The url link above wil take you to a list of problems from Math Memos. The problems are “Chicken and Goats”, “Sums and Differences” and the “Movie Theater”. Each can be solved with problem-solving strategies like drawing a picture, making a chart, and through guess and check. Each of them also creates a rich opportunity for students to compare and evaluate the benefits of each of the strategies. (For more ideas on how to facilitate a discussion on the different strategies that students use, watch Metacognition and Math: Develop Student Problem-Solving Strategies.)

In addition to developing student strategies, sense-making and perseverance in problem-solving, these problems can all be used to connect student algorithms to equations and systems of equations. For example – students who come up with a way to use guess have implicitly set up two equations and are testing various possible values for certain variables. They are demonstrating algebraic thinking, though perhaps without the understanding of how to use formal algebraic notion and manipulation to make their process more efficient. Similarly, students who use charts are essentially testing various ordered pairs until they find the ones that meet all of the conditions in the problem.

Marilyn Burns says that “Algebra is the generalization of arithmetic” and these problems open up the door to helping students make connections between the methods they use and more formal algebraic manipulation.

Because each of these problems come from Math Memos, they each have a full teacher write-up including different possible solution methods, samples of student work, and suggestions from a teacher who used it in an adult numeracy/HSE class.

The following is a problem from the NYS Regents exam:

Two friends went to a restaurant and ordered one plain pizza and two sodas. Their bill totaled $15.95. Later that day, five friends went to the same restaurant. They ordered three plain pizzas and each person had one soda. Their bill totaled $45.90.

What is the price of one plain pizza?

There is no write up on Math Memos for using this problem with adult numeracy students (yet!), but it presents a similar opportunity for students to solve the problem using guess and check and an arithmetic algorithm which could then be connected to the generalization of an algebraic solution.