Math Background

Lesson: Using Ratios and Percents
Introducing the Concept

Your students have already worked with fractions and decimals, but they might not see the connection between them and ratios and percents in their daily lives. To spark their interest, discuss topics like test scores, sports statistics, or percent of students earning As and Bs.

Materials: none

Preparation: none

Prerequisite Skills and Concepts: Students should know equivalent fractions, simplest form, and multiplying fractions. They should also know how to multiply decimals.

Tell students that they will learn to write a ratio as a percent and a percent as a ratio.

On the chalkboard show students a drawing of a group of five geometric shapes—3 squares and 2 circles.

  • Say: We are going to talk about some ratios and percents concerning these shapes.
  • Ask: Who can tell me what is the ratio of squares to the total number of shapes?
    Students may identify that 3 out of 5 are squares. If they don't, remind them that there are a total of 5 shapes and 3 of them are squares. They may write three-fifths , 3 to 5, or 3:5.
  • Ask: How can we write three-fifths as a percent?
    (Since percent means “per hundred,” we should change three-fifths to an equivalent fraction with a denominator of 100.)
  • Ask: Who can explain how to do this?
    Students may say that both the numerator and the denominator should be multiplied by 20. Make sure they understand that the numerator must be multiplied by the same factor as the denominator. three-fifths = three-fifths x twenty-twentieths = sixty-hundredths
  • Ask: What percent is equivalent to sixty-hundredths ?
    Students may know that a fraction with a denominator of 100 can be written in percent form. sixty-hundredths = 60%. If necessary, review this fact with the class.
  • Say: In the group of geometric shapes, we know that the 3 squares represent 60% of the group.
  • Ask: What percent of the group do the circles represent?
    Students may answer 40%. If they don't, tell them that 100% − 60% = 40%.
  • Ask: How do we write 40% in fraction form?
    Students may answer forty-hundredths .
  • Say: forty-hundredths is an equivalent ratio for 40%.
  • Ask: How do we write forty-hundredths in simplest form?
    Have a volunteer demonstrate on the chalkboard.

    forty-hundredths = forty-hundredths ÷ twenty-twentieths = two-fifths

    Some students may take two steps to simplify to two-fifths .

    forty-hundredths = forty-hundredths ÷ ten-tenths = four-tenths = four-tenths ÷ two-halves = two-fifths

    Place the following equivalency table on the board, partially completed with these numbers: three-fourths , one-fifth , sixteen-twentieths , nine-tenths , 5%, 34%, 12%, 80%.

    Equivalent Ratios and Percents
     Ratio three-fourths one-fifth sixteen-twentieths nine-tenths        
     Percent       5% 34% 12% 80%

    Ask students to complete the table, writing the ratios as percents and the percents as ratios. The ratios should be in simplest form.

    Students should complete the table with these numbers: 75%, 20%, 80%, 90%, one-twentieth , seventeen-fiftieths , three-twenty-fifths , and four-fifths .


Houghton Mifflin Math Grade 5