## Balanced Equations

### Judy FoxCitrus County Schools

#### Description

If your students have a hard time understanding variables, this lesson is for you. It is wonderful for the visual student. In the lesson students will use weights and a balance scale to show how the sides of an equation are equal.

#### Objectives

The student describes, extends, and creates numerical and geometric patterns using a variety of models (for example, lists, tables, charts).

#### Materials

-Worksheet: Basic Balanced Equations (located in the associated file) one per student
-Balance Scales or pan balance- one scale per 4 to 6 students
-Weights for the balance scales 50 for each scale used
-Math Journal

#### Preparations

1. Copy worksheet: Balanced Equations (located in the associated file) one per student.
2. Locate Balance Scales or pan balance-one scale per 4 to 6 students.
3. Get out weights (or counters that are of equal weight)for the balance scales 50 for each scale used.
4. Divide the class into small groups of 4 to 6.

#### Procedures

1. Tell the class that they will be doing simple algebraic problems today. Show the class the balance scale and the weights. Ask how they think that they are connected with Algebra?

2. Tell the students that the balance scale is like an equation. What is on one side of the equation is equal to what is on the other side of the equation, just like the balance scale what ever weight you put on one side needs to be the same amount of weight you put on the other side.

3. Model by having a student drop five weights on one side of the balance scale. Ask what needs to go on the other side to make it balance out? Have the student drop in the weights counting after each one (one – two- three – four – five) Yes, five. Now the balance scale is equal. Now ask the class what the = sign means. Put on the board 5=5.

4. Now model a few easy problems such as 2+4=6.Beging by putting this equation on the board. Ask the class if they agree with what you wrote. Now place two weights on to one side of the balance scale and four more weights to this. Now place six weights to the other side. Ask the class if they are balanced or equal. Yes, they are because 6=6. You may want to demonstrate another problem or two such as 3+5=8 or 4+3=7.

5. Write the equation 6+X=10 on the board. Ask the class what the X is doing in a math problem? Wait on answers then explain that the X is called a variable. A Variable in nothing more than a symbol, usually a letter that represents a number. They way you would say this equation is six plus X is equal to ten, or six plus something is equal to ten. Explain that you can use any letter for the variable.

6. Now model using the balance scale the equation 6+X=10. Place 6 weights on one side of the balance scale, and ten weights on the other side. Now ask the class how many more weights do you need to put in with the six for it to be equal with the ten weights? Yes four weights. Put in one at a time counting out the weights. (one-two-three-four) So ten is equal to ten. Go back to the board and write under the equation 6+X=10, 6+4=10, X=10. You may model using similar problems, changing the variable. Samples may include: 7+Y=13, or 15= 9+A.

7. Now write the equation 6+2=4+Y on the board. Tell the class to remember what is on one side of the equation has to equal what is on the other side of the equation. Model this equation with the use of the balance scale.

8. Put the class into small groups of four to six students. Distribute a balance scale and 25 counters/weights per group and the worksheet Balanced Equations to each student. Model how to do the first problem together. The students need to complete the remainder of the worksheet in their groups. While the students are working the teacher needs to circulate around the class helping where needed.

9. When the students have finished the worksheet have them make an entry in their Math Journal. Tell them to explain how to solve the equation 3+Z=7. They may use diagrams or models to help explain how the solve the equation. These diagrams and models should be labeled. Students should use the include, but limited to the vocabulary words agebra, manipulatives, variable, equation, equal, balance scales, symbols, addition, number sentence, addition, and subtraction.

#### Assessments

The student will solve problems involving equations or simple inequalities using manipulatives, diagrams, or models, symbolic expressions or written phrases.
Use the worksheet in the associated file along with the student’s math journal.

#### Attached Files

Worksheet: Balanced Equations & Rubric for Journal entry.     File Extension: pdf