Deepening the Understanding of Algebraic Reasoning

withPat Milot, Leah Dubecki

& Agnes Grafton

A bike is travelling at 35 km/h.

A car is travelling at 80 km/h and begins 180 km behind the bike.

How long will it take the car to catch up to the bike?

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Exploring Different Representations

Quadratic Tiling Patterns

• Open envelope A • Distribute the contents equally

Step 1:• Which representations belong together?• How do you know?

Quadratic Tiling Patterns

Step 2: Examine the various representations.

What information does each representation tell you about the quadratic function it represents?

Step 3:Match the algebraic and pictorial representations.

I spy a representation that:

1. Shows me that quadratics do not form a straight line.2. Shows me the factored form.3. Shows me the “completed square”.4. Helps me see that x is a variable.5. Helps me see that a polynomial is a sum of functions.6. Shows me that the first differences of a quadratic are

constant.7. Shows me that the second differences of a quadratic

are linear.

Contact Information

• Pat Milot patmilot@emis3.ca• Leah Dubecki ldubecki@bhncdsb.ca• Agnes Grafton agrafton@bhncdsb.ca