Solving Equations Using Algebra Tiles: Teacher Notes

Overview

In this activity students review the guess and check method for solving equations and see how to solve equations using algebra tiles.

Important Mathematical Ideas

  • An unknown in an equation can be represented using a letter or symbol.
  • An unknown in a linear equation represents a number that solves the equation (i.e., makes the equation true).
  • An equation is true when the values of the expressions on the left side and the right side are equal.
  • Algebra tiles can be used to model and solve linear equations

Prior Knowledge

  • Familiarity with the vocabulary of algebra (e.g., algebra, variable, term, and algebraic expression) as needed throughout the unit.
  • Representing statements (words) as algebraic expressions.
  • Using the zero principle as it connects to the "balance method" of equation solving.
  • Adding, subtracting, multiplying and dividing integers.
  • Substituting into and evaluating formulas.
  • Understanding how to solve equations and verify answers using left side/right side equivalence.
  • Solving equations using the methods of inspection, balance and guess and check.

Common Misconceptions

  • Solving equations involves “moving to the other side and changing the sign”.
  • Inability to deal with integer or fraction operations required to solve equations.
  • Inability to deal with equations where the coefficient of the unknown is negative.
  • In order to solve an equation, the unknown must be on the left side.
  • There can be more than one solution to a linear equation.

Curriculum Notes

  • This unit involves solving simple equations using the balance method and inverse operations. Solving equations that involve the distributive property is done in Unit 7 after students have had experiences with simplifying algebraic expressions. Further practice with equation solving is revisited in Unit 8 as this applies to determining the measures of angles using geometric properties.

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.,variable, expression, equation, solve, solution, simplify, zero pairs, balancing).
  • Additional Resources
  • Paying Attention to Algebraic Reasoning
  • Paying Attention to Algebraic Reasoning Adobe Presenter

Minds On

Task 1: Expression or Equation

  • Students will:
  • sort given items as expressions or equations
  • check with provided answers
  • Common Error
  • not recognizing an equation is made up of expressions on either or both sides

Journal Prompt and Sample Responses

What is the same and what is different about expressions and equations?

  • Same
  • both contain variables and numbers
  • bothcontain operations such as add, subtract, multiply and divide
  • Different
  • Expressions have no equal signs but equations always do

Task 2:The Mystery of the Unknown Quantity

  • Uses guess and check method to solve equations

Journal Prompt and Sample Response

1)Describe how the “equal” sign in the equation is like a balance.

An equal sign means that the value of the expression or quantity on the left side of the equation is the same as the value of the expression or quantity on the right side. For a weigh scale to remain balanced, the mass on the left side needs to be the same as the mass on the right side.

2)Describe how the “guess and check” method is used to solve an equation.

Solving an equation means finding the value of the unknown that makes the equation true. For example to solve 2a + 3 = 13, I might guess that a = 4 and then substitute 4 into the left side of the equation and evaluate.

2(4) + 3 = 8 +3 = 11. I see that this is close to but less than 13, so I try a larger value for a. Trying a = 5, I get 2(5) + 3 = 10 +3 = 13 Now I know that the solution to 2a + 3 = 4 is a = 5

3)Determine whether the solution to x - 3 = 4 is the same as the solution to

4 = x - 3. Explain.

Yes, the solutions are the same. By guess and check I see that

7 – 3 = 4. x = 7 is the solution to

x – 3 = 4. When I check with x = 7 in 4 = x – 3, I find it is also true that 4 = 7 – 3. I see from this that the expressions on the left side and the right side of an equation are interchangeable.

Action

Task 3: Rex and Tex Zero Pairs

  • Use zero pairs to solve equations
  • uses yellow for positive and red for negative
  • students can make their own algebra tiles
  • Algebra Tiles Template in Colour
  • Algebra Tiles Template in Black and White
  • some students may need additional support with their integer skills
  • Gap Closing Intermediate/SeniorTopic 3 Integers
  • Student Book
  • Facilitator's Guide
  • some students may need additional support solving equations
  • Gap Closing Intermediate/Senior Module 7 Solving Equations
  • Student Book
  • Facilitator's Guide

Journal Prompts and Sample Responses

1)Define “zero pairs”. This is also called the zero principle

Zero pairs are terms that are opposite, like 4 and -4, or 2x and -2x. Their sum equals zero

2)Draw pictures or create screenshots of the different types of zero pairs you saw. Be sure to label the tiles with their values

3)Describe what “isolate the variable” means

Isolate the variable means to get the variable by itself on one side of the equal sign.

4)What does it mean to check your solution? How do you check your solution?

To check your solution means to test if your answer is correct. Substitute the value of your answer into the equation in place of the variable. If this results in an equation that is true, then the solution is correct.

Discussion Notes

  • Students will:
  • understand what “isolating the variable “ means
  • recognize and use the zero principle
  • know how to check their solution
  • Common errors:
  • not keeping equality by performing the same operation to both sides of the equation
  • confusion of what to do when the variable is on the right side of the equation

Consolidation

Task 4:Virtual Algebra Tiles Practice

  • interactive, online tool for students to practice using algebra tiles

Journal Prompts and Sample Responses

1)How did you know when the equations you were modeling were in balance and ready to be solved?

The inequality sign in the middle turned into an equal sign.

2)How did you make zero pairs with this tool?

I addedtiles of the opposite sign to each side of the equation.

3)What happened when you dragged tiles in a zero pair onto each other?

The tiles disappeared.

Task 5:Algebra Tiles - More Practice

  • Students solve the given equations using their own algebra tiles
  • Students can use Mindomo to develop a Mind Map or a web showing the representations, and strategies to solve equations
  • Answers are provided

Task 6: Assignment 1 – Solving Equations Using Algebra Tiles

  • Posted with Unit
  • See sample Solutions in Teacher Notes posted on the vLE

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 6 Activity 2 Page 1 of 4