Solving Equations ALGEBRA 1 SOLVING EQUATIONS
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1 Solving Equations In this activity, students use cups and counters to model one-step equations and solve them using addition. MATERIALS Transparency/Page: Equation Models Transparency/Page: Equation Mat blank transparency transparency pen overhead counters two-dimensional cups (Transparency: Cup) plastic or paper cups (one cup per student pair) two-color counters (approximately 30 per student pair) plastic baggies VOCABULARY zero pair Addition Property of Equality TIME: 40 minutes IN TEACHING TIP: For this activity, students will model one-step equations and solve them by using addition. You may repeat this activity with equations that require the use of subtraction, multiplication, division, or a combination of these operations. TEACHING TIP: This activity uses an equation mat, counters, and cups to model solving equations. You may wish to practice with students in advance to ensure that they are comfortable with each of these tools and understand what they represent. Glencoe/McGraw-Hill 1
2 INTRODUCE Explain to students that today they will use cups and counters to model and solve algebraic equations. Display Transparency: Equation Models and Transparency: Equation Mat. Go over the model concepts with students, making sure that they understand the principles. Transparency: Equation Models Tell students that you will model each side of an equation in the boxes on the mat. Remove the Transparency: Equation Models. Place a cup and 5 positive counters on the left side of the mat transparency. Explain to students that the cup represents an unknown value, x. Transparency: Equation Mat Ask students to name the sum shown. (x + 5) Place 9 positive counters on the right side of the mat. Tell students that the mat is a model of the equation x + 5 = 9. Write the equation below the mat. Remind students that to solve an equation, they must isolate the variable on one side of the equation. Place 5 negative counters on each side of the mat. Point out that both sides of the model are still equal because you added the same number to both sides. Glencoe/McGraw-Hill 2
3 Ask students what property of equality this illustrates. (Addition Property of Equality) Write x ( 5) = 9 + ( 5) below the mat. Ask students if removing zero pairs from either side affects the value of that side. (No, because 0 is the additive identity.) Remove the 5 zero pairs from each side. Ask students to describe the simplified form of the equation. (x = 4) Write the solution at the base of the mat. TEACHING TIP: You may wish to have students write each step of the solution as you model it. Glencoe/McGraw-Hill 3
4 Model the original equation on the mat. Place 4 positive counters on the cup. Point out that both sides are equivalent and that this is a check of the solution 4. Clear the mat and blank transparency. Place 1 cup and 3 positive counters on the left side of the mat and 8 negative counters on the right side of the mat. Ask students what equation is represented. (x + 3 = 8) Write the equation (and the subsequent steps) below the mat. Ask students what you must do to each side to be able to remove all counters from the left side (isolate the cup, or variable, on one side). (Add 3 negative counters, or -3 to each side.) Add the counters and then remove the zero pairs. Ask students to state the solution. ( 11) Model the original equation (x + 3 = 8) on the mat. Place 11 negative counters on the cup and point out that both sides are equivalent. Remind students that this is a way to check the solution. Pose additional equations and solutions and have one or two volunteers model and solve the problems. Glencoe/McGraw-Hill 4
5 DISCUSS AND DO Have students move into pairs. Have a student volunteer distribute one plastic or paper cup and colored counters to each student pair. TEACHING TIP: You may want to prepare the materials for this activity ahead of time. Place one plastic or paper cup and approximately 30 two-color counters in plastic baggies. You will need one set of materials for each pair of students. Have students lay out their Equation Mats and take out recording sheets (notebook paper, blank paper, or math journals). Write several equations on the overhead transparency. Use these or similar equations: x + 4 = 13 Transparency: Equation Mat x 2 = 5 x 4 = 8 x + 9 = 2 Have students models and solve each equation, drawing pictures of their models and solutions on their recording sheets. Tell students to record each step in their solution process. Glencoe/McGraw-Hill 5
6 CONCLUDE Call the class together. Have student pairs come to the front of the room and use cups and counters to model the equations and solutions on an overhead transparency. Glencoe/McGraw-Hill 6
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