Algebra Introduction: Teacher Notes

Overview

In this activity students represent algebraic expressions using concrete materials and vice-versa.

Important Mathematical Ideas

  • A variable in an algebraic expression can be represented using a symbol or a letter.
  • A variable in an algebraic expression can represent a variety of values.
  • Algebraic expressions of degree 1, 2 or 3 can be represented geometrically using concrete materials.

Prior Knowledge

  • Familiarity with the vocabulary of algebra (e.g., algebra, variable, term, algebraic expression) as needed throughout the unit.
  • Representing statements (words) as algebraic expressions.
  • Using the zero principle.
  • Adding, subtracting, multiplying and dividing integers.

Common Misconceptions

  • An x-tile is a specific length rather than a variable length.
  • An x2-tile is a specific area rather than a variable area.
  • Confusing length and area

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

  • The zero principle is a critical aspect of this unit and it may be new learning for some students. Students may have trouble representing zero in many ways; e.g.,3+(+3),x + (-x)
  • 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., algebra, variable, term, algebraic expression, zero principle).
  • Additional resources Paying Attention to Algebraic Reasoning and Paying Attention to Algebraic Reasoning Adobe Presenter

Minds On

Task 1: Who Cares about AlgebraVideo

  • The video can be viewed as a whole class instead of individually
  • Before and after viewing, discuss why algebra is important
  • Responses could be posted on the class bulletin board

Journal Prompt and Sample Response

In your journal describe at least four examples you see in the video that answer the question, ’Whocares about algebra?'

I see that algebra can be used in to build equations which can be used for many things (e.g., making a computer, launching a rocket into space, getting oil out of the ground and designing a car).

Action

Task 2: AlgebraicExpressions Gizmo

  • This interactive tool allows students to review how to translate words to expressions and expressions to words
  • to use ministry licensed Gizmos teachers will need to set up a Class Code to create an account to give students a password
  • Students can work through the examples in pairs and justify their answers to one another
  • Consider posing various scenarios and having students write the associated algebraic expressions on their individual white boards. Since students may write their answers differently this provides opportunities for discussion (e.g., for ‘five more than a number', you can ask, “Are these the same or different: 5 + n; x + 5?”; or for ‘five less than a number', “Are these the same or different: 5 - n; x - 5?”)

Journal Prompt and Sample Response

In your journal summarize your learning from the Algebraic Expressions Gizmo.

I can translate a word phrase into an algebraic expression, (e.g., a number divided by 6 can be written as n ÷ 6). I can also translate an algebraic expression into a word phrase (e.g., n + 5 means a number increased by five).

Task 3: Discussion Prompt and Notes

  • Explain why, in the Algebraic Expressions Gizmo, ‘a number' is used in place of the variable. When is order important?
  • Students will:
  • understand that a variable can represent any number in an algebraic expression
  • acknowledge that with certain operations the order is important (i.e., n – 6 is not the same as 6 – n; x ÷ 4 is not the same as 4 ÷ x (non-commutative))

Task 4: Assignment 1 - Using the Zero Principle to Add Integers

  • students will solve integer addition problems using the zero principle
  • Integer Tiles Addition – an interactive learning activity from the National Library of Virtual Manipulatives
  • this website uses black for positive and red for negative
  • students need to pay attention to the colours being used for positives and negatives whenever they use a different resource
  • some students may need additional support with their integer skills
  • Gap Closing Intermediate/Senior Module 3 Integers
  • Student Book
  • Facilitator's Guide
  • A Concrete Introduction to the Abstract Concepts of Integers and Algebra using algebra tiles

Journal Prompts and Sample Responses

1)Find three different ways to create an answer of -2.

Answers will vary.

2)Describe how the zero principle is helpful when adding integers.

I dragged each of the red squares over to the black squares. One red and one black square equal zero; there were two red squares left when I was done. My answer is -2.

Task 5: Investigation – Algebra Tiles

  • Students will:
  • model algebraic expressions usingAlgebra Tiles: Modelling Expressions virtual algebra tiles
  • feedback is provided
  • copy screen shots of their work into their journal
  • A template is provided for students to make their own paper algebra tiles to use in this unit
  • Algebra Tiles Template in Colour or Algebra Tiles Template in Black and White
  • have students cut the tiles from the template and keep the tiles in a zip lock bag
  • Consider having students work through the exercises in pairs and justify their answers to one another

Journal Prompt and Sample Response

Do five problems at the Medium level and paste in your journal.

Task 6: Discussion Prompts and Sample Responses

1)Use your algebra tiles to represent the following:

  1. twice a number, increased by three
  1. twice a number that has been increased by three

2)An explanation of the similarities and differences between the two representations:

Both representations have two
x tiles and some unit tiles.

The second representation has twice as many unit tiles.

Discussion Notes

  • Solutions should include:
  • two different representations
  • an explanation of the similarity between the two representations
  • an explanation of the difference between the two representations
  • Common Errors:
  • both representations are the same – not seeing the difference in the language

Consolidation

Task 7:Algebra Tiles: Modelling Expressions Practice

  • Online algebra practice using virtual algebra tiles
  • answers are provided

Task 8:Assignment 2 – Representing Expressions with Algebra Tiles

  • Posted with Unit
  • See sample Solutions in Teacher Notes posted on the vLE
  • Rather than submit the assignment, students can do the assignment in pairs on chart paper

Task 9: 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 1 Page 1 of 5