KATHY CAMPBELL

Lesson Planning & Today’s Lesson

THE NATIONAL MIDDLE SCHOOL ASSOCIATION SUCCESSFUL LEARNING FOR YOUNG

ADOLESCENTS

High Expectations All students can learn. Based on Standards of Learning Curriculum

Frameworks Active Learning

Students remain engaged. Relevant Challenging

High, yet achievable goals Exercise higher order thinking skills.

Integrative Assessment & Evaluation

EFFECTIVE LESSONSObjectives are based on SOL’s.Lessons are well-planned.

ResearchVirginia Department of Education (from website)

Test Release Items Enhanced Scope/Sequence PLUS lesson plans Middle School Math Strategies

textbooksstudent textsmath for teachers textbooks

professional journalsonline resources

Revise and Personalize

LESSON PRESENTATION

PROBABILITY: GRAB A HANDFUL

Related Standard of Learning 7.16, 7.18

7th Grade

Students collect data about the handful of cubes and use the data to explore the mean, median and mode.

7.16: TSW create and solve problems involving the measures of central tendency (mean, median, mode) and the range of a set of data

7.18: TSW make inferences, conjectures, and predictions based on analysis of a set of data

OverviewRelated Standards of

Learning

PREREQUISITE UNDERSTANDING/KNOWLEDGE/SKILLS

Students must know how to construct a bar graph or line plot

mean (average

)

outliers mode

mediancentral

tendency

range

MATER

IAL

S

Post-it Notes (small) Linking cubes Recording sheet

INSTRUCTIONAL ACTIVITYNote: This activity is a modified version of a lesson found in the Probability and

Statistics Teachers Resource Guide, developed by the Virginia Department of

Education.

Have students grab a large handful of cubes from a bucket or bag.

Each student should connect all of his/her cubes and write the number of cubes in the cube-train on a Post-it Note.

Students then take their Post-it’s to the whiteboard and construct a bar graph or line plot (using notes as bars/line plots.

Students then line up at the front of the room according to the number of cubes each student has. They should line up in front of each other when there is more than one student with the same number of cubes. (human plot should be similar to line plot on board)

INSTRUCTIONAL ACTIVITY CONTINUED

Teacher leads the group through a discussion of the measures of central tendency (mean, median, mode) using vocabulary words. While discussing range, students learn about outliers

Before discussing, students should be asked what they know. Assessing prior knowledge is key.

They also should be encouraged to predict the median and the mean. The mode is easily illustrated on the human line plot and the line plot or bar graph on the board.

INSTRUCTIONAL ACTIVITY CONTINUED

Before the median discussion begins, ask students to spread out in one line.

Ask students to move out from the line in pairs – one from each end at the same time. The idea with this is that students will see how, as you approach the center, there will be one or two students remaining. They will experience what the center really is. The movement away from center makes this very clear to students. Discussion should follow regarding the median and what it represents.

INSTRUCTIONAL ACTIVITY CONTINUED

Before illustrating the mean, students should again discuss what they re really trying to find. Encourage students to share ways they could find the mean using cubes.

Then have students share linking cubes with each other until all students have a similar number of cubes. They share until sharing anymore isn’t helpful to reach the same number of cubes for each student. More than likely, two groups will exist. Some students will have trains of one number and the other group will have trains of another number. At this time, students discuss the mean and also use the term average.

CLOSURE

End the lesson by reviewing the measures of central tendency students have learned and stating again the actual answers for this collection of data. Students should be encouraged to discuss how changes in the data would affect the measures of central tendency. Ask students to complete the Recording Sheet.

ASSESSMENTS

Informal assessments throughout the discussion part of the activity.

The recording sheet can be used as an assessment

Further assessments for understanding: Students look up statistics on the internet

Weather data Sports statistics Population data

Use this data to create problems asking students to determine which measure of central tendency would be best to use to describe the data set, and have them find it

VA Dept. of Education release data test items

TECHNOLOGY OPTION

Have students complete a spreadsheet with give data

LESSON CONCLUSION

AN EFFECTIVE LESSON

I CONSIDER THIS LESSON EFFECTIVE BECAUSE IT IS DEVELOPMENTALLY APPROPRIATE FOR

MIDDLE SCHOOL LEARNERS

High expectations based on SOL’sRelevant, challengingActive learning multisensory

Guided practiceHands onInductive learningCooperative learningDiscussions Visual stimulusGraphic organizerstechnology

ATTACHMENT: RECORDING SHEET

Name: Date:

  Number of cubes I grabbed in

one handful:

 

Number of students participating in this activity:  

Total number of cubes grabbed by the students:  

Using the data, I discovered the following:

Range of the data:

Identify any outliers, and tell why they are outliers.

   Mode(s) of the data:

How did you know?  

 Median of the data:

What is the meaning of median?

Mean of the data:

Why is the mean also called the average?

Which measure of central tendency best represents the data and why?

 

RESOURCES Virginia Department of Education

Enhanced Scope & Sequence http://www.doe.virginia.gov/VDOE/Assessment/Release2008/VA_Spr08Released_G7Math.pdf

Virginia Department of Education Release Test Items http://www.doe.virginia.gov/VDOE/Assessment/Release2008/VA_Spr08Released_G7Math.pdf

T/TAC Online SOL Enhanced Scope and Sequence http://ttaconline.org/staff/sol/sol.asp

National Middle School Association – This We Believe http://www.nmsa.org/AboutNMSA/ThisWeBelieve/tabid/1273/Default.aspx

THANK YOU FOR YOUR ATTENTION.

The end