Math Background

Lesson: Percents
Introducing the Concept

Reacquaint students with some physical models for percents, such as a 10 x 10 square grid, a meterstick, and money. Spending some time making sure your students understand the relationships among fractions, decimals, and percents is well worth the effort. Having students remember certain relationships between specific fractions, decimals, and percents is also very helpful (for example, one-fourth = 0.25 = 25%).

Prerequisite Skills: Students should know how to use inverse operations to solve multiplication equations. They should also know that the word percent means “divide by 100” and is a synonym for the word hundredths.

  • Ask: Who can tell me what a tax is?
    Students will probably say it is an extra amount you have to pay in order to use or get something. If not, explain it to them.

    Write the following problem on the board.
    The sales tax for a state is 6% of the cost of an item. If a softball bat costs $32.00, how much would you pay in sales tax?

  • Say: We can solve problems like this by using the formula P = R x B, where P equals the amount of the tax, tip, or discount; B equals the original price; and R equals the rate, or percent, of the tax, tip or discount.
    Discuss the problem, focusing on what we are given (the percent, or tax rate, and the original price), and what we need to find (the amount of tax charged for purchasing the item).
  • Ask: Do we know what P is in this particular problem? (no) What is B? ($32) What is R? (6%) Solve the equation for P at your desks.
    Mention the need to change 6% to 0.06 when solving for P. After students have had a chance to solve the equation, have a student do it on the board for all to see.

    Write the following problem on the board for students to solve at their desks.
    A store is having a 25% sale on all items. If a pair of jeans costs $42, what is the sale price?

  • Say: Before solving this problem, let's estimate what the pair of jeans will cost. Who can give me an estimate and explain how you got that estimate?
    Students may need to be reminded that 25% is equal to one-fourth. They should then be able to follow steps similar to the following: one-fourth of $40 is $10, so one-fourth of $42 is about $10. $42 − $10 = $32, so a good estimate would be around $32.
  • Say: Great. Now let's solve for the exact amount. What is our unknown? (P) What is B? ($42) And what is R? (25%) When you find the amount, what will you have to do to find the sale price? (Subtract the amount from the original price.)

    Have students solve a few more problems in which the amount is unknown and the rate, or percent, and price are known.

Houghton Mifflin Math Grade 6