3x 2x + 3 = 7 – 1x + 3 = 7 We call this step like because to set up we already put “combining terms” together terms that are the same (cups are same terms just like 2x and 3x are same terms) Ask the students what to do next as they already have practice solving one-step equations. Repeat the process as many times as needed for your students using the cups and counters for two-step equations that combine like terms. Direct students to complete questions 1- 6 of the Balance Mat Practice “Equation worksheet. Provide assistance where needed 2” Explain to the students that up to this point, they have been solving equations with only addition and subtraction. The equation 2x = 12 involves multiplication. Ask the class what the x’s” in our model, two cups.) Then, set up term “2x” means. (“Two or, the model of the equation by adding 2 cups on the left side of the mat and putting 12 counters on the right side to form a balanced equation. Ask the students to tell you the next step in solving this equation, using the model. (Divide 12 counters on the right side into two equal groups to match the two cups on the left side). Because 2 cups are equal to 12 counters, 1 cup must equal 6 counters. Provide as much additional practice as a group as needed using equations such as 3x = 15, model it with the procedure outlined in the previous step. When the students are ready for individual practice, assign equations 7 -9 on the worksheet. Explain to the students that so far, they have been solving equations with only positive numbers, but now they will see how to solve equations that include negative numbers. Display 3 positive counters (3 ones) to the students and ask them the value of the 3 counters. Then, place 3 negative counters (minus ones) next to the 3 positive counters and ask the students the value of the 6 counters all together. They should respond by they do not, be sure to place each positive saying “zero.” If counter directly next to a negative counter so they can see why the value is zero. Refer to the combination of a positive and a negative together as a Ask “zero pair.” the students to make zero in any form with their counters. Some will simply use 1 positive and 1 negative counter, while others may use 5 (or any equal number) of each. Allow students to share their zero pairs with each other.
3x – 2x + 3 = 7 1x + 3 = 7 We call this step “combining like terms” because to set up we already put together terms that are the same (cups are same terms just like 2x and 3x are same terms) Ask the students what to do next as they already have practice solving one-step equations. Repeat the process as many times as needed for your students using the cups and counters for two-step equations that combine like terms. Direct students to complete questions 1- 6 of the “Equation Balance Mat Practice 2” worksheet. Provide assistance where needed Explain to the students that up to this point, they have been solving equations with only addition and subtraction. The equation 2x = 12 involves multiplication. Ask the class what the term “2x” means. (“Two x’s” or, in our model, two cups.) Then, set up the model of the equation by adding 2 cups on the left side of the mat and putting 12 counters on the right side to form a balanced equation. Ask the students to tell you the next step in solving this equation, using the model. (Divide 12 counters on the right side into two equal groups to match the two cups on the left side). Because 2 cups are equal to 12 counters, 1 cup must equal 6 counters. Provide as much additional practice as a group as needed using equations such as 3x = 15, model it with the procedure outlined in the previous step. When the students are ready for individual practice, assign equations 7 -9 on the worksheet. Explain to the students that so far, they have been solving equations with only positive numbers, but now they will see how to solve equations that include negative numbers. Display 3 positive counters (3 ones) to the students and ask them the value of the 3 counters. Then, place 3 negative counters (minus ones) next to the 3 positive counters and ask the students the value of the 6 counters all together. They should respond by saying “zero.” If they do not, be sure to place each positive counter directly next to a negative counter so they can see why the value is zero. Refer to the combination of a positive and a negative together as a “zero pair.” Ask the students to make zero in any form with their counters. Some will simply use 1 positive and 1 negative counter, while others may use 5 (or any equal number) of each. Allow students to share their zero pairs with each other.
prac-2-eq-bal-mat-6-13.docx