Grade 4: Fraction Equivalence & Comparison

Objective

Students will make sense of the size and location of fractions with denominators 2, 3, 4, 5, 6, 8, 10, and 12 by using number lines and simple diagrams. They will practice comparing fractions using benchmarks (1/2 and 1) and explaining why two fractions are equivalent.

Materials

• This resource (Section A Checkpoint tasks and Practice Problems, printed or read aloud)
• Whiteboard or chart paper and markers
• Straightedges or rulers (for drawing number lines)
• Paper and pencils for each student

Warm-up (~5 min)

Do a quick mental-math "Number Talk" focused on doubling and halving, since this unit builds fluency with the factors 2, 4, 5, 6, 8, 10, and 12.

• Say each of the following one at a time and ask students to solve it mentally, then share their answer and how they got it:
• Double 3
• Double 6
• Half of 12
• Double 5
• Half of 8
• Briefly note that today's lesson uses these same numbers as denominators of fractions.

Main Activity (~25 min)

Work through the following tasks as a whole class or in pairs, drawing each number line on the board as described.

Task 1 – Label the point (10 min)

1. Draw a number line from 0 to 1 partitioned into 8 equal parts. Mark a point on the 7th tick mark from 0.
2. Draw a second number line showing whole-number points 0, 1, 2, with each whole partitioned into 5 equal parts. Mark a point on the 8th tick mark from 0.
3. Ask students, in pairs, to figure out what fraction each point represents and to explain their reasoning on paper.
4. Reveal the answers: the first point is 7/8 (8 equal parts in 1, point on the 7th tick mark). The second point is 8/5 (5 equal parts in each whole, point on the 8th tick mark).
5. Discuss: remind students that tick marks show distance from 0, and that a fraction can be greater than 1.

Task 2 – Compare using benchmarks (8 min)

1. Write on the board: Is 7/12 greater than or less than 2/8?
2. Have students discuss with a partner and use a number line if helpful.
3. Share the reasoning: 7/12 is more than halfway to 1 (half of 12 is 6, so 7/12 > 6/12 = 1/2), while 2/8 is less than 1/2. So 7/12 is greater.

Task 3 – Explain equivalence (7 min)

1. Write on the board: Explain why 1/3 is equivalent to 4/12.
2. Ask students to sketch a number line divided into thirds, then imagine dividing each third into 4 equal pieces.
3. Share the reasoning: each third becomes 4 twelfths, and 1/3 lands on the same point as 4/12 on the number line, so they are equivalent.

Wrap-up / Exit Ticket (~10 min)

Have each student complete this exit ticket independently on paper:

1. Label the point on a number line partitioned into 4 equal parts, with a point on some tick mark (draw one on the board with the point on the 3rd tick mark from 0). Ask: What fraction does the point represent? Explain your reasoning.
2. Answer: 3/4, since there are 4 equal parts and the point is on the 3rd tick mark from 0.
3. Explain or show why 2/4 and 1/2 are equivalent fractions.
4. Sample answer: A diagram split into 4 equal parts with 2 shaded represents 2/4; the same shaded region can be seen as 1 of 2 equal (larger) parts, representing 1/2.

Collect papers to check for understanding of tick-mark reasoning and equivalence.

If Time Remains

Give students this extension task from the resource: Circle the greater fraction in each pair and explain or show your reasoning using a diagram or number line if helpful.

• a. Compare two fractions of the student's choice using denominators from today's lesson (e.g., pick two fractions with denominators 2, 3, 4, 5, 6, 8, 10, or 12).
• b. Have students explain their reasoning by referring to benchmarks (1/2 or 1) or by drawing a quick number line, as practiced in the Main Activity.

Invite a few volunteers to share their comparisons and reasoning with the class.