Math Background

Lesson: Percents
Developing the Concept

Now that students know how to find the amount of a tip, tax or discount using the formula P = R x B, it is time for them to solve for B given P and R, or solve for R given P and B.

Preparation Write the equation P = R x B on the board. Review what was done yesterday.

  • Say: Yesterday we used the formula P = R x B to solve for P. Today we are going to use this same formula, but instead solve for R or B, whichever is unknown. Who remembers how to solve a multiplication equation like 3x n = 15? (Write 3 x n = 15 on the board.)
    Students should say they divide both sides by 3, since dividing by 3 is the inverse of multiplying by 3.

    Write the following problem on the board.
    A dress that originally sold for $140 is on sale for $84. What is the percent discount?

  • Say: In the problem on the board, what is unknown? (R) What is the original price B? ($140) What is the discount amount P? ($56)
    Students may not know the discount amount. You may need to discuss with students that the discount amount is equal to the original price minus the sales price, or $140 − $84, which is $56.
  • Say: Now if I substitute these numbers into the equation, what does the equation become? (56 = R x 140) Solve the equation for R at your desks.
    The value students will get for R is 0.4. This will need to be changed to a percent, so remind students that 0.4 = 0.40, or forty hundredths, and 40 hundredths is 40%.

    Write this next problem on the board.
    A friend is treating you lunch, so you offer to leave the tip. Your friend tells you a 15% tip would be $3.60. What was the cost of lunch?

  • Ask: What information do we have?
    Students should say that the rate for the tip is 15% and the amount of the tip is $3.60.
  • Ask: Who can write the equation for the problem we want to solve? (3.6 = 0.15 x B) Try solving this equation at your desk.

    Have a volunteer solve the equation at the board. The cost of the lunch, B, was $24.
    Have students do similar problems at their desks.

Wrap-Up and Assessment Hints
Getting students to recognize which piece of information is missing in a problem requires them to ask themselves what P, R, and B are for each problem. Have them verbalize this information and explain their reasoning.

Point out to students that some problems have more than one step. For example, in problems where they need to find the rate, or percent, of a discount, the original price and sale price may be given. Students will need to calculate the amount of the discount before using the formula. In problems where students are asked to find the sale price of an item, they need to subtract the amount of the discount from the original price after using the formula.

Houghton Mifflin Math Grade 6