1. Kathy Campbell Lesson Planning & Today’s Lesson

2. 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

3. Effective Lessons Objectives are based on SOL’s. Lessons are well-planned. Research Virginia Department of Education (from website) Test Release Items Enhanced Scope/Sequence PLUS lesson plans Middle School Math Strategies textbooks student texts math for teachers textbooks professional journals online resources Revise and Personalize

4. Lesson presentation

5. Probability: Grab a Handful Related Standard of Learning 7.16, 7.18 7th Grade

6. 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 Overview Related Standards of Learning

7. Prerequisite Understanding/Knowledge/Skills Students must know how to construct a bar graph or line plot

8. vocabulary outliers range mode mean (average) median central tendency

9. Post-it Notes (small) Linking cubes Recording sheet Materials

10. Instructional Activity Note: 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)

11. 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.

12. 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.

13. 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.

14. 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.

15. 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

16. Technology option Have students complete a spreadsheet with give data

17. Lesson Conclusion

18. An effective lesson

19. I consider this lesson effective because it is developmentally appropriate for middle school learners High expectations based on SOL’s Relevant, challenging Active learning multisensory Guided practice Hands on Inductive learning Cooperative learning Discussions Visual stimulus Graphic organizers technology

20. 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?

21. 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

22. Thank you for your attention. The end