Practice 1
Answer and teaching response
1/3 · One half of two thirds is one third.
Resize every ingredient by the same batch factor
Create a new ingredient card for a fractional batch while preserving the relationship between all original amounts.
Get the student and teacher materialsPrepare the group
Learning goal: Produce a consistent scaled ingredient table and show how the batch factor acts on each starting amount.
You will need: Pencil and paper. This is an invented measurement recipe for a paper task; no food preparation is required.
Start with this question
One batch uses 3/4 cup of oats and 1/2 cup of seeds. Write the ingredient card for half a batch.
Use 3/8 cup of oats and 1/4 cup of seeds. Each starting amount is multiplied by the same factor, 1/2.
- Identify what one batch means: the two listed ingredient amounts belong together. Half a batch changes both amounts rather than removing half a cup from each.
- Take half of 3/4 cup. Split each quarter into two eighths; half of the six eighths is three eighths.
- Take half of 1/2 cup to get 1/4 cup. Record the common factor beside both rows so the new card preserves the original recipe relationship.
- Check by doubling both new amounts. Two portions of 3/8 cup recover 3/4 cup, and two portions of 1/4 cup recover 1/2 cup.
Run the 15-minute workshop
- 3 minutes. Compare half a batch with subtracting half a cup, and ask which instruction preserves the recipe.
- 4 minutes. Complete both rows of the worked ingredient card using fraction strips or equal shares.
- 5 minutes. Calculate the first three ingredient changes and check the expected size before calculating.
- 3 minutes. Complete the independent batch card, then reverse the scaling to check both ingredients.
A useful error to discuss
A learner might say: For half a batch, subtract 1/2 cup from every ingredient.
A batch factor describes a proportional change, not a fixed amount removed. Subtracting half a cup would erase the seeds and leave only a quarter cup of oats.
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
1 1/8 · One batch plus another half batch gives 3/4 + 3/8 = 9/8 cups.
Practice 3
Answer and teaching response
2 1/2 · Two copies of five quarters make ten quarters.
Independent check
Answer and teaching response
1/2 · Oats: 2/3 × 3/4 = 1/2 cup. Seeds: 1/3 × 3/4 = 1/4 cup.
Transfer the idea
If one ingredient is doubled but the other stays unchanged, has the whole recipe been doubled? Explain using the original two-row card.
Discuss a possible response
No. A doubled batch needs twice every listed ingredient. Changing only one row alters the ingredient relationship rather than making a larger copy of the same batch.
Choose the next teaching step
Look for:
- Applies the same factor to every ingredient.
- Predicts whether each new amount should be smaller, equal or larger before calculating.
If the idea is not secure: Start with one half of each amount and physically pair equal portions before introducing other factors.
If the learner is ready: Make a three-quarter-batch card for the worked example: oats 9/16 cup and seeds 3/8 cup; verify both products.
Materials for your group
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