Sneaking Up the Line
Eric the Sheep is at the end of a line of 50 sheep waiting to be shorn. But being an impatient sort of a 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 2 sheep behind him in line. If at some point it is possible for Eric to move only 1 place, he does that instead of moving ahead 2 places.
How many sheep get shorn before Eric?
1.
Predict a solution “in your head.”
2.
Use manipulatives or anything else to solve these 2 problems:
Number in front of Eric
Number shorn before Eric
6 11
3.
What pattern did you notice that could help you solve the original problem in which Eric is at the end of a line of 50 sheep?
4.
Explore other numbers and put the results into a table.
Number in front of Eric
Number shorn before Eric
5.
Describe how you could work out the answer for any number of sheep.
6.
Work out the solution for the boxes left blank.
Number in front of Eric
Number shorn before Eric
37 296 1000
13 21
7695
7. Eric gets more (and more) impatient! Explore how your rule changes if Eric sneaks past 3 at a time, 4 at a time, or even 10 at a time. A soon as someone tells you how many sheep are in front of Eric and how many he sneaks past at a time, describe how you could work out the answer.