Lesson 6 Relate Fractions to Benchmarks

    • Let’s compare the size of fractions to and to 1.

Warm-up Notice and Wonder: A Point on a Number Line

What do you notice? What do you wonder?

Number line. 10 evenly spaced tick marks. First tick mark, 0. Point at seventh tick mark, unlabeled.

Activity 1 Greater Than or Less Than 1?

For each diagram:

  1. Name a fraction the point represents.

  2. Is that fraction greater than or less than 1?

  3. How far is it from 1?

  1. Number line. 21 evenly spaced tick marks. First tick mark, 0. Point at tenth tick mark, unlabeled. Eleventh tick mark, 1

  2. Number line. 0 to 2, by fifths. Point plotted at sixth tick mark from 0.

  3. Number line. 11 tick marks. 0 on first tick mark. 1 half on fifth tick mark. Point on tenth tick mark. 

  4. Number line. 11 evenly spaced tick marks. First tick mark, 0. Second tick mark, 1 fourth. Point at sixth tick mark, unlabeled.

Activity 2 Card Sort: Where Do They Belong?

3 stacks of cards.

Sort the cards from your teacher into three groups: less than , equal to , and greater than .
Be prepared to explain how you know.
Record your sorting results here after you have discussed them with another group.

less than

equal to

greater than

Complete the following sentences after class discussion:

  • A fraction is less than when …

  • A fraction is greater than when …

  • A fraction is between and 1 when …

Activity 3 Greater Than or Less Than ?

For each diagram:

  1. Name a fraction the point represents.

  2. Is that fraction greater than or less than ?

  3. How far is it from ?

  1. Number line. Scale, 0 to 1, by sixths. Point at second tick mark.

  2.  Number line. Evenly spaced by fourths. 11 evenly spaced tick marks. Point at fifth tick mark, no label.

  3. Number line. 11 evenly spaced tick marks. First tick mark, 0. Point at fourth tick mark, unlabeled. Eighth tick mark, 7 eighth.

  4. Number line from 0 to 1. 7 evenly spaced tick marks. First tick mark, 0. Point at third tick mark, unlabeled. Last tick mark, 1.

Practice Problem

Problem 1

For each question, explain your reasoning. Use a number line if you find it helpful.

  1. Is more or less than ?

    Number line. Scale, from 0 to 1.

  2. Is more or less than 1?

    Number line. Scale, from 0 to 1.