Intent

This activity will help you assess how well students understand meaningful algebraic expressions.

Mathematics

As in Ox Expressions, students approach the use of variables from another perspective, generating meaningful algebraic expressions from a given set of variables. They see that, when used in context, combinations of variables can represent more than a sequence of numeric steps. Students also strengthen their skill with substitution into algebraic expressions. Finally, the activity offers another context for working with the distributive property.

Progression

Students complete the activity on their own. After this individual work, while students share their expressions and summary phrases, the teacher can gauge their understanding to determine what to debrief and what to emphasize. The activity concludes with identification of examples of the distributive property.

Approximate Time

10 minutes for introduction

20 minutes for activity (at home)

15 minutes for discussion

Classroom Organization

Individuals, followed by whole-class discussion

Doing the Activity

This activity is similar to Ox Expressions, but more structured. One difference is that the numeric values have been stripped from the list of variables. You might watch how students adapt their work to this change and inquire whether this makes the activity easier or more challenging.

Tell students that in this activity, they will work on problems similar to those in Ox Expressions, using algebraic expressions and summary phrases.

Discussing and Debriefing the Activity

You might begin by having students share in their groups. While you are listening, watch for students who write statements of arithmetic procedures rather than summary statements. For example, in Question 5, students should recognize that FM gives the number of men in a wagon train and should not simply describe the expression as the number of families in a wagon train times the number of men per family.

In Question 7, students should recognize that the expression WL has no meaning in this context, even though one can multiply the numbers that might be associated with the variables W and L.

The extent of the discussion will depend on what happened in the earlier discussion of Ox Expressions. If students had difficulty with that, continue to emphasize the issue of meaningful expressions and the creation of summary phrases. The suggested supplemental activities can help students who need more experience with relating variables to their meanings and creating good summary phrases.

This activity also lends itself to using sentence strips, or another public display, of student replies. Responses to Question 8 can be posted as challenge tasks—posting only the ox expression or the summary phrase, of course.

Use the discussion of this activity to reinforce students’ understanding of the distributive property. For example, focus on Question 2 to bring out that the solution can be written as either B(W + M + C) or BW + BM + BC, and identify this as another example of the distributive property. If either of these expressions did not arise in students’ work, challenge the class to seek another expression for the summary phrase “the water consumed in a day by a family.” Ask, How could you get the total amount of water by finding the separate totals for the women, for the men, and for the children?

Ask whether students can explain why the expressions B(W + M + C) and BW + BM + BC are both correct. Use this opportunity to review the phrase equivalent expressions and to bring out that the equivalence of the expressions is an example of the distributive property. You might also suggest that students assign specific numbers to the variables and use substitution to help confirm the equivalence of the two expressions. Having different groups use different values will make the confirmation even more powerful.

Key Question

How could you get the total amount of water by finding the separate totals for the women, for the men, and for the children?

Supplemental Activities

Classroom Expressions (reinforcement) asks students to create summary phrases and algebraic expressions using a set of variables that relate to a classroom setting. The activity also introduces the notation of subscripts.

Variables of Your Own (reinforcement) asks students to make up a set of variables, and to write algebraic expressions and summary phrases, in a context of their own choosing.