A focused Grade 6 learning session for Solving Percent Problems using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving solving percent problems.
Solving Percent Problems means choosing a model, naming what each number means, and explaining the strategy.
Question: In the bar model above, the shaded region represents \(75\) students. How many students are there in total?
Why it works: Shaded portion is \(75\%\) of the total. If \(75\%\) equals \(75\) students, then \(100\%=\frac{75}{0.75}=100\) students.
Answer: \(100\)
Question: The shaded portion represents apples. How many apples are there?
Answer: \(80\)
Question: Which store offers the larger percent discount?
| Store | Original Price | Sale Price |
|---|---|---|
| Store A | $\(50\) | $\(40\) |
| Store B | $\(60\) | $\(42\) |
Answer: Store B (\(30\%\) off)
Question: A sweater originally costs \($40\). It is on sale for \(25\%\) off. What is the sale price?
Why it works: \(25\%\) of \($40\) is \(0.25\times40=$10\). Sale price is \($40-$10=$30\).
Answer: \($30\)
Solving Percent 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 sweater originally costs \($40\). It is on sale for \(25\%\) off. What is the sale price?
Answer C: \($30\)
\(25\%\) of \($40\) is \(0.25\times40=$10\). Sale price is \($40-$10=$30\).
Sarah scored \(45\) correct answers out of \(60\) questions on a math test. What percent of the questions did she answer correctly?
Answer C: \(75\%\)
To find the percent: \(\frac{45}{60}=\frac{3}{4}=0.75=75\%\).
In the bar model above, the shaded region represents \(75\) students. How many students are there in total?
Answer A: \(100\)
Shaded portion is \(75\%\) of the total. If \(75\%\) equals \(75\) students, then \(100\%=\frac{75}{0.75}=100\) students.
A jacket costs \($80\) after a \(20\%\) discount. What was the original price?
Answer D: \($100\)
If the discount is \(20\%\), the customer pays \(80\%\) of the original price. So \(0.80 \times \text{original} = $80\). Original \(= $80 \div 0.80 = $100\).
What is \(15\%\) of \($200\)?
Answer C: \($30\)
\(15\% \times $200 = 0.15 \times 200 = $30\).
A restaurant bill comes to \($45\). The customer wants to leave a \(20\%\) tip. How much is the tip?
Answer B: \($9.00\)
\(20\%\) of \($45 = 0.20 \times 45 = $9.00\).
Out of \(250\) students at a school, \(30\%\) participate in sports. How many students participate in sports?
Answer C: \(75\)
\(30\%\) of \(250 = 0.30 \times 250 = 75\) students.
A game costs \($60\). During a sale, it is discounted by \(35\%\). What is the sale price?
Answer C: \($39\)
\(35\%\) of \($60 = 0.35 \times 60 = $21\). Sale price is \($60 - $21 = $39\).
If a book's price increases from \($20\) to \($24\), what is the percent increase?
Answer A: \(20\%\)
Increase is \($24 - $20 = $4\). Percent increase is \(\frac{4}{20} = 0.20 = 20\%\).
What is the discount amount on the pants?
Answer D: \($12\)
\(15\%\) of \($80 = 0.15 \times 80 = $12\).
Marcus earns a commission of \(5\%\) on his sales. If he sold \($2000\) worth of items, how much commission does he earn?
Answer B: \($100\)
Commission is \(5\%\) of \($2000 = 0.05 \times 2000 = $100\).
