Pythagorean Theorem, Proportion & Algebraic Equations (Gr.8)

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Curriculum

Grade 8:

B1.3 estimate and calculate square roots, in various contexts

B2.8 compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts

C2.3 solve equations that involve multiple terms, whole numbers, and decimal numbers in various contexts, and verify solutions

E2.4 describe the Pythagorean relationship using various geometric models, and apply the theorem to solve problems involving an unknown side length for a given right triangle

Knowledgehook's Math Background, Misconception Charts and Gap Closing Resources

These resources are available in your Knowledgehook account. They are also linked in this Google Doc. However, you must be logged into your browser or app with your DSB1 account to access this file.

Knowledgehook's math background charts explore the big ideas in detail and address best practices and tips for remediation. Their misconceptions charts include tips for understanding, preventing, and/or remediating common learning gaps, misconceptions, and errors for this topic. The Remediation questions can be assigned to students in order to assess individual students' specific remediation needs.

Topics for this unit:

Describing and Representing a Percent
Equivalent Forms of Rates
Equivalent Forms of Ratios
Perfect Squares and Roots
Pythagorean Theorem
Solving Proportion Problems
Solving Simple Linear Equations

Grade 7 & 8 Knowledgehook Support Charts

Marian Small's Gap Closing

Gap Closing resources are designed for students who need additional support in mathematics. For each topic in the resource, there is a diagnostic and a set of intervention materials. Diagnostics are designed to uncover the typical problems students have with a specific topic.

Solving Equations

Powers & Roots

Proportional Reasoning

Facilitator's Guide

Student Book

Pedagogy

Lesson Resources for Pythagorean Theorem

Pythagorean Theorem

(Open on iPad or MacBook)

iBook by Kyle Pearce

(open on iPad or MacBook)

teacher.desmos.com/activitybuilder/custom/5d23bd86cbc7a96547fb27ca

Pythagorean Theorem Desmos Activity

Lesson from the Ontario Association of Mathematics Educators (OAME)

Grade 8 - Coding Lesson - Coding with the Pythagorean Theorem In this lesson, students will increase their knowledge of the Pythagorean Theorem while working on their coding skills. (Specific Expectations: A1, B1.3, C3.1, E2.4)

Visual Lesson Approaches to Support Student Understanding

Online simulations that power inquiry and understanding

Gizmos

Gizmos for this topic include:

Square Roots

Modeling and Solving Two-Step Equations

Pythagorean Theorem

Pythagorean Theorem with Geoboards

Solving Algebraic Equations I

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

Desmos

access create your free teacher account at teacher.desmos.com
See a brief introductory video and a support page

Some activities for this topic include:

Connections to Real-Life Contexts with 3-Act Math Tasks

3-Act math tasks are a great way to weave together proportional reasoning and mathematical modelling. Visit the Mathematical Modelling page on this site for lots of 3-act math task resources.

3-Act Tasks Involving Pythagorean Theorem:

Corner to Corner

Taco Cart

(and tons more online…)

Assessment Ideas

Introductory Video

Knowledgehook

Knowledgehook is an Instructional Guidance System (IGS) that uses engaging assessments to unlock insights and expert guidance for math teachers.

Create assessments from question banks aligned with the new 2020 Ontario Mathematics Curriculum
Assign work as "Game Shows" (class-wide activity similar to Kahoot) or as self-paced "Missions"
Reports and built-in individualized gap closing materials activities support teachers in remediation efforts
Parental portal allows parents to view their child's progress and send encouraging messages
DSB1 premium upgrade (You must be logged into Google with your DSB1 account to see this document.)
Teacher Essentials support document

You can use Google Forms to quickly document evidence of learning during your conversations with and observations of your students. This PDF includes links to several Google Forms organized by strand. You'll need to copy and modify them to include your students' names.

Google Forms for Documenting Student Learning.pdf

Use ongoing, progressive rubrics (provided below) to record student progress based on triangulated data, like observations and conversations.

sample template for Reasoning & Proving Rubric

Rubrics for each of the new overall expectations

Here's a great blog post by Damian Cooper called What is “Triangulation” in the Assessment Context? which will help support our understanding of how we can assess as we move towards giving students messier and more real problems where the process of problem-solving is valued in addition to "the right answer."

Documenting Conversations & Observations - Tracking Sheets.pdf

Use Showbie to create Problem-Solving Portfolios where students can work on problems with increasing complexity as they master the concepts and monitor their progress.