Mission 5 · Unit 3

Ratios and Rates

6.RP.A.1 · Unit 3
Today's objective: Describe relationships between two quantities using ratio language.
Need a hint?
Re-read the problem and underline the numbers and the question. Pick one representation (model, table, or equation), show your steps, and check that your answer makes sense for the situation.

The school is hosting a Smoothie Bar for the end-of-year celebration. The recipe calls for 3 cups of strawberries for every 5 cups of yogurt. The planning committee expects 60 students and each student gets one 8-oz cup. Your team must scale the recipe using ratio tables, tape diagrams, and equivalent ratios to figure out exactly how many cups of each ingredient to buy.

Smoothie Bar Recipe 3 cups strawberries : 5 cups yogurt 🍓 Strawberry 3 cups 🥛 Yogurt 5 cups Tape Diagram Strawberry 1 1 1 Yogurt 1 1 1 1 1 Ratio Table Strawberry Yogurt 3 5 6 10 x2 x2

Team Roles

Facilitator Reads the smoothie recipe problem, ensures everyone uses ratio language ("for every," "per," "to"), and tracks the timer.
Model Builder Draws the tape diagram with equal-size parts, builds the ratio table, and labels each row with the multiplier used.
Precision Checker Checks that the tape diagram parts are equal size, verifies every row of the ratio table by multiplication, and confirms the final totals.
Reporter Prepares the defense: states the ratio in three ways (words, colon, fraction), explains the scaling strategy, and reads the final shopping list.

Investigation

The Problem

The smoothie recipe uses 3 cups of strawberries for every 5 cups of yogurt. Each batch makes 8 cups total (3 + 5 = 8). The school needs enough for 60 students, each getting one 8-oz cup (= 1 cup). That means 60 cups total.

Your tasks:

  1. Write the ratio of strawberries to yogurt in three ways: words, colon, and fraction.
  2. Draw a tape diagram showing the 3:5 relationship.
  3. Build a ratio table from 1 batch (8 cups) up to 60 cups.
  4. Calculate: how many cups of strawberries and how many cups of yogurt for 60 students?
  5. Determine the number of batches needed.
Ratio Table: Scaling Up Batches Strawberry Yogurt Total Cups 1 3 5 8 2 6 10 16 5 15 25 40 ? ? ? 60 How many batches make 60 cups? 60 / 8 = ?

Step-by-Step Investigation Guide

  1. Write the ratio three ways Words: "3 cups of strawberries for every 5 cups of yogurt." Colon: 3 : 5. Fraction: 3/5 (strawberries to yogurt). Also write the part-to-whole ratios: 3/8 and 5/8.

    What is the difference between a part-to-part ratio and a part-to-whole ratio?

  2. Draw a tape diagram Draw one tape with 3 equal parts for strawberries and another tape (same-size parts) with 5 parts for yogurt. Each part represents the same amount. Label the total as 8 parts.

    If the parts are equal size, what does ONE part represent in the actual recipe?

  3. Build a ratio table Start with 1 batch: 3 strawberry, 5 yogurt, 8 total. Multiply both by 2, 3, 4, and so on. Fill in rows until you find the one where total = 60.

    Why must you multiply BOTH columns by the same number? What happens if you only scale one?

  4. Find the number of batches 60 total cups / 8 cups per batch = 7.5 batches. Since you cannot make half a batch, discuss: do you round up to 8 batches (and have leftovers) or find a way to make exactly 7.5 batches?

    Is 7.5 batches a problem? Can you actually measure 1.5 cups of strawberries?

  5. Calculate final amounts For 7.5 batches: strawberries = 3 x 7.5 = 22.5 cups. Yogurt = 5 x 7.5 = 37.5 cups. Check: 22.5 + 37.5 = 60 cups. OR for 8 batches: 24 + 40 = 64 cups (4 extra).

    Which is better for the school: exact amounts with half-cups, or full batches with extra? Why?

  6. Make a recommendation Write a shopping list: how many cups of each ingredient? State your reasoning. Consider: if strawberries come in 4-cup containers and yogurt in 8-cup containers, how many of each do they need to buy?

    How does packaging size affect your recommendation?

Language Support

Key Vocabulary

Ratio: A comparison of two quantities (like 3 to 5)
Equivalent ratio: A ratio with the same relationship but different numbers (6:10 = 3:5)
Rate: A ratio that compares different units (cups per batch)
Tape diagram: A drawing of bars (tapes) showing how quantities compare
Scale up: Multiply both parts of a ratio by the same number to make it bigger
For every: Ratio language meaning "each time you have ___, you also have ___"

Sentence Frames

  • "The ratio of strawberries to yogurt is ___ to ___, which means for every ___ cups of strawberries, there are ___ cups of yogurt."
  • "To scale up, I multiplied both parts by ___, so the equivalent ratio is ___ : ___."
  • "In the tape diagram, each part represents ___ cups because ___."
  • "We recommend buying ___ cups of strawberries and ___ cups of yogurt because ___."

Multiple Representations

Tape Diagram

Equal-size bars showing the 3:5 part-to-part relationship visually.

Ratio Table

Organized columns showing equivalent ratios by multiplying both sides.

Equation

Total = batches x 8. Strawberries = batches x 3. Yogurt = batches x 5.

Work Space

Ratio (3 ways):


Tape Diagram:



Ratio Table:




Calculations:



Shopping List and Recommendation: