100 ◆ Reasoning About Problems
Reasoning About Remainders
Remainders are difficult. But they don’t have to be. Start out by teaching
remainder problems with pictures. Students should be able to reason about
the numbers by seeing them. They should talk about various situations
to understand that we either round up, round down, drop or leave the
remainder (see Figures 6.21 and 6.22).
Figure 6.21 Act Out, Sketch or Diagram the Problem
There were 24 fish in the tank at the pet store. The clerk took them out and
put them in smaller bowls with 5 fish in each bowl. How many bowls did
he use?Figure 6.22 Act Out, Sketch or Diagram the Problem
Figuring out remainders:
Pick a problem
Record it. Solve it. Write the Remainder. Interpret it!
Problems Model Remainder Round Up/Down/
Drop/Leave
Version 1:
The 3rd graders
are going on a
field trip. There
are 67 students
and 5 adults.
Each minivan fits
15 people. How
many minivans
do they need?72/15 =
So we need 5
buses because 4
would only fit
60 people and
12 would be left
over.12 In this case, we
have to round up.
We need 5 buses
because the 12
people need a
place to sit.Graphic organizers can help students to think through the process.