Lesson 4: Mean and Median

COURSE/LEVEL: 6th grade math

TOPIC: Mean and Median

GOAL OF LESSON: The goal of this lesson is to further develop students’ skills with finding the mean and median of sets of data and introduce them to box and whisker plots.

INSTRUCTIONAL OBJECTIVES: Students Will Be Able To (SWBAT):

Order given sets of data.
Understand the meanings of the terms mean and median.
Work in partners to find the means and medians of given sets of data and use an online tool to illustrate their findings with box and whisker plots.

NY State Standards for Mathematics:

6.PS.10 Work in collaboration with others to solve problems.
6.PS.13 Model problems with pictures/diagrams or physical objects.
6.CM.3 Organize and accurately label work.
6.CM.10 Use appropriate vocabulary when describing objects, relationships, mathematical solutions, and rationale.
6.CN.4 Understand multiple representations and how they are related.
6.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations.
6.S.5 Determine the mean, mode and median for a given set of data.
6.S.7 Read and interpret graphs.

NCTM Standards:

Standard 2: Mathematics as Communication: In grades 5-8, the study of mathematics should include opportunities to communicate so that students can:
- develop common understandings of mathematical ideas, including the role of definitions.
Standard 6: Number Systems and Number Theory: In grades 5-8, the mathematics curriculum should include the study of number systems and number theory so that students can:
- develop and use order relations for whole numbers, fractions, decimals, integers, and rational numbers.
Standard 10 Statistics: In grades 5-8, the mathematics curriculum should include exploration of statistics in real-world situations so that students can:
- systematically collect, organize, and describe data.
- make inferences and convincing arguments that are based on data analysis.

ISTE NETS-S Standards:

1. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
c. Use models and simulations to explore complex systems and issues.
2. Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.
d. Contribute to project teams to produce original works or solve problems.
3. Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.
a. Plan strategies to guide inquiry.

b. Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media.
4. Critical Thinking, Problem Solving, and Decision Making: Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.
b. Plan and manage activities to develop a solution or complete a project.

c. Collect and analyze data to identify solutions and/or make informed decisions.
6. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems, and operations.
a. Understand and use technology systems.

b. Select and use applications effectively and productively.

MATERIALS:

Notebooks/Pens/Pencils
Whiteboard w/markers and eraser (if no SMART Board).
Computers with Internet access (preferably a lab so each pair of students has their own computer).
Computer with Internet access hooked up to an overhead projector/SMART board.

RATIONALE: The NYS Mathematics Standards state that students should work in collaboration with others to solve problems, and they will be working in pairs to find means and medians during this lesson. Students will be modeling problems with the box and whisker plots using the online tool. They will be organizing their work as they find the means and medians of sets of data. Students will also learn and review the vocabulary words mean and median. Through the online tool, students will see how data points can be plotted on a simple number line and translated into a box and whisker plot; the online tool shows the median simultaneously on both representations. They will determine means and medians and read the graphs on the tool. The ISTE NETS-S state that students should use models and simulations, and the digital resource in this lesson is just that. Students will be using technology and using the application effectively and productively to visualize means and medians of sets of data. They will also be fulfilling standard two by working with others to solve problems.

PROCEDURES:

Introduction:

1. Tell students that we are going to continue learning about means and medians of sets of data. Review the two terms:
Mean: the quotient obtained when the sum of the numbers in a set is divided by the number of addends. (AKA: We add them all up and then divide by the number of things we added)

Median: The middle number of a set of numbers arranged in increasing or decreasing order; if there is no middle number, the median is the average of the two middle numbers.
2. Give the class a few sets of data to review and find the mean and median. Circulate the room as they work. Go over the answers by calling on students once everyone is finished.
3. Tell them that we are going to go down to the computer lab quietly. Once everyone has arrived there, divide the class into pairs so that each pair of students is working at one computer.

Presentation:

4. Tell the students to go to our class site and click the “Interactive Tools” tab. Tell them to click on the last link called Illuminations: Mean and Median.
5. Bring Illuminations: Mean and Median up on the SMART Board (or computer projector). Make sure you uncheck the mean and median box so that the answers are not displayed. Tell the students to do the same. Ask the students to call out numbers (one at a time) for you to add to the number line on the tool. The students can do this on their computers with you if they want.
6. Once you have put all of the numbers in the boxes under the number line, click “apply,” and all of the points will appear on the number line. Add all of the numbers together and divide by however many points you made on the number line to find the mean with the class.
7. Now have the students help you put all of the numbers in order and write the ordered list on the board. Show them how they can check their work using the tool. Click the “sort” button, and the tool will put the numbers in order for you. Now have them find the median by locating the number in the middle of the ordered data set (dividing the middle two numbers if there is an even number of data entries in the set).
8. Finally, reveal the answers on the tool by checking the mean and median box. The answers will appear on the number line and the box and whisker plot, and the median will be lined up between the two representations.

Application:

9. Hand out the practice sheet so that each student has the data sets. Tell the students to work in their pairs to find the means and medians of each data set. In class, they will do the odd numbered problems, and for homework they will complete the even numbered problems.
10. Remind the students that they must uncheck the mean and median box on the tool while they are finding the mean and median of their sets of data. Then they can re-check the box after they have found the answer to compare what they got to the answer the tool gives. Circulate the room as they work to keep them on task.

ASSESSMENT: I will check each student’s work that they email me tonight (because they will finish the same sheet for homework).

ASSIGNMENT: Students will complete the even numbered problems on the sheet for homework and scan all of their work (from in class and at home) into their computers and email me their completed and scanned work as an attachment. Tell them to check their work using the tool from Illuminations that we used in class.

Name: ___________________________ Math-Aids.Com Mean and Median

1) 58, 95, 45, 16, 46 Mean ____ Median ____	2) 42, 29, 56, 60, 86, 38, 83, 70 Mean ____ Median ____
3) 95, 27, 70, 79, 24 Mean ____ Median ____	4) 96, 26, 52, 11, 30, 32, 33 Mean ____ Median ____
5) 55, 80, 40, 82, 64, 40, 60, 99 Mean ____ Median ____	6) 40, 95, 41, 94, 86, 34 Mean ____ Median ____
7) 88, 38, 29, 21, 39 Mean ____ Median ____	8) 74, 50, 84, 40, 70, 71, 72, 35 Mean ____ Median ____
9) 29, 88, 52, 66, 29, 40, 74 Mean ____ Median ____	10) 86, 39, 89, 37, 43, 70, 28 Mean ____ Median ____
11) 53, 71, 32, 55, 79, 48, 94, 19, 80 Mean ____ Median ____	12) 26, 84, 73, 36, 31, 56 Mean ____ Median ____
13) 77, 57, 90, 30, 25, 52, 40 Mean ____ Median ____	14) 59, 67, 91, 20, 98 Mean ____ Median ____

Worksheet Generated From: Math-Aids.com

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