Fraction Classroom · 2.0.0 · Student pages
More equal pieces, smaller pieces
Compare unit fractions and same-numerator fractions with equal wholes to challenge whole-number denominator reasoning.
Anonymous group code: __________ Date: __________
Quick diagnosis
Try all three. Explain with words, a sketch, or objects.
d2. Compare 3/4 and 3/8 of the same whole. What stays the same, and what changes?
d3. Does a larger denominator always mean a smaller fraction? Test the claim with 1/2 and 7/8.
Worked examples
Study the example that matches the difficulty. Keep the other for a second session.
w1. Order 1/2, 1/4, and 1/8 from least to greatest.
- Start with three identical whole strips.
- Partition them into 2, 4, and 8 equal parts.
- Compare one part from each strip.
- The eighth is smallest and the half is largest.
Worked example: 1/8 < 1/4 < 1/2.
w2. Compare 2/3 and 2/6 without finding a common denominator.
- Use two identical whole strips.
- A third is larger than a sixth of the same whole.
- Take two of each type of piece.
- Two larger pieces cover more than two smaller pieces.
Worked example: 2/3 > 2/6.
Practice
For a short session, choose three tasks. Use the others for a second try or follow-up.
p1. Compare 1/4 and 1/6 of the same whole using <, >, or =. Explain with sharing.
p2. Put 1/3, 1/8, and 1/4 in increasing order.
p3. Which covers more of one whole: two sixths or two eighths? Explain.
p4. Choose a denominator from 3, 4, or 8 to make 1/__ smaller than 1/6.
p5. A student says 5/8 < 1/4 because eighths are smaller than fourths. Is the conclusion correct?
p6. Draw 3/4 and 3/6 on equal-sized strips. Circle the greater amount and describe the matching piece counts.
Transfer check
Try one independently. Save the other for a later check.