Expressions and Equations Standard 1a

Use properties of operations to generate equivalent expressions

Standard 1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients

Goal: Students will be able to simplify expressions by combining like terms with rational numbers.

DEVELOP UNDERSTANDING: Organizing Your Closet Activity

(Adapted from: Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics Network. DuPage Regional Office of Education. May 2007)

o Directions:1. 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.

2. 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.

3. Using the defined variables, students will write an expression to represent the number of items in each category.

4. Students will be given a basket full of clean clothes to put into the closet. Using the developed pattern, students need to put clothes away in the proper spot. Students will write a new expression representing the clothes in the closet after adding new items to the closet.

5. Questions to ask: What characteristics are alike/different?

Anticipation for Develop Understanding:

Have extra pictures available for unprepared students. The different categories students may use (ex. colors, seasons, types). Vocabulary – mathematical expression, variable, average Making the transition from the semi-concrete pictures to the symbolic expressions.

SOLIDIFY UNDERSTANDING: Modeling Like Terms Activity

o Directions: Write an algebraic expression that illustrates the model. o Simplify the algebraic expression by combining like terms.

Anticipation for Solidify Understanding:

You may want to separate the tasks to differentiate or have the students complete only certain problems.

Have manipulatives available for students to access. Perimeter may need to be reviewed. Vocabulary: deposit, withdrawal, credit, debit Making sure that all students write the algebraic expressions, and not just do it in their

head. Students may miss some quantities because numbers are written out in word form.

SOLIDIFY UNDERSTANDING: Vocabulary Flip Cards (Teacher Note: Could be used for a Homework Assignment)

o Directions: Identify vocabulary using the vocabulary flip cards template. Have students create flip cards on index cards while introducing vocabulary.

Term – the parts of a variable expression that are separated by addition or subtraction signs.

Coefficient – the numerical factor of a term. Like terms – terms in an expression that have the same variable raised to the same

power (variable factor). Constant term – a term that has no variable factor.

Anticipation for Solidify Understanding:

None

PRACTICE UNDERSTANDING: Combining Like Terms Worksheet

Anticipation for Practice Understanding:

Some students may still need to model problems using manipulatives.

Name ___________________ Date _____ Period ____ Organizing Your Closet

Your mom is very upset with you because your closet is a total disaster. She’s telling you that you will not attend the school dance unless you have your closet organized.

1. Using the pictures of items you have cut out of the magazine, organize them into 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 a mathematical expression to describe your closet.

4. Explain why you cannot combine different categories.

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 mathematical 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.

Extension

In this activity, you have used the math skill of combining like terms (variables). Apply what you have learned to simplify the following mathematical expressions.

7. a + a + a + b + b + c + a + b 8. 2a + b + 3c + 4a + c

Clean Laundry Basket

Item Cost ($)shoes 45shirts 25pants 35hats 15belts 10Misc. 5

Name __________________________ Date ___________________ Period: _______

Modeling Like Terms Activity (EE.1a)

Directions: Look at each picture and do both part A and part B.A. Write an algebraic expression that illustrates the model given belowB. Simplify the expression by combining like terms

1. A. ___________________________

B. ____________________________

2.

A. ______________________

B. ______________________

Name __________________________ Date ___________________ Period: _______

Modeling Like Terms Activity (EE.1)

Directions: Each triangle is made of 3 different colored sticks of different sizes [white (w), black (b) and gray (g)].

A. Write an expression that illustrates the perimeter of each triangle using w, b and g. B. Simplify the expression by combining like terms

3.

A. ___________________________

B. ____________________________ A.

4.

A. ____________________________

B. ____________________________

5. A. ____________________________

B. ____________________________

6. A. ____________________________

B. ____________________________

Name __________________________ Date ___________________ Period: _______

Modeling Like Terms Activity (EE.1)

DirectionA. Convert each transaction into an expressionB. Simplify the expression by combining like terms

7. A deposit of 15 pesos, 12 euros, and 19 dollars is combined with a deposit of 13 euros, ten

pesos, and six dollars.

A. ____________________________

B. ____________________________

8. A deposit of 18 euros, 26 pesos, and 35 dollars is combined with a deposit of nine dollars, five

pesos, and seven euros.

A. ____________________________

B. ____________________________

9. A deposit of 12 euros of credit and debit of 18 dollars, is combined with a withdrawal of nine

euros and seven dollars. (credit means add and debit means subtract)

A. ____________________________

B. ____________________________

10. A deposit of 45 pesos and 28 dollars is combined with a withdrawal of 15 pesos and 12 dollars.

A. ____________________________

B. ____________________________

VOCABULARY FLIP CARDS

Name ______________________________ Date ___________ Period ________

TERM

The parts of an algebraic expression that are separated by addition or subtraction signs

Example: In the algebraic expression

, the terms are

and .

COEFFICIENT

The numerical factor of a term.

Example:In the algebraic expression,

, and are the coefficients.

LIKE TERMS

Terms in an expression that have the same variable raised to the same power (variable factor).

Example:, , are like terms., , are like terms.

CONSTANTTERMS

A term that has no variable factor.

Example:In the algebraic expression,

, is the constantbecause it has no variable factor.

COMBINING LIKE TERMS

DirectionsA. Convert each transaction or triangle into an expressionB. Simplify the expression by combining like terms

1. A. ____________________________B. ____________________________

2. A deposit of eight euros, 20 pesos and 15 dollars is combined with a deposit of nine euros, five pesos, and seven dollars.

A. ____________________________B. ____________________________

3. A deposit of 19 euros and 7 dollars is combined with a withdrawal of 10 pesos and 2 dollars.

A. ____________________________B. ____________________________

Directions: Simplify each expression by combining like terms.

4. 5d + 3d = ________________________

5. 6x + 5y – 2x = ____________________

6. n + 3n – 4m + 6m = ________________

7. 2p + 6 – 7p + 10 = ________________

8. f – 6 – 8f +6 = ____________________

9. 5d + 18d – 4r – 7r = ___________________

10. 4x + 14 + 2y + 2x + 3y – 8 = ___________________

11. 9y – 2x + 15 + 7x – 5y – 11 = ___________________

12. (5r + 6) + (4r + 3) + (3r + 7) = ___________________

13. (5g + 6r) + (4r + 2) + (3g + 5) = ___________________

14. A pot of water has a temperature of 25 °C. How many degrees should you raise the temperature to boil the water at 100 °C?

15. Your goal is to save $50. So far, you’ve saved $34. You’ve spent $13.75 at the movies last weekend. How much money do you need to save to reach your goal?