Generating MCAS practice problems



Generating MCAS practice problems

Each week your assignment is to generate two MCAS practice problems. The purpose of this document is to make the content as clear as possible.

Problem 1: must be open ended and at the grade level you teach at (so 8th grade in all likelihood). Additionally it should include:

the problem itself

the category and substrand that the problem as a whole addresses.

the problem below is from Geometry and is in the first substrand

of "identify, describe, compare and classify geometric figures"

to make things simple, we will call that 8.G.1 indicating grade 8,

Geometry, first substrand

a complete solution to the problem

a break down of the solution into components and the strand that relates to each

component.

The reason for the last requirement is to help people identify the particular place in the solution where students might have problems as well as what type of work might be needed in order to get them up to speed in that area.

This may be clarified with an example.

Sample Problem: a right triangle has a hypotenuse of 7 units. What must the lengths of its other sides be in order for it to be an isosceles triangle?

This problem might be put in Grade 10, Geometry, section 1 or 10.G.1.

Now let's look at what a student possibly needs to get a correct solution:

1) know what a right triangle is (8.G.1) as well as which part the hypotenuse is. Know what an isosceles triangle is.

2) assign a variable to the other two sides (perhaps 8.A.1)

3) know the Pythagorean Theorem and apply it here (10.G.5)

x2 + x2 = 72

4) solve the equation for x (10.P.5) x = 7/Ö2

(possible a substrand in here dealing with exponents and radicals, 10.N.1)

5) pick the appropriate solution (discard the negative value)

One might also, in light of the fact that the problem is entirely verbally stated, argue that there is a Communication component initially.

comments:

there are strands here from both 8th and 10th grades. You might ask" shouldn't the problem reflect a single grade?". My answer would be NO, math is a cumulative part of education. All education leading up to the 10th grade may contribute. The effectiveness of all prior instructors may play a role. We're all in this together!!

The sequential nature of the solution is referred to by one of my colleagues as scaffolding. Each part builds on the other; if it falls down, we need to identify the weak component.

Problem 2: must be at a grade level other than the one you teach at! May be multiple choice. Should get you thinking about what people are working on at other levels. Should also indicate the category and sub areas involved, as discussed above.

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