Grades 3–5
How can a bigger recipe keep the same proportions?
A recipe describes amounts that belong together. A pretend batch might use two cups of oats and one cup of berries. The oats make up two of the three cupfuls in that whole batch.
In the diagramScale every ingredient togetherPretend recipe arithmetic · not cooking directionsONE BATCH2 cups oats1 cup berries2 matching batches4 cups oats + 2 cups berriesSame 2:1 proportion; every amount × 2.
Two matching batches need two copies of every amount: four cups of oats and two cups of berries. Doubling only the oats changes the mixture. Keeping the same proportions means using the same multiplier for every ingredient.
The larger plan also needs enough resources. If oats cost one token per cup and berries cost two, the two-batch plan costs eight tokens. A seven-token budget is one token too small, even though the ingredient proportions are correct.
Proportions describe how the parts fit together; a budget describes what can be paid for. Both matter to the plan. Ingredient arithmetic alone does not tell us how long a real recipe should cook or which equipment it needs.
Sources
- Common Core State Standards Initiative — Grade 3: Number and Operations—Fractions
- NRICH, University of Cambridge — Tray Bake
- Common Core State Standards Initiative — Grade 3 Operations and Algebraic Thinking, 3.OA.A.3
- New York City Council — How the city budget works