Friday, May 29, 2015

Math problems of the week: 6th grade Smarter Balanced "number sense" problems

It turns out the Montgomery Public Schools isn’t the only institution going deeper with K12 math. So is the Smarter Balanced Consortium and its Common Core-aligned tests. Here are two sample items from a 6th grade number sense assessment (one from the beginning, one from the end):

Stimulus: The student is presented with a context involving a negative number or zero.
Example Stem: A Fahrenheit thermometer shows that the temperature is 15 degrees below zero.
Enter the integer that represents the temperature in degrees Fahrenheit.

Stimulus: The student is presented with statements involving absolute value in a real-world context.
Example Stem: Sea level is defined as being at an elevation of 0 feet. Objects can be above or below sea level.
• Submarine J is 35.6 feet below sea level.
• Submarine Q is 21.5 feet below sea level.
• Submarine Z is 43.8 feet below sea level.

Determine whether each statement comparing the submarines is true.
Submarine J is deeper than Submarine Q because |–35.6| > |–21.5|.
Submarine Q is deeper than Submarine Z because |–21.5| > |–43.8|.
Submarine J is deeper than Submarine Z because |–35.6| > |–43.8|.

OILF's Extra Credit:

Is it possible that what’s challenging about negative numbers and absolute value aren’t the “deep” concepts that underlie them, but, rather, the more complicated operations on them that emerge in a curriculum less focused on “number sense” and more on (shudder!) mathematical procedures?