Fraction Classroom · 2.0.0 · Student pages
Split every part, keep the amount
Repartition shaded strips to explain why equivalent fractions multiply both counts by the same factor.
Anonymous group code: __________ Date: __________
Quick diagnosis
Try all three. Explain with words, a sketch, or objects.
d2. Which equals 2/5: 3/6 or 4/10? Explain the transformation.
d3. Complete 3/4 = __/12. What happened to each fourth?
Worked examples
Study the example that matches the difficulty. Keep the other for a second session.
w1. Show why 2/3 = 8/12 with one strip.
- Divide one strip into three equal parts and shade two.
- Split every third into four equal pieces.
- Count twelve equal pieces across the whole and eight shaded pieces.
- Write 2/3 = (2 × 4)/(3 × 4) = 8/12.
Worked example: Each third becomes four twelfths; two shaded thirds become eight shaded twelfths.
w2. A student says 6/8 = 3/8 after grouping shaded pieces in pairs. Repair the reasoning.
- Start with eight equal parts, six shaded.
- Group every pair of neighboring eighths into one fourth.
- The whole has four groups and the shaded region has three groups.
- Divide both counts by 2 to write 6/8 = 3/4.
Worked example: 6/8 = 3/4. Group all eight eighths in pairs, not only the shaded six.
Practice
For a short session, choose three tasks. Use the others for a second try or follow-up.
p1. Split each fourth in a 3/4 strip into two equal parts. Write the new fraction.
p2. Complete 1/3 = 4/__. Explain your factor.
p3. Repair the statement 1/3 = 2/4. Give a true equivalent fraction with numerator 2.
p4. Group a strip with 8 of 12 equal parts shaded into groups of four small parts. Name the shaded fraction using the larger parts.
p5. Are 3/6 and 2/4 equivalent? Explain using a common familiar fraction.
p6. Give two fractions equivalent to 2/3 with different denominators. Describe how you made each.
Transfer check
Try one independently. Save the other for a later check.