### Sandi KingBay District Schools

#### Description

Using information about the planets and our solar system, students explore median, mode, mean, and range. Calculators assist students in finding the range and mean.

#### Objectives

The student identifies the mean, median and mode from a set of data.

The student identifies the range on a line graph.

The student uses a calculator to determine the range and mean of a set of data.

#### Materials

- Calculators (one per student or pair of students)

- Transparencies, one made from each of the five teacher modeling documents (download and print from the attached file)

- Planet Characteristics data wall chart or student charts (See instructions in the lesson plan Nine Around the Sun.)

- Student Web lesson, Jupiter Is Average

#### Preparations

1. Locate calculators (one per student or pair of students).

2. Locate and practice using an overhead calculator. This is very important for all learners, but especially essential for visual learners. Talk to your media specialist about locating or purchasing an overhead calculator.

4. Make transparencies, one made from each of the five teacher modeling documents from the attached file Student work sheets, 5 in all (downloaded and printed from the attached file), one per student.

5. Download and print Summative Assessment #2 from the unit assessment package, “Outer Space and Cyber Space,- one per student. (See Extensions.)

6. The Planet Characteristics data wall chart or student data charts should be available. (See instructions in the Lesson Plan “Nine Around the Sun.”)

8. Locate and preview the Student Web Lesson, Jupiter Is Average.

9. Attempt to locate a lab or multiple computers that can be used each day for the Web lesson, or see your media person for a projection device to do lessons whole group. (Student Web Lessons are most effective when done in pairs.)

10. Any visuals that can be located to demonstrate averages will assist visual learners. Suggestions are your gradebook (mean) and pictures of a road median (median).

#### Procedures

NOTE - This is the mathematics lesson plan for the unit, Outer Space and Cyber Space. This lesson is the math content that compliments the science and language arts content lessons from the unit. Data from the science lesson, Nine Around the Sun, will be used with the math concepts presented in this lesson.

Day 1

1. If you are doing this lesson as part of the unit, Outer Space and Cyber Space, give the diagnostic assessment before beginning any instruction. The diagnostic is not to be graded, but rather should be used as a tool for planning and meeting the students' needs.

Day 2

1. Introduce median, mode, mean, and range by asking inquiry questions, such as: “When you have completed several math papers and I have all the grades in my gradebook, how do I know what grade to put on your report card? What do I mean when I say the word average? Why is the grassy place in the middle of a busy road called the median? Is average good or bad? What is a batting average? When baseball players figure their batting average, what do they do? If I drive an average of 30 miles each week, can you tell how far I drive in one day? If I’m buying a new dress and the price is within my range, what does range mean?”

2. Introduce the vocabulary words median, mode, mean, range, and average. Display the vocabulary cards from the associated files. Describe average, and then continue with the other four words. Be sure students know that these are words that describe a way to determine the average. As you discuss each of the vocabulary words, ask students for a reason or time that they might use that kind of method for finding the average. Suggestions might include the following:

Median – If I were catching a baseball, I’d like to know the median (middle) of the area where it might be hit. Then I would know where to stand in order to have the best chance of catching the ball.

Mode – If we are running laps on the track, we may want to know how fast the average runners are going. Instead of looking at the group of a couple of runners in the lead or at the end, the average runner would be in the largest group in the middle. This large middle group would be the mode.

Mean – If we did well on some math tests and poorly on others, we would want the good tests to be counted as much as the bad ones. The mean will give us the fairest score counting all the good and not so good.

Range – If we were fishing, we would want to know how far we could cast our line and bait. The range will let us know the furthest point we can reach with our cast.

3. Display the vocabulary cards on the word wall where they are available for students to reference as needed.

Day 3

1. Teach median. Direct students' attention to the vocabulary card introduced on Day 2. Remind the students that the median is the middle.

* To figure the median, list all the numbers in order, progressing from lowest to highest. Since we are looking for the middle number, cross a number off the top, then off the bottom, then off the top, and then off the bottom of our list of numbers until the only number left is the one in the middle.

* Use the transparency, Median Modeling, to demonstrate this procedure. Teachers should model writing all the numbers in ascending order, then crossing off the top and bottom number until only the middle (median) is left.

* At this point, students complete part A of the worksheet, Median in the Middle. Notice that all the number lists in part A have an odd number of numerals so there is always a middle (median) without any more procedures.

* As students are working, circulate and formatively assess students. Give corrective feedback: “Remember to cross off the top, then bottom, then top, then bottom until you get to the middle.” Also give affirmative feedback: “Great! You knew to write the numbers in order first.”

2. Use the Median Modeling transparency, part B to present the problem of what to do with even numbers that do not have a middle listed.

* Ask for students' ideas as to how to find the median. Try student suggestions and lead a discussion as to why or why not the procedure worked.

* If a student describes finding the middle of the two numbers that are in the middle, extend the idea by showing how to add the two numbers and then divide by 2. If no student suggests this method, the teacher will eventually have to offer this method as a solution.

* Using the Median Modeling transparency, part B, demonstrate how to complete this procedure. Remember to demonstrate how to list the numbers in ascending order, cross off the top and bottom, then add the two middle numbers and divide by 2.

* Students are now ready to complete part B of the worksheet. Remember to conduct an oral formative assessment and give corrective and affirmative feedback as students are working to complete the worksheet.

3. Collect the completed median worksheets and counsel any students who need further help. Give individuals written formative feedback on each worksheet. Affirmative and corrective feedback should be written.

4. Complete the median section of the Student Web Lesson, Jupiter Is Average. A link to this Student Web Lesson is available in the Weblinks section of this lesson plan.

* This can be done whole group using a computer connected to a TV or projector, but for best results, students working in pairs gain the most value from the Web lesson. Pairs of students assist each other in successfully completing only the portion of the lesson assigned. Students with special needs (poor reading skills, poor computer skills, etc.) can be paired with students who can assist.

Day 4

1. Review median by asking the class the median of these numbers: 7, 14, 7, 16, 8. After students give their responses, select a student to demonstrate how they got their answer. They can write on the board or on a transparency. As the student is demonstrating, ask other students to verbalize why the student is doing what he is doing. Give corrective and affirmative feedback.

2. Teach mode. Follow the same procedure as was used with median.

* Direct students' attention to the vocabulary card introduced on Day 2. Remind the students that the mode is the number that appears most often.

* To figure the mode, list all the numbers in order progressing from lowest to highest. Since we are looking for the number that is listed the most, grouping the numbers in this order will assist in counting all the numerals.

* Use the transparency, Mode Modeling to demonstrate this procedure. Teachers should model writing all the numbers in ascending order, then locating the number that appears most often.

* A number must appear more than once to be the mode. There can be more than one mode.

* One of the problems with using the mode for the average is the fact that there can be many modes for a list of numbers. At this point, students complete the worksheet, More Mode. As students are working, circulate and formatively assess their understanding of mode. Give corrective feedback: “Remember to list the numbers in order first.” Also, give affirmative feedback: “Great! You found the number that appears most often.” Give feedback as your oral formative assessment.

3. Collect the completed mode worksheets and counsel any students who need further help. Give written formative feedback. This formative assessment is given on an individual basis. Affirmative and corrective feedback is given.

4. Complete the mode section of the Student Web Lesson, Jupiter Is Average. This can be done whole group using a computer connected to a TV or projector, but for best results, students working in pairs gain the most value from the web lesson. Pairs of students assist each other in successfully completing only the portion of the lesson assigned. Students with special needs (poor reading skills, poor computer skills, etc.) can be paired with students who can assist. See the link in Weblinks.

Day 5

1. Review median and mode by asking the class to find the median and mode of these numbers: 7, 14, 7, 16, 8.

* After students give their responses, select students to demonstrate how they got their answer. They can write on the board or on a transparency.

* As the students are demonstrating, ask other students to verbalize why the student is doing what he is. This formative assessment should have both corrective and affirmative feedback.

* The median and the mode will not be the same number. This is a good time to discuss the pros and cons of using each way of finding the average.

2. Teach mean. Follow the same procedure as was used with median and mode.

* Direct students' attention to the vocabulary card introduced on Day 2. Remind the students that the mean is the sum of the numbers divided by the number of numbers.

* To figure the mean, first add all the numbers in the list. Then count how many numbers are listed. Finally, divide the sum by the number of numbers.

* Use the transparency, Mean Modeling, to demonstrate this procedure. Teachers should model adding all the numbers, counting the numbers, and dividing the sum by the number of numbers.

* At this point, students complete the worksheet, Mean Isn’t Bad. As students are working, circulate and formatively assess students' understanding of mean. Give corrective feedback: “Remember to add the numbers first.” Give affirmative feedback: “Great! You divided the sum by the number of numbers.” Give feedback as your formative assessment.

3. Collect the completed mean worksheets and counsel any students who need further help, giving written feedback to individuals. This formative assessment must be done indivually and must include both affirmative and corrective feedback.

4. Complete the mean section of the Student Web Lesson, Jupiter Is Average.

Day 6

1. At this point in the science portion of the unit, Outer Space and Cyber Space, you have constructed a wall chart of the characteristics of the planets. Students have individual data charts that correspond with the data on the wall chart. When reviewing median, mode, and mean, use the data from these charts. This will integrate the study of the planets with the need to be able to figure the median, mode, and mean in the real world.

* Examples might include the following:
- Which planet is the median if we are looking at the distance from the sun?
- Looking at the gravitational pull of each planet, what is the mode?
- Looking at the number of moons for each planet, what is the mean?

2. Teach range. Follow the same procedure as was used with median, mode, and mean. Direct students' attention to the vocabulary card introduced on Day 2.

* Remind the students that the range is the difference between the largest number and the smallest number.

* The range can be figured in two ways. If the numbers are small, the range can be figured using a line graph. Find the largest and smallest numbers that have points on the graph. Subtract the smallest number from the largest number. The difference is the range. Use the transparency, Range Modeling, to demonstrate this procedure.

* Teachers should model finding the lowest and highest points on the line graph. Find the numbers that correspond with these points. Subtract the lowest number from the highest number. The difference is the range.

* At this point, students complete part A of the worksheet, Different Range. As students are working, circulate and conduct a formative assessment giving corrective feedback, such as “Remember to find the number that corresponds with the lowest point.” Give affirmative remarks, such as “Great! You remembered to subtract the lowest from the highest.” Provide oral feedback.

3. The second way to figure the range is to subtract the smallest number from the largest one using any set of data.

* Use the transparency, Range Modeling, to demonstrate this procedure. Teachers model creating a subtraction problem using the data given.

* Discuss how the data method and the line graph method produce the same solution. At this point, students complete part B of the worksheet, Different Range. As students are working, circulate and give affirmative and corrective feedback as your formative assessment.

4. Collect the completed range worksheets and counsel any students who need further help giving written feedback.

5. Complete the range section of the Student Web Lesson, Jupiter Is Average.

Day 7

1. Review median, mode, mean, and range using the data charts and wall charts that students have been creating in the science portion of this unit. Describe a procedure and ask which type of average is being described.

* For example: Finding the middle number as the average is which type of average? What is the easiest way to find the median? What is another word that helps us remember what mode means? What type of average do baseball players use when they figure their batting average? (Hint: They add all their hits and divide by their total number at bats.)

2. Discuss the fact that to find the median and mode, we just line the numbers up in order and find the middle (median) or find the one that is their most (mode), but when finding the mean and range, we must add, subtract, and divide. Sometimes the numbers we are using are huge and difficult to use or there are a lot of numbers in the data.

*Establish that finding the mean and range of many numbers or large numbers is an appropriate use of a calculator. (Numbers on the worksheet were selected to force the use of calculators in order to meet the standard.)

3. Distribute individual calculators. Using an overhead calculator, review the various keys and functions. Have students use their calculators as you demonstrate.

4. Use the teacher information transparency, Calculator Modeling, and an overhead calculator to model how to find the mean and range using a calculator.

5. Students complete the worksheet, Let’s Calculate It. As students are working, circulate and give affirmative feedback , "Yes. You remembered to add them all before you divided." Also, give corrective feedback, such as, "Count the number of figures and divide by that number." Provide feedback as you formatively assess.

6. Collect the completed worksheets and counsel any students who need further help giving written feedback.

7. Complete the calculator section of the Student Web Lesson, Jupiter Is Average. At this point every child should have completed the Student Web Lesson. The Web lesson can be used as review or additional practice with any students that may still be struggling.

Day 8

1. Review median, mode, mean, and range for the summative assessment to be given on Day 9. Use the data gathered and presented on the planet wall chart and individual data charts when reviewing the mathematics concepts.

* Students should use a calculator when figuring mean and range.

* Be sure to have a line graph for figuring the range on smaller numbers, such as the number of satellites. A line graph for this purpose is available in the attached files.

* Since this is the final opportunity for formative assessment and feedback, give verbal whole group feedback, but also give individual feedback when individual students show a need. The goal of formative assessments is to assess individual students and address individual needs.

Day 9

1. Give Summative Assessment #2,Our Planets Aren’t Average, located in the associated files that accompany the unit Outer Space and Cyber Space. (See Extensions for the link.)

#### Assessments

A diagnostic assessment is given before giving instructions on the first day. The diagnostic is designed to address the two science standards taught in this lesson, as well as three mathematics standards, four language arts standards, and Goal 3 standards 1 and 2. The assessment tool is available from the associated files that accompanies the unit, Outer Space and Cyber Space. Instructions for administering the assessment are included. The link to the unit is available in the Extensions section of this lesson plan.

Formative assessment is given daily as students calculate median, mode, mean, and range. Affirmative and corrective feedback is given daily, both to individuals and to groups. Examples and criteria are available in each day's plan.

The summative assessment is given at the completion of day 8 of this lesson plan. It is a constructed response assessment. The assessment tool is available from the associated files that accompany the unit, Outer Space and Cyber Space. Instructions for administering and scoring the assessment are included. The link to the unit is available in the Extensions section of this lesson plan.

#### Extensions

1. This is the math content lesson from the unit, Outer Space and Cyber Space. The data collected from the science lesson plan, Nine Around the Sun is used extensively in this math lesson plan while learning to figure the median, mode, mean, and range.

2. Students can work in cooperative groups while using calculators. Peers helping peers often ends in better understanding for all group members. (If your students are not frequent users of calculators, a review lesson in calculator use may be necessary.)

3. Review of division may be necessary.

4. For advanced learners, the Student Web Lesson, The Mean Green Machine, gives additional practice in finding the mean using a calculator.

5. The Beacon Unit Plan associated with this lesson can be viewed by clicking on the link located at the top of this page or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=2943. Once you select the unit’s link, scroll to the bottom of the unit plan page to find the section, “Associated Files.” This section contains links to the Unit Plan Overview, Diagnostic and Summative Assessments, and other associated files (if any).

Using data from our solar system, students explore median, mode, mean, and range. Students learn to use an on-line calculator to determine the mean and range.
Jupiter is Average

#### Attached Files

Teacher information     File Extension: pdf

Vocabulary posters     File Extension: pdf

Modeling Transparency Masters     File Extension: pdf

Worksheets     File Extension: pdf

Satellite Line Graphs     File Extension: pdf