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Fraction Classroom · 2.4.0 · Student pages

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.

Anonymous group code: __________   Date: __________

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?

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

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

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.

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.