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Guess my rule! - 1
Students use pattern finding and algebraic skills while learning that there is more than one way to continue any sequence. (Date Revised: Wednesday, June 27, 2001).
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Divisibility 1
First with numbers, students conjecture that (a^n - 1) is divisible by (a-1). Students prove that (a-1) is a factor of (a^n - 1) with elementary algebra, and apply the result to understanding the arithmetic test for divisibility by 9. (Date Revised: Thursday, March 15, 2001).
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Sally Snail: Travel at constant rate
This set introduces the concept of constant rate. It represents constant rate by increases of both distance and time with equal increments. It connects this representation with the graphical representation of constant rate. It also emphasizes the connection of constant rate with proportional relations. (Date Revised: Thursday, March 15, 2001).
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Triangle with restricted angle sum
In this very short problem, students employ proof by contradiction in a non-formal way, while examining relationships among angles in triangles. (Date Revised: Tuesday, February 27, 2001).
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Powers of two
Students use a simple context (balance scales) to see that all counting numbers can be expressed as sums of powers of 2. This can be used as an introduction to exponents or the base-2 number system. (Date Revised: Thursday, May 31, 2001).
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Area of regular polygons
Students use congruence tests, area of a triangle, and trigonometry (the tangent ratio) to find formulas for the areas of regular pentagons and hexagons. They generalize the formulas to other regular polygons. (Date Revised: Tuesday, November 06, 2001).
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Finding the line of best fit
Students compare two models for a data set (women's tennis earnings) using the absolute value of the residuals (or error). Then they use technology (calculator or software) to find the least squares regression line, and they compare one of the earlier models to that line using squares of the residuals. (Note, the problem set "Tennis, anyone?" makes an excellent precursor to this one.) (Date Revised: Monday, November 19, 2001).
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Setting up proportions
Students learn how to properly set up proportions by first organizing the three given values and the unknown value. Some solving of set-up proportions is required. (Date Revised: Thursday, February 07, 2002).
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Numerical Patterns and Sequences