Introduction
Tables of Equivalent Ratios 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 tables of equivalent ratios.
What Is Tables of Equivalent Ratios?
Tables of Equivalent Ratios 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 Tables of Equivalent Ratios
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: The table shows the ratio of pancakes to cups of milk needed. Which value completes the table?
| Pancakes | Cups of Milk |
|---|---|
| \(4\) | \(1\) |
| \(8\) | \(2\) |
| \(12\) | \(?\) |
- A. \(1\)
- B. \(3\)
- C. \(4\)
- D. \(6\)
Why it works: Every \(4\) pancakes require \(1\) cup of milk, so \(12\) pancakes require \(12\div4=3\) cups.
Answer: \(3\)
Visual Model 2
Question: A recipe uses a ratio of \(2\) cups of flour to \(3\) cups of sugar. The table shows how much flour is needed for different amounts of sugar. What is the missing value?
| Flour (cups) | Sugar (cups) |
|---|---|
| \(2\) | \(3\) |
| \(4\) | \(6\) |
| \(?\) | \(12\) |
- A. \(6\)
- B. \(8\)
- C. \(10\)
- D. \(12\)
Why it works: The ratio \(2:3\) is constant. When sugar is \(12\), multiply by \(4\): \(2\times4=8\) cups of flour.
Answer: \(8\)
Worked Examples
Example 1
Question: A runner completes \(5\) miles in \(50\) minutes. The table below shows equivalent distances and times. Which time is missing?
| Distance (miles) | Time (minutes) |
|---|---|
| \(5\) | \(50\) |
| \(10\) | \(100\) |
| \(15\) | \(?\) |
- A. \(120\)
- B. \(140\)
- C. \(150\)
- D. \(160\)
- The ratio is \(5:50\) or \(1:10\).
- For \(15\) miles: \(15\times10=150\) minutes.
Answer: \(150\)
Example 2
Question: The table shows the cost of different numbers of apples at a farmer's market. How much do \(9\) apples cost?
| Number of Apples | Cost ($) |
|---|---|
| \(3\) | \(1.50\) |
| \(6\) | \(3.00\) |
| \(9\) | \(?\) |
- A. \($3.50\)
- B. \($4.00\)
- C. \($4.50\)
- D. \($5.00\)
- Each apple costs \($0.50\).
- So \(9\) apples cost \(9\times0.50=$4.50\).
Answer: \($4.50\)
Example 3
Question: A factory produces \(24\) widgets in \(4\) hours. The table shows equivalent production rates. What is the missing number of widgets?
| Widgets | Hours |
|---|---|
| \(24\) | \(4\) |
| \(?\) | \(8\) |
| \(72\) | \(12\) |
- A. \(36\)
- B. \(64\)
- C. \(60\)
- D. \(48\)
- The ratio is \(24:4\) or \(6:1\).
- For \(8\) hours: \(6\times8=48\) widgets.
Answer: \(48\)
Real-World Word Problems
Problem 1
Question: A gardener plants flowers in a ratio of roses to tulips of \(4:5\). If the gardener plants \(16\) roses, how many tulips are planted?
| Roses | Tulips |
|---|---|
| \(4\) | \(5\) |
| \(8\) | \(10\) |
| \(16\) | \(?\) |
- A. \(18\)
- B. \(24\)
- C. \(22\)
- D. \(20\)
Why it works: The ratio is \(4:5\). When roses are \(16\) (multiply by \(4\)), tulips are \(5\times4=20\).
Answer: \(20\)
Problem 2
Question: A recipe for lemonade uses lemons and water in the ratio \(2:9\). The table shows ingredients for different batch sizes. Find the missing value:
| Lemons | Water (cups) |
|---|---|
| \(2\) | \(9\) |
| \(4\) | \(18\) |
| \(?\) | \(27\) |
- A. \(5\)
- B. \(6\)
- C. \(8\)
- D. \(10\)
Why it works: The ratio is \(2:9\). When water is \(27\) (multiply by \(3\)), lemons are \(2\times3=6\).
Answer: \(6\)
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
A swimming pool needs chlorine. The ratio of chlorine to water is \(2\) to \(50\). Complete the table:
| Chlorine (oz) | Water (gal) |
|---|---|
| \(2\) | \(50\) |
| \(4\) | \(100\) |
| \(6\) | \(?\) |
- A. \(120\)
- B. \(150\)
- C. \(180\)
- D. \(200\)
Question 2
A coffee shop blends espresso and milk in a ratio of \(3:7\). How much milk is needed with \(6\) shots of espresso?
| Espresso (shots) | Milk (oz) |
|---|---|
| \(3\) | \(7\) |
| \(6\) | \(?\) |
- A. \(10\)
- B. \(12\)
- C. \(14\)
- D. \(16\)
Question 3
A book club reads pages at a constant rate. The table shows how many pages are read in different times:
| Pages Read | Time (hours) |
|---|---|
| \(45\) | \(1.5\) |
| \(90\) | \(3\) |
| \(?\) | \(4.5\) |
- A. \(120\)
- B. \(130\)
- C. \(135\)
- D. \(150\)
Question 4
A car travels at a constant speed. The table shows equivalent distances and times:
| Distance (miles) | Time (hours) |
|---|---|
| \(60\) | \(1\) |
| \(120\) | \(2\) |
| \(?\) | \(3\) |
- A. \(160\)
- B. \(180\)
- C. \(200\)
- D. \(220\)
Question 5
At a party, the ratio of sodas to juices is \(5:3\). If there are \(20\) sodas, how many juices are there?
| Sodas | Juices |
|---|---|
| \(5\) | \(3\) |
| \(10\) | \(6\) |
| \(20\) | \(?\) |
- A. \(10\)
- B. \(16\)
- C. \(14\)
- D. \(12\)
Question 6
A teacher grades papers at a constant rate. The table shows how many papers are graded over time:
| Papers Graded | Time (minutes) |
|---|---|
| \(12\) | \(20\) |
| \(24\) | \(40\) |
| \(30\) | \(?\) |
- A. \(45\)
- B. \(50\)
- C. \(60\)
- D. \(75\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(150\)
The ratio is \(2:50\) or \(1:25\). For \(6\) oz of chlorine: \(6\times25=150\) gallons.
Question 2
Answer: \(14\)
The ratio is \(3:7\). When espresso is \(6\) (multiply by \(2\)), milk is \(7\times2=14\) oz.
Question 3
Answer: \(135\)
The rate is \(45\div1.5=30\) pages per hour. In \(4.5\) hours: \(30\times4.5=135\) pages.
Question 4
Answer: \(180\)
The car travels \(60\) miles per hour. In \(3\) hours: \(60\times3=180\) miles.
Question 5
Answer: \(12\)
The ratio is \(5:3\). When sodas are \(20\) (multiply by \(4\)), juices are \(3\times4=12\).
Question 6
Answer: \(50\)
The rate is \(12:20\) or \(3:5\). For \(30\) papers: \(30\div3=10\), so \(10\times5=50\) minutes.
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
Tables of Equivalent Ratios 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.
