Friday, May 28, 2010

Math problem of the week: Core-Plus Math vs. traditional math on triangles

1. The first assignment on proving triangle similarity in Core Plus Mathematics, Contemporary Math in Context (a unified high school "core curriculum appropriate for all students") Course 2 (year 2), Part B, p. 395:

Imagine that you and a classmate each draw a triangle with three angles of one triangle congruent to three angles of the other triangle Do you think the two triangles will be similar? Make a conjecture.

a. Now conduct the following experiment. Have each member of your group draw a sement (no two with the same langth). Use a protractor to draw a 50o angle at one end of the segment. Then draw a 60o angle at the other end of the segment to form a triangle.

-What should be the measure of the third triangle? Check you answer.
-Are these two triangles similar to one another? What evidence can you give to support your view?

b. Repeat Part a with angles measuring 40o and 120o. Are these triangles similar? Give evidence to support your claim.

2. The first assignment on proving triangle similarity in Weeks & Atkins A Course in Geometry (a high school geometry text first published in 1961), p. 233:

P, Q are points on the sides AB, AC, respectively of the Δ ABC such that AP = 6 in. and AQ = 8 in. If AB = 16 in. and AC = 12 in., prove that the Δ APQ and ACB are similar. Is PQ parallel to BC?
[No accompanying diagram]

3. Extra Credit:

Discuss the perils of having today's students draw solo conclusions based only on rigid axioms and rigid logic rather than through empirical hands-on investigations in groups.

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