# Percent instructional ideas, sample activities, and assessment

This page includes information on tasks to facilitate the development of percent: percent related to fractional and decimal equivalents and how they are represented in media and life. This includes ideas for investigation and activities with supporting materials: percent circles, disks, paper folding, area models, measurement models, and number lines to represent values as percent, fractions, and decimals.

*Related resources*

- percent concepts & misconceptions
- developmental ideas
- development of spatial abilities
- operations of fractions, decimals, percents, ...
- Fraction activities to represent fractional values

*Worksheet samples*:

- Percentage strips 10%
- Percentage strips 50%
- Percentage strips 100%
- Percentage circle
- Percentage wheel
- Hundred chart
- Percentage and 1oo
^{ths}(.01) charts - What percent of polka dots are which color?

### Equivalent percent, fractions, & decimals

It is really helpful for learners to be able to recognize equivalent fractions and decimals as hundredths and switch from one to another to understand and operate on percents.

Percentage strips, percentage wheels, and other representations can be used to represent equivalent fractional, decimal, and percentage values. Verify their answers by showing the equal the fractional number of fractional parts of in the circle.

Ask. Can you show equivalent fractions?

Give the learners a fraction strip, or other material to use to demonstrate a percentage and its fractional and decimal equivalents.

If they can't prompt them by showing them that the inside circle is 1/4, then ask them if that helps them know what the middle section and outer section is. Then ask what that has to do with equivalent fractions.

## Sample activities

- Use different representations to compare fractions as equal, greater, or less:
- Discuss: How is it possible to get the same percentage off on purchases and have different discounts? 50% of ten is different than 50% of 100
- Discuss: What should we know when - We get a notice from the utility department that the rates are going to increase 25%. How much additional money do we need to save to pay our bill?
- Two merchants are selling the same item. One for $9.99 and the other for $19.95. One person says that's almost 100% more expensive and another says it is about 50% less. Who is more accurate? Could they both be equal? Would it be different if the prices were $20 & $20?
- Use 100Percentage bars: Make percentage bars for each of the landmark percents. Do five more of your own: 25/50, 48/50, 50/75, 50/80, 50/85, square percentage, 1oo
^{ths}or .01 paper to represent landmark values: 1%, 10%, 25%, & 50%. - Select a landmark percentage. Make a diagram to represent a situation for your percent. For example select a room, gym, auditorium, write a situation that would fit the percentage. There is an auditorium with four chair carts. Each holds 25 chairs and three are filled and one is almost full, but missing one chair. What percentage of chairs is missing and what percentage of chairs are racked? What other problems can you create? What about a theater with 400 seats? Stadium with 40 000? Find five different events that people attend and the number of people that attended each event and write a problem for each to share.
- Use the ideas in the activity above to create other problems: Examples:
- Representations for percentage of different colors of shoes (black, white, other).
- Give a group a page of flowers (5, 10, 20, 25) to color and a limited number of colored (3, 4, 5 (red, orange, violet, blue, yellow)) crayons, markers, or pencils and have them color all the flowers. Then determine the percentage of different colors of flowers.

- Find or take a picture of a parking lot. Determine the percentage of parking spaces that have cars. What percentage would describe the following situations: Empty, full, half full, full, full with cars parking in the lanes …
- A parking attendant wants to program an electronic sign that displays a percentage and full (25% full, 100% full ...). Identify the information needed to write a program. (Number of parking spaces, number occupied, number available, fraction occupied, fraction available, … )
- The owner of a parking garage hears of the idea and says she could use the idea to help drivers get to a parking space faster if it would display the information by floors. If there are five floors, what information needs to be known to write the software program?
- After a few days the owner of the parking garage returns with a new idea and request. She says, your program is working great and is wondering if you would help to calculate additional information for her to make pricing decision. She says she knows there are less parked cars during the night, but doesn’t know what percentage of occupancy the garage has at different hours during a day. She says knowing the percentage of cars at two hour intervals starting at midnight is what she would like to see. She would like you to identify the information needed to chart the actual information. (Number of parking spaces, number occupied, number available, fraction occupied, fraction available, % occupied, % available)

- Find information for attendance to an event at a stadium or arena. Figure how to divide the spectators into two groups. Home and visiting fans, wearing dark colors or light colors, … use your data to make percentage bars and a ratio table to show how the number of fans for each of the two conditions would change if the total attendance varied. Bad/good weather day, time of day matinée/early night, late night, different events, attendance for different Major League Baseball series home team vs. different aways teams …
- Graph the percentage of fans as they arrive to a stadium and leave the stadium. Football stadiums that sell out. Get a time lapse video and determine the attendance at ten minute intervals and graph it.
- Make a survey, then use it to survey fellow classmates or another group and display the data as percentages. Such as: those who like different books, shows, sports, food, … Graph, percentage bars, and ratio tables to show how the data could be used to extrapolate from one class to multiple classes, schools, communities, … and identify why the accuracy might decrease as the numbers grow larger.
- Get
*raw stats*from a sporting event and determine some appropriate percentages with the data. Explain which percentages you believe are important to know or not and why or why not.- Put your calculations on a spread sheet? App? Already have one, check out its accuracy and see if there are values that can be entered that can make it calculate nonsense.

- Make a ratio table to determine tips: 10%, 15%, 20%, 25% for values of $2 to $20…
- Collect personal examples or create problems from Online menus to make problems to determine tips for a party of four. What would they tip individually and all together?

- Like big numbers? Find a budget: school, state, national, … select five categories and figure what percentage of the total budget each category is.
- How does the battery icon on an electronic device represent fractions, percentages, and how can it be used to determine usage time?
- Food labels have much information on them. Select four ingredients and make percentage bars or graphs to show the percentage of the ingredient in a food.
- Find a business or service person that will cooperate with you to collect and share approximate data for you to use to represent in different ways as percentages.
- Grocery store: kinds of goods sold each day; library or media center: kinds of media used each day; automobile dealership: kinds of cars and truck sold in a year; restaurant kinds of meals served each day; other ideas …

# Activity sheets

## Percentage strips:

What percentages can you represent with a strip?

## Percentage strips:

## Percentage strips:

## Percentage circle

Represent percentages with the circle?

## Percentage Wheel

Cut out each disk. Cut along the radius line. Slide each disk inside the other. Rotate the wheels to show different percentages of a circle.

## Percentage chart

What percentages can you represent on the square?

## Percentage and 1oo^{ths} (.01) charts

## Percentage of polka-dots

What percentage of different colors are in this group?

Green

Pink

Yellow

Blue

What is one?