Interpreting and Evaluating - January 2009, Stage 4&5

This month our problems involve aspects of the process of interpreting the information in a question and examining in various ways the solution or methods used to get the solution. For example, are the assumptions and arguments made correct or appropriate? How does the solution relate to the initial problem? Can we make sense of someone else's finding? Can we compare strategies used?

Problems

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Making Sixty

Stage: 4 Challenge Level: Challenge Level:1

Why does this fold create an angle of sixty degrees?

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More or Less?

Stage: 4 Challenge Level: Challenge Level:1

Are these estimates of physical quantities accurate?

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Time to Evolve

Stage: 4 Challenge Level: Challenge Level:1

How many generations would link an evolutionist to a very distant ancestor?

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Beelines

Stage: 4 Challenge Level: Challenge Level:1

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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Why 24?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

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Napkin

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .

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Partly Circles

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the same and what is different about these circle questions? What connections can you make?

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Bendy Quad

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

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OK! Now Prove It

Stage: 5 Challenge Level: Challenge Level:1

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

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Mind Your Ps and Qs

Stage: 5 Short Challenge Level: Challenge Level:2 Challenge Level:2

Sort these mathematical propositions into a series of 8 correct statements.

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Chi-squared Faker

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

How would you massage the data in this Chi-squared test to both accept and reject the hypothesis?

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So Big

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

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Rain or Shine

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.