This activity is aligned to NCTM Standards - Grades 6-8: Algebra, Problem Solving, Reasoning and Proof, and Communication and to California Mathematics Standards Grade 7: Algebra and Functions #1 and Mathematical Reasoning #1.1, 1.2, 2.4, 2.5, 2.6.

Glencoe's Interactive Mathematics text provides an activity (Units 7-12, p. 16) called "Fruit for Thought." During the 1996-97 school year the mathematics department used a similar problem, The Variable Dilemma as an open-ended assessment question. (This is the the rubric we developed for that assessment question.) Whether presented with fruit or letters as variables, it is an interesting problem for students to solve.

Introducing the Activity

    Using variables:

Each group of 4 students is given a "Fruit for Thought" chart to record the digits from 0 - 9 which correspond to the fruit used in the equations. They are instructed to turn to page 16 to begin determining the values that each fruit represents. Remind the students that there is a unique digit corresponding to each fruit.

As groups determine values ask them to write down their process. What were they thinking?

Give time for the groups to work through the solution.

As a class discuss the answers.

Processing the Activity

Discuss the properties that this exercise uses.

1. adding 0 to any number gives the same number - Additive Identity
2. multiplying by 1 gives the same number - Multiplicative Identity

Discuss other properties that the students have learned about numbers

1. Commutative Property for Addition
2. Commutative Property for Multiplication
3. Distributive Property of Multiplication over Addition
4. Additive Inverse
5. Multiplicative Inverse
6. Closure

Here are some pages from the Math Forum that students might find interesting to read on the different properties.

Basic Real Number Properties
Properties
Identifying Algebraic Properties
Reciprocals

Other Links:

Whole Numbers and Their Basic Properties - Math League Multimedia
Definitions of the properties with accompanying examples.

Make 24 If You Can - Don Link
This is an Excel spreadsheet that implements a game similar to the card-based 24 Game by Suntex International Inc.