Lesson 4.1Percents Greater Than 100%
Start hereWords, worked example, and sentence starters
Learning target I can explain a percent as a rate per 100, model it on a decimal grid or tape diagram, and interpret percents greater than 100%.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| PercentSpanish: Porcentaje | A ratio that compares a number to 100. The word means “per hundred,” and the symbol is %. | 100% = one whole |
| Per hundredSpanish: 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. | 23% = 23/100 |
| Decimal gridSpanish: Cuadrícula decimal | A 10-by-10 grid of 100 squares. Shading squares shows a percent directly, one square per percent. | 40 shaded squares out of 100 = 40% |
| Part-to-wholeSpanish: Parte a todo | A comparison of one part against the whole amount. In a percent, the whole is always 100%. | The whole = 100%; the part = the percent |
| Greater than 100%Spanish: Mayor que 100 % | More than one whole. A percent above 100 means the amount is larger than the thing it is being compared to. | 150% = one and a half wholes |
| Equivalent ratioSpanish: Razón equivalente | A ratio with the same value, made by multiplying or dividing both terms by the same number. | 2 : 5 → 40 : 100 |
How it worksWorked examplewriting 'times as much' as a percent
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A puppy weighs 2.5 times as much as a kitten. What percent of the kitten's weight is the puppy?
- The kitten's weight is the whole, so it stands for one hundred percent.
- Break 2.5 into pieces: 2 wholes plus one half of a whole.
- Each whole is one hundred percent; the half is fifty percent.
- Add the pieces: two hundred percent plus fifty percent.
Answer: The puppy weighs 250% of the kitten's weight.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A sunflower is 1.5 times as tall as a cornstalk. What percent of the cornstalk's height is it?
- The whole here is the , so it stands for %.
- Break 1.5 apart: whole plus of a whole.
- Whole piece: % Half piece: %
- Add the pieces: %
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The whole in this problem is , so it stands for one hundred percent.
- The amount is times as much, so the percent is .
- This percent is greater than one hundred because .
- I drew tape diagrams to show the amount.
Word bank percentper hundredwholeparttape diagramone wholegreater thantimes as muchcompareequivalent ratioshadebaseline
Watch outA common mistake
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.
Lesson 4.1Percents Greater Than 100%
Apply Day · Version ASupported practice
Learning target I can explain a percent as a rate per 100, model it on a decimal grid or tape diagram, and interpret percents greater than 100%.
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1Complete each step, then write the final answer.
5 out of every 10 kids like soccer best. What percent of the kids is that?
Show your workHint Multiply both terms by 10. Read the number out of 100.
Final answer: -
2Complete each step, then write the final answer.
A puppy weighs 3 times as much as a kitten. What percent of the kitten's weight is the puppy's weight?
Show your workHint The kitten is the whole, or 100%. The puppy is 3 wholes.
Final answer: -
3Complete each step, then write the final answer.
9 out of every 10 students brought a lunch. What percent of the students brought a lunch?
Show your workHint Multiply 9 and 10 by 10. Read the number out of 100.
Final answer:
Lesson 4.1Percents Greater Than 100%
Apply Day · Version BCore practice
Learning target I can explain a percent as a rate per 100, model it on a decimal grid or tape diagram, and interpret percents greater than 100%.
-
1Complete each step, then write the final answer.
Ana says 9 out of every 20 is 9%. Is she right? What percent is 9 out of every 20?
Show your workFinal answer: -
2Complete each step, then write the final answer.
Write 3 out of every 50 as a percent.
Show your workFinal answer: -
3Complete each step, then write the final answer.
In a survey, 3 out of every 4 students have a pet. What percent of the students have a pet?
Show your workFinal answer:
Lesson 4.1Percents Greater Than 100%
Apply Day · ChallengeExtension
Learning target I can explain a percent as a rate per 100, model it on a decimal grid or tape diagram, and interpret percents greater than 100%.
-
1Circle the letter of the best answer. Show how you know.
A robotics club had a fundraising goal of $500. By Friday, they collected $750. What percent of their goal did they achieve?
- A50%
- B75%
- C125%
- D150%
Work -
2Complete each step, then write the final answer.
Jen says 21 out of 15 cannot be a percent, because 21 is more than 15. What percent is 21 out of 15?
Show your workFinal answer: -
3Complete each step, then write the final answer.
A club planned to sell 80 tickets. It sold 92 tickets. What percent of the plan did the club sell?
Show your workFinal answer: