Sneaking Up the Line
Goal: Think like a mathematician! Look for a process that repeats then generalize the repetition.
Eric the Sheep is at the end of a line of 50 sheep waiting to be shorn. Being an impatient sort of sheep, Eric sneaks up the line two places every time the shearer takes a sheep from the front to be shorn. So, for example, while the first sheep is being shorn, Eric moves ahead so that there are two sheep behind him in line. If at some point it is possible for Eric to move only one place, he does this instead of moving ahead two places. How many sheep get shorn before Eric? Describe how you could work out the answer for any number of sheep. (Have students model sneaking up the line with manipulatives or by drawing the process to sense regularity.)
Source: Maths 300 online resource published by Curriculum Corporation www.maths300.esa.edu.au
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In this Eric the Sheep activity, I lined up several students and gave one child a sign “Eric the Sheep” and I pretended to shave the first student and let Eric sneak up. That helped the third graders understand the problem. This was our second lesson. I reduced the number of sheep to 15, and gave the children unifix cubes for the sheep and one of Eric. The acting out and concrete materials helped; however I still had about a third of the kids not really understanding what the others were doing. It was really difficult for most of the kids to understand that they could combine the reduction of 2 and 1 more. I think I should have used a word problem that only required one step vs. two, although we did have three pairs of kids who could draw and explain.
We used this story to introduce Recognizing Repetition. We read the story 3 times (once with eyes closed) , talked about the story (what is it about) documented on easel paper, and then I chose a student to represent Eric. She held a red cube, the remainder of students were other sheep (holding white cubes). We clustered the into 10s~ dropping the cubes in the 1 (sheep shorn) and 2 (move 2 up) pattern. We did this util we noticed the repetition and thought we could generalize. Students returned to their table groups and were asked to draw the repetition, share and discuss.