Mathematics Big Idea and Major Topic: Simplify and Evaluate Expressions
More specific statement of the topic: Develop rules for combining like terms.
What the students already know: Basic math skills (adding, subtracting, dividing, and multiplying)
Know what variables are.
What part will the students have to figure out on their own? Defining like terms and be able to communicate their rules for defining and combining like terms.
Context: Organizing their closets
Statement of the task: Students must organize their messy closet filled with clothes into
3-5 categories. The categories represent different variables.
Students need to bring in at least 15 pictures from magazines, clip art, etc to represent items in their messy closet. Using the pictures of clothing students need to organize them in 3-5 categories. After students have categorized the clothing, they will explain the criteria for organization and establish variables to represent the categories. Using the defined variables, students will write an expression to represent the number of items in each category.
Then, students will be given a basket full of clean clothes to put into the closet. Using the developed rule, students need to put clothes away in proper spot. Students will write a new expression representing the clothes in the closet after adding new items to the closet.
Where might they get stuck? Making the transition from the semi-concrete pictures to the symbolic expressions.
What questions can I use to prompt them without giving away answers?
What characteristics are alike/different?
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
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Your mom is very upset with you because your closet is a total disaster. She’s telling you that you will not attend school dance unless you have your closet organized.
1.
Using the pictures of items you have cut out of the magazine, organize them in 3-5 categories.
2.
Explain what your rule is for sorting the items in the closet.
3.
Assign a variable to each category and write an expression to describe your closet.
4.
Explain why you cannot combine different categories.
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
2

5.
You are now given a basket full of clean clothes/items.
Using the rule you have developed, sort the clothes and add them to the items in your closet. Write a new expression.
6.
The following are the average cost of clothes/items.
Using the dollar amount of clothes/items evaluate the total value of your closet.
Item Cost ($) shoes shirts pants hats belts
45
25
35
15
10
Misc. 5
Extension
In this activity, you have used the math skill of combining like terms(variables). Apply what you have learned to simplify the following expressions.
7.
a + a + a + b + b + c + a + b
8.
2a + b + 3c + 4a + c
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
3

Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
4