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K12MATH009: Algebra I

Unit 1: Connecting Patterns and Functions   Suppose you want to lose weight because you currently weigh 115 pounds and you want to wrestle in the 105-pound weight class. If you knew you could lose 3.5 pounds each week, an expression would assist in creating a weight-loss strategy to reach your goal.
 
Imagine you and your friends are talented at making dresses and you want to start your own business. You are all very interested in earning money; however, you are a little nervous since the start-up fees and costs to make each dress are very expensive. Your job is to determine a price to charge for each dress that would be fair to the customer but would still earn you a profit. Luckily, one of your friend’s fathers has offered his basement to use as a workshop for free, so you will not need to worry about renting shop space. It will cost approximately $25 per dress for materials, which you can purchase through a wholesale company. Before you determine what to charge for each dress, you must test a couple of different prices and determine which one will be most appealing to your market but still be enable you to earn a decent profit. A variety of strategies within this unit could assist you in accomplishing this endeavor.

This unit covers expressions, displays, basic equations and inequalities, functions, and units.

Unit 1 Time Advisory
Completing this unit should take you approximately 10.5 hours.

☐    Subunit 1.1: 50 minutes

☐    Subunit 1.2: 3 hours

☐    Subunit 1.2.1: 15 minutes

 

☐    Subunit 1.2.2: 15 minutes

☐    Subunit 1.2.3: 40 minutes

☐    Subunit 1.2.4: 30 minutes

☐    Subunit 1.2.5: 80 minutes

☐    Subunit 1.3: 1 hour and 50 minutes

☐    Subunit 1.3.1: 70 minutes

☐    Subunit 1.3.2: 40 minutes

☐    Subunit 1.4: 45 minutes

☐    Subunit 1.5: 20 minutes

☐    Subunit 1.6: 3.75 hours

☐    Subunit 1.6.1: 15 minutes

☐    Subunit 1.6.2: 50 minutes

☐    Subunit 1.6.3: 15 minutes

☐    Subunit 1.6.4: 15 minutes

☐    Subunit 1.6.5: 25 minutes

☐    Subunit 1.6.6: 75 minutes

 

☐    Subunit 1.6.7: 30 minutes

Unit1 Learning Outcomes
Upon successful completion of this unit, you will be able to: - utilize units as a way to determine precision of a problem. - choose and interpret the scale of a data display. - classify parts of an expression. - write and evaluate an expression. - write an equation and inequality. - determine whether a relation is a function. - determine the domain and range of a function. - write an equation in function notation.

Standards Addressed (Common Core): - CCSS.Math.Content.HSN-Q.A.1 - CCSS.Math.Content.HSN-Q.A.3 - CCSS.Math.Content.HSA-SSE.A.1 - CCSS.Math.Content.HSA-SSE.A.2 - CCSS.Math.Content.HSA-CED.A.1 - CCSS.Math.Content.HSA-CED.A.3 - CCSS.Math.Content.HSF-IF.A.1 - CCSS.Math.Content.HSF-IF.A.2 - CCSS.Math.Content.HSF-IF.A.3 - CCSS.ELA-Literacy.RST.9-10.2 - CCSS.ELA-Literacy.RST.9-10.4

1.1 Order of Operations   If Dominic goes grocery shopping and buys 2 bags of oranges for $5.99 each and a loaf of bread for $1.50 and has a coupon for the bread for $0.50 and then has to pay 6% tax on the food, the order of which these numbers are used to compute the bill is very important. This is the order of operations. If everyone did not follow the correct order, a variety of amounts would be calculated and the cashier would not know how much the customer would need to pay.

The order of operations is the foundation for almost every mathematical topic covered in this course, as well as other future mathematical courses. It helps serve as the one way of interpreting mathematical statements so that everyone performs the operations in the correct order as well in the correct direction.

Subunit 1.1 covers the rules of the order of operations when performing a problem manually and then suggests learning how to check a solution using a calculator.

  • Explanation: Henrico County Public Schools’s “Module – Expressions: Lesson 2: Order of Operations” Link: Henrico County Public Schools’s “Module – Expressions: Lesson 2: Order of Operations” (HTML and PPT)
     
    Instructions: Please click on the link above and then click on “Notes: Order of Operations.” This is a PowerPoint presentation that details the rules of the order of operations, provides some guided practice, and a self-reflection quiz that appears at the end. Checking your answers on the calculator will ensure that you also know how to enter problems using technology. If you are struggling with this practice, at the same link you can complete the order of operations worksheet, view the study guide, or complete the additional order of operations documents. Some of these documents do not provide an answer key, but you can check your answers on the calculator.

    Completing this PowerPoint exercise itself should take approximately 20 minutes.

    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Checkpoint: Henrico County Public Schools’s “Module – Expressions: Lesson 2: Order of Operations” Link: Henrico County Public Schools’s “Module – Expressions: Lesson 2: Order of Operations” (HTML)
     
    Instructions: Please click on the link above and then click on “ExamView Quiz: Order of Operations.” When completed, this can be automatically scored with a click of the “Check Your Work” button. Once scored, the site will also provide the correct answers for any that were wrong. Once the quiz is scored, you should rework the problems by using the “Retake” button or retry the problems using the answers and working backward. Once corrected, you could start the quiz again or just attempt to rework the problems you answered incorrectly.
     
    Finishing this quiz should take approximately 30 minutes.

    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.2 Expressions   Algebraic expressions are how we speak on a daily basis. “I’m two years older than my sister” translates to 2 + x where x is the age of the sister. “My paycheck was $60 less than last week” translates to x – 60 where x is the amount of last week’s paycheck. “The bill from the restaurant is being split amongst four people” can be translated to x / 4 where x is the cost of the bill. “I have to double the recipe for the amount of people I have to serve” can be translated to 2x where x is the amount of the original recipe.

Even though variables mixed with numbers can be intimidating at times, those variables, numbers, and operations, are a part of our daily life and conversation and can help us solve many problems.

1.2.1 Definition of Expression   Subunit 1.2.1 explains what makes up an expression and the possible ways of viewing expressions using certain operations. This section will assist you in writing equations and inequalities in later sections and units.

  • Explanation: Henrico County Public Schools’s “Module – Expressions: Lesson 1: Variables and Expressions” Link: Henrico County Public Schools’s “Module – Expressions: Lesson 1: Variables and Expressions” (HTML and PPT)
     
    Instructions: Please click on the link above and then click on “Notes: Translating Expressions.” Watch the first five slides of this PowerPoint presentation, which provides a quick explanation to what is included in an expression.
     
    Watching this PowerPoint exercise should take approximately 5 minutes.

    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Illustrative Mathematics’s “Delivery Trucks” Link: Illustrative Mathematics’s “Delivery Trucks” (HTML)
                                                      
    Instructions: Please click on the link above to complete this task, which allows you to explore the structure of algebraic expressions in the context of a real-world example. The solution to the task is found toward the bottom of the page.
     
    Completing this task should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.2.2 Parts of an Expression   Simplifying by combining like terms is a process we use daily without realizing that algebra is involved. When cleaning out the dishwasher, we put the dishes in one spot and the silverware in another spot and we even break it down more, the bowls with the bowls and the forks with the forks.
 
If you work at a daycare and are chaperoning a trip to McDonald’s where the toddler class has 5 boys and 7 girls and the primary class has 2 boys and 9 girls, you would tell the cashier when ordering the happy meals that you have 7 boys and 16 girls, so that you get the appropriate toy for each child.
 
There is no difference when viewing an expression with variables and numbers. The variables are like representing the boys and the girls and the coefficients are representing the amount of each. The plus sign represents the amount of happy meals I have so that McDonald’s knows how many need to be included in my bill.
 
Subunit 1.2.2 focuses on the rules of combining like terms to simplify an expression while still utilizing the order of operations learned in a previous section.

  • Explanation: Khan Academy’s “Combining Like Terms” Link: Khan Academy’s “Combining Like Terms” (YouTube)
     
    Instructions: Please click on the link above and then play the video, which explains the beginning stages of combining like terms. Pay attention to what pieces are part of the expressions as well as the pictures representing the variables.
     
    Watching the video takes approximately 5 minutes.
     
    Standards Addressed (Common Core):

     Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Illustrative Mathematics’s “Mixing Candies” Link: Illustrative Mathematics’s “Mixing Candies” (HTML)

    Instructions: Please click on the link above and complete the task, which allows you to explore the meaning associated with pieces of an expression. The solution to the task is found toward the bottom of the page.
     
    Completing this task should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.2.3 Evaluating an Expression   In a shopping ad for Kohl’s, it states that the sale price for all jeans is $25 and the sale price for all shoes is $30. I could easily calculate that if I want 4 pairs of jeans and 2 pairs of shoes, I would spend $160 without tax. I just evaluated an expression because the jeans could be x and the shoes could be y to create 25x + 30y where I plug in how many I want of each for the variables.
 
Your everyday life includes expressions whether or not you are writing them down using variables, numbers, and operations.
 
Subunit 1.2.3 will show you how to evaluate an expression and then simplify if possible using the order of operations.

  • Explanation: Khan Academy’s “Example: Evaluating an Expression” Link: Khan Academy’s “Example: Evaluating an Expression” (YouTube)
     
    Instructions: Please click on the link above and then play the video, which explains how to substitute values into an expression for a specified variable.
     
    Watching this video takes approximately 5 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Did I Get This? Activity: Khan Academy’s “Evaluating Expressions in One Variable” Link: Khan Academy’s “Evaluating Expressions in One Variable” (HTML)
     
    Instructions: Please click on the link above and then answer the problems provided. This site will automatically inform you after each problem if you are correct with the click of the “Check Answer” button. Try problems until you get five correct answers in a row without using the “I’d Like a Hint” button.
     
    Completing these practice problems should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Explanation: Khan Academy’s “Example: Evaluating Expressions with 2 Variables” Link: Khan Academy’s “Example: Evaluating Expressions with 2 Variables” (YouTube)
     
    Instructions: Please click on the link above and then play the video, which explains how to substitute values into an expression that has more than one variable.
     
    Watching this video should take approximately 5 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Did I Get This? Activity: Khan Academy’s “Evaluating Expressions in 2 Variables” Link: Khan Academy’s “Evaluating Expressions in 2 Variables” (HTML)
     
    Instructions: Please click on the link above and then answer the problems provided. This site will automatically inform you after each problem if you are correct with the click of the “Check Answer” button. Try problems until you get five correct answers in a row without using the “I’d Like a Hint” button.
     
    This practice should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Illustrative Mathematics’s “Animal Populations” Link: Illustrative Mathematics’s “Animal Populations” (HTML)
     
    Instructions: Please click on the link above and then complete the task, which allows you to explore evaluating an expression without any specified numbers. The solution to the task is found toward the bottom of the page.
     
    Completing this task should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.2.4 Simplifying an Expression   Think back to the McDonald’s scenario. If you know how many boys’ Happy Meals you need and you know how many girls’ Happy Meals you need and you know the cost of each Happy Meal, a distribution expression, cost (boys’ amount + girls’ amount) is made. This type of algebraic structure is used daily even if you are not writing variables on paper.
 
In subunit 1.2.4, you will combine some of the topics learned in previous sections and classes, such as the order of operations, combining like terms, and the distributive property, to simplify expressions.

  • Explanation: Khan Academy’s “Combining Like Terms and the Distributive Property” Link: Khan Academy’s “Combining Like Terms and the Distributive Property” (YouTube)
     
    Instructions: Please click on the link above and then play the video, which explains how to simplify an expression by combining like terms and using the order of operations.
     
    Watching this video should take approximately 5 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Did I Get This? Activity: Khan Academy’s “Combining Like Terms with Distribution” Link: Khan Academy’s “Combining Like Terms with Distribution” (YouTube)
     
    Instructions: Please click on the link above and then answer the problems provided. This site will automatically inform you after each problem if you are correct with the click of the “Check Answer” button. Try problems until you get five correct answers in a row without using the “I’d Like a Hint” button.
                                                   
    Completing this activity should take approximately 15 minutes.
     
    Standards Addressed (Common Core):

     Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Illustrative Mathematics’s “Taxes and Sales” Link: Illustrative Mathematics’s “Taxes and Sales” (HTML)
     
    Instructions: Please click on the link above and complete the task, which allows you to explore different scenarios of a real-world situation using an expression and the order of operations. The solution to the task is toward the bottom of the page.
     
    Completing this task should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.2.5 Writing an Expression   When you go to a store, you get a receipt to explain your charges, which is computed by the program installed in the cash register that has the expression needed to be used to obtain your total sales amount. Expressions are all around us in the daily activities of our lives.
 
In subunit 1.2.5, you will learn how to translate words into a mathematical expression.

  • Explanation: Henrico County Public Schools's “Module – Expressions: Lesson 1: Variables and Expressions” Link: Henrico County Public Schools’s “Module – Expressions: Lesson 1: Variables and Expressions” (PPT and PDF)
     
    Instructions: Please click on the link above and then click on “Notes: Translating Expressions.” This is a PowerPoint presentation that details the steps in translating words or numbers into an expression, provides some guided practice, and then offers a self-reflection quiz at the end. Begin with slide 6. If you are struggling with this practice, you can view the “Words for Operations” PDF, complete the Variables and Expressions Worksheet available in a word document or PDF, or view the Variables and Expressions Study Guide available in a word document or PDF. The worksheet and study guide do not have an answer key, but there is enough assistance through this site to guide you so that you could use these as supplemental practices.
     
    Completing this PowerPoint exercise should take approximately 20 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Checkpoint: Henrico County Public Schools’s “Module – Expressions: Lesson 1: Variables and Expressions” Link: Henrico County Public Schools’s “Module – Expressions: Lesson 1: Variables and Expressions” (HTML)
     
    Instructions: Please click on the link above and then click on “ExamView Quiz: Translating Expressions.” When completed, this can be automatically scored with a click of the “Check Your Work” button. Once scored, the site will also provide the correct answers for any that were wrong. Once the quiz is scored, you should rework the problems by using the “Retake” button or retry the problems using the answers and working backward. Once corrected, you could start the quiz again or just attempt to rework the problems you answered incorrectly.
     
    Finishing this quiz should take approximately 60 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.3 Unit Analysis  

When asked for the temperature, we use an answer such as 60 degrees; when asked how much something costs, we respond with something such as 60 dollars; when asked for how fast we were driving, we say something like 60 miles per hour. We attach units to our responses.

 

Many problems involve determining a variable that is representing an unknown value, so it is important to consider what the answer represents. The same applies when viewing graphs because they help us visualize data. To ensure everyone views the data the same, it is important to label the graphs’ axes and their scales. 

1.3.1 Converting Units Using Dimensional Analysis   If you were trying to purchase carpet for your bedroom and measured your floor in feet, but when you went to the store, the dimensions were posted in inches, you would have to convert to see how much carpet you had to purchase. Sometimes the units you have are not the units that will help you solve a problem. In these cases, you have to convert to the units needed.
 
In subunit 1.3.1, you will learn how to convert units using a horizontal analysis method. This method is used a lot in chemistry, so in the video, the presenter will reference to this subject.

  • Explanation: Education Portal’s “Unit Conversion and Dimensional Analysis” Link: Education Portal’s “Unit Conversion and Dimensional Analysis” (Flash)
     
    Instructions: Please click on the link above and then click on the video tab. This video explains how to convert units using dimensional analysis. A calculator can be used to perform the calculations. While watching the video, you should pause it to attempt the problems yourself. You can use a calculator to perform the calculations.
     
    Watching this video should take approximately 20 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Checkpoint: Education Portal’s “Unit Conversion and Dimensional Analysis” Link: Education Portal’s “Unit Conversion and Dimensional Analysis” (HTML)
     
    Instructions: Please click on the link above and then click on the quiz tab. Answer the five provided quiz questions. Choose your answer and click “Check Answer.” If correct, click “Next,” and if incorrect, you have two options: change your answer and click “Check Answer” or click on “Watch The Correct Answer” to receive a hint. You can use a calculator to perform the calculations.
     
    Completing this practice quiz should take approximately 20 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Checkpoint: The Community College of Baltimore County’s “Practice Problems on Unit Conversion Using Dimensional Analysis (Factor Label Method)” Link: The Community College of Baltimore County’s “Practice Problems on Unit Conversion Using Dimensional Analysis (Factor Label Method)” (PDF)
     
    Instructions: Please click on the link above and answer the practice problems provided. Worked out solutions are included at the end of the document. You can use a calculator to perform the calculations.
     
    Working through these practice problems should take approximately 30 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.3.2 Significant Digits   In math and science, exaggerating a number’s accuracy can lead to errors. If you go to the store and the bill is $4.07, you can’t just give the cashier $4.00 and say you rounded the bill. If you go to the home improvement store and need 35.45 yards of carpet, you won’t just buy 35 yards. Carefully providing accurate measurements and calculations is a concept we have to use in real-world situations. In subunit 1.3.3, you will learn the importance of numbers in a topic called significant digits.

  • Explanation: Suite 101’s “The Importance of Significant Digits” Link: Suite 101’s “The Importance of Significant Digits” (HTML)
     
    Instructions: Please click on the link above and read the article on the importance of significant digits.
     
    Reading this article should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Explanation: Khan Academy’s “Significant Figures” Link: Khan Academy’s “Significant Figures” (YouTube)
     
    Instructions: Please click on the link above and then play the video, which explains how to determine how many significant digits are in a given number.
     
    Watching this video should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Explanation: Khan Academy’s “More on Significant Figures” Link: Khan Academy’s “More on Significant Figures” (YouTube)
     
    Instructions: Please click on the link above and then play the video, which continues the explanation on determining how many significant digits are in a given number.
     
    Watching this video should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Did I Get This? Activity: Khan Academy’s “Significant Figures” Link: Khan Academy’s “Significant Figures” (HTML)
     
    Instructions: Please click on the link above and then answer the problems provided. This site will automatically inform you after each problem if you are correct with the click of the “Check Answer” button. Try problems until you get five correct answers in a row without using the “I’d Like a Hint” button.
     
    Completing these practice problems should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.4 Writing Equations   Three plus two is five. The bill is $43.00 plus a tip of $7.00 is $50.00. We are surrounded by equations, and even though we don’t walk around all the time writing equations in the form of variables and numbers, we are using them in our daily activities.
 
In subunit 1.4, you will use key terms and knowledge of expressions to expand on writing equations.

  • Explanation: HippoCampus’s “Algebra I – An Open Course" Link: HippoCampus’s “Algebra I – An Open Course” (HTML)
     
    Instructions: Please click on the link above and then click on “Algebra 1 – An Open Course (2011) under the “Presentations” tab. Then click on “Writing Expressions and Equations” under “Solve Linear Equations.” Then play the video, which shows how to set up an equation using a real-world example.
     
    Watching this video should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: HippoCampus's “Algebra I – An Open Course” Link: HippoCampus’s “Algebra I – An Open Course” (HTML)
     
    Instructions: Please click on the link above and then click on “Algebra 1 – An Open Course (2011) under the “Worked Examples” tab. Then click on “Writing Expressions and Equations 1” under “Solve Linear Equations.” Then play the video, which contains examples of writing equations. While watching the video, you should pause it to attempt the problems yourself. You can use a calculator to perform the calculations.
     
    Watching this video and working through the problems should take approximately 15 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: HippoCampus’s “Algebra I – An Open Course” Link: HippoCampus’s “Algebra I – An Open Course” (HTML)
     
    Instructions: Please click on the link above and then click on “Algebra 1 – An Open Course (2011)” under the “Worked Examples” tab. Then click on “Writing Expressions and Equations 2” under Solve Linear Equations.” Then play the video, which contains examples of writing equations. While watching the video, you should pause it to attempt the problems yourself. You can use a calculator to perform the calculations.
     
    Watching this video and working through the problems should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Checkpoint: The Mathematics Common Core Toolbox’s “Isabella’s Credit Card” Link: The Mathematics Common Core Toolbox’s “Isabella’s Credit Card” (HTML)
     
    Instructions: Please click on the link above, then click on “High school tasks,” and then click “Isabella’s credit card.” At the top of the page, click on “Part a,” then “Part b,” then “Part c.” Directions for each task are at the top of the page and the site will provide a score if you are correct. There is also a scoring button at the top of the page that you can click on for assistance in case you cannot determine the correct answers.
     
    Completing this task should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.5 Writing Inequalities   We speak in inequalities on a daily basis. “I spent over $100 at the store” can be translated to x > 100; “there needs to be five or more students signed up for the ski trip or it will be cancelled” can be translated to x >5; “you have to be less than 40 pounds to get on a children’s ride” can be translated to x < 40; and “you can only miss 4 or less points to earn an A” can be translated to x < 4.
 
In subunit 1.5, you will use your skills in writing equations to write inequalities. 

  • Activity: HippoCampus’s “Algebra I – An Open Course” Link: HippoCampus’s “Algebra I – An Open Course” (HTML)
     
    Instructions: Please click on the link above and then click on “Algebra 1 – An Open Course (2011)” under the “Presentations” tab. Then click on “Writing and Using Inequalities” under “Analyze, Solve, and Graph Inequalities.” Then play the video, which explains the concept of inequalities and the steps in setting up an inequality.
     
    Watching this video should take approximately 5 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: HippoCampus's “Algebra I – An Open Course” Link: HippoCampus's “Algebra I – An Open Course” (HTML)
     
    Instructions: Please click on the link above and then click on “Algebra 1 – An Open Course (2011)” under the “Worked Examples” tab. Then click on “Writing and Using Inequalities 2” under “Analyze, Solve, and Graph Inequalities.” Then play the video, which contains examples of writing equations. While watching the video, you should pause it to attempt the problems yourself. You can use a calculator to perform the calculations.
     
    Watching this video should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: HippoCampus’s “Algebra I – An Open Course” Link: HippoCampus’s “Algebra I – An Open Course” (HTML)
     
    Instructions: Please click on the link above and then click on “Algebra 1 – An Open Course (2011)” under the “Worked Examples” tab. Then click on “Writing and Using Inequalities 3” under “Analyze, Solve, and Graph Inequalities.” Then play the video, which contains examples of writing equations. While watching the video, you should pause it to attempt the problems yourself. You can use a calculator to perform the calculations.
     
    Watching this video and working through the problems should take approximately 5 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.6 Functions   Sometimes it is difficult to model real-world situations, and the best way is to try to fit data through functions. “The volume of a sphere depends on its radius.” “The amount of money John makes depends upon the number of hours he works.” “The grade that Marissa received in the class depends upon the number of points she has earned.” These are examples of functional relationships where one variable depends upon another variable. In this unit, you will learn concepts of functions.

1.6.1 What Is a Function?   In subunit 1.6.1, you will extend your knowledge of ordered pairs and graphs to determining if they represent a function.

  • Explanation: Henrico County Public Schools’s “Module – Relations and Functions: Lesson 5: Functions” Link: Henrico County Public Schools’s “Module – Relations and Functions: Lesson 5: Functions” (HTML and PPT)
     
    Instructions: Please click on the link above and then click on the “Notes: Functions” PowerPoint presentation. This is an overview of most of the concepts you will view in this unit.
     
    Watching this PowerPoint presentation should take approximately 15 minutes.
               
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

1.6.2 Is the Relation a Function?   You can’t be in two places at once; sometimes it would be nice, but it can’t happen. This is similar to the concept of functions because for every input, there can only be one output (every x can only have one y).
 
In subunit 1.6.2, you will learn how to determine if a relation is a function.

  • Explanation: HippoCampus’s “Algebra I – An Open Course” Link: HippoCampus’s “Algebra I – An Open Course” (HTML and Flash)

    Instructions: Please click on the link above and then click on “Algebra 1 – An Open Course (2011)” under the “Presentations” tab. Then click on “Representing Functions and Relations” under “Functions and Patterns.” Then play the video, which explains how to determine if a relation is a function.
     
    Watching this video should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: HippoCampus’s “Algebra I – An Open Course” Link: HippoCampus’s “Algebra I – An Open Course” (HTML and Flash)
     
    Instructions: Please click on the link above and then click on “Algebra 1 – An Open Course (2011)” under the “Worked Examples” tab. Then click on “Representing Functions and Relations 1” under “Functions and Patterns.” Then play the video, which provides an example of how to determine if a given relation is a function when written as a table. Once the prompt is read, you should pause it to attempt the problems yourself. You can use a calculator to perform the calculations.
     
    Watching this video and working through the problems should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: HippoCampus’s “Algebra I – An Open Course” Link: HippoCampus’s “Algebra I – An Open Course” (HTML and Flash)
     
    Instructions: Please click on the link above and then click on “Algebra 1 – An Open Course (2011)” under the “Worked Examples” tab. Then click on “Representing Functions and Relations 2” under “Functions and Patterns.” Then play the video, which provides an example of how to determine if a given relation is a function when graphed on a coordinate plane. Once the prompt is read, you should pause it to attempt the problems yourself. You can use a calculator to perform the calculations.
     
    Watching this video and working through the problems should take approximately 5 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Illustrative Mathematics’s “The Customers” Link: Illustrative Mathematics’s “The Customers” (HTML)
     
    Instructions: Please click on the link above and complete the task, which allows you to determine if a function exists using real-world context. The solution to this task is found toward the end of the page.
     
    Completing this task should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Illustrative Mathematics’s “Foxes and Rabbits” Link: Illustrative Mathematics’s “Foxes and Rabbits” (HTML)
     
    Instructions: Please click on the link above and complete the task, which allows you to determine if a function exists using real-world context. The solution for this task is found toward the end of the page.
     
    Completing this task should take approximately 15 minutes.
     
    Standards Addressed (Common Core):

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1.6.3 Function Notation   You, or someone you know, might have one nickname at home and a different nickname at school. You might know a friend as Lizzy, but her family calls her Elizabeth. She is the same person no matter what name she is called. We see a similar idea in function notation. We are used to viewing equations in y = , but now we will see a function notation such as f(x) = . We are used to writing ordered pairs such as (5, 4), but now we might see the format f(5) = 4. These are all different ways of referring to a function.
 
In subunit 1.6.3, you will learn the meaning of function notation and how to work with that format.

  • Explanation: cK-12’s “Function Notation” Link: cK-12’s “Function Notation” (HTML)
     
    Instructions: Please click on the link above and then click on the “Function Notation – Overview” video, which introduces function notation, another method of writing y in an equation.
     
    Watching this video should take approximately 5 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Illustrative Mathematics’s “Interpreting the Graph” Link: Illustrative Mathematics’s “Interpreting the Graph” (HTML)
     
    Instructions: Please click on the link above and complete the task, which allows you to interpret a graph using function notation. The solution is toward the bottom of the page.
     
    Completing this task should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

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1.6.4 Domain and Range   Your teacher assigns everyone a partner for the activity. No one can switch partners. Brady’s partner is Margie. Donna’s partner is Jose. Indigo’s partner is Tray. This is similar to the domain and range concept of functions where x values are paired with y values.
 
In subunit 1.6.4, you will determine the domain and range of functions.

  • Explanation: HippoCampus’s “Algebra I – An Open Course” Link: HippoCampus’s “Algebra I – An Open Course” (HTML)
     
    Instructions: Please click on the link above and then click on “Algebra 1 – An Open Course (2011)” under the “Presentations” tab. Then click on “Domain and Range” under “Functions and Patterns.” Then play the video, which explains how to determine the domain and range of a function.
     
    Watching this video should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Illustrative Mathematics’s “Points on a Graph” Link: Illustrative Mathematics’s “Points on a Graph” (HTML)
     
    Instructions: Please click on the link above and complete the task, which allows you to rewrite function notation as an ordered pair. The solution for this task is found toward the bottom of the page.
                                       
    Completing this task should take approximately 5 minutes.
     
    Standards Addressed (Common Core):

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1.6.5 Vertical Line Test   There are several methods to determine if a function exists. In subunit 1.6.5, you will learn how to determine if a function exists by using the vertical line test.

  • Explanation: cK-12’s “Vertical Line Test” Link: cK-12’s “Vertical Line Test” (HTML and YouTube)
     
    Instructions: Please click on the link above and then click on the video, which explains how to determine whether there is a function using the Vertical Line Test.
     
    Watching this video should take approximately 5 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Checkpoint: cK-12’s “Vertical Line Test” Link: cK-12’s “Vertical Line Test” (HTML)
     
    Instructions: Please click on the link above and scroll down to complete the practice sections. The practice is available with and without the video and also gives you a preview to piecewise functions.
     
    Completing these exercises should take approximately 20 minutes.
     
    Standards Addressed (Common Core):

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1.6.6 Sequences   - Explanation: Utah Electronic High School’s “Sequences as Functions” Link: Utah Electronic High School’s “Sequences as Functions” (HTML)
 
Instructions: Please click the link and read the chapter on sequences as functions. Why are sequences functions?
 
Reading the chapter should take approximately 15 minutes.
 
Standards Addressed (Common Core):

-   [CCSS.Math.Content.HSF-IF.A.3](http://www.corestandards.org/Math/Content/HSF/IF/A/3)

Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Checkpoint: Mathematics Vision Project’s “Arithmetic and Geometric Sequences” Link: Mathematics Vision Project’s “Arithmetic and Geometric Sequences” (PDF)
     
    Instructions: Click on the link and scroll down to the Growing Dots activity on page 4. Read this introduction and then go on to the Ready Set Go activity on page 5. Complete problems 1-12. If you want additional practice, you can do any of the other activities in this packet.
     
    Completing the activity should take approximately 60 minutes.
     
    Standards Addressed (Common Core):

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1.6.7 Modeling   Even though math concepts seem like they don’t relate to real life, they control a lot of what is happening in our world. In subunit 1.6.7, you will explore some situations where functions are utilized.

  • Activity: Illustrative Mathematics’s “Cell Phones” Link: Illustrative Mathematics’s “Cell Phones” (HTML)
     
    Instructions: Please click on the link above and complete the task, which allows you to practice a mixture of function concepts in a real-world situation. The solution to this task is found toward the bottom of the page.
     
    Completing this task should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Illustrative Mathematics’s “Yam in the Oven” Link: Illustrative Mathematics’s “Yam in the Oven” (HTML)
     
    Instructions: Please click on the link above and complete the task, which allows you to practice a mixture of function concepts in a real-world situation. The solution is found toward the bottom of the page.
     
    Completing task should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Activity: Illustrative Mathematics’s “The Parking Lot” Link: Illustrative Mathematics’s “The Parking Lot” (HTML)
     
    Instructions: Please click on the link above and complete the task, which allows you to practice a mixture of function concepts in a real-world situation. The solution is found toward the bottom of the page.
     
    Completing task should take approximately 10 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.