Practice 1
Answer and teaching response
6 · Each cup has three third-cup servings; two cups give six.
Plan how many fixed-size servings a supply can make
Treat the serving size as the repeated unit, count how many fit in the supply and keep that count distinct from the amount per serving.
Get the student and teacher materialsPrepare the group
Learning goal: Produce a serving plan that names total supply, amount per serving and number of servings, with a multiplication check.
You will need: Paper strips and a pencil. Use cups as a stated mathematical unit; the invented quantities do not require handling food or liquid.
Start with this question
A supply contains 3 cups. Each serving must contain exactly 1/4 cup. How many servings can be made?
12 servings. Each cup contains four quarter-cup units, so three cups contain twelve such units.
- Label the supply as 3 cups and the serving size as 1/4 cup per serving. The requested answer counts servings, not cups.
- Partition one cup into four equal quarter-cup parts. Repeat that same-sized partition for all three whole cups.
- Count twelve parts of the required size. The division 3 ÷ 1/4 asks how many quarter-cup servings fit; it does not ask to share three cups among four recipients.
- Check with multiplication: 12 servings × 1/4 cup per serving = 3 cups. That equation confirms both the quantity and the unit interpretation.
Run the 15-minute workshop
- 3 minutes. Compare the questions three cups shared among four groups and three cups served in quarter-cup portions.
- 4 minutes. Partition the supply strips and write the division and multiplication check with units.
- 5 minutes. Make the first three serving plans and explain how changing serving size changes the count.
- 3 minutes. Complete the independent plan and recover the whole supply by multiplication.
A useful error to discuss
A learner might say: Divide 3 by 4 to get 3/4 of a serving.
Four is the number of quarter-cup units in one whole cup, not the recipient count. Draw those units in each cup and count how often the fixed serving size fits.
Practise, then check independently
Try the first three tasks with the worked model. Try the final task without help. Enter a number, fraction or mixed number, such as 3/4 or 1 1/4. The number check does not assess your drawing or explanation.
Practice 2
Answer and teaching response
10 · Five whole cups contain ten half-cup units.
Practice 3
Answer and teaching response
8 · Eight equal eighth-cup portions fill the whole cup.
Independent check
Answer and teaching response
24 · Four groups of six servings give twenty-four; 24 × 1/6 cup = 4 cups.
Transfer the idea
Keep the 3-cup supply but change each serving from 1/4 cup to 1/2 cup. What happens to the serving count, and why?
Discuss a possible response
It changes from 12 to 6. Each new serving combines two of the earlier quarter-cup portions, so twice the serving size produces half as many servings from the same supply.
Choose the next teaching step
Look for:
- Labels the divisor as an amount per serving.
- Reports a count and checks count × serving size = total supply.
If the idea is not secure: Draw one whole cup first and count its unit-fraction portions before repeating the pattern for additional cups.
If the learner is ready: For a fixed supply of 2 cups, compare half-, third- and quarter-cup portions: the counts are 4, 6 and 8. Explain the pattern in units.
Materials for your group
Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.