Session 10, Grades 6-8, Part C:
Patterns That Illustrate Algebraic Thinking (25 minutes)

Many students find that a context or situation helps them think about algebraic ideas. In the next problem, we'll look at different representations of a situation that lead to a solution. Note 6

In this section we'll analyze problems at the grade 6-8 level for their algebraic content. For each problem, find a mathematical solution, then answer questions (a)-(d) listed below. If it is helpful, print this page and refer to the questions as you work on each problem.

 a. How would you solve the problem? b. What is the algebraic content in the problem? c. How do you think your students might solve the problem? What different representations might they use? d. What question or questions might you ask to get at "doing and undoing"?

Here's the problem:

A group of 8 adults and 2 children needs to cross a river. They have a small boat that can hold either 1 adult, 1 child, or 2 children.

Problem C1

How many one-way trips does it take for the entire group of 8 adults and 2 children to cross the river? Tell how you found your answer.

 Problem C2 How many trips in all for 6 adults and 2 children?

 Problem C3 How many trips for 15 adults and 2 children?

 Problem C4 How many trips for 23 adults and 2 children?

 Problem C5 How many trips for 100 adults and 2 children?

 Problem C6 Tell how you would find the number of one-way trips needed for any number of adults and 2 children to cross the river.

 Problems taken from MathScape (New York: Glencoe/McGraw-Hill, 2000). www.glencoe.com/sec/math
 Session 10, Grades 6-8: Index | Notes | Solutions | Video