Activity 10.6-10.7
Thursday, February 16, 2017 5:03 AM
A: Read SRH pp. 317-318, 324-325.
Do Ch. 10 EMP #33-34, 43.
B: Do Ch. 10 EMP #66, 69-70.
Housekeeping
10 minutes: 3.45-3.55pm
• Return folder #1
• Comments on the folder?
○ What do you do to show that a claim is true? show that it always
holds true (use a definition, theorem/properties or show for all
possible cases),
○ What do you do to disprove a claim? Give a counterexample! One
is enough!
○ Extra credit problem is an opportunity to improve your grade. We
don’t usually have many of them, so when one is assigned, be sure
to attempt it.
Activity 10.5: Pythagorean presentations
30 minutes: 3.55-4.25pm
Blank sheets of paper
• Instructor present the first proof.
• 3 groups that are ready to present their proofs. Each group to take 5 minutes.
○ The rest of the class listen and ask questions. Do not copy the proofs. They
will be posted on blackboard. Simply take short notes if need be.
• Let the rest of the groups work on their proofs. Submit a copy to instructor
• Get ready to present on Wednesday
Activity 10.6: Investigating Circles
15 minutes: 4.25-4.40pm
Blank sheets of paper
• Ask a volunteer to read the introductory paragraphs
• Assign the definitions as follows:
○ Group #1 def. 1 & 2
○ Group #2 def 3 & 4
○ Group #3 def 5 & 6
○ Group #4 def 5 & 6
○ Group #5 def. 3 & 4
○ Group #6 def. 1 & 2
• Figure out the definitions in your groups. Make sure your definitions meet the
necessary and sufficient conditions. Exchange for partners doing same ones to critique
each other. Collect after 10 minutes to discuss in next class. If no time, email by
Wednesday!
Activity 10.7: Investigating the Circumference-to-Diameter Ratio
25 minutes: 4.40-5.05pm
2 Coffee Cans
Measuring Tape
• A volunteer to read through the activity introductory statements.
• Model the process of measuring diameter and circumference. Be as precise as you can be.
**Use centimeters!
• When you have the average of your C/D results, please write it on the board. Create slots for
groups to write their average values.
• Discuss where the averages are close to. How come they aren't all pi? Measurement errors
• So C/D = pi. Solve the equation for C. Rewrite in terms of the radius. C=piD=2pir
Reflection
Joanna observed my class and gave feedback
Attendance
Alberto, Ashley Rose
Allen, Mackenzie E
Aurilia, Justine A
Bruce, Lydia
Critelli, Eve M
Czarnecki, Rylie
Fikert, Justina
Gershman, Emily
Gold, Hannah Michelle
Groome, Caroline Marie
Kotkin, Emily T
Norman, Cody
O'Connor, Abigail
Polkowitz, Allison L
Rachlin, Kelly
Ross, Rian D
Sievers, Michelle
Son, Yerin L
Supey, Katie Ann
Walter, Kylie E
Wang, Fengzhang
I finished all activities as planned and had time about 13 minutes to revisit definitions of 10.6. We had
interesting discussions as student critiqued each others' definitions. One group had said a tangent
touches at least one point of the circle. We had to define the term then agreed that it touches at exactly
one point.
I have to revisit the definition of a chord and show that not passing through the center is not a necessary
condition; however, containing interior points on the circle is necessary and as such, the diameter is a
chord.
Some students had misconceptions about are and circumference of circle. They confused the two.
Another one though C=pi.r.D
Assigning 10.5 to be done out of class was not a great idea, only three groups out of five were able to
complete the assignment.