In November, PARCC, one of the two multi-state consortia developing Common Core assessments, released some more sample questions. *CCSSI Mathematics* has good analysis of them. As they right note, this is an exercise in factoring, not in multiplication. The 10 x 10 grid prohibits a student from arranging the tiles in a 2 x 24 or 4 x 12 grid. Only the 6 x 8 or 8 x 6 rectangular shape is possible.

I have one more criticism to add for his math problem: the user interface is awful. To answer the question, the students need to click on at least 48 squares. This is a tedious task. With a pencil, the students could easily shade them in broad strokes across columns or rows. The user interface does not permit them to select tiles by click-and-drag or using the keyboard. To un-select the tiles, the student must click each one. So an error in selecting them, could require a child to make more than 48 mouse-clicks.

Then there is part C:

Again, *CCSSI Mathematics *has a good criticism of the age-inappropriate nature of these CC standards. Setting that aside, as the item is written, the answer range is quite broad. Consider this:

This is a multiplication question that Andy *could* have written. It doesn’t represent the problem in C, but the item-writers did not require the test subject to do so. All they asked for was an multiplication equation that used ? to represent the number of row. Is this a correct answer? Or this:

Neither demonstrates any understanding of the problem posed in C, but they are mathematically accurate multiplication equations that Andy could have written. And quite sophisticated ones indeed.

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Chris, I also have issues with the term “rectangular array”. Thus this is not only a math problem, but a reading comprehension problem and depends on how you interpret the meaning of rectangular array. For example in part A, when I first read it, I thought, gee I could just randomly choose individual squares, as each individual square could be its own rectangular array. You could instead say “contiguous rectangular array” but then your vocabulary might exceed the students’ capacity. Finally, there’s the issue of English Language Learners. If this test is not offered in your native language, god help you.

By the way, what grade level is this sample question intended for?

Great stuff!

3rd grade.

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