A focused Grade 6 learning session for What Is a Ratio? using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving what is a ratio?.
What Is a Ratio? means choosing a model, naming what each number means, and explaining the strategy.
Question: The ratio bar shows red and blue sections. What is the ratio of red to blue?
Why it works: Look at the lengths in the bar: red takes \(2\) equal units and blue takes \(3\) equal units. Red to blue is \(2:3\).
Answer: \(2:3\)
Question: What is the ratio of blue marbles to red marbles in simplest form?
| Type | Count |
|---|---|
| Red marbles | 12 |
| Blue marbles | 8 |
Answer: \(2:3\)
Question: The bar shows two sections. Section A is \(\frac{2}{5}\) of the bar and section B is \(\frac{3}{5}\). What is the ratio of A to B?
Answer: \(2:3\)
Question: A fruit basket contains \(6\) apples and \(4\) oranges. What is the ratio of apples to oranges in simplest form?
Why it works: Great start: keep the order the same, apples first and oranges second. Both \(6\) and \(4\) can be divided by \(2\), so \(6:4\) becomes \(3:2\).
Answer: \(3:2\)
What Is a Ratio? 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 fruit basket contains \(6\) apples and \(4\) oranges. What is the ratio of apples to oranges in simplest form?
Answer D: \(3:2\)
Great start: keep the order the same, apples first and oranges second. Both \(6\) and \(4\) can be divided by \(2\), so \(6:4\) becomes \(3:2\).
A classroom has \(8\) boys and \(10\) girls. Write the ratio of boys to girls in the form "\(a\) to \(b\)".
Answer D: \(8\) to \(10\)
Read the words carefully: "boys to girls" means the boys number comes first. There are \(8\) boys and \(10\) girls, so the ratio is \(8\) to \(10\).
Which ratio is equivalent to \(5:15\)?
Answer D: \(1:3\)
A helpful way to check is to simplify. Divide both parts of \(5:15\) by \(5\): \(\frac{5}{5}:\frac{15}{5}=1:3\).
A recipe calls for \(2\) cups of flour for every \(3\) cups of sugar. Which fraction represents the ratio of flour to the total amount of flour and sugar?
Answer C: \(\frac{2}{5}\)
First find the total amount of flour and sugar: \(2+3=5\) cups. Flour is \(2\) of those \(5\) cups, so the ratio is \(\frac{2}{5}\).
The ratio bar shows red and blue sections. What is the ratio of red to blue?
Answer D: \(2:3\)
Look at the lengths in the bar: red takes \(2\) equal units and blue takes \(3\) equal units. Red to blue is \(2:3\).
A soccer team wins \(12\) games and loses \(4\) games. In simplest form, what is the ratio of wins to total games?
Answer D: \(3:4\)
Do not compare wins to losses here; the question asks for wins to total games. The total is \(12+4=16\), and \(12:16\) simplifies to \(3:4\).
Which of the following ratios is in simplest form?
Answer D: \(5:7\)
A ratio is in simplest form when the two numbers have no common factor greater than \(1\). The numbers \(5\) and \(7\) share no common factor except \(1\), so \(5:7\) is already simplified.
The diagram shows orange and green counters. What is the ratio of orange to green in fraction form?
Answer D: \(\frac{3}{4}\)
Count the counters by color: \(3\) orange and \(4\) green. Since the question asks orange to green, write \(\frac{3}{4}\).
A punch recipe mixes \(1\) part juice with \(4\) parts water. If you use \(8\) cups of juice, how much water should you use?
Answer C: \(32\) cups
Use the ratio as a recipe: for every \(1\) cup of juice, there are \(4\) cups of water. With \(8\) cups of juice, multiply \(8 \times 4=32\) cups of water.
Simplify the ratio \(18:27\).
Answer D: \(2:3\)
The greatest common factor of \(18\) and \(27\) is \(9\). Divide both parts by \(9\) to get \(\frac{18}{9}:\frac{27}{9}=2:3\).
A store sells pens at a ratio of red to blue of \(7:5\). If there are \(35\) red pens, how many blue pens are there?
Answer D: \(25\) pens
Match \(35\) red pens to the \(7\) red parts: \(35\div7=5\), so each part is worth \(5\) pens. Blue has \(5\) parts, so \(5\times5=25\) blue pens.
