## Summer Daze

• Lesson
6-8
1

Students begin by breaking down a typical summer day into a variety of activities and the amount of time they spend on each.  They then translate their activity times into a simplified fraction, a decimal, and a percent.  Students create a pie chart for this information that is unique to them.  Students who struggle with the calculations will have the opportunity to practice these conversions by playing a game that can easily be differentiated for various levels of learners.

Lead students in a discussion about how they spend a typical summer day. You may want to have students create a list of activities on the board, but mainly you want to get students thinking about their recurring activities, such as sleeping, eating, watching television, texting, etc. Hand out a copy of the How I Spent My Summer Daze activity sheet to each student.

Students record their typical summer activities in the first column on the activity sheet. In the second column, they estimate the number of hours they spend on each activity in a typical day. Have students assign values to the nearest hour to make the calculations easier. Remind students that there are exactly 24 hours in a day, so each person's times should total exactly 24. You may wish to stipulate that they list at least 6 items. As they complete the Hours column, circulate among students to check their work. This is very important to do with students who may be struggling because each column builds on the previous ones—any mistakes will be carried forward into subsequent columns. Stronger students can probably work through the remainder of the activity sheet with little or no help.

Help students recall their facts by asking questions like these:

• How would I write 10 hours a day as a fraction?
[10/24.]
• Which is the part and which is the whole?
[10 is the part of the day we are talking about; 24 is the whole number of hours in a day.]
• Are the numerator and denominator divisible by the same number?
[In this case, they are both divisible by 2. You might prompt students by asking if both numbers are even.]
• If I want to convert a fraction to a decimal, do I divide the numerator by the denominator or the denominator by the numerator?
[Numerator divided by denominator. Students may have learned to divide the larger number by the smaller. For those students this may be a hard concept to grasp.]
• What should I multiply by to convert a decimal to a percent?
[100. Percent relates things to 100 or 100%.]
• How many degrees are in a full circle?
[360°. Most students will probably know this fact.]
• How would I find the number of degrees given the percent?
[Multiply. You are looking for "some percent of 360°," and of means multiply. Take advantage of the opportunity to connect the word of with multiplication.]

During any of these discussions feel free to have a student explain their methods or reasoning to the class using their own words.

To create the pie charts, use circular objects, such as coffee filters. This gets students more excited about the activity just because it’s something different. No matter what you use for the pie charts, emphasize the importance of accuracy. Let students know they will create their chart using pencil first. They will go back over it with black marker when they are sure they have drawn their chart accurately.

Have students fold their circle in half twice to find the middle, and then draw a radius to start. Since some students may not be comfortable with protractors, show at least two measurements on the board or overhead. A common mistake is for students to read the degree measures on the protractor from the wrong direction. Once students have sketched all of the sections on their pie chart in pencil, they can go back over the lines with a black marker and then fill in the wedges with different colors. Have students label each section of their pie chart with the name of the activity it represents and its percent (e.g., Sleep 34%).

Students will likely complete the activity at different times. As students finish, ask them to practice the calculations reviewed in this lesson by playing Concentration. The game can be played individually or in pairs. If students are playing in pairs, match those with similar abilities for the best learning experience. You may also choose to allow a struggling student to practice on his/her own. Use the game to differentiate instruction based on the individual needs of your students.

Students should use the game to practice converting fractions and percents. The game can also be set to practice reducing fractions if you have students who need additional help with that concept. There is also the option to play with all the cards on the board visible, so the student can focus on the match itself without having to also remember where the cards are located. It would be helpful to play the game yourself a few times to familiarize yourself with the various settings.

When all students have finished their pie charts, take a moment to have a whole class discussion about the skills and topics explored during this activity.

Assessment Options

1. Collect the activity sheets. Check the accuracy of students' calculations and pie charts to assess their understanding of the topic.
2. Have students present their pie charts in a quick, informal presentation to the class.
3. Create a class competition using the Concentration applet. This should be used only as an informal assessment.
4. Give students a written assignment in which they consider how the activity and the results might be different if minutes were used instead of hours. Would the table look different? Would the pie chart?

Extensions

1. This activity can be changed from a typical summer day to an actual school day or other specific day. This allows for the activity to be done later in the year. You may also have students keep track of the amount of time they spend on each activity for a day so they could create a more realistic or accurate chart.
2. Combine all data from a class into one large pie chart. Students can then compare how much time they spend on an activity compared to the entire class.

Questions for Students

1. What information does the pie chart give us very quickly?

[There are a variety of answers here, including the number of activities, the activity we spend the most time on, an overview of a typical day, etc. This question can be answered as a class discussion—ask students to observe their finished products and describe what they see.]

2. What other way could we have displayed the same information?

[Students should suggest bar graph, histogram, etc. They should also recognize that something like a scatter plot would not be a good choice because there is only one data set.]

3. What is the advantage of presenting your data in a pie chart?

[Again, there are a number of possible responses to this question, including seeing where the majority of your time is spent and seeing where you are spending too much time. The main advantage of a pie chart is the visual way in which it relates the parts (or activities) to the whole (or day). If students do not mention this advantage, make sure to point it out, since this is one feature that really sets a pie chart apart from the other types of graphs/charts.]

Teacher Reflection

• Did you challenge the high achievers? How?
• Was your lesson developmentally appropriate? If not, what was inappropriate? How would you change it?
• How did your lesson address auditory, tactile and visual learning styles?
• How did students demonstrate understanding of the materials presented?
• Did the lesson integrate and use technology effectively in instruction and assessment?

### Learning Objectives

Students will:

• Practice writing hours per day as a fraction of a day in lowest terms.
• Calculate a decimal from a fraction.
• Calculate a percent from a decimal.
• Calculate the number of degrees of a pie chart that each of their activities should be allotted.
• Create a pie chart using their calculations and a protractor.
• Practice conversions between fractions, decimals and percents in a game setting.

### NCTM Standards and Expectations

• Work flexibly with fractions, decimals, and percents to solve problems.
• Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

### Common Core State Standards – Mathematics

• CCSS.Math.Content.7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers.

• CCSS.Math.Content.7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or$2.50, for a new salary of \$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.