A focused Grade 6 learning session for Solving Rate and Ratio Word Problems using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving solving rate and ratio word problems.
Solving Rate and Ratio Word Problems means choosing a model, naming what each number means, and explaining the strategy.
Question: A recipe uses \(2\) cups of flour for every \(3\) eggs. How many cups of flour are needed for \(12\) eggs?
Why it works: The ratio is \(2:3\) (flour to eggs). For \(12\) eggs, multiply both parts by \(4\): \(2 \times 4 = 8\) cups of flour.
Answer: \(8\) cups
Question: A rectangular garden is divided into a length-to-width ratio of \(5:3\). If the width is \(12\) feet, what is the length?
Answer: \(20\) feet
Question: A recipe serves \(2\) people and uses \(\frac{1}{2}\) cup of milk. How much milk is needed to serve \(8\) people?
Answer: \(2\) cups
Question: A printer prints \(30\) pages in \(5\) minutes. At this rate, how many pages will it print in \(12\) minutes?
Why it works: The unit rate is \(30\div5=6\) pages per minute. In \(12\) minutes the printer prints \(6\times12=72\) pages.
Answer: \(72\)
Solving Rate and Ratio Word Problems 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 printer prints \(30\) pages in \(5\) minutes. At this rate, how many pages will it print in \(12\) minutes?
Answer D: \(72\)
The unit rate is \(30\div5=6\) pages per minute. In \(12\) minutes the printer prints \(6\times12=72\) pages.
A recipe uses \(2\) cups of flour for every \(3\) eggs. How many cups of flour are needed for \(12\) eggs?
Answer C: \(8\)
The ratio is \(2:3\) (flour to eggs). For \(12\) eggs, multiply both parts by \(4\): \(2 \times 4 = 8\) cups of flour.
A sports team won \(15\) games and lost \(5\) games. What is the ratio of wins to total games played?
Answer B: \(3:4\)
Total games: \(15 + 5 = 20\). Ratio of wins to total is \(15:20\), which simplifies to \(3:4\) by dividing both by \(5\).
Store A sells \(8\) oranges for $2. Store B sells \(12\) oranges for $3. Which store offers the better price per orange?
Answer C: Both are the same
Store A: \(2 \div 8 = 0.25\) per orange. Store B: \(3 \div 12 = 0.25\) per orange. Same unit rate.
If \(\frac{4}{6} = \frac{x}{15}\), what is the value of \(x\)?
Answer D: \(10\)
Cross-multiply: \(4 \times 15 = 6 \times x\), so \(60 = 6x\), thus \(x = 10\).
A model train is built at a scale of \(1:50\). If the model is \(8\) inches long, how many inches long is the real train?
Answer C: \(400\)
At a scale of \(1:50\), the real object is \(50\) times larger. \(8 \times 50 = 400\) inches.
The table below shows a proportional relationship between distance and time. What is the missing value?
Answer C: \(270\)
Rate is \(90 \div 2 = 45\) miles per hour. For \(6\) hours: \(45 \times 6 = 270\) miles.
Maria buys \(\frac{1}{2}\) kilogram of almonds for $6. What is the unit price per kilogram?
Answer C: $12
Unit rate: \(6 \div \frac{1}{2} = 6 \times 2 = 12\) dollars per kilogram.
A car travels \(120\) miles in \(2\) hours. At the same rate, how far will it travel in \(5\) hours?
Answer B: \(300\) miles
Step 1: Rate is \(120 \div 2 = 60\) mph. Step 2: Distance in \(5\) hours is \(60 \times 5 = 300\) miles.
In a classroom, the ratio of boys to girls is \(4:3\). If there are \(8\) boys, how many girls are there?
Answer B: \(6\)
Ratio \(4:3\) with \(8\) boys means multiply by \(2\): \(4 \times 2 = 8\) boys, \(3 \times 2 = 6\) girls.
A rectangular garden is divided into a length-to-width ratio of \(5:3\). If the width is \(12\) feet, what is the length?
Answer A: \(20\) feet
Ratio \(5:3\) with width \(12\) means each part is \(12 \div 3 = 4\) feet. Length is \(5 \times 4 = 20\) feet.
