The full lesson plan and activity sheets with teacher guides is available on Teachers Pay Teachers. Use this link.

**Brief Lesson Description**:

Students start off by observing the similarities and differences of longitude and latitude lines on maps and globes. They will develop and use a hemisphere model to construct explanations as to why longitude and latitude lines are measured in degrees. Students will construct latitude and longitude lines with their model using string, a protractor, and thumbtacks. Then, students read a passage about longitude and latitude and complete a Venn Diagram. Using the Venn diagram, students will write sentences constructed from the vocabulary words explaining the characteristics and significance of longitude and latitude lines. Next, students will use ratio and rate reasoning to solve problems related to longitude and latitude. These ratio and rate reasoning problems will also require students to write, read, and evaluate expressions in which letters stand for numbers, use variables to represent numbers and write expressions, and understand that a variable can represent an unknown number. Finally, using a coordinate grid world map, students will understand that positive and negative numbers are used together to describe quantities having opposite directions or values and use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

**Common Core Math Standards Integrated in the Lesson Plan:**

- CCSS.MATH.CONTENT.6.G.A.4-Represent 3D figures using nets
- CCSS.MATH.CONTENT.4.MD.C.5– Understand concepts of angle and measure angles.
- CCSS.MATH.CONTENT.4.MD.C.6– Measure angles in whole-number degrees using a protractor.
- CCSS.MATH.CONTENT.6.RP.A.3-Use ratio and rate reasoning to solve real-world and mathematical problems
- CCSS.MATH.CONTENT.6.NS.C.5-Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
- CCSS.MATH.CONTENT.6.NS.C.6.C– Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
- CCSS.MATH.CONTENT.6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.
- CCSS.MATH.CONTENT.6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set

#### Resources (also in found in the lesson plan):

**Developing a model: **

How to Develop a Longitude/Latitude 3D model to Explain Why They’re Measured in Degrees.

**Map Projection Videos:**

**Map Projection Activities (Geometry connection): **

This website gives instructions on how to create your own planar projection, cylindrical projection, and conical.

This website gives instructions how to make different globes of several geometric shapes using nets.

**Proportional Reasoning books: **

I found this book helpful when researching strategies of how to implement more mathematics into my lessons. One standard that is essential for understanding in both math and science is proportional reasoning. However, my knowledge of how to teach this skill was limited. I was taught how to use the cross-multiplication trick to solve the problems. Through researching proportional teaching strategies for a graduate class I was taking, I found out that cross multiplication is not “real algebra” but a trick. Tina Cardone calls it illegal algebra and explains why as well as adding her ideas on how to teach it. Below this, I will list the my references for the paper I wrote about this topic in my graduate class.

*Nix the Tricks:A guide to avoiding shortcuts that cut out math concept development** *by Tina Cardone

**Other References:**

- Bassarear, T. (2012).
*Mathematics for elementary school teachers*(5th ed., pp. 315-332). Belmont, CA: Brooks/Cole. - Cardone, T. (2015).
*Nix the tricks: A guide to avoiding shortcuts that cut out math concept development*(Second ed., pp. 24-25). - Cramer, K. & Post, T. (1993, May). Connecting Research To Teaching Proportional Reasoning.
*Mathematics Teacher,*86(5), 404-407. - Cramer, K., Post, T., & Currier, S. (1993). Learning and Teaching Ratio and Proportion: Research Implications. In D. Owens (Ed.),
*Research Ideas For the Classroom*(pp. 159-178). NY: Macmillan Publishing Company. - Grade 6 Mathematics Module 1, Topic B, Lesson 10. (n.d.). Retrieved December 12, 2015, from https://www.engageny.org/resource/grade-6-mathematics-module-1-topic-b-lesson-10
- Heller, P., Ahlgren, A., Post, T., Behr, M., & Lesh, R. (n.d.). Proportional reasoning: The effect of two context variables, rate type, and problem setting. J. Res. Sci. Teach. Journal of Research in Science Teaching, 205-220. Retrieved December 12, 2015, from http://www.cehd.umn.edu/ci/rationalnumberproject/89_6.html
- HOFFER, A. (1988). Ratios and proportional thinking. In T. Post (Ed.),
*Teaching mathematics in grades K-8: Research based methods*(pp. 285-313). Boston: Allyn & Bacon. - Lesh, R., Post, T., & Behr, M. (1988). Proportional Reasoning. In J. Hiebert & M. Behr (Eds.)
*Number Concepts and Operations in the Middle Grades*(pp. 93-118). Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics. - Lobato, J., Druken, B., & Jacobson, E. (2011, April 8). Middle School Teachers’ Knowledge of Proportional Reasoning for Teaching. Retrieved December 12, 2015, from http://www.kaputcenter.umassd.edu/downloads/products/workshops/AERA2011/Lobato_Orrill_Druken_Erikson_AERA_2011.pdf
- NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS. (1989).
*Curriculum and evaluation standards for school mathematics.*Reston, VA: Author - Parish, Linda. Facilitating the Development of Proportional Reasoning through Teaching Ratio. Retrieved December 12, 2015, from http://files.eric.ed.gov/fulltext/ED520962.pdf
- Scale City | Scale Models in the Real World. (n.d.). Retrieved November 14, 2015, from http://www.pbslearningmedia.org/resource/mket.math.rp.miniland/scale-models-in-the-real-world/