Mission 6 · Unit 3

Unit Rates

6.RP.A.2 · Unit 3

Today's objective: Find and compare unit rates to solve real-world problems.

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 6th-grade teachers are ordering T-shirts for the end-of-year trip. They found three online stores with different deals:
Store A: 5 shirts for $60
Store B: 8 shirts for $88
Store C: 12 shirts for $150
They need 30 shirts total. Your team must find the unit rate (price per shirt) for each store, decide which store is the best deal, and calculate the total cost for 30 shirts from each store.

Team Roles

Facilitator Reads the T-shirt problem aloud, assigns one store per calculator (if available), and makes sure all three unit rates are found before comparing.

Model Builder Draws a double number line for at least one store, builds a comparison table showing all three stores, and labels the unit rate for each.

Precision Checker Verifies each division (price / shirts = unit rate), checks that 30-shirt totals are correct, and confirms the cheapest store is labeled right.

Reporter Prepares the defense: states each unit rate, shows the comparison table, explains the recommendation, and discusses one surprise the team found.

Investigation

The Problem

Three stores sell T-shirts at different rates:

Store A: 5 shirts for $60
Store B: 8 shirts for $88
Store C: 12 shirts for $150

The teachers need 30 shirts.

Your tasks:

Find the unit rate (price per 1 shirt) for each store.
Draw a double number line for one store to show how unit rate works.
Build a comparison table with all three stores.
Calculate the cost of 30 shirts from each store.
Recommend the best deal and defend your choice.

Step-by-Step Investigation Guide

Find the unit rate for Store A Divide the total cost by the number of shirts: $60 / 5 shirts = $__ per shirt. This is the unit rate: the cost for exactly 1 shirt.
What does "per" mean in "dollars per shirt"? What are the two units in this rate?
Find the unit rate for Store B $88 / 8 shirts = $__ per shirt. Is this more or less than Store A? By how much?
Why is dividing the key step to find a unit rate?
Find the unit rate for Store C $150 / 12 shirts = $__ per shirt. This one does not come out as a whole number. Round to the nearest cent.
When you get a decimal in the unit rate, how do you decide how many places to round?
Draw a double number line Pick any store. Draw one line for shirts (0, 1, 2, 3...) and one line for dollars ($0, unit rate, 2x unit rate...). Mark equal jumps. Circle the unit rate at 1 shirt.
Why is a double number line helpful for seeing the unit rate?
Calculate 30-shirt cost for each store Multiply: unit rate x 30 shirts. Store A: $12 x 30 = $___. Store B: $11 x 30 = $___. Store C: $12.50 x 30 = $___.
How much money does the school save by choosing the cheapest store vs. the most expensive?
Make a recommendation Which store is the best deal? Is the cheapest store always the best choice? (Consider: does Store C offer free shipping? Better quality?) Write your recommendation with math evidence.
Are there real-life reasons to pick a more expensive option sometimes?

Language Support

Key Vocabulary

Unit rate: A rate where the second quantity is 1 (like $12 per 1 shirt)

Rate: A ratio that compares two different units (dollars and shirts)

Per: For each one ("per shirt" means "for each shirt")

Better buy: The option with the lower unit rate (costs less per item)

Double number line: Two number lines lined up to show how two quantities relate

Compare: Look at two or more things to see which is greater, lesser, or equal

Sentence Frames

"The unit rate for Store ___ is $___ per shirt because $__ divided by __ shirts = $__."
"Store ___ is the better buy because its unit rate of $___ is the lowest."
"For 30 shirts, Store ___ costs $___ because $__ per shirt times 30 = $__."
"The school saves $___ by choosing Store ___ instead of Store ___."

Multiple Representations

Double Number Line

Two aligned lines showing shirts and dollars. Unit rate is at 1 shirt.

Comparison Table

Columns for store, original rate, unit rate, and 30-shirt cost.

Division Equation

Total price / number of shirts = price per shirt. Then unit rate x 30.

Timed Lab Phases

Launch phase

Click a phase, then press Start.

03:00

Read the T-shirt problem aloud. Assign roles. Underline the three prices and the question. Predict: which store LOOKS cheapest before calculating?

Can you tell which store is cheapest without dividing? Why or why not?

Before moving on: every team member knows the three store deals and what a unit rate means.

Calculate all three unit rates. Model Builder draws a double number line for one store. Build a comparison table with columns: Store, Deal, Unit Rate, 30-Shirt Cost.

Which division was hardest? How did you handle the decimal for Store C?

Before moving on: three unit rates found and double number line drawn.

Calculate 30-shirt cost for each store. Find the savings (most expensive - cheapest). Precision Checker verifies all multiplication. Write the recommendation.

How much does the school save with the best deal vs. the worst? Is it worth the effort to compare?

Before moving on: all costs calculated, savings found, and recommendation written.

Reporter prepares: state each unit rate, show the comparison table, point to the double number line, and explain the savings and recommendation.

If Store C offered free shipping (saving $20), would your recommendation change?

Before moving on: Reporter can present in under 60 seconds with the table visible.

Extension Challenge

Store B offers a bulk discount: if you buy 24 or more shirts, the price drops to $10 per shirt. Store A offers buy 5 get 1 free (so 6 shirts for $60). Recalculate: which store is now the best deal for 30 shirts? Show all your work.

"What If?" Variations

you needed 50 shirts instead of 30? Would the same store still be cheapest?
Store C had a 20% off coupon? What would the new unit rate be?
the schools wanted to compare miles per gallon for buses instead of price per shirt? How would the setup change?

Real-Life Connection

Shoppers compare unit rates in the grocery store every day. When one box of cereal is $4.50 for 15 oz and another is $5.40 for 20 oz, unit rate ($0.30/oz vs. $0.27/oz) reveals the true better buy -- even though the first box looks cheaper.

Defense Preparation

Defense Questions

What is the unit rate for each store? Show your division.
Explain your double number line. Where is the unit rate marked?
How much do 30 shirts cost from each store?
How much money does the school save by choosing the best deal?
Could there ever be a reason to choose a more expensive store?

Sentence Starters for Your Defense

"The unit rate for Store ___ is $__ per shirt because..."
"Store ___ is the best deal because its unit rate is the lowest at $__."
"For 30 shirts, the school would pay $___ at Store ___ and save $___ compared to Store ___."
"On the double number line, you can see the unit rate at..."

What Makes a Strong Defense

Unit RatesAll three calculated correctly with division shown

ModelsDouble number line and comparison table are accurate

RecommendationBest deal identified with savings explained

Exit Product

Submit a one-page lab note with:

Unit rate for all three stores with division shown
Double number line for one store
Comparison table (store, deal, unit rate, 30-shirt cost)
Total savings calculation (most expensive - cheapest)
Written recommendation with reasoning
Three-sentence defense: claim, evidence, and real-world reasoning

Work Space

Unit Rate Calculations:

Store A: $60 / 5 =

Store B: $88 / 8 =

Store C: $150 / 12 =

Double Number Line:

30-Shirt Costs:

Recommendation and Defense: