4.1 Small Group · Group 1
Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems
Understand Percent · Percent · Procedural Fluency · Real-World Applications
- Percent means per hundred. Any part-to-whole comparison becomes a percent by rewriting it as an equivalent ratio whose second term is 100. A decimal grid makes that visible: 100 squares, one for each percent. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
- Students voted on a mascot, and 4 out of every 10 voters chose the tiger. I want to know how many that is out of 100.
- "4 out of every 10" is a ratio, so I write an equivalent ratio with 100 as the second term. Multiplying both terms by 10 gives 40 out of 100.
- On a decimal grid of 100 squares, I shade 40 squares — one square for each percent.
- 40 out of 100 is written 40%. So 40% of the students voted for the tiger.
- Understand Percent (Comprender el porcentaje) — A percent is a ratio that compares a number to 100, so every percent answers the question “how many out of 100?”
- Percent (Porcentaje) — A ratio that compares a number to 100. The word means “per hundred,” and the symbol is %.
- Per hundred (Por cada cien) — The meaning hidden inside the word percent: for every group of 100. It is why every percent can be written as a fraction over 100.
- Decimal grid (Cuadrícula decimal) — A 10-by-10 grid of 100 squares. Shading squares shows a percent directly, one square per percent.
- Part-to-whole (Parte a todo) — A comparison of one part against the whole amount. In a percent, the whole is always 100%.
- Greater than 100% (Mayor que 100 %) — More than one whole. A percent above 100 means the amount is larger than the thing it is being compared to.
- A common mistake with percent is scaling only one term of the ratio: reading 7 out of 10 as 7%. A percent compares to 100, so BOTH terms must be multiplied by the same factor — 10 × 10 = 100, so 7 × 10 = 70, giving 70%. Reading it as 7% describes seats that are nearly empty when they are nearly full. A second mistake is treating a percent as an amount: 150% of a 200-point goal is 1.5 × 200 = 300 points, not 150 points.
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1 MULTIPLE CHOICE
The orange kitten weighs 1.5 times as much as the gray kitten. What percent of the gray kitten's weight is that?
- A150%
- B15%
- C50%
- D1.5%
Work- 1Whole100% is what number?
- 2Find 10%Divide by 10.
- 3BuildAdd or multiply to the percent.
- 4CheckIs it under or over the whole?
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2 MULTIPLE CHOICE
What percent is 9 out of 100?
- A9%
- B90%
- C0.9%
- D19%
✏️ Workspace & Solution Steps -
3 MULTIPLE CHOICE
Which is exactly one whole?
- A100%
- B50%
- C10%
- D1%
✏️ Workspace & Solution Steps -
4 MULTIPLE CHOICE
A recipe makes 200% of what you need. That means it makes…
- ATwice as much as you need
- BHalf of what you need
- CExactly what you need
- DTwo servings total
✏️ Workspace & Solution Steps
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5 ERROR ANALYSIS
Find the error
- 1Setup:7 out of every 10 seats are taken. What percent is that?
- 2Step 1:A percent compares to 100.
- 3Step 2:7 out of 10 = 7%.
- 4Step 3:So 7% of the seats are taken.
Which step contains the error? Explain the mathematical misconception and write the correct calculation below.
✏️ Corrected Mathematical Work & Explanation -
6 OPEN RESPONSE
A car dealership sold 50 cars last month: 20 sedans, 15 SUVs, 10 trucks, and 5 vans. The owner will order 100 cars for next month and wants the order to match last month's sales pattern. Write each type as a percent, then say how many of each to order — and explain why percents make this easier than the raw counts.
✏️ Mathematical Justification & Response
Writing Task: Justify why your mathematical solution is accurate and complete.