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 road sign in the image.
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
 The
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."
 Many students need help in understanding
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.
 You should help them to
understand why the sign doesn't make sense.
Comments on doing the
Activity
 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 the sign? 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 secondgraders: 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 made no sense.
This problem and the Bus
problem that follows are good examples of
problems you should do with your students to reinforce
and make sure that the answers are meaningful to them.
Source: Original Version 1.0
developed at CIESE
Center for
Innovation in Engineering & Science Education
(2007)
Revised
10.26.19 currently under
construction
