Expressions: Simplify

Objective  I will simplify algebraic expressions 

Essential Question Why are the expressions 2(x - 1) + 3(x - 1) and 5(x - 1) equivalent?

Develop the Concept 

How many wheels are they in the NYC parking lot?

• If f stands for vehicles with four wheels, write an expression for the number of wheels on 4-wheel vehicles. 
  
• If t stands for vehicles with two wheels, write an expression for the number of wheels on 2-wheel vehicles. 
• Write an expression that represents the total number of wheels in the parking lot. 

Objective  I will simplify algebraic expressions 

Essential Question Why are the expressions 2(x - 1) + 3(x - 1) and 5(x - 1) equivalent?

Lesson Vocabulary  

term
like terms  
constant
simplest form
expression

Modeling Expressions

Percent

Percents Part 2

Visual Percents

http://www.mathplayground.com/visualpercent.html

Essential Questions


 How can two amounts of change be the same but the percents of change be different?




 Which method of finding the total price of a bill with a 20% tip do you prefer?
 What are two methods you could use to find the sale price of an item that is discounted by a percent? How can you use a formula to find simple interest?

Percents

This chapter focuses on content from the Ratios and Proportional Relationships (RP) domain and addresses the following grade 7 standards: 7.RP.2, 7.RP.2, 7.RP.3, 7.EE.2, 7.EE.3.

Essential Question  How can percent help you understand situations involving money?

How do you find the percent of a number?

Find percent of a number by writing a percent as a fraction

Will 5% of 300 be greater than or less than 300? Why?

What is 5% written as a fraction in simplest form?

 What expression can be used to find 1/20  of 300? 

Find percent of a number by writing a percent as a decimal

Will 25% of 180 be greater than or less than 180? Why?

What is 25% written as a decimal?

How would you find 25% of 180?

Use percents greater than 100%

Will 120% of 75 be greater than or less than 75? Why?

What is 120% written as a fraction?

What expression is used to find 120% of 75?

Exit Ticket

Proportional Reasoning Summative Task

Proportional Reasoning Summative Task.

Length: 3 days
Due: Friday December 12, 2014

You will need to save the following documents and save them in your google docs.  Make sure you give each document the propor name.

1. Summative Task
2. Report Outline
3. Rubric

Task

Unit 2 Proportional Reasoning Summative Task from Jessica Garcia

Report Outline

Throw a dinner party report from Jessica Garcia

Rubic

Intro into Percents and test make-ups

Percents

This chapter focuses on content from the Ratios and Proportional Relationships (RP) domain and addresses the following grade 7 standards: 7.RP.2, 7.RP.2, 7.RP.3, 7.EE.2, 7.EE.3.

Essential Question

Each chapter has an Essential Question that keeps students focused on the big idea of the chapter. For Chapter 2, the Essential Question is "How can percent help you understand situations involving money?"

Chapter Vocabulary 

discount (Lesson 7)
gratuity (Lesson 6)
markdown (Lesson 7)
markup (Lesson 6)
percent equation (Lesson 4)
percent error (Lesson 5)
percent of change (Lesson 5)
percent of decrease (Lesson 5)
percent of increase (Lesson 5)
percent proportion (Lesson 3)
principal (Lesson 8)
sales tax (Lesson 6)
selling price (Lesson 6)
simple interest (Lesson 8)
tip (Lesson 6)

Proportional and Reasoning Book Test.  Download for corrections.




P

Direct Variation

Common Core State Standards

7.RP.2   Recognize and represent proportional relationships between quantities.

7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Essential Question How can you determine if a linear function is a direct variation from an equation

Objective use direct variation to solve problems

Lesson Vocabulary

direct variation

constant of variation

constant of proportionality