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Let’s Examine Conjectures About Numbers Using Algebraic & Geometric
Reasoning
NCTM ANNUAL MEEETING NEW ORLEANS LA APRIL 9-12, 2014
Margaret J. Kenney ([email protected]) BOSTON COLLEGE, CHESTNUT HILL, MA
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Standards for
Mathematical Practice 1. Make sense of problems
and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
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4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
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3 + 5 5 + 7
11 + 13 17 + 19
29 + 31 41 + 43 59 + 61 71 + 73
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0 - 1 1 - 2 2 - 4
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Conjectures:
• On a 5x5 geoboard there are more than 50 squares.
• On a 5x5 geoboard there’s a path more than 50 units long that does not intersect with itself.
• On an nxn geoboard the maximum number of interior points for a triangle is a triangular number.
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