Success criteria
- I can identify whether the question asks for sharing or measuring groups.
- I can draw a model for unit-fraction and general fraction division.
- I can rename fractions as common-sized parts and compare their group counts.
- I can interpret the quotient in the original context.
Explain
1/3 ÷ 4 asks us to share one third among four groups, so each share is smaller. 3 ÷ 1/4 asks how many quarter-size pieces fit in three wholes, so the count is larger. Draw both before using a rule.
The measurement question also works when neither fraction is a unit fraction. For 2/3 ÷ 4/9, rename both amounts as the same-sized pieces. The dividend has 6 pieces of size 1/9 and each group uses 4 of those pieces. Therefore the number of groups is 6/4 = 3/2. The reciprocal rule is a shortcut for this common-parts reasoning, not a replacement for understanding the quotient.
Independent practice
For 1/3 ÷ 4, enter the denominator of the simplified answer.
The complete answer is 1/12.
How many 1/4-metre pieces fit into 3 metres?
Which expression describes sharing one half of a cake among three people?
The amount being shared is one half; the number of equal groups is three.
For 2/3 ÷ 4/9, enter the numerator of the simplified quotient.
The quotient is 3/2.
For 2/3 ÷ 4/9, enter the denominator of the simplified quotient.
The quotient is 3/2.
Transfer
Write two mini-stories using the same numbers: one sharing story and one measurement story. Then model 3/5 ÷ 2/5 with common-sized parts and verify that the quotient is 3/2.
Delayed check
After four days, solve one unit-fraction case and one general fraction divided by fraction. Draw common-sized parts first, state what the quotient counts, and use the inverse multiplication to check.
Evidence and next step
Save the paired stories and models at jeremy/portfolio/math/unit-3/unit-fraction-division.md.
- Both structures chosen and explained independently → continue.
- Computation correct but story mismatched → sort six new prompts into sharing versus measuring.
- Model uncertain → use paper strips before symbols.