Setting the Stage
- Have your students sit in
groups or teams. Hand
out the student page to each student.
- Ask the students to carefully
look at the cartoon. Ask
them to figure out two things that are problematic
with the sign. In other words, (1) what was the
mistake that was made and (2) why is the sign making
the driver smile?
Doing the Activity
students should try to answer the question on their
own in the space provided. Then they should discuss
with their group members and come up with the
group's best answer. One of the group members can be
the spokesperson for the group. As you go
around to each group and see what they are writing
down, you might notice comments such as: "There should
be a comma between the 1 and the 8 in 1802 not
realizing that "Founded" makes reference to a year."
- They many need help in seeing that adding
years + feet + people does not produce a meaningful
number independent of whether the numbers are added
properly or not.
Debriefing the activity
- Each group shares their
answers with the rest of the class.
- The teacher helps them to
understand why the sign doesn't make sense.
Comments on doing the
- What the students will probably see is that
the sum should be 6,122 instead of 5,122. They
should be able to explain that the thousands column
was not added properly. More challenging for the
students is answering the second part.
(What else is "wrong" with it?
Why is the driver smiling?)
- Understanding the road sign is a
prerequisite for realizing that finding a sum for this
problem does not make sense. For example, students
could be asked what 3 apples + 5 shoes + 7 doorknobs
equals? They might be tempted to say "15 items" which
could be argued as correct. But the overriding
question of whether it makes sense to do this addition
is the main point of this discussion.
- In a research project this
question was posed to 41 second-graders: There are 26
Sheep and 10 goats on a ship. How old is the captain?
About 90% of the children gave the same answer: 36.
And these were good students! They had scored well
above average on a math part of a statewide,
standardized achievement test. However, in the sheeps/goats
problem the children appeared to follow the rule: If
in doubt add the numbers in the problem. These came
out a traditional classroom environment. In the group
of students who were seeped in a constructivist
approach, a quarter of them said that the problem was
This problem and the Bus problem that
follows are good examples of problems you should do
with your students to reinforce that make sure that
answers are meaningful and "make sense."