Introduction
What Is a Rate? is an important Grade 6 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with what is a rate?.
What Is What Is a Rate??
What Is a Rate? means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding What Is a Rate?
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Based on the graph, what is the unit rate in miles per hour?
- A. \(\frac{1}{2}\) mile per hour
- B. \(2\) miles per hour
- C. \(1\) mile per hour
- D. \(\frac{2}{3}\) 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
Visual Model 2
Question: Based on the table, what is the rate in miles per gallon?
| Gallons | \(2\) | \(4\) | \(6\) |
|---|---|---|---|
| Miles | \(48\) | \(96\) | \(144\) |
- A. \(20\) miles per gallon
- B. \(96\) miles per gallon
- C. \(48\) miles per gallon
- D. \(24\) miles per gallon
Why it works: Divide miles by gallons: \(48 \div 2 = 24\) miles per gallon.
Answer: \(24\) miles per gallon
Worked Examples
Example 1
Question: Based on the double number line, what is the rate in dollars per hour?
- A. \(\frac{5}{3}\) dollars per hour
- B. \(\frac{3}{5}\) dollars per hour
- C. \(5\) dollars per hour
- D. \(15\) 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.
Answer: \(\frac{5}{3}\) dollars per hour
Example 2
Question: What is the unit rate in dollars per pound?
| Pounds | \(2\) | \(5\) | \(10\) |
|---|---|---|---|
| Cost ($) | \(3\) | \(7.50\) | \(15\) |
- A. \($1.00\) per pound
- B. \($1.25\) per pound
- C. \($1.50\) per pound
- D. \($2.50\) per pound
- Divide cost by pounds: \(3 \div 2 = 1.50\) dollars per pound.
Answer: $1.50 per pound
Example 3
Question: Based on the table, what is the unit rate in gallons per hour?
| Hours | \(1\) | \(2\) | \(3\) | \(4\) |
|---|---|---|---|---|
| Gallons | \(12\) | \(24\) | \(36\) | \(48\) |
- A. \(8\) gallons per hour
- B. \(36\) gallons per hour
- C. \(24\) gallons per hour
- D. \(12\) gallons per hour
- Divide gallons by hours: \(12 \div 1 = 12\) gallons per hour.
Answer: \(12\) gallons per hour
Real-World Word Problems
Problem 1
Question: A car travels \(180\) miles in \(3\) hours. Which of the following is the rate written in simplest form as miles per hour?
- A. \(60\) miles per hour
- B. \(90\) miles per hour
- C. \(180\) miles per hour
- D. \(540\) 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
Problem 2
Question: A recipe calls for \(2\) cups of flour for every \(3\) eggs. Is this a rate or a simple ratio? Explain.
- A. It is a rate because the units are different
- B. It is a simple ratio because we compare number to number
- C. It is a rate because it involves two quantities
- D. It is a simple ratio because the units are both measurements of quantity
Why it works: 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.
Answer: It is a rate because the units are different
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Which of the following is a rate?
- A. \(3\) boys to \(4\) girls
- B. \(60\) miles per hour
- C. \(5\) red marbles to \(2\) blue marbles
- D. \(8\) pencils to \(3\) pens
Question 2
A factory makes \(360\) toys in \(6\) hours. What is the rate in toys per hour?
- A. \(60\) toys per hour
- B. \(54\) toys per hour
- C. \(80\) toys per hour
- D. \(360\) toys per hour
Question 3
A painter paints \(48\) square feet in \(2\) hours. What is the rate in square feet per hour?
- A. \(20\) square feet per hour
- B. \(96\) square feet per hour
- C. \(50\) square feet per hour
- D. \(24\) square feet per hour
Question 4
A store sells \(8\) notebooks for \($6.40\). What is the unit price per notebook?
- A. \($0.50\) per notebook
- B. \($0.70\) per notebook
- C. \($0.80\) per notebook
- D. \($1.00\) per notebook
Question 5
A basketball player scores \(42\) points in \(6\) games. What is the average rate in points per game?
- A. \(6\) points per game
- B. \(36\) points per game
- C. \(7\) points per game
- D. \(48\) points per game
Question 6
A farmer harvests \(288\) pounds of wheat in \(4\) hours. What is the rate in pounds per hour?
- A. \(72\) pounds per hour
- B. \(70\) pounds per hour
- C. \(60\) pounds per hour
- D. \(284\) pounds per hour
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(60\) 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.
Question 2
Answer: \(60\) toys per hour
Divide toys by hours: \(360 \div 6 = 60\) toys per hour.
Question 3
Answer: \(24\) square feet per hour
Divide area by time: \(48 \div 2 = 24\) square feet per hour.
Question 4
Answer: $0.80 per notebook
Divide total cost by number of notebooks: \(6.40 \div 8 = 0.80\) dollars per notebook.
Question 5
Answer: \(7\) points per game
Divide total points by number of games: \(42 \div 6 = 7\) points per game.
Question 6
Answer: \(72\) pounds per hour
Divide weight by time: \(288 \div 4 = 72\) pounds per hour.
Connection to Standards
This lesson supports Grade 6 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
What Is a Rate? becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
