The Road Sign Problem

Teacher's page

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

  • 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."
  • 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 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 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 senseless.

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."

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