A focused Grade 6 learning session for What Is a Rate? using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving what is a rate?.
What Is a Rate? means choosing a model, naming what each number means, and explaining the strategy.
Question: Based on the graph, what is the unit rate in miles per hour?
Why it works: From the graph, at 3 hours the distance is 2 miles. The unit rate is \(2 \div 3 = \frac{2}{3}\) miles per hour.
Answer: \(\frac{2}{3}\) miles per hour
Question: Based on the double number line, what is the rate in dollars per hour?
Answer: \(\frac{5}{3}\) dollars per hour
Question: What is the unit rate in dollars per pound?
| Pounds | \(2\) | \(5\) | \(10\) |
|---|---|---|---|
| Cost ($) | \(3\) | \(7.50\) | \(15\) |
Answer: $1.50 per pound
Question: A car travels \(180\) miles in \(3\) hours. Which of the following is the rate written in simplest form as miles per hour?
Why it works: A rate compares two quantities with different units. Divide the distance by the time: \(180\div3=60\) miles per hour.
Answer: \(60\) miles per hour
What Is a Rate? becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A car travels \(180\) miles in \(3\) hours. Which of the following is the rate written in simplest form as miles per hour?
Answer A: \(60\) miles per hour
A rate compares two quantities with different units. Divide the distance by the time: \(180\div3=60\) miles per hour.
A recipe calls for \(2\) cups of flour for every \(3\) eggs. Is this a rate or a simple ratio? Explain.
Answer A: It is a rate because the units are different
A rate compares two quantities measured in different units. Here, cups of flour are compared to eggs, so the comparison is a rate: \(2\) cups of flour for every \(3\) eggs.
Which of the following is a rate?
Answer B: \(60\) miles per hour
A rate compares quantities with different units. Option B compares distance (miles) to time (hours), which are different units. All other options compare quantities in the same category.
A factory makes \(360\) toys in \(6\) hours. What is the rate in toys per hour?
Answer A: \(60\) toys per hour
Divide toys by hours: \(360 \div 6 = 60\) toys per hour.
Based on the graph, what is the unit rate in miles per hour?
Answer D: \(\frac{2}{3}\) miles per hour
From the graph, at 3 hours the distance is 2 miles. The unit rate is \(2 \div 3 = \frac{2}{3}\) miles per hour.
A painter paints \(48\) square feet in \(2\) hours. What is the rate in square feet per hour?
Answer D: \(24\) square feet per hour
Divide area by time: \(48 \div 2 = 24\) square feet per hour.
Based on the table, what is the rate in miles per gallon?
Answer D: \(24\) miles per gallon
Divide miles by gallons: \(48 \div 2 = 24\) miles per gallon.
Based on the double number line, what is the rate in dollars per hour?
Answer A: \(\frac{5}{3}\) dollars per hour
From the double number line, 3 hours corresponds to 5 dollars. The rate is \(5 \div 3 = \frac{5}{3}\) dollars per hour.
A store sells \(8\) notebooks for \($6.40\). What is the unit price per notebook?
Answer C: \($0.80\) per notebook
Divide total cost by number of notebooks: \(6.40 \div 8 = 0.80\) dollars per notebook.
What is the unit rate in dollars per pound?
Answer C: \($1.50\) per pound
Divide cost by pounds: \(3 \div 2 = 1.50\) dollars per pound.
A basketball player scores \(42\) points in \(6\) games. What is the average rate in points per game?
Answer C: \(7\) points per game
Divide total points by number of games: \(42 \div 6 = 7\) points per game.
