Geometry Algebra Connections: Teacher Notes

Overview

In this activity students use algebra skills to solve linear equations using geometric properties of parallel lines and polygons.

Important Mathematical Ideas

  • Algebra skills are useful to solve problems.

Prior Knowledge

  • Applying angle relationships for intersecting lines (e.g., supplementary angles, complementary angles, vertically opposite angles) to determine angle measures.
  • Applying angle properties of triangles (e.g., angle sum, isosceles triangle, equilateral triangle) to determine angle measures.
  • Applying angle relationships for parallel lines and transversals (e.g., alternate, corresponding, co-interior and vertically opposite angles) to determine angle measures.
  • Solving linear equations.
  • Applying algebra skills.

Common Misconceptions

  • The sum of the exterior angles of a polygon changes based on the number of sides.
  • The interior angles of a polygon are always equal to each other even when the polygon is not regular.

Information to Support/ Enhance/ Extend Learning

  • Students are asked to keep a journal for each unit in the course. It should contain notes of important mathematical ideas with examples and new vocabulary.
  • ePortfolio may be used for these journal entries.
  • Students can make individual choices whether this is a paper or digital personal resource.
  • Consider a variety of formats as alternatives to journal entries (e.g., student note, pair/share, group discussion, exit card, poster, electronic posting).
  • Develop a Word Wall and continue it throughout the unit as new vocabulary and terms arise that require clarification (e.g., equation, algebra).

Minds On

Task 1: Review

  • Students will:
  • review solving equations using their algebra skills
  • check answers with feedback provided
  • Some students may require more practice solving equations before moving on:
  • Gap Closing I/S: Solving Equations
  • Student Book
  • Facilitator’s Guide
  • Can be organized as a Think/Pair/Share or as a Coach and Be Coached activity.

Action

Task 2: Find the measures of the angles for the quadrilateral

  • Students will:
  • identify a geometric property that can be used to solve the problem
  • write an algebraic equation to represent the geometric property
  • solve their algebraic equation
  • compare their solution with the sample provided
  • Can be done as a Think/Pair/Share.

Task 3: Riddle involving angles

  • Students will:
  • represent the problem using a diagram and an equation
  • state a geometric property that can be used to solve the problem
  • solve their equation
  • check their solution with the feedback provided
  • Can be organized as a Gallery Walk.

Discussion Prompt and Sample Responses

1) Create a riddle involving angles for your classmates to solve for an unknown and the measures of the angle(s), using at least one geometric property.

2) Create a full solution to your riddle.

  • Solutions should include:
  • a diagram
  • an algebraic expression to represent the angles, where it is appropriate
  • the geometric property used to solve for the measures of the angle(s)
  • an algebraic equation to represent the geometric property
  • the steps to solve the equation
  • the measures of the angle(s)
  • Common Errors:
  • diagram does not match the riddle
  • incorrect use of the geometric property identified
  • algebraic equation does not match the diagram
  • error(s) in the solution to the equation
  • solution is correct but answer is incorrectly stated

Consolidation

Task 4: Practice Exercise: Connecting Algebra to Geometry Problems

  • Students will:
  • complete Connecting Algebra to Geometry Practice Problems handout
  • identify a geometric property that can be used to solve the problem
  • write an algebraic equation to represent the property
  • solve their equation
  • determine the measure of the angles
  • check solutions with provided sample solutions
  • Consider organizing Practice Exercise as a Coach and Be Coached activity.

Task 5: Assignment 1: Exterior and Interior Angles of Polygons

  • Assignment posted in unit.
  • Sample solutions posted in Teacher Notes in the vLE.

Task 6: Assignment 2 Riddle Response Discussion Prompt and Possible Solutions

1) Read through your classmates' solutions to your angle riddle.

2) Select two different solutions to your riddle.

3) For each:

  • Describe how your solution was similar or different.
  • Explain how or why you agree or disagree with their solution.
  • Solutions should include:
  • two different solutions to their riddle
  • a comparison of how the solutions were the same or different
  • an explanation why they agree or disagree with the solution

Task 7: Student Reflection

  • Students are asked to reflect on their understanding of this topic.
  • These reflections can be used as assessment for learning to help determine next steps for individual students.

Grade 9 Applied Blended Learning: Unit 8 Activity 4 Page 1 of 3