Percent Building Blocks
Benchmark Percent Review:
On this page, you will explore and learn about how to put together the things you have learned about benchmark percents so far to figure out almost any percent question. Before you do, take a few minutes to practice with your benchmark percents. Here is a model you can use and some warm-up questions.
For each of the warm-up questions, do the following:
1) Guess (estimate). About how big will the answer be?
2) Use what you've learned about benchmark percents to find the answer. You may want to draw your own picture!
3) Use the model to check your answer by dragging the black and orange dots.
On this page, you will explore and learn about how to put together the things you have learned about benchmark percents so far to figure out almost any percent question. Before you do, take a few minutes to practice with your benchmark percents. Here is a model you can use and some warm-up questions.
For each of the warm-up questions, do the following:
1) Guess (estimate). About how big will the answer be?
2) Use what you've learned about benchmark percents to find the answer. You may want to draw your own picture!
3) Use the model to check your answer by dragging the black and orange dots.
Warm up questions:
1. What is 10% of 140?
2. If 75% of a number is 60, what is the number?
3. What percent of 80 is 8?
4. What is 50% of 104?
5. If 45% of the people in a group eat breakfast every morning, what percent of the people do not eat breakfast every morning?
6. If you have a 10% off coupon at a store and you buy something that normally costs $32, how much do you save?
7. There were 120 people signed up for a conference, but only 75% of them showed up. How many people did not show up?
Click here for the answers to these warm-up questions.
1. What is 10% of 140?
2. If 75% of a number is 60, what is the number?
3. What percent of 80 is 8?
4. What is 50% of 104?
5. If 45% of the people in a group eat breakfast every morning, what percent of the people do not eat breakfast every morning?
6. If you have a 10% off coupon at a store and you buy something that normally costs $32, how much do you save?
7. There were 120 people signed up for a conference, but only 75% of them showed up. How many people did not show up?
Click here for the answers to these warm-up questions.
Building New Percents
You have seen how helpful it is to think of benchmark percents as fractions. You can find 25% or 1/4 of a number by dividing it by 4. You can find 75% or 3/4 of a number by finding 25% and then multiplying it by 3. You can find 10% of a number by dividing it by 10. Now we're going to look at how you can use the percents you know to build other percents.
The model below shows three ways of writing 10%.
10% of the rectangle is 1/10 or one orange block out of ten blocks all together.
The decimal for one-tenth is 0.1.
You can drag the orange dot to shade in more blocks. What percent do you think you will see when you shade in two blocks? What fraction will you see? What decimal will you see? Make your predictions and then drag the orange dot to check them.
Make predictions about what you will see if you drag the orange dot to shade in three blocks and then check them.
What patterns do you see? Keep dragging the orange dot to see if your patterns continue.
What do you think will happen if you drag the orange dot past the end of the black rectangle? Will your patterns continue? Check it out.
The model below shows three ways of writing 10%.
10% of the rectangle is 1/10 or one orange block out of ten blocks all together.
The decimal for one-tenth is 0.1.
You can drag the orange dot to shade in more blocks. What percent do you think you will see when you shade in two blocks? What fraction will you see? What decimal will you see? Make your predictions and then drag the orange dot to check them.
Make predictions about what you will see if you drag the orange dot to shade in three blocks and then check them.
What patterns do you see? Keep dragging the orange dot to see if your patterns continue.
What do you think will happen if you drag the orange dot past the end of the black rectangle? Will your patterns continue? Check it out.
Finding Other Percents
How can you use what you know about 10% to find other percents of a number? Below is a calculator that will find some different percents. Play with it to see how it works and then try the activities. (Note: changing the whole will erase all the answers in the table.)
Multiples of Ten Percent |
Calculator Activities:
Activity 1 - Looking for patterns: 1. Type a number of your choice and click all the buttons to find the values of 10%, 20%, 30%, etc. of that number. What patterns do you see? 2. Write down your patterns and then choose another number and check whether it also follows the patterns you found. 3. Keep trying numbers until you are sure you have found some patterns that always work. (Hint: If you are stuck getting started, here are some good numbers to try: 50, 100, 120, 150, 200, 4, 40, 400.) Activity 2 - Making predictions: 1. Choose a number and predict what 10% of that number will be. Check your answer using the calculator. 2. Now that you know 10%, predict what 20% will be. Check your answer using the calculator. 3. Now predict 30% before clicking the button. 4. Keep going. Can you predict all the percents correctly? 5. Pick another number and do it again. Continue until you feel confident that you can do predict for any number. 6. For an extra challenge, mix up the order of your predictions. Can you predict 30% before you predict 20%? Can you predict 70% before you predict 10%? (Note: This might be easier with some numbers than with others. What kinds of numbers are easier to work with? What kinds are harder?) |
Activity 3 - The backwards challenge:
Try these challenges. Each challenge names a percent and you have to figure out another percent and the whole. Make an estimate first and then reason about it using what you've learned about these percents. When you think you know the answers, put your prediction in the calculator and click the button representing the percent in the challenge to check. Keep trying until you can predict the answer!
1. 30% of the whole is 18. What is 20%? What is the whole?
2. 80% of the whole is 32. What is 40%? What is the whole?
3. 40% of the whole is 20. What is 60%? What is the whole?
4. 70% of the whole is 21. What is 10%? What is the whole?
5. 60% of the whole is 120. What is 30%? What is the whole?
Try these challenges. Each challenge names a percent and you have to figure out another percent and the whole. Make an estimate first and then reason about it using what you've learned about these percents. When you think you know the answers, put your prediction in the calculator and click the button representing the percent in the challenge to check. Keep trying until you can predict the answer!
1. 30% of the whole is 18. What is 20%? What is the whole?
2. 80% of the whole is 32. What is 40%? What is the whole?
3. 40% of the whole is 20. What is 60%? What is the whole?
4. 70% of the whole is 21. What is 10%? What is the whole?
5. 60% of the whole is 120. What is 30%? What is the whole?
The Percents in Between
Now that you can find any multiple of 10% (like 20%, 30%, etc.), what about the percents in between those? Can you figure out how to find 5% of a number? What about 1%? Here's a model to help you think about what the relationships are between the percents you know and the percents in between.
What percent of the grid is shaded orange before you start playing with it? (If you aren't sure, drag the green dot up to "Show Percent." Drag it back down to "Hide Percent" after you have checked. You can show the percent any time you want, but try to figure it out yourself first!)
What percent of the grid is shaded orange before you start playing with it? (If you aren't sure, drag the green dot up to "Show Percent." Drag it back down to "Hide Percent" after you have checked. You can show the percent any time you want, but try to figure it out yourself first!)
Try dragging the black dot back and forth to change what percent of the grid is shaded.
When you are ready, try to predict what the grid will look like with only 5% shaded orange. Then move the blue dot down to "1 box at a time" and see if you can make the grid 5% orange by dragging the black dot. If you aren't sure whether you've done it, drag the green dot up to show the percent.)
What will it look like to shade 1% of the grid? Try it.
When you are ready, try to predict what the grid will look like with only 5% shaded orange. Then move the blue dot down to "1 box at a time" and see if you can make the grid 5% orange by dragging the black dot. If you aren't sure whether you've done it, drag the green dot up to show the percent.)
What will it look like to shade 1% of the grid? Try it.
Another Calculator
Here is another percent calculator to play with. Just like with the others, make predictions before you click the buttons. Pick a number, then predict what 5% and 1% of the number will be. You can use the the 10% button to help you get started. Play with this calculator until you feel confident finding 5% and 1% of a number.
5% and 1%
Strategies for finding 5% and 1%
What strategies did you use to figure out 5% and 1%? Here are some strategies other people came up with. Not all of them work! For each one, decide whether you think it works and then use the calculator above to check. To check a strategy with the calculator, use the strategy and then see if the calculator gives you the same answer. Make sure you try each strategy with at least two different numbers to convince yourself that it works or it doesn't. (You can use your own calculator as well if you need to.)
1. To find 5% of a number, divide it by 5.
2. To find 5% of a number, divide it by 10 and then divide it by 2.
3. To find 5% of a number, divide it by 2 and then divide it by 10.
4. To find 5% of a number, find 10% of the number and then find half of that.
5. To find 5% of a number, multiply it by 0.5.
6. To find 5% of a number, multiply it by 0.05.
7. To find 1% of a number, divide it by 1.
8. To find 1% of a number, divide it by 100.
9. To find 1% of a number, divide it by 10 and then divide it by 10 again.
10. To find 1% of a number, find 10% and then divide that by 10.
11. To find 1% of a number, multiply it by 0.1.
12. To find 1% of a number, multiply it by 0.01
Click here to check your answers on these strategies and read some explanations.
What strategies did you use to figure out 5% and 1%? Here are some strategies other people came up with. Not all of them work! For each one, decide whether you think it works and then use the calculator above to check. To check a strategy with the calculator, use the strategy and then see if the calculator gives you the same answer. Make sure you try each strategy with at least two different numbers to convince yourself that it works or it doesn't. (You can use your own calculator as well if you need to.)
1. To find 5% of a number, divide it by 5.
2. To find 5% of a number, divide it by 10 and then divide it by 2.
3. To find 5% of a number, divide it by 2 and then divide it by 10.
4. To find 5% of a number, find 10% of the number and then find half of that.
5. To find 5% of a number, multiply it by 0.5.
6. To find 5% of a number, multiply it by 0.05.
7. To find 1% of a number, divide it by 1.
8. To find 1% of a number, divide it by 100.
9. To find 1% of a number, divide it by 10 and then divide it by 10 again.
10. To find 1% of a number, find 10% and then divide that by 10.
11. To find 1% of a number, multiply it by 0.1.
12. To find 1% of a number, multiply it by 0.01
Click here to check your answers on these strategies and read some explanations.
Putting It All Together
Now you have the tools you need to build any percent you want! Benchmark percents can be put together to build more percents. For example, to build 15% of a number, you can add together 10% and 5% of the number. Here's a picture to show that this works:
Try it yourself:
Here are some percent challenges to try and a new calculator to use to check your work. Try using different strategies - sometimes one strategy works better for some numbers and another works better for others. It's always a good idea to start by estimating!
Here are some percent challenges to try and a new calculator to use to check your work. Try using different strategies - sometimes one strategy works better for some numbers and another works better for others. It's always a good idea to start by estimating!
1. Find 15% of 20.
2. Find 35% of 80. 3. Find 6% of 40. 4. Find 12% of 40. 5. Find 19% of 50. |
% |
Here are some more challenges. You can still use the calculator to check your answers by putting in your answers as the whole or the percent. If you don't get it right, try again! Don't forget to estimate first!
6. If 60 is 15%, what is the whole?
7. What percent is 45 of 50? 8. If 30 is 25%, what is the whole? |
9. What percent is 30 of 40?
10. What percent is 30 0f 20? 11. If 35 is 35%, what is the whole? |
Want to do more? Choose your own numbers to challenge yourself, make your predictions, and then check them with the percent calculator!
More Visuals!
Want to play more with what fractions, decimals, and percents look like? Go back to: www.visnos.com/demos/percentage-fraction-decimals-grid and play around. Try out some of the buttons you haven't played with before!
Here's a fun challenge:
1) Click the button with the red number cube to create a random pattern of shaded boxes.
2) Estimate what percent of the boxes are shaded.
3) Click the button that looks like a blue arrow pointing to the left.
4) Decide if you want to revise your estimate.
5) Click the percent button to see how close you were.
Here's a reminder of what some of the buttons do.
Want to play more with what fractions, decimals, and percents look like? Go back to: www.visnos.com/demos/percentage-fraction-decimals-grid and play around. Try out some of the buttons you haven't played with before!
Here's a fun challenge:
1) Click the button with the red number cube to create a random pattern of shaded boxes.
2) Estimate what percent of the boxes are shaded.
3) Click the button that looks like a blue arrow pointing to the left.
4) Decide if you want to revise your estimate.
5) Click the percent button to see how close you were.
Here's a reminder of what some of the buttons do.