In our basic algebra unit, you learned that a variable is a letter that represents an unknown value; and a coefficient is a number that is multiplied by a variable. A solution is the value for the variable that makes the equation or inequality true. To solve for the variable, you must isolate it (get it by itself). To undo operations, you perform inverse or opposite operations. You must perform the same operations to both sides of the equation in order to keep them equal to one another. In the advanced algebra unit, you will solve problems that involve combining like terms, applying the distributive property and moving variables to one side of an equation.

### Monday, November 6

Common Core Standards and Extended Standards

8.EE.7 Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form × = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

8.EE.C.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

EE.68.6a Solve a 1-step linear equation (e.g., y + 3 = 5).

EE.68.3a Solve an algebraic expression or inequality involving variables.

EE.68.1b Apply properties of operations to generate equivalent expressions (e.g., 3(2 + x) = 6 + 3x; y + y + y = 3y).

EE.68.3c Solve an algebraic expression using concrete objects.

Student Objectives

I can solve multi-step equations.

Bellwork

Students will complete *Math Minute 37*.

Lesson (Special Solutions/Rational Coefficients/Negative Distributions)

1. Go over homework.

2. Journal entry and demonstration: solving equations with negatives and equations with rational coefficients

3. Guided practice with dry erase boards and markers: multi-step equations with rational coefficients and negative distributions

4. Journal entry and demonstration: examples of equations with infinite solutions and no solutions

5. Cooperative small group practice: equations with rational coefficients & negative distributions footloose challenge (task cards)

6. Independent practice: special solutions create a face

7. Independent practice: solving equations with negative distributions/rational coefficients worksheet, special solutions worksheet

8. Blended learning: Like Terms Matching, Combining Like Terms Practice Quiz, Combining Like Terms Practice, Matching Action, Like Terms Invaders, linear equations with variables on both sides, Hot Math Practice Problems

Closing

Journal entry/writing prompt: “List and describe at least 3 specific skills and/or vocabulary terms you have learned in this unit. Include examples.”

Homework

Finish the special solutions worksheet. Finish the equations with rational coefficients/negative distributions worksheet. On Wednesday, there will be a test over advanced equations. Work on the IXL module 7 to-do list.

### Tuesday, November 7

Common Core Standards and Extended Standards

8.EE.7 Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form × = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

8.EE.C.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

EE.68.6a Solve a 1-step linear equation (e.g., y + 3 = 5).

EE.68.3a Solve an algebraic expression or inequality involving variables.

EE.68.1b Apply properties of operations to generate equivalent expressions (e.g., 3(2 + x) = 6 + 3x; y + y + y = 3y).

EE.68.3c Solve an algebraic expression using concrete objects.

Student Objectives

I can solve multi-step equations.

Bellwork

Students will complete *Math Minute 38*.

Lesson (Advanced Equations Review)

1. Go over homework.

2. Advanced equations review

Closing

Exit ticket:

Homework

Tomorrow, there will be a test over advanced equations. Work on the IXL module 7 to-do list. The advanced equations review sheet is due tomorrow.

Links

Check out the instructional videos on my “solving equations” links page. You can locate this page by typing “solving equations” into the search box on any page of my website. There are also links in the module 7 folder of our Schoology course.

### Wednesday, November 8

Common Core Standards and Extended Standards

8.EE.7 Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form × = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.EE.68.6a Solve a 1-step linear equation (e.g., y + 3 = 5).

8.EE.C.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

EE.68.3a Solve an algebraic expression or inequality involving variables.

EE.68.1b Apply properties of operations to generate equivalent expressions (e.g., 3(2 + x) = 6 + 3x; y + y + y = 3y).

EE.68.3c Solve an algebraic expression using concrete objects.

Student Objectives

I can solve multi-step equations.

Bellwork

Students will complete *Math Minute 39*.

Lesson (Advanced Equations Unit Test)

1. Go over homework. Answer questions.

2. Brief review of key concepts & skills

3. Advanced equations unit test

4. STAR math benchmark

5. Early finishers: work on IXL module 3 to-do list

Closing

n/a

Homework

Work on the IXL module 3 to-do list.

The remainder of this week will be devoted to learning about proportional relationships.

A proportional relationship can be described as a relationship between two variables in which the rate of change is constant. This is also called direct variation. The inputs or x-values (in this case, minutes) are called domains, and the outputs or y-values (in this case, feet) are called ranges. In the chart on the left above, we multiply the number of minutes by 3 to get the number of feet traveled. This rate of change remains constant in the chart on the left. The graph of a proportional relationship is a straight line through the origin.. The slope of the line is constant. Proportional relationships model a wide range of situations including measurement conversions (ex. feet to inches). The equation for a proportional relationship can be written in the form of *y=kx*, where *k* is the rate of change, slope, or constant of proportionality.

### Thursday, November 9

Common Core Standards and Extended Standards

8.EE.6 Understand the connections between proportional relationships, lines, and linear equations.

Create and solve ratios.

Represent proportional relationships.

Use ratios to solve real-world problems.

Ratios and proportional relationships can be used to determine unknown quantities.

8.F.4 Use functions to model relationships between quantities.

Specific input will yield specific output.

Compare/contrast two different input/output relationships.

Equations of linear and non-linear functions

Construct a linear graph using a table or equation.

Construct a linear graph as described verbally.

Student Objectives

Given a graph, chart, or equation, I can determine if the relationship between the values is proportional.

Given a chart of values representing a proportional relationship, I can identify the pattern (the rate of change/constant of proportionality) between the outputs (x-values) and inputs (y-values).

Bellwork

Students will complete *Math Minute 40*.

Lesson (Introduction to Proportional Relationships/Lesson 3.1)

1. Student exploration: Mine Shaft 1 Puzzle from Lure of the Labyrinth

2. Journal entry: vocabulary for the lesson-ratio and proportion (stop at proportional relationship)

3. Modified concept attainment lesson (examples and non-examples, emphasis on essential characteristics: “Proportional Relationships Characteristics Exploration” in Smart Notebook. Students will completed a guided notes form as this lesson is presented.

4.

5. Team/partner practice: Comparing Rates of Change War

6. Independent practice: *GoMath* page 74

Closing

Homework

Complete page 74 in your *GoMath* workbook. There will be a brief quiz over proportional relationships on Tuesday. It will cover tables, graphs, and equations. Students will need to be able to identify the rate of change/slope, input, output, equation, and graph when given a table of values.

Links

Check out the instructional videos on my proportional relationships links page. You can locate this page by typing “proportional relationships” into the search box on any page of my website. Work on the IXL module 3 to-do list.

### Friday, November 10

Common Core Standards and Extended Standards

8.EE.6 Understand the connections between proportional relationships, lines, and linear equations.

Create and solve ratios.

Represent proportional relationships.

Use ratios to solve real-world problems.

Ratios and proportional relationships can be used to determine unknown quantities.

8.F.4 Use functions to model relationships between quantities.

Specific input will yield specific output.

Compare/contrast two different input/output relationships.

Equations of linear and non-linear functions

Construct a linear graph using a table or equation.

Construct a linear graph as described verbally.

Student Objectives

Given a graph, chart, or equation, I can determine if the relationship between the values is proportional.

Given a chart of values representing a proportional relationship, I can identify the rate of change.

Bellwork

Students will complete *Math Minute 41*.

Lesson (Representing Proportional Relationships/Lesson 3.1)

1. Go over homework.

2. Generate interest: real-world video from *GoMath* page 67

3. Guided practice with real-world application: “Who has the best job?” task from Illustrative Mathematics

4. Direct instruction and guided notes: proportional relationships interactive notes

5. Guided practice: proportional relationships text messaging plans task

6. Cooperative practice: proportional relationships sorting activity

7. Independent practice: HRW homework assignment 3.1

Closing

“Peaches and Plums” task from Illustrative Mathematics

Homework

Complete pages 75 and 76 in your math workbook. There will be a brief quiz over proportional relationships on Tuesday. It will cover tables, graphs, and equations. Students will need to be able to identify the rate of change/slope, input, output, equation, and graph when given a table of values. Work on the IXL module 3 to-do list.

Links

Check out the instructional videos on my proportional relationships links page. You can locate this page by typing “proportional relationships” into the search box on any page of my website.