Fraction Classroom · 2.0.0 · Student pages
Estimate before finding equal units
Use a benchmark estimate to catch denominator-addition errors, then combine or subtract equivalent fractions.
Anonymous group code: __________ Date: __________
Quick diagnosis
Try all three. Explain with words, a sketch, or objects.
d2. A student says 1/2 + 1/3 = 2/5. Give a quick reason the result cannot be right.
d3. To subtract 5/6 − 1/4, can the numerators be subtracted directly while keeping one denominator?
Worked examples
Study the example that matches the difficulty. Keep the other for a second session.
w1. Estimate, then calculate 3/4 + 2/3.
- Both fractions exceed half, so the sum is greater than 1. Both are at most 3/4, so the sum is at most 1 1/2.
- Use twelfths: 3/4 = 9/12 and 2/3 = 8/12.
- Add the counts of twelfths: 9/12 + 8/12 = 17/12.
- Group 12 twelfths as one whole and check that 1 5/12 fits the estimate.
Worked example: 17/12 = 1 5/12, between 1 and 1 1/2.
w2. Estimate, then calculate 7/8 − 1/3.
- Compare 7/8 with 5/6: 7/8 is greater, and 5/6 − 1/3 = 1/2, so the answer is above half.
- Rename the fractions as 21/24 and 8/24.
- Subtract equal-sized parts: 21/24 − 8/24 = 13/24.
- Since half is 12/24, the answer is only 1/24 above the benchmark.
Worked example: 13/24, a little more than 1/2.
Practice
For a short session, choose three tasks. Use the others for a second try or follow-up.
p1. Estimate whether 5/6 + 1/4 is below or above 1, then find the exact sum.
p2. Find 2/3 − 1/6. Explain why renaming 2/3 is needed.
p3. A student gives 3/8 for 1/2 + 1/6. Use an estimate to reject it, then repair the calculation.
p4. Calculate 5/6 − 3/4. Is the difference greater or less than 1/4?
p5. Both 12 and 24 are possible common denominators for 1/3 + 1/4. Solve using one and show why the other gives the same amount.
p6. Complete __ + 1/4 = 5/6. Estimate the missing amount relative to 1/2, then calculate.
Transfer check
Try one independently. Save the other for a later check.