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Fraction Classroom · 2.4.0 · Teacher answers & responses

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.

Both ingredients use the same batch factor. The new quantities differ because their starting amounts differ.IngredientOne batchFactorNew amountOats3/4 cup× 1/23/8 cupSeeds1/2 cup× 1/21/4 cup
Both ingredients use the same batch factor. The new quantities differ because their starting amounts differ.

Build the idea

model. One batch uses 3/4 cup of oats and 1/2 cup of seeds. Write the ingredient card for half a batch.

  1. 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.
  2. Take half of 3/4 cup. Split each quarter into two eighths; half of the six eighths is three eighths.
  3. 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.
  4. 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.

Worked example: Use 3/8 cup of oats and 1/4 cup of seeds. Each starting amount is multiplied by the same factor, 1/2.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. One batch uses 2/3 cup of an ingredient. How many cups are needed for half a batch?

Answer: 1/3

Teacher response: One half of two thirds is one third.

p2. One batch uses 3/4 cup. How many cups are needed for 1 1/2 batches?

Answer: 1 1/8

Teacher response: One batch plus another half batch gives 3/4 + 3/8 = 9/8 cups.

p3. One batch uses 1 1/4 cups. How many cups are needed for twice the batch?

Answer: 2 1/2

Teacher response: Two copies of five quarters make ten quarters.

e1. A batch uses 2/3 cup of oats and 1/3 cup of seeds. For 3/4 of a batch, enter the oats amount in cups and record the seeds amount on paper.

Answer: 1/2

Look for:

  • Applies the same factor to every ingredient.
  • Predicts whether each new amount should be smaller, equal or larger before calculating.

Teacher response: Oats: 2/3 × 3/4 = 1/2 cup. Seeds: 1/3 × 3/4 = 1/4 cup.

Transfer the idea

transfer. If one ingredient is doubled but the other stays unchanged, has the whole recipe been doubled? Explain using the original two-row card.

Answer: 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.

Run the 15-minute workshop

teach-1. 3 minutes: Compare half a batch with subtracting half a cup, and ask which instruction preserves the recipe.

teach-2. 4 minutes: Complete both rows of the worked ingredient card using fraction strips or equal shares.

teach-3. 5 minutes: Calculate the first three ingredient changes and check the expected size before calculating.

teach-4. 3 minutes: Complete the independent batch card, then reverse the scaling to check both ingredients.

Respond to the learner

misconception. For half a batch, subtract 1/2 cup from every ingredient.

Teacher response: 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.

support. Start with one half of each amount and physically pair equal portions before introducing other factors.

extend. Make a three-quarter-batch card for the worked example: oats 9/16 cup and seeds 3/8 cup; verify both products.

Teaching notes