Benchmark Percent Review
On this page, you will explore and learn about how to use 10% as a benchmark. Before you do, take a few minutes to practice with the benchmark percents you have already learned about. Here is the model you’ve been working with and some warm-up questions. Try to use the things you have learned about benchmark percents and their relationships to answer the questions before you investigate them on the model. You can also try drawing your own pictures!
Warm up questions:
- What is 25% of 200?
- If 50% of a number is 75, what is the number?
- What percent of 140 is 105%
- What is 75% of 116?
- If 75% of the people in a group wear glasses, what percent of the people do not wear glasses?
- If you get a 25% discount on a gym membership that normally costs $200, how much do you pay for it?
- There were 8 students enrolled in a math class. Then enrollment went up by 75%. How many students are there now?
Click here for answers to these warm up questions.
Introducing 10%
Here is a new model. Play with it a little to see how it works.
As you play with the model, write down what you notice and what you wonder about. Here are some things you might want to think about:
- How does 10% compare with the other benchmark percents that you’ve been working with?
- The shaded part is 10%. What percent is unshaded?
- What fraction do you think is equal to 10%?
Use the model to fill in the blanks in these sentences:
8. 10% of 100 is ____.
9. 15 is 10% of ____.
10. 10% of 50 is ____.
11. 20 is 10% of ____.
Look at the four percents you’ve figured out so far. Can you figure out what fraction 10% is equal to? (Hint: try to figure out what you have to divide a number by to get 10% of it. Or see if you can figure out how many times 10% fits in to the whole.)
If you’re not sure what fraction 10% is, click here to find out. If you feel pretty sure you know, try filling in the missing numbers in the table that follows. Use a calculator if you need to. (The first row is filled in for you.) What patterns do you notice?
| 10% | 100% |
|---|---|
| 10 | 100 |
| 120 | |
| 180 | |
| 6 | |
| 14 | |
| 3500 | |
| 350 | |
| 35 |
Click here for the filled in table if you want to check your answers.
What patterns did you notice in the table?
Investigating Patterns
Below are two special calculators. The first one finds 10% of a number. The second one tells you what the whole number is if you know 10%. Play with both calculators. Put in any number you want and try to predict what the calculator will say before you click the button. Can you figure out any patterns that can help you think about 10%?
What strategies do you have for thinking about 10%? Here are some numbers to try in the calculators to check your strategies. If your strategies work for all of these numbers, they will probably work for any number! Remember to make a prediction before you click the button! If you strategy doesn’t give you the right answer, can you make your strategy better?
Numbers to try:
| 30 | 3 | 0.3 | 0.30 | 0.0300 |
| 1234 | 123.4 | 12.34 | 1.234 | 0.1234 |
(Did something weird happen with zeros? If you’re confused about the zeros, click here.)
Pictures of Percents
Below are some pictures that show percents. For each one, pick the answer choice that best describes the colored part. An alternative version that is more accessible to those with visual impairments is available.
Click here to check your answers.
An accessible version of the answer key is available.
Creative Challenge!
Here is a website where you can make your own pictures of percents: www.visnos.com/demos/percentage-fraction-decimals-grid
This picture that follows shows what some of the buttons do. If you want to find out what the other ones do, try them out! Some challenges to try follow the picture.
Challenges:
Here are some creative challenges. Make your picture first and then click on the fraction, decimal, and percent buttons to see if you were successful. (And then click them again before you start the next challenge.)
- Make a picture on a square grid that is more than 25% orange but less than 50% orange.
- Make a picture on a square grid that is exactly 10% orange, but don’t have any of the orange boxes touch each other!
- Make a picture on a circle with slices that is more than 10% orange but less than 25% orange.
- Make a picture on a circle that is 10% white. (You can also click and drag to color in a bunch of pieces at once.) What percent orange is your picture?