Lesson 5

Fractions on Number Lines

Est. Class Sessions: 1–2

Summarizing the Lesson

Display the Representing Fractions in Many Ways Master. Tell students to note that the representations in the last row have been left blank and can be divided into equal shares to show any fraction. Representations for thirds (in the first row) can be divided to show sixths, and representations for fifths (in the second row) can be divided to show tenths. Ask a student to choose a fraction and show it using one of the representations on the page: symbols, circles, rectangles, or number lines. Then ask other students to represent the same fraction using one of the other representations on the display. Continue until the fraction has been represented several ways.

As each student shows his or her representation, ask questions such as:

X
  • What fraction have you represented? (Possible response: 9/4)
  • How does what you have written or drawn show the fraction? (Possible response: I shaded 9 of the fourths in the three rectangles and if I count each part by fourths it is 1/4, 2/4, 3/4, 4/4, 5/4, 6/4, 7/4, 8/4, 9/4.)
  • Use the word “numerator” in your explanation. (Possible response: 9 is the numerator and it tells that I should shade 9 of the fourths that are shown.)
  • Use the word “denominator” in your explanation. (Possible response: The denominator 4 tells me that the unit whole is divided into four equal pieces.)
  • Is there another name for this fraction? How do you know? (21/4; Possible response: The number line is divided into fourths and there are 9/4. 4 of the fourths makes 1 whole, so 8 of the fourths makes 2 wholes. Then there is one more fourth of another whole. 2 wholes and a fourth is 21/4.)

Select other students to present additional fractions and repeat the process. Encourage students to show proper fractions, improper fractions, and mixed numbers using a variety of representations.

Student Guide:
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SG_Mini
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Student Activity Book:
Master: