Outcome #2

Algebraic Expressions and Equations

Description

This outcome covers the following:

Like Terms
Distributive Property
Solving Equations
Creating expressions/equations based on words and visual representations
Finding Points of Intersection of 2 lines (using Comparison)

Curriculum Expectations: C1.1, C1.2, C1.3, C1.4, C1.5

Emerging

I can create simple expressions and generalize relationships expressed in words, numbers and visual representations in various context.

I can substitute values into an expression and solve.

I can solve one step equations and simple two step equations.

Notes/Examples:

Creating expressions based on visual representations will link to Lines Outcome
Eg: Create an expression using the following pattern (shown below)

Equations such as: 4x = 24 and 3x + 1 = 16

Developing

I can simplify algebraic expressions by applying properties of operations of numbers (collecting like terms).

I can solve simple two step equations with context.

Notes/Examples:

A cost to rent a paddle boat at a campground is $3 per hour plus a flat fee of $5. How many hours can Diaz rent the boat if he has $20?

Proficient

I can solve difficult two step equations with context and verify the solution

I can simplify algebraic expressions by applying properties of operations of numbers (distributive property).

Notes/Examples:

Eg. Solve for x, and verify your solution:

3x + 5 + 4x = 19

Sample Question: Give equations of 5 lines. Which lines does the point (x, y) satisfy (show by substitution) and then verify by graphing that you were correct.
Sample Question: Show how expanding and simplifying can help graph a line (consider showing students slope/point form here)

y = 3(x - 4) + 2

= 3x - 12 + 2

= 3x - 10

Exceeding

I can create and solve equations using the distributive property, with variables on both sides, and unit fractions, and verify their solutions.

Notes/Examples:

Sample Problem: Determine the POI of two lines (Using Comparison Method)
Sample Problem: The equal sides of an isosceles triangle are 3 m shorter than the base. If the perimeter of the triangle is 42 m, how long is each side?
Examples: Solve for x and verify your answer.

Sample Problem: The perimeter of the triangle is 34 cm. Determine the side lengths of the triangle.

Extending

I can solve multistep equations (with and without fractions, distributive property, variables on both sides) and verify their solutions.

Notes/Examples:

Consider linking this level to other outcomes in the course.
Questions should require deep understanding of the outcome and may require multiple steps to solve.
Eg. Solve for x:

Sample Assessments

(Approaching Standard)

(Reaching Standard)

(Reaching Standard -> Extending Understanding)

Lesson Ideas

Solve Me Mobiles

Visual puzzles that help teach solving equation skills (without actually writing the equation).

Consider using these as warm up activities prior to officially teaching equations.

Visual Patterns

This website provides lots of examples of both linear and non-linear patterns. Use them to help generate algebraic expressions.

Consider using some of these as warm up activities prior to diving into this Outcome.

(How do you see the pattern growing? What stays the same?)

Solving Equations Question Progression

These questions work well as a Thinking Classroom activity

Algebra Without Numbers

3 Puzzles that can be used to practice algebraic skills

Collecting Like Terms Lesson

This is a "bare bones" smartboard lesson on collecting like terms, to be tailored to suit your class

Version 2 - this has more details using the algebra tiles

Calendar Algebra Trick

Wow the class with your this math trick.

Then show them how it works with a little algebra. This will require representing a number on the calendar with a variable and collecting like terms.

Rats Game

This is a great game for any topic.

This version is an algebra review.

Questions

Smartboard File

Algebra Review Activity

Option 1: Where's Waldo?

Option 2: QR Code Scavenger Hunt

Instructions and Documents: Instructions

Website: Where's Waldo?

Algebraic Expressions and Equations - Traffic Light Activity

A series of questions with different difficulty levels. Suggested to be used in Pass 2, at the end of the outcome. Final answers are given on the last page.

Questions

Multi-step Equations Task

This task can be delivered in groups or as a gallery walk. Students can jump in at the level they are at and progress to more difficult questions.

Google Doc version

PDF version

A classroom activity that can be used to reinforce adding like terms. In this whole class activity, students take turns choosing polynomials that will create the smallest coefficients possible. But watch out for player "injuries" and "trades"!

Teacher Notes

Printables

Warm Up Intro Equation Questions

The intent of these questions is to provide warm up questions in your class in advance of starting the algebra unit.

Use a question or two each day to get students thinking about algebraic concepts and gradually build skills by using picture/equation challenges.

Polynomial Expressions

This activity can be used to help students practice simplifying algebraic expression. This resource is adapted from resources found on the open middle website developed by Robert Kaplinsky.