assess students' prior knowledge, ask students to recall where they
have heard of or used ratios before. Their answers may include the
- Ratios compare the relative sizes of two numbers.
- Ratios compare wins to losses in the World Series; for example, the Braves are ahead in the series three games to one.
- Ratios can describe the number of students to a teacher in a classroom or the number of boys to girls in a classroom.
Record student answers on chart paper for future reference.
Discuss the meaning of ratio in each of the examples from the
class list. Explain that a fraction expresses a ratio when it is
written as a quotient of one number divided by the other number, and
that there are several ways to write ratios. Note the ways in which
students have used fractions to express such relationships.
Organize the class into groups of three or four. Provide a
measuring tape or yardstick and some string (about two yards or so) to
each group. Encourage students to assist one another in measuring their
total body heights with the string, as well as their heights from their
feet to their navels. Have them record their measurements on a chart.
Have students write their two measurements as a ratio. Explain
the history of the Golden Ratio (The Golden Ratio is a ratio of the
length to width and is approximately 1.618. This ratio not only appears
in art and architecture, but also in natural structures including the
human body). Then describe that the Golden Ratio is the ratio of a
person's total height to height from their feet to their navels. The
students may have heard of this as well as other ratios said to exist
in the human body.
See how the students “measure up” to the Golden Ratio.
As an independent assignment, invite the students to measure
other lengths, such as the distance from their waist to the floor and
from the top of their head to their waist, to see whether a similar
ratio exists between those measurements. This activity provides extra
practice in writing ratios and in developing a better understanding of
how ratios are used.
Enter the class data on a chart. Graph the ratios by individual
student and compare the different groups of students, such as girls to
boys or students of one age to students of another.