− Lead students to subtract 6 from both sides of the equation. − Write ‘ x + 6 – 6 = 10 – 6’ on the board. − Relate the subtraction of 6 from both sides of the equation to the second scale pictured. − Have students simplify the equation and see that they get x = 4. − Write ‘ x = 4’ on the board. − Relate this back to the picture of the last scale. − Point out to students that they can check if x = 4 is a solution of the equation by substituting 4 for x in the expression x + 6. Have a student do this and work out the answer on the board. He/she should get an answer of 10. − Conclude that x = 4 is a solution of the equation x + 6 = 10.
Learn
Using the balance method to solve algebraic equations
Learning Outcome: •
Use the balance method to solve an algebraic equation
(a) Stage: Pictorial Representation Relate the activity to the pictures of the scale and the cubes. − Have students look at the algebraic equation in (a) and the first scale. − Guide students to see that they need to ‘remove’ the same number of connecting cubes from both sides of the scale until only the unknown number remains on one side. − Lead them to see that there are 10 cubes on the right and 6 cubes on the left, and that there is 1 box on the left pan that contains an unknown number of cubes, x . − Point out that they can relate the equation to a part-whole bar model as shown in the thought bubble. Guide them to see that x and 6 are both parts of the whole, 10. To find the unknown x , we have to subtract the known part, 6, from the whole, 10. − Together look at the second scale, and lead students to see that in order to have just the box on the left pan, 6 cubes must be removed. − Remind them that if 6 cubes are removed from the left pan, 6 cubes will have to be removed from the right pan, to keep the scale balanced. − Have students look at the last scale. − Point out that after 6 cubes are removed from each side of the scale, there is now 1 box on the left pan and 4 cubes on the right pan. − Lead students to see that since the box of x cubes on the left balances the 4 cubes on the right, there must be 4 cubes in the box. Stage: Abstract Representation Students will see how the algebraic equation relates to the pictorial representation. This association is important as it helps students to visualize the balancing of the scale when they are solving the algebraic equation using the balance method. This method serves as the foundation to solving complex algebraic equations in the later stages.
(b) Stage: Pictorial Representation Relate the activity to the pictures.
− Have students look at the algebraic equation in (b) on PR1ME p. 27 and recall the steps they used in (a) to solve the equation. − Lead students to recognize that they need to ‘remove’ the same number of connecting cubes from both sides of the scale until only the unknown number remains on one side. − Have students see that there are 10 cubes on the right pan and 4 cubes on the left pan. Guide them to also see that there are 3 boxes on the left pan, each containing an unknown number of cubes, x . − Point out that they can relate the equation to a part-whole bar model in the thought bubble. − Have students look at the second scale and lead them to understand that in order to have 3 boxes remain on the left pan, 4 cubes will have to be removed from it. Remind them that when 4 cubes are removed from the left pan, 4 cubes will also have to be removed from the right pan, to keep the scale balanced. − Have students look at the third scale and see that after 4 cubes are removed from each side, 3 boxes remain on the left pan and 6 cubes on the right pan. − Guide students to see that to find the number of cubes in 1 box, we need to divide the left side by 3. We must also divide the right side by 3 to keep the pan balanced. − Have students look at the last scale and see that after dividing both sides by 3, there is 1 box on the left pan and 2 cubes on the right pan. − Lead them to see that since the box of x cubes on the left balances the 2 cubes on the right pan, there must be 2 cubes in the box.
Write ‘Solve x + 6 = 10.’ on the board.
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− Relate x + 6 = 10 to the first scale pictured on the page. − Have students see that to solve the equation, we must find the value of the unknown letter x that will make the values on both sides of the equal sign the same. − Guide students to see that this is the same as subtracting numbers from both sides of the equation until only the unknown value x is left on one side.
Grade 7 I Teacher’s Guide 41
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