**Written by Laura Grimwad, Rockdale County

# Stage 1  Desired Results

Established Goals:

(M5A1)  Students will represent and interpret the relationships between quantities algebraically.

(M5P1) Using the appropriate technology, students will solve problems that arise in mathematics

and in other contexts.

(M5P2)  Students will investigate, develop, and evaluate mathematical arguments.

(M5P3)  Students will use the language of mathematics to express ideas precisely.

(M5P5)  Students will create and use pictures, manipulatives, models, and symbols to organize,

record, and communicate mathematical ideas.

Enduring Understandings:

## Students will understand that

• variables, such as n or x, are used to represent unknown quantities in algebraic expressions
• relationships exist between variables and quantities in algebraic expressions
• word problems can be solved using variables
• variables can be used to investigate, develop, and evaluate mathematical arguments

Essential Questions:

• What is a variable?
• How are variables used in algebraic expressions?

Knowledge:

## §         the mathematical term: Variables

• the relationship between variables in algebraic expressions
• how to create an algebraic expression using variables from a word problem

## Students will be able to(VERBS)

• explain what a variable is and when one should be used
• substitute unknown amounts with variables
• write variable expressions from word problems

Stage 2  Assessment Evidence

1.  Students work with partners to write an expression for the following problem using a variable and explain what the variable stands for:

Will gave some fiction books to a book drive.  Then he gave 5 more nonfiction books.

Call on several students to share and assess student understanding.

2.  Student pairs write their own word problem and trade with another student pair.  The students will write an expression for the traded problem using a variable and explain what the variable stands for.  Students will return their problems to original student pair who will check the work.  Have student pairs share any that may be questionable.  Discuss the questionable problems with class.  If none are questionable, then call on several pairs to share their problem and the responses they received.

3.  Students write an expression giving a value for a variable, along with an expression to solve. (Ex: If n = 3, what is n + 7?) Share with another pair and have the other pair solve.  Give back to original pair to check.  Ask for students to share their expression and the responses they received. Assess understanding through class conversation and questioning.

## Other Evidence:

·   Teacher observation of students working on tasks.

·   Assessment of student work.

·   Student pairs create problems to swap with other pairs to solve.

·   Assess understanding through class conversation and questioning.

·   Orally review vocabulary words.

·    Read Essential Question and call on several students to give their interpretations.  Ask for any misunderstandings.

## Stage 3  Learning Plan

Begin with the following hook:  Use overhead (Attachment 1).  In the top picture you have two cars that together cost \$2.00.  In the bottom picture, you have a car and a dog that together cost \$5.00.  What is the price for a car?  What is the price for the dog?  Explain how you found your answer.    Students work with pairs to investigate, develop, and evaluate mathematical arguments.

Vocabulary:  Variables.  Use the activating strategy as an example. Car + Car = \$2.00;

Car + Dog = \$5.00.  Instead of using numbers, students used representations to find out the value.  Have students give their definition of a variable.  Be sure students understand that a variable is a letter or symbol that can stand for any number.  Example:  8 + B = 12.  Be sure students understand that variables are used when an exact amount is not known.

Allow students to work in pairs.  Read a simple story problem to students.  Have the students write an expression using variables.

Dexter had three baseballs.  After practice, he found several more baseballs.  Write an expression using a variable.  Explain what the variable stands for.

(3 + B); The variable stands for the number of baseballs Dexter found after practice.

On her birthday, Kristin brought 30 cupcakes to school.  She gave a cupcake to each student in her class.  Write an expression using a variable.  Explain what the variable stands for.

(30  C);  The variable stands for the number of cupcakes given out.

Call on several students to share their expression and explain what the variable stands for.  Ask class for thumbs up if they agree.  Check for understanding and clear any misconceptions.

Ask students:  If p = 88, what is p  30?  Have students rewrite the expression substituting the value for the variable in the expression, then solve.

Give Attached Sheet (Attachment 2) to assess student understanding.

***Intermath connection:

Toothpicks are used to build a rectangular grid that is 20 toothpicks long and 10 toothpicks wide. The grid is filled with squares that have 1 toothpick on each side. What is the total number of toothpicks used?
If a represents the number of toothpicks in the length of a grid and b represents the number of toothpicks in the width of a grid (again, the grid is filled with squares that have 1 toothpick on each side), write an expression representing the total number of toothpicks in any rectangular grid of this sort.

Attachment 1:

Attachment 2:

Variables and Expressions                                                                                                                                                      Name:  ______________________________

 Write an expression using a variable.  Explain what the variable stands for. Word Problem Expression The variable stands for Raul collected comic books and kept them in a shoebox.  He had 21 of them.  His mom put more comic books into the box. Raul had          Mom put more    (21)       +            (X)   21 +  X X stands for more comic books. Starr had 25 pencils.  She sold some of them. Starr had           She sold some     (25)                (P)   25  P P stands for the number of pencils Starr sold. Lonnie had 17 baseball cards. He got a few more at the store. A number of cups were on the table.  Kelly put 4 of them away. Substitute the given value for each variable.  Write the value of each expression. Expression Explain The expression value is If n = 12, what is 6 + n? If n = 12, then put 12 where the n is and 6 + 12 equals 18. 18 because 6 + 12 = 18 If s = 14, what is s  8? If m = 25, what is 75  m? If x = 7, what is x + x + 6?