PR1ME I Whole Class (cont.) WEEK 2 I DAY 1
(c) Stage: Abstract Representation
Stage: Abstract Representations Having gone through the previous stages, students will see how the algebraic equation relates to the pictorial representations.
Students use the balance method to solve algebraic equations that involve fractions. After going through these examples and the two methods of solving algebraic equations, students will realize that even though both methods give the same answer, it is more efficient to use the balance method to solve algebraic equations. Compared to the guess and check method, the balance method usually involves fewer steps.
Write ‘Solve 3 x + 4 = 10.’ on the board.
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− Relate 3 x + 4 = 10 to the first scale picture on PR1ME p. 27. − Explain that even though there is a number in front of the letter, the steps used to solve the equation are the same as those used in (a). − Remind students that to solve the equation, we must carry out the same operations on both sides of the equation until only the unknown value x is left on one side of the equation. − Guide students to first subtract 4 from both sides of the equation. − Write ‘3 x + 4 – 4 = 10 – 4’ on the board. − Relate the subtraction of 4 from both sides of the equation back to the second scale picture. − Demonstrate how to simplify the equation before moving on to the next step. − Write ‘3 x = 6’ on the board. − Guide students to see that since there is a ‘3’ in front of the x , we need to divide both sides of the equation by 3 in order to find the value of x . − Write ‘3 x ÷ 3 = 6 ÷ 3’ on the board. − Have students look at the third scale picture to relate the division by 3 on both sides of the equation back to the pictorial representation. − Have students simplify the equation and see that they get x = 2. − Write ‘ x = 2’ on the board. − Have students look at the last scale picture. − Highlight to students that they can check if x = 2 is a solution of the equation by substituting 2 for x in the expression 3 x + 4. − Have a student substitute 2 for x in the expression 3 x + 4 and work out the answer on the board. He/she should get an answer of 10. − Conclude that x = 2 is a solution of the equation 3 x + 4 = 10.
1 2 q – 5 = 10.’ on the board.
Write ‘Solve
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− Guide students in recalling the steps they used in (a) and (b) to solve the equation. − Explain that even though this equation involves fractions, the steps used to solve the equation are the same as those used in (a) and (b). − Remind students that we must carry out the same operations on both sides of the equation until only the unknown value q is left on one side of the equation. − Lead students to first add 5 to both sides of the equation. − Write ‘ 1 2 q – 5 + 5 = 10 + 5’ on the board. − Point out to them to simplify the equation first before moving on to the next step. − Write ‘ 1 2 q = 15’ on the board. − Then, guide students to see that since the fraction involved is 1 2 , we need to multiply both
sides of the equation by 2 in order to find the value of q . Help struggling students to recall that multiplying
1 2 by 2 gives 1. So, multiplying
1 2
q
by 2 will give q .
1 2 q × 2 = 15 × 2’ on the board.
Write ‘
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− Have students simplify the equation and see that they get q = 30. − Write ‘ q = 30’ on the board. − Remind students that they can check if q = 30 is a solution of the equation by substituting 30 for q in the expression q – 5. Get a student to substitute 30 for q in the expression 1 2 q – 5 and work out the answer on the board. He/she should get an answer of 10. − Conclude that q = 30 is a solution of the equation 1 2 − 1 2 q – 5 = 10.
42 Scholar Zone Summer: Math
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