Setting the Stage

• Have your students sit in their teams. (See organizing for cooperative technology activities.)
• Tell the students that you saw this signpost one day as you approached Hillsdale. As you passed the sign you realized that there was something wrong with it. So you pulled over and looked at it again. This time not only did you notice the mistake, but also you realized there was a more serious problem with the sign. Ask the students to figure out two things: (1) what was the mistake and (2) what was the "serious" problem.
• Discuss the problem with your group members and answer both parts of the question in the space provided.

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 thousandths column was not added properly. More challenging for students who focus on getting the "right" (and only?) answer, is answering the second part. You will quickly be able to assess the students number sense. Some possible answers to your followup question: "what else is wrong with this? What was the more "serious" problem?

As you go around to each group and see what they are writing down, you might notice answers like this

• There should be a comma between the 1 and the 8 next to Founded. (The same student did not know what founded meant.)

However, students who are focused on getting the answer may overlook the fact that finding the sum of the three numbers does not make any sense. This problem and the bus problem that follows are good examples to see if sense making is part of the students agenda.

Debriefing

Understanding the 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 doornobs 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.

Given this discussion, the next problem (School trip) should be approached from a sense making perspective.