Fraction Classroom · 2.0.0 · Student pages
Use a benchmark, then justify
Sort fractions around one half and one, then recognize when a shared benchmark does not settle a comparison.
Anonymous group code: __________ Date: __________
Quick diagnosis
Try all three. Explain with words, a sketch, or objects.
d2. Compare 3/8 and 5/6 using one half.
d3. Both 2/3 and 3/4 are above 1/2. Does that fact alone tell which is larger?
Worked examples
Study the example that matches the difficulty. Keep the other for a second session.
w1. Compare 2/5 and 7/12 using one half.
- Two groups of 2 fifths make 4/5, less than a whole, so 2/5 is below half.
- Half of twelve equal parts is six parts; 7/12 exceeds 6/12.
- One fraction is below 1/2 and the other above it.
- Place 2/5 to the left of 7/12.
Worked example: 2/5 < 7/12.
w2. Compare 5/6 and 7/8 by thinking about what is missing from 1.
- Both fractions are one equal part short of a whole.
- Write the missing amounts: 1/6 and 1/8.
- A sixth of the same whole is larger than an eighth.
- Removing the larger gap leaves the smaller fraction.
Worked example: 5/6 < 7/8 because 1/6 is a larger missing amount than 1/8.
Practice
For a short session, choose three tasks. Use the others for a second try or follow-up.
p1. Sort 2/5, 4/8, and 5/6 as below, equal to, or above 1/2.
p2. Compare 3/10 and 3/5 using one half.
p3. Which is closer to 1: 4/5 or 5/6? Explain with missing parts.
p4. A student says 1/3 = 2/5 because both are below 1/2. Explain the mistake and compare them.
p5. Choose a benchmark of 0, 1/2, or 1 that separates 7/8 and 9/8. Write a comparison.
p6. Give one fraction below 1/2 and one above 1/2, both with denominator 5. Explain your choices.
Transfer check
Try one independently. Save the other for a later check.