1. Unit 6: Measurement and Geometry By Kimberly Govea Edited by Verlinda Ruble

2. What is Measurement? Here is a definition of measurement… A comparison between an attribute (like length, weight, etc) of the object being measured and the same attribute of a unit of measure. Example: comparing the length of a crayon to the length of an inch.

3. Question…. What are some attributes that we measure? For example, length is one attribute that we measure.

4. Commonalities… Although we measure different attributes (volume, length, weight, time, etc.), measurement has many commonalities. What did you find were common tools/skills necessary to all types of measurement?

5. Commonalities… Use of standard units Use of tools to measure Importance of precision (reliability) and accuracy (how close it is to the actual measurement) Estimation Use of manipulatives and visual aids

6. Reflect … What is your comfort level with measurement? Do you feel comfortable using different tools to measure?

7. Reflect … Do you feel pretty confident in your ability to estimate with different units—like the length of a room in feet, the weight of a person, the area of a field, etc?

8. Real Life… In what ways do you use measurement in your daily life?

9. Brainstorm… Let’s brainstorm some hands-on activities for measuring in the following areas… Length Weight Area/Perimeter Here is a link to practice area http://enlvm.usu.edu/ma/nav/activity.jsp?sid=__s hared&cid=emready@perimeter_and_area&lid=2& aid=1687844154 http://enlvm.usu.edu/ma/nav/activity.jsp?sid=__s hared&cid=emready@perimeter_and_area&lid=2& aid=1687844154 Volume Time

10. Making Tools… The author suggests having students make and use their own measurement tools. This type of activity helps the students to focus on the attribute being measured, rather than on the marks/numbers that are on the measuring tool… Let’s think of some non-standard units students could use for length, weight, volume, area, and time. Share your ideas!

11. Estimation… Suppose this small yellow shape is your measuring tool and you are going to use it to measure the blue line. Estimate how many units long the line is. _________________________________

12. Now use the same tool to estimate the green shape…

13. Question: Why should students make an estimate before making a measurement?

14. Importance of Estimation… We depend on estimation enormously in our daily lives (perhaps more than real measuring tools) Estimation focuses students on the attribute being measured. It also motivates students to measure the object. It also helps students to develop familiarity with the unit of measurement.

15. Question: In what ways do you use estimation in your life?

16. Area and Perimeter Field Trip… Let’s take a trip! Click on this link: Explore some of the interactive lesson activities in this website. We will meet back in 5 minutes… http://enlvm.usu.edu/ma/nav/toc.jsp?sid=__shared&cid=e mready@perimeter_and_area&bb=published

17. Virtual Field Trip Question… How do activities such as these contribute to students' understanding of the concepts of perimeter and area?

18. Geometry…Geometry…

19. Reflect… Do you remember studying geometry in elementary or middle school? What types of experiences do you recall?

20. Patch Tool Field Trip… Click on the link: 1. Patch Tool: http://illuminations.nctm.org/ActivityDeta il.aspx?ID=27 http://illuminations.nctm.org/ActivityDeta il.aspx?ID=27 We will meet back in 5 minutes…

21. Question… Why are these types of activities valuable for children?

22. Sorting Shapes… What are some ways that children can sort shapes?

23. Unit 6 Project Here’s a chance to apply your understanding of the geometric principles you learned about in this unit.

24. Project 6:Unit on Measurement Imagine you are beginning to teach a unit on measurement to third-grade students. You want them to understand the common concepts behind measurement, regardless of whether one is measuring weight, length, time, angles, volume, area, etc. What do you think is important to explain to them so they will understand that measurement has some common skills and tools necessary? Think about how you might incorporate the following into your presentation: –Use of standard units –Use of tools to measure –Importance of precision and accuracy –Estimation –Use of manipulatives and other visual aides

25. Project 6 continued The van Hiele Levels of Geometric Thinking is very important in math instruction and has its foundation in an appreciation for developmental differences in individuals based on both their experiences and maturation. Explain, in your own words, some of the key points of the van Hiele Levels and why they are important when working with students on geometric concepts. Note the link is under the Unit 6 Project directions.

26. Format for Project 4–6 (total, including the title and reference pages) typed, double- spaced pages, written in complete sentences using Standard American English, and organized into paragraphs.

27. More on Format The Kaplan Writing Center is a free resource to you. A title page (contains three items: a running head (a short version of the title) and page number, the paper's title, and the author's name) The paper itself, including at least one in-text citation for each reference used to support your essay A reference page including at least one source (see the APA Quick Reference for help with citations)

28. More Format for Project 6 Use standard margins: 1" on all sides. Use standard 12-point font size, Arial or Times New Roman. Use standard double-spacing: average of 22 lines per page, and between 20 and 24 lines per page. Use left-aligned text. Do not right-justify. There should be no subtitles or spaces between paragraphs within the paper.

29. Rubric for Project 6 Project Grading Criteria: A/116-125 pts or A-/113-115 pts Well written project that demonstrates knowledge and understanding of topics from the unit and addresses all components listed in the directions. Project refers to additional information researched and provides relevant classroom and pedagogical application. Meets or surpasses minimum requirements for length, follows required format and contains no spelling or grammatical errors. Writing is clear with smooth transitions; includes introductory and concluding paragraphs. Accurate citation of sources if necessary.

30. Thank you for coming! To do by Tuesday: Reading : his unit’s readings focus on concepts of measurement, including the skills necessary for measuring length, area, volume, mass, angles, and time. Additionally, you will read about geometry including the underlying logic necessary in geometric thinking. Web Resources You will have the option to access a web site for online graph paper. Video : View the video "Measurement Lesson". Discussion : You will consider some real-world applications and examples of measurement and geometry in students' lives. Seminar (if you are here tonight, then you can cross this one off your to do list). Project : You’ll have the opportunity to apply your understanding of geometric and measurement concepts by completing an exercise and also composing an essay applying your understanding of the developmental stages of geometric thought.