Lesson 13 Whole Numbers and Fractions

    • Let’s find fractions and whole numbers that are equivalent.

Warm-up Notice and Wonder: Four Number Lines

What do you notice? What do you wonder?

4 number lines. Evenly spaced tick marks. 0 to 3 ones by ones, 0 to 6 halves by halves, 0 to 9 thirds by thirds, 0 to 12 fourths by fourths.

Activity 1 Hidden Whole Numbers

Problem 1

On each number line, circle the fractions that are equivalent to whole numbers. Explain how you know.

  1. Number line. Scale 0 to 6 halves by halves, evenly spaced tick marks. First tick mark, 0. Last tick mark, 6 halves.
  2. Number line. Scale 0 to 9 thirds by thirds, evenly spaced tick marks. First tick mark, 0. Last tick mark, 9 thirds.
  3. Number line. Scale 0 to 12 fourths by fourths, evenly spaced tick marks. First tick mark, 0. Last tick mark, 12 fourths.

Problem 2

We can write to show that and are at the same location on the number line, so they are equivalent.

Write 5 other equations that show fractions that are equivalent to whole numbers. Use the number lines if they are helpful.

Number line. Evenly spaced tick marks labeled 0 to 3.  First tick mark, 0. Last tick mark, 3.
Number line. Evenly spaced tick marks labeled 0 to 3.  First tick mark, 0. Last tick mark, 3.

Problem 3

Decide if each fraction is equivalent to a whole number. Use number lines if they are helpful.

Number line. Evenly spaced tick marks labeled 0 to 3.  First tick mark, 0. Last tick mark, 3.
Number line. Evenly spaced tick marks labeled 0 to 3.  First tick mark, 0. Last tick mark, 3.

Activity 2 Write Them as Fractions

Two students looking at an equation on chart paper.

Work with your group to complete the table. In each column, write fractions that are equivalent to the whole number in the top row. 

  • Step 1: Write two fractions that are equivalent to each whole number (six fractions in all). Pass your paper to your right.

  • Step 2: When you receive your neighbor’s paper, write a new fraction that is equivalent to a whole number.

  • Repeat Step 2 until the table is complete.

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Practice Problem

Problem 1

  1. Write 10 as a fraction in 2 different ways.

  2. Is equivalent to a whole number?