Friday, June 12, 2015

Math problem of the week: 6th grade Common Core-inspired test question

More from the Smarter Balanced Consortium and its Common Core-aligned tests: the final items on a 6th grade number sense assessment.

Stimulus: The student is presented with statements about two rational numbers and their position on a number line in relation to each other.

Example Stem: Select True or False for each statement.

The numbers 7 and –12 are both located to the right of 0 on the number line.

The number –12 is located to the right of 5 on the number line.

The number –12 is located to the left of –8 on the number line.


Extra Credit:

Discuss how confusing mathematical conventions with mathematical concepts is similar to confusing mathematical labels with mathematical concepts.

1 comment:

Auntie Ann said...

I was looking over our kid's "summer math packet" and page 1 reinforces exactly this point.

It starts out with a blurb about Geometric formula (yes, they capped Geometric), then gets it right when it defines some formulas for perimeter and area:

"Perimeter of a square = 4s, where s is the length of one side."

It then goes on to show the formulas for rectangles and area of a triangle.

But, when it comes to the actual problems they want the kids to do, it runs off the rails, explicitly teaching the kids to look at the letters to figure out the formula:

"First identify the formula to use from the letters given, then use that formula to find the area of the figure given its dimensions.

"7.) b = 7 in., h = 4 in."

According to the formulas given at the top, that can only refer to a triangle. Teaching the convention is the point, not teaching the concept.

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p.s. Far worse, however, in a packet for rising 8th graders, page 3 has such challenging problems as:

1) 4 + 3
2) -12 + 4
3) 19 + (-3) +6

Page 5 has:

1) (-10)4
6) (-1)(-7)

Page 6 has the best question ever...

Write the reciprocal of the following:

2) 1

etc. These are problems I would expect any 5th grader to be able to do. No wonder kids can't hack algebra in 8th grade...or 9th...or college.