Angry Birds – Parabolas

by Jon Orr

[UPDATED – Sept. 25 2015]

We have just spent a week working with quadratics in MPM2D and today I had students create their own angry birds level.

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The only real requirement was for them to create at least two flight paths and model them with quadratic equations.

I was hoping to see how they relate the equation to the graph. This worked out better than expected. Most students did not initially make their curves symmetric…..and that gave us a chance to discuss symmetry and these questions

  • Where would the zeros be?
  • Where is your vertex? Where are the zeros in relation to your vertex?
  • What could the equation be then?

Most students started creating their flight paths with placing the zeros on the graph….then picking a vertex. The best part of the day was discussing how students knew where their vertex was.

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Most knew that the axis of symmetry had to be half way between the zeros and also knew the vertex was on the axis. The issues, and then real thinking came when they went to create the equation to match. For example if Alexis wanted her bird to take off from x = 0 and land when x = 24 …she also wanted her highest height to be 7.5 units high. She wrote the equation y = – (x)(x – 24) and assumed she was correct. This assumption gave us lots to discuss!

I asked her to show me how she knew the vertex is (12,7.5) and she had a hard time. “I knew the x value was 12 but I just picked that height”. So I asked her to use the equation and find which height does go with an x value of 12. She did and then we graphed….
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Something clicked in her….”Aaah! The a-value must not just be -1″ and then that led us into discussing what the a-value should be and how we can get it more accurately! We did this…

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I loved that we discovered and struggled to find the correct a-value instead of me just giving an example and them copying.

I floated from group to group having similar conversations. Some students created their equations first and then found the vertex from the equation and plotted that.

Extensions

Some students started to ask if they could use different birds!!

  • The blue bird once tapped would split off and create three more birds with three new flight paths.
  • The yellow bird once tapped we assumed would make a straight line with a linear equation.

Pictures are from 2010….new pictures coming!!!

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Hottest Cup – TI-nSpire Temperature Probe

by Jon Orr

Collecting Data in MAP4C!

Student teams have been challenged to design a new coffee cup that will keep coffee warm.

The winner of the challenge will be the cup that keeps coffee warm the longest.

Requirements

  • The cup must hold at least 190ml
  • You must use only the material provided.

Teacher Handout – Includes student assignment and teacher notes on using TI-n Spire with the temperature probe.

 

CSI at JMSS

by Jon Orr

Grade 10 Principles of Mathematics at JMSS will be involved in an ongoing mock crime scene investigation. Throughout the semester clues will be discovered and evidence will be analyzed using Linear Systems, Analytic Geometry, Quadratic Relations, and Trigonometry. A full list of evidence and An introductory video revealing some evidence can be seen below. Statements from the 4 witnesses/suspects can also be downloaded below. As a Grade 10 math student it is your job to discover what happened and who the murderer is! Good Luck.

1. Car tire mark found on the road. 5.  Video evidence that may be related. (REVEALED) – (Need QuickTIME)
2. Picture of suspect and shadow caught on camera. (REVEALED) 6. GPS locations of all four suspects. Statements about locations have been given. (REVEALED)
3. Blood spatter found at the scene of the crime. Re-created in classroom lab. 7. Victim: Mrs. Curl – an ex JMSS math teacher. Also the ex-math department head.
4. Suspects found on location immediately after time of death

  • Mr. Roesch
  • Mr. Orr
  • Ms. Koiminek
  • Mr. Coates
The following are statements taken from each of the suspects found at the scene

  • Mr. Roesch: “I never liked that Mrs. Curl. I never forgave her for making me use that darn Smart Board in my classroom. I didn’t kill her though”
  • Mr. Coates:   “I always like Mrs. Curl. I can’t see why anyone would want to hurt her. I definitely didn’t kill her.”
  • Mr. Orr:         “When she left the school last year she it left ME with double the work!!! I’LL NEVER FORGIVE HER FOR THAT!”
  • Ms. Kominek:“I never really knew Mrs. Curl, but I know I didn’t like her”