know where to start. This is the progression
that we created for SMP 8.
We used a Geometry
Nspired activity as a guide for our exploration. A good GeoGebra
exploration is Equations
We started by noting what changes and
what stays the same as we move point P
around in the coordinate plane:
• The triangle is always right.
• The hypotenuse is always 5.
• The legs change.
• One vertex is always at the origin.
Then I ask some questions: What path does
P follow? What can we say that’s
always true about the coordinates of P?
We trace point P as it moves around
the coordinate plane and students begin to generalize the results, connecting
the equation of the circle to the Pythagorean theorem: x2 + y2
Eventually, students move the circle
around in the coordinate plane, changing the radius and center, noticing and
noting how the equation of the circle changes. How does the equation of the
circle change when the center is translated from the origin?
Finally, I ask my students how to write
the equation of a circle, given its center and radius.
“Ask, Don’t Tell” learning opportunities allow
the mathematics that we study to unfold through questions, conjectures, and
exploration. “Ask, Don’t Tell” learning opportunities begin to activate
students as owners of their learning.
are some of your favorite places to find “Ask Don’t Tell” learning
opportunities for your students? Here are some of ours:
We use many of the
formative assessment lessons from the Shell Center.
• Mary Bourassa started a site for sharing Which One Doesn’t Belong? items.
• Nanette Johnson, Robert Kaplinsky, and Bryan
Anderson have created a site to share Open
• Jo Boaler and the Youcubed team have shared a Week of
Inspirational Math for beginning the school year by
inspiring students with inquiry-based activities.
Toward the end of the school year, one student
reflected, “I think that interacting in class helped
me further my learning experience. I was nervous to speak up because I was
afraid of being wrong but now I understand that instead of getting in trouble
for being wrong, the others in my class will help me find the right answer
without actually telling me the answer.”
What #AskDontTell opportunities do and can you provide?
a National Board Certified Teacher, teaches and learns mathematics at Northwest
Rankin High School and is a curriculum specialist at the Rankin County School
District in Brandon, Mississippi. She is an instructor for TI’s Teachers
Teaching with Technology (T3) program. She enjoys learning alongside
the Illustrative Mathematics community, and she is
a recipient of the Presidential Award for Excellence in Mathematics and Science
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