Pythagorean Theorem- Grade 8 Math Unit Plan – Elementary Ed. Resource Sharing

Math Final Unit Plan

Group Members: Lauren La Prairie, Laurel Apps, KW

Key concepts:

Pythagorean theorem ☀ Coast Salish canoeing routes ☀ Astronomy ☀ Spiralling

Purpose of Unit: Our focus for this unit was to instruct grade 8s on how to use Pythagorean theorem by grounding it in the local Coast Salish knowledge present on Vancouver Island. Between canoeing and following island patterns, as well as some well-known Coast Salish constellations, there are ample opportunities for place-based instruction that naturally uses this mathematical principle. By helping grade 8s internalize this concept by grounding them in familiar local funds of knowledge, we hope to give them meaningful reference points to the topic for life long recollections of this theorem’s utility.

Big Idea: “Discrete linear relationships can be represented in many connected ways and used to identify and make generalizations.”

Many of the big ideas in grade 8 are very subtle in their connections to the main curricular content, and this one was no exception. We chose this big idea because it values the role of linear trajectories in coordinates, plotting points (as in stars) and the straight line expectations of the hypotenuse of triangles when pushed one step further.

First Peoples Principles of Learning: “Learning recognizes the role of indigenous knowledge.”

We wanted to make Coast Salish funds of knowledge integral to our unit plan, so that we wouldn’t feel we were “sprinkling” indigenous content in after the fact, ie. straight up tokenism. This unit plan aims to teach mapping canoe routes as a vital, lifelong skill rather than a one off nod to Indigenous ways of knowing. Similarly with constellations, we feel that we can tap into tweens love of the mystic and the undeniable power of star exploration and discovery, incorporating elements of play into the realm of mathematical inquiry to heighten their investment in the topic. To ground our trajectory, we relied largely on the AMAZING FNESC math teach resource guide, which has excellent lesson plans for using the pythagorean theorem as a way to plot canoe routes, and as a way to understand the relationship between stars within Coast Salish constellations.

Core Competencies:

Understanding & Solving:

Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

Connecting & Reflecting:

Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts

Previous Knowledge:

Cartesian coordinates and graphing (grade 7)
Perimeter and angle measurement & classification (grade 6)

Learning Objectives: We want our students to develop lifelong referents to Pythagorean theorem by developing rich connections to its application when used as a tool for navigation and understanding the environments they live in. By rooting our lesson in Coast Salish funds of knowledge, largely pulled from FNESC and the BC curriculum, students should leave this unit confident that they could elaborate on how this theorem has practical applications for them going forward. Our main unit plan made changes to our resources’ original lesson ideas by incorporating increased student voice and choice, giving them more opportunities for creative exploration and control for instance in the storyboarding activity or the spiral art project. This is largely evident through their storyboarding, creating their own questions for the class and free exploration outside.

Additional relevant details about how this unit would integrate with other topics

PHE! So many opportunities to “participate in different types of physical activities,” from canoeing, to walking, to climbing around their local area to find relevant triangles. Further, PHE 8 asks teachers’ to focus on emergency preparedness, a vital component to outdoor explorations and especially canoe trips. Canoe trips are a great way to integrate financial literacy as well into the planning stages, budgeting out needs and wants to keep safe, warm and fed while afloat.

Luckily one of the key pieces of content in Science 8 is facilitating discussion around local indigenous landmarks in the form of “local geological formations” and, “significant local geological events,” a perfect opportunity for cross-curricular exploration as students find triangles throughout maps of the Saanich peninsula and other local landmarks, as well as in constellations.

Social Studies 8 is another key area that we can incorporate knowledge of canoeing and its history and present day implications. Specifically, we figured the big idea, “Contacts and conflicts between peoples stimulated significant cultural, social, political change,” would be an excellent starting point for exploring the implications of navigation on our current local landscape.

In Art 8, teachers need to spark their students to understand, “creative growth requires patience, readiness to take risks, and willingness to try new approaches,” seen best in the culminating activity around creating spiral art.

How we will involve family, how it is personalized to the needs of individuals

As with any unit, when there are opportunities to invite parents into leading lessons that can supplement your instruction and heighten those memories for your students, the better. Many in this area will work in areas directly related to geological formations and navigation around the island, and to have them lend their wisdom onto what types of math work they use to carry out their day to day work would be an amazing enrichment opportunity for our students. Due to the voice and choice component of many of the units, we hope to have this reach a wide range of mathematical proficiencies.

Assessment plans

Formative:

Math journals
Exit slips
Student created questions and comprehension of others’ questions

Summative:

Final table of hypotenuse lengths associated with corresponding spiral art piece

Lesson	Title	Main goals Unit accomplished over the course of 2 weeks, 4 lessons per week
1	Exploration	This first lesson is Exploratory, we want students to work together through a class brainstorm on the following questions; What do we know about triangles? Length of sides? Angles, degrees? Where are triangles present in everyday life? How do we use triangles when traveling? Leave lots of room for their own wonderings! Compile what they know so far on a class graphic organizer (you can just use chart paper) and encourage them to add to it later as they gain more insight (~15 minutes). Now! For the fun part, we’re heading outside! During this outdoor exploration, encourage students to find right angles in nature and draw the one they found in their daily math journals (~20 minutes). Finally, for the last part, hand them sticky notes to contribute to the class exit slip which includes the theorem on it to spark their ongoing consideration of the topic going forward. *Exit slip(chart paper and sticky notes)*– what questions do you have about Pythagorean Theorem and how we use it in the world?
2	Truth & Proofs	Exploration of why Pythagorean Theorem is true/proofs and manipulatives to help this exploration, crank out the protractors and calculators! Ideally this would start as student led exploration as they try their hand at some basic Pythagorean word problems (see appendix). Follow up lesson with a group discussion about persisting wonderings, difficulties, and students offer up how they solved problems to the whole group. This video clip would supplement/support the use of manipulatives in lesson activities for introducing Pythagorean Theorem to students (such as using tiles for proof through simplification; tangram proof; geometric proof): https://www.youtube.com/watch?v=YompsDlEdtc *Assessment*: formative, fingers on chest 1-4 (not getting at all= 1, totally nailing it= 4)
3	Pythagorean Story Boarding	Start by showing this clip on how Pythagoras HIMSELF came to make history: https://www.youtube.com/watch?v=KVnuUjat4ZU After the video, it’s time for your students to make a creative splash! Let them know they have the remainder of class to come up with their own story board (written or comic style) depicting their own story using this theorem. Let them know that next class they will be presenting it in groups to their peers! This is a great way to sneak some ELA into your math lessons. *Criteria for story:* must include theorem in some capacity (1) must present a real life problem needing solving in this way (2)
4	Storyboard showcase!	Students take the lead! In small groups students share their respective storyboards. This is meant as an editing session! Practice giving constructive feedback. *End of activity:* Provide 2 stars and a wish to at least two other students
5	Student led questions	In this lesson, students create and present their own real life pythagorean theorem questions, engaging with peers across the classroom. This should be entirely student led so they can learn from their peers. Make sure to have all of your class graphic organizers posted around the room during this time and circulate among their discussion. Give students an opportunity to reflect on their initial wondering from the first lesson. Have they gotten closer to understanding their question? *Provide the following checklist to students to refer to throughout lesson:* Create a word problem using pythagorean theorem Create a solution for your problem Share with at least one other peer, attempt their question Answer in math journal- reflect on your initial wondering from the first lesson. Have you gotten closer to understanding their question?
6	First Nations’ “Crossing the River” canoeing lesson	Refer to expanded lesson: https://drive.google.com/file/d/1uCaWvYNOD0YhBndecpf_8FnLDT19SW8V/view?usp=sharing
7	Coast Salish Astronomy	Read aloud, “Txamsm Brings Light to the World” (FNESC math document, pg. 60) which discusses how Raven put stars into the sky. Use bentwood boxes through your retelling and orient them around your class at different vantage points (2D plain). Then get class to form different triangles between each box (the sun box, moon box, new stars) and practice their fluency. Next, showcase the interior BC constellation from the Ntlakyapamuk (or Thompson peoples) in the southern British Columbia Interior of the three hunters chasing a grizzly bear. This constellation uses the same stars that the ursa major constellation does. Have students chart triangle distances between the stars throughout this constellation. Distances according to paper dimensions (everyone can do) Distances according to scientific dimensions (extending) Put constellation work in math journal.
8	Spiral Creation	Refer to expanded lesson: https://drive.google.com/file/d/1a-kc8ujuS_gi36J7SpqDD0Pw1dHsCILi/view?usp=sharing