A focused Grade 6 learning session for Tables of Equivalent Ratios using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving tables of equivalent ratios.
Tables of Equivalent Ratios means choosing a model, naming what each number means, and explaining the strategy.
Question: The table shows the ratio of pancakes to cups of milk needed. Which value completes the table?
| Pancakes | Cups of Milk |
|---|---|
| \(4\) | \(1\) |
| \(8\) | \(2\) |
| \(12\) | \(?\) |
Why it works: Every \(4\) pancakes require \(1\) cup of milk, so \(12\) pancakes require \(12\div4=3\) cups.
Answer: \(3\)
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) |
|---|---|
| \(5\) | \(50\) |
| \(10\) | \(100\) |
| \(15\) | \(?\) |
Answer: \(150\)
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 ($) |
|---|---|
| \(3\) | \(1.50\) |
| \(6\) | \(3.00\) |
| \(9\) | \(?\) |
Answer: \($4.50\)
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 |
|---|---|
| \(4\) | \(5\) |
| \(8\) | \(10\) |
| \(16\) | \(?\) |
Why it works: The ratio is \(4:5\). When roses are \(16\) (multiply by \(4\)), tulips are \(5\times4=20\).
Answer: \(20\)
Tables of Equivalent Ratios 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.
The table shows the ratio of pancakes to cups of milk needed. Which value completes the table?
Answer B: \(3\)
Every \(4\) pancakes require \(1\) cup of milk, so \(12\) pancakes require \(12\div4=3\) cups.
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?
Answer B: \(8\)
The ratio \(2:3\) is constant. When sugar is \(12\), multiply by \(4\): \(2\times4=8\) cups of flour.
A runner completes \(5\) miles in \(50\) minutes. The table below shows equivalent distances and times. Which time is missing?
Answer C: \(150\)
The ratio is \(5:50\) or \(1:10\). For \(15\) miles: \(15\times10=150\) minutes.
The table shows the cost of different numbers of apples at a farmer's market. How much do \(9\) apples cost?
Answer C: \($4.50\)
Each apple costs \($0.50\). So \(9\) apples cost \(9\times0.50=$4.50\).
A factory produces \(24\) widgets in \(4\) hours. The table shows equivalent production rates. What is the missing number of widgets?
Answer D: \(48\)
The ratio is \(24:4\) or \(6:1\). For \(8\) hours: \(6\times8=48\) widgets.
A swimming pool needs chlorine. The ratio of chlorine to water is \(2\) to \(50\). Complete the table:
Answer B: \(150\)
The ratio is \(2:50\) or \(1:25\). For \(6\) oz of chlorine: \(6\times25=150\) gallons.
A coffee shop blends espresso and milk in a ratio of \(3:7\). How much milk is needed with \(6\) shots of espresso?
Answer C: \(14\)
The ratio is \(3:7\). When espresso is \(6\) (multiply by \(2\)), milk is \(7\times2=14\) oz.
A book club reads pages at a constant rate. The table shows how many pages are read in different times:
Answer C: \(135\)
The rate is \(45\div1.5=30\) pages per hour. In \(4.5\) hours: \(30\times4.5=135\) pages.
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?
Answer D: \(20\)
The ratio is \(4:5\). When roses are \(16\) (multiply by \(4\)), tulips are \(5\times4=20\).
A car travels at a constant speed. The table shows equivalent distances and times:
Answer B: \(180\)
The car travels \(60\) miles per hour. In \(3\) hours: \(60\times3=180\) miles.
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:
Answer B: \(6\)
The ratio is \(2:9\). When water is \(27\) (multiply by \(3\)), lemons are \(2\times3=6\).
