106 ◆ Reasoning About Problems
Mike and Mary are having a math discussion. They are talking about
which number will make this equation true. Mike says that the answer
would be 56. Mary says the answer would be 8.
64 = b × 8
Part A: Who is correct?
Answer: _________________________
Part B: Explain your thinking with numbers, words and pictures.Figure 6.28 Reasoning About Numbers
Figure 6.29 Reasoning About Numbers
A busy candy store in downtown New York City sells about 25 lbs.
of chocolate a day. During the month of February, they sell three
times as many pounds of chocolate a day. Which of the following
is true?A. Every week (7 days), they sell over 200 lbs. of chocolate.
B. In February, they sell 1,000 pounds a week.
C. In February, they sell about 500 pounds a week.
D. Every week (7 days), they sell 125 lbs. of chocolate.Adapted from NAEP, 2011
Reasoning about numbers: greatest differences or smallest sum
(etc... .)
These problems are popular abroad in many top-performing math
countries (see Figures 6.30 and 6.31).
Another genre of reasoning problems is where students have to pick
which statement is true given a variety of options (see Figures 6.28 and
6.29). This problem is centered around comprehension and language.