For years I have turned a blind eye to what happens inside J's math class--so long as I get to decide what we do at home. Just recently I've learned what I've been missing. Without my lifting a finger or wagging a tongue, a minor miracle has occurred. The interim math teacher who took over mid-year appears to have been giving J some above grade-level classwork. Given what the alternative would look like (the school uses Connected Math), I'm all the more appreciative.
Friday, June 10, 2011
Consider the final algebra problems in 8th grade Connected Math vs. the worksheet that J brought home three days ago:
I. The final four problems in the final algebra chapter in 8th grade Connected Math: "Frogs, Fleas, and Painted Cubes," p. 87:
1. What patterns would you expect for a quadratic function
a. in tables of (x, y) value pairs?
b. in graphs of (x, y) value pairs?
c. in equations relating x and y?
2. How are equations, tables, and graphs for quadratic relations different from those for
a. linear relations?
b. exponential relations?
3. For a quadratic relation in the form ax2 + bx + c, how can you tell whether the graph will have a maximum or minimum point?
4. What strategies can be used to solve quadratic equations such as 3x2 - 5x -3 and x2 + 4x = 7 using
a. tables of values of a quadratic function?
b. graphs of a quadratic function?
II. The last four problems in J's sheet: (source unknown)
Write the following functions in the form y = a(x + h)2 + k. Find the vertex.
y = x2 + 4x -9
y = x2 - 6x + 16
y = x2 - 8x - 1
y = x2 + x + 2
III. Extra Credit
Consider the likely performance of a language-delayed, high functioning autistic child on each problem set. How might estimates of mathematical ability in autistic children depend on whether the instrument involves Reform Math problems?