Math Background

Fractions, Ratios, Rates, and Percents: Tips and Tricks

  • To help model percents, have students shade in percent and decimal equivalents on grid paper, using a 10 x 10 grid. When they have hands-on experience making models, students better understand the meaning of percent. Some examples of shaded grids are shown below.
    shaded grids
  • Students have previously used a number line to compare fractions. Make use of a large number line, labeled from zero to one, and put it in a prominent place in the room so that students can become familiar with the fractional and decimal locations between 0 and 1.
    number line
  • Have students create their own 0 to 1 number lines for making comparisons of fractions, decimals, and percents. Divide the number line into twenty equal parts between 0 and 1, each mark representing one-twentieth or 5%. Students can locate fractions, decimals, and percents on the number line. This will help them visualize the relationships between the numbers. They can keep the number line in their notebooks for future reference.
  • To provide a model for ratios, have students select a paragraph of reading material. Have them count all the words in the paragraph. Then ask them to count all the one-syllable words. Next have them count all the two-syllable words. Ask questions such as, What is the ratio of two-syllable words to one-syllable words? What is the ratio of one-syllable words to words with more than two syllables?
  • Provide examples of real-world models for percent and ratio. These could include items such as ratios used in advertising, as in “Seven out of ten dentists prefer a certain toothpaste”; statistics that show the percentage of U.S. homes with VCRs, televisions, and video-game systems; or basketball free-throw shooting percentages. For example, Rick Barry retired from the National Basketball Association with a career free-throw shooting percentage of 90%. Over the course of his career, he made 9 free throws for every 10 free throws he took.
  • A good activity for reinforcing the relationships between fractions, percents, and decimals is to have students complete an equivalency chart. This chart could include common fractions and percents. A four-column chart that provides space for a 10-by-10 grid picture will help students visualize the meaning and size of the numbers. Students can keep the chart in their notebooks for future reference.

Houghton Mifflin Math Grade 5