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This Unit Covers
This is the first of 11 units in the 4MAT 4 Geometry Curriculum Series from About Learning.
These skills are essential for communicating geometrically: Identify points, lines, planes Use segments and congruence Use midpoint and distance formulas Measure and classify angles Describe angle pair relationships Classify polygons Find perimeter, circumference, and area Using inductive reasoning Analyze conditional statements Apply deductive reasoning Use postulates and diagrams Reason using properties of Algebra Prove statements about segments and angles Prove angle-pair relationships
Unit 1 - Reasoning
Research confirms that the brain is not likely to remember new information and even more unlikely to recall that information if the human brain cannot associate this information to personal experiences in a meaningful and relevant way. As an educator, it would be egregious not to recognize the implications of this research and act on it. The following introduction gives explanations of how to create meaning for students through an established context.
The gateway to any content area is vocabulary. Setting this up in a meaningful and relevant way for the students is critical and will minimize the number of times students question why they are learning this new information. It is our intention to set up the importance vocabulary plays in being able to reason and logically support your hypothesis. This is essential to not only Geometric Proofs but ALL reasoning in the real world. We would challenge anyone to find a task that does not have reasoning behind it.
This first unit begins with an activity called "Friplet". Providing students a made up word, students will not be able to efficiently or effectively reason because no contextual reference exists. By entering into this experience, students begin to see the challenge of vocabulary that is foreign to them. When the teacher finally provides students with a definition of this made up word, students now have a contextual reference. We believe this is an effective connect activity because it would be extremely rare to have any student who is not familiar with what a cell phone is and the possible uses of a cell phone. By beginning a unit with something that teenagers are highly familiar with and can easily connect to personally, we have engaged all students, created a contextual reference, and put all students on a level playing field.
This activity provides a seamless and natural progression from Friplets to Geometry vocabulary. Teachers will need to be reminding students how easy it was to reason (prove) when you understand the vocabulary. We would then recommend telling students that this course is designed so that students build knowledge in Geometry while learning how to argue and reason using supporting details and facts. To do this we will start the year by building our understanding of vocabulary. As you introduce vocabulary to students, keep reminding them of the Friplet activity and how the vocabulary that is going to be introduced will enhance our ability to effectively argue (reason).
Example: Yesterday we discussed the vocabulary words complementary and supplementary. It is much easier to reason (argue) when we understand vocabulary. It is difficult to master skills when you don't know what the words mean. We found this out with the Friplet activity. Today we are going to define a few more vocabulary words such as polygon, convex, concave, and regular. Understanding them will help us to use them in our future reasoning.
This dialogue should happen as you bring in new vocabulary throughout this unit. In doing so you keep students connected to why vocabulary is essential to their learning.
The Concept is Reasoning. The Content is the essentials of Geometry and proof. There is a relationship between reasoning and proof and the relationship is vocabulary and logic!
Learning Outcomes
Students will: Explore terminology that is not familiar to them. Gain insight on the importance of understanding and using common vocabulary. Understand that to communicate effectively, vocabulary must be defined and commonly understood. Understand the vocabulary necessary to reason effectively in Geometry. Practice the concepts taught. Apply their knowledge of the vocabulary in this unit by completing an ABC book. Collaborate to fine-tune projects. Share their projects.
Teacher Notes
This unit is authored by Michael Arlien and Colleen Hodenfield, authors of the 4MAT 4 Geometry Curriculum Series and 4MAT 4 Algebra Curriculum Series. This is the first unit of 11 conceptual Geometry units.
"l'll help with driving my sister to practice and school." "I'll get groceries for you when you need something quick." "I'll get myself to my job so you don't have to take me." "I'll..." After Mikey spent 30 minutes explaining the reasons for why he should get a car of his own, his parents realized he had some legitimate points and went ahead and got him one. Knowing the facts, laying them out in a orderly fashion with a good conclusion are the essentials of good reasoning and proof.
Why is it important to understand common Geometric vocabulary and logic when reasoning?
