Can everyone get a cup?
How do we turn a quantity into a decision?
The situation
A class event has 3 liters of juice. A recipe calls for ⅔ liter of juice per batch. Each batch makes 1½ liters of finished drink. Cups hold ¼ liter. There are 24 students.
Assume quantities can be measured exactly and every student wants one full cup. Fractional batches are allowed in the first case.
Estimate an answer and record what you think matters. You do not need a finished method yet.
Your investigation
- Decide whether everyone can get a full cup. Show a diagram and label liters, batches, and cups.
- Find a second method. Explain where multiplication and division each enter your reasoning.
- The organizer now allows only complete batches. Does your recommendation change?
- Reserve ½ liter of finished drink for spills. What is the largest class size you can serve under each batching rule?
Support cards
Open one when your teacher invites you to. Use the idea, then return to your own work.
Find a way in
How many batches can 3 liters of juice make? A batch is not a liter and not a cup. Keep units next to every quantity.
Choose a representation
Draw three 1-liter strips, divide each into thirds, and group two thirds per batch. Then make a new model for the finished drink.
A tool to formalize
Division asks how many groups of a chosen size fit. Multiplication can scale the number of batches by the drink produced per batch. Check each equation using its units.
Challenge a claim
FICTIONAL GENERATED-STYLE RESPONSE · NOT LIVE AI“There are 4½ batches, so there are 4½ cups. That is not enough for 24 students.”
Identify the exact assumption or step you accept or reject. A confident explanation is not a mathematical check.
Defend and revise
Make a claim in one sentence. Support it with a labeled model and a calculation. State an assumption. Have a partner try to find a case that breaks your claim. Revise in a different color.
Close the support cards. Explain the key idea on your own, then solve the changed case your teacher selects. The group’s answer is not evidence that every person understands.
Make the mathematics portable
Create your own drink recipe. Choose juice per batch, finished drink per batch, and cup size so exactly 24 full cups are possible. Describe whether fractional batches are allowed.
With 2 liters of juice and the same recipe, how many full cups can you serve? How does a complete-batches-only rule change the result?