104 ◆ Reasoning About Problems
Two Argument Problems
Two argument problems are great! They get students to think and reason
to themselves and out loud. The makeup of these problems is to have a
central problem with students, approaching it from different perspectives.
The students have to read the problem and then make sense of it and
decide who is correct. For example (see Figures 6.25 and 6.27).
Linda answered the following problem like this:2500
− 498
2,198Can you find and fix her error?*Mary multiplied 478 × 20. She got 5,039. Use estimation to explain
why this answer is not reasonable.Mary Jo said that^3 ⁄ 8 is bigger than^2 ⁄ 4 because 8 is bigger than 4. Kylie
said that you can’t just say that. You must look at the size of the frac-
tion. Who is correct? Use your tools to explain your thinking.Figure 6.25 Fraction Bars
1(^1) ⁄ 2 1 ⁄ 2
(^1) ⁄ 3 1 ⁄ 3 1 ⁄ 3
(^1) ⁄ 4 1 ⁄ 4 1 ⁄ 4 1 ⁄ 4
(^1) ⁄ 5 1 ⁄ 5 1 ⁄ 5 1 ⁄ 5 1 ⁄ 5
(^1) ⁄ 6 1 ⁄ 6 1 ⁄ 6 1 ⁄ 6 1 ⁄ 6 1 ⁄ 6
(^1) ⁄ 8 1 ⁄ 8 1 ⁄ 8 1 ⁄ 8 1 ⁄ 8 1 ⁄ 8 1 ⁄ 8 1 ⁄ 8
(^1) ⁄ 10 1 ⁄ 10 1 ⁄ 10 1 ⁄ 10 1 ⁄ 10 1 ⁄ 10 1 ⁄ 10 1 ⁄ 10 1 ⁄ 10 1 ⁄ 10
(^1) ⁄ 12 1 ⁄ 12 1 ⁄ 12 1 ⁄ 12 1 ⁄ 12 1 ⁄ 12 1 ⁄ 12 1 ⁄ 12 1 ⁄ 12 1 ⁄ 12 1 ⁄ 12 1 ⁄ 12
Luke read the following problem: Grandma Betsy made some brownies.
On Monday her grandchildren ate^1 ⁄ 3 of them. On Tuesday they ate another
(^1) ⁄ 3 of them. How much did they eat altogether both days? Luke said (^2) ⁄ 6 of the
brownies. Kelly said that didn’t make sense. Who is correct and why?