Skip navigation.

2nd Quarter, Math Level 1 (9th grade math)

00.00 Start Here (Math Level 1)

Course Description

The fundamental purpose of Mathematics I is to formalize and extend the mathematics that students learned in 8th grade.  Students will focus on linear expressions, equations, and functions but also be introduced to exponential functions. They will solve systems of equations and inequalities. They will review learn the basic terms of geometry and solve problems involving angles, triangles, parallel lines, perimeter and area. In addition, they will use the Pythagorean Theorem to solve problems and find the distance and midpoint between two points. They will review transformations and use this knowledge to understand triangle congruence.  Finally, they will study the statitistical concepts of spread, frequency tables, histograms, box plots. scatter plots, correlation and causation, and standard deviation. Students should experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

Class Overview

This integrated Secondary Mathematics I course is based on the New Utah State Standards Initiative.

Credit

This course is worth .25 credits, or nine weeks of Mathematics I. There are four Mathematics II quarter classes available. Taking all four will add up to one credit or one year of Mathematics I. In order to earn credit for each quarter, you must commit to following the EHS Honor Code: "As a student of the Electronic High School, I agree to turn in my assignments in a timely manner, do my own work, not share my work with others, and treat all students, teachers, and staff with respect." This course is for ninth grade students. After completing the work for the class, students must pass a proctored final exam to earn credit. There is not a paper-based textbook assigned for this course. If you find that having a textbook is useful, you can check out a textbook from most local libraries. You can also search for topics on the Internet to find many useful resources.

Prerequisites

You should have successfully completed 8th grade math.

Supplies needed

  • Graph paper (this can also be downloaded)
  • Scientific or Graphing Calculator (You can download scientific and graphing calculator simulators or find online versions, but as you will need a graphing calculator for the rest of your high school career, you may consider buying one now.)
  • Access to a printer to print the daily assignments is vital. Most assignments are NOT interactive and must be printed out to complete.
  • Ability to scan or photograph a completed assignment to submit electronically.

Organization of Secondary Math Level 1

Units: There are 10 units for the full credit of Secondary Math 2.

Quarter 1 has two units.
Quarter 2 has two unit.
Quarter 3 has three units.
​Quarter 4 has three units.

Schedule: When you enroll in a quarter class, you are given 10 weeks to finish all the requirements needed to earn the credit for a quarter. There are no "required" due dates for the assignments in this course. However, there is a pacing guide provided for you that will help you stay on track to being successful and finishing the course within the 10 week time frame. The pacing guide is located in the Syllabus in Module 1. Before you begin, go over the pacing guide to help you set up your own due dates for the assignments. Give your parents permission to nag you about it. You don't want to be one of those students who does a whole lot of work, but never finishes the course.

This Quarter Class

The units in this class have lessons, assignments, quizzes and a unit test.

Lessons: Each lesson provides instruction on a given topic. Many include instructional videos (hosted on YouTube) and one or more assignments for independent practice.

Assignments: Print, then complete the practice worksheet, showing how you arrived at your answer. In order to earn full points on each problem, you are required to show step by step the process needed to arrive at your answer. Then circle your answer so it is easily seen. I do give partial credit for showing your work--so ALWAYS show your work even if you think it is obvious. Assignments are submitted by uploading the digital assignment through the course website by following the instructions within each assignment. Under some circumstances, you may snail-mail a hard copy of the assignment to the instructor. If you choose this option, be sure to make a copy for yourself, as the instructor will NOT return your assignment. Also, please send the instructor an e-mail if you must mail an assignment.

Quizzes: Some quizzes are taken online. Others are more like the assignments. Print, then complete the quiz, showing all of your work as to how you arrived at your answer. In order to earn full points on each problem, you are required to show step by step the process needed to arrive at your answer. Then circle your answer so it is easily seen. I do give partial credit for showing your work--so ALWAYS show your work even if you think it is obvious. Quizzes are submitted by uploading the digital assignment through the course website by following the instructions within each quiz.

Proctored Final

Each quarter class has a proctored final exam and is worth 25% of the final grade.

Information about the Final Exam

  1. You must get approval from your teacher before you are allowed to take the final exam.
  2. You must complete every assignment and have an overall grade of C in the course to be approved to take the final exam.
  3. The final exam is a comprehensive exam that must be taken with an approved proctor.
  4. You are allowed to have a page of notes. You also will need a calculator and scratch paper.
  5. You must pass the final exam with a 60% in order to pass the class.
  6. The final exam is worth 25% of your final grade.
  7. The exam is timed. You will have 2.0 hours to complete the exam. You must finish it in one attempt.

Final Grade

Assignments and quizzes are worth 75% of the final grade. The proctored final test is worth 25% of the final grade.

Grading Scale

You earn a grade based on a modified total points percentage method. This means that the total number of points you earned is divided by the total number of points possible, times 100%. That will make up 75% of your final grade. The final exam is the remaining 25%. These scores are combined for a total percentage of the class. This percentage is translated into a grade based on this standard scale:

94-100% A
90-93% A-
87-89% B+
83-86% B
80-82% B-
77-79% C+
73-76% C
70-72% C-
67-69% D+
63-66% D
60-62% D-
0-59% no credit

00.01 Curriculum Standards (Math Level 1)

Overview information on the Utah Mathematics Level I Core is here.

00.01.01 Student Software Needs

 

Students need access to a robust internet connection and a modern web browser.

This class may also require the Apple QuickTime plug-in to view media.

For students using a school-issued Chromebook, ask your technical support folks to download the QuickTime plug-in and enable the plug-in for your Chromebook.

$0.00

00.02 About Me (Math Level 1)

teacher-scored 10 points possible 10 minutes

{\color{Red} CAREFULLY } {\color{Red} FOLLOW } {\color{Red} THE } {\color{Red} DIRECTIONS } {\color{Red} BELOW!! }

About Me Assignment: This assignment gives me, as your teacher, a chance to get to know you better! To complete and submit this assignment copy the material between the asterisks into a blank word-processing document. Answer the questions using complete sentences, appropriate punctuation and sentence structure. Please write your answers in either BOLD or a {\color{Magenta}DIFFERENT } {\color{Magenta}COLOR }. Save the document. Finally, select all, copy, then paste the entire document into the box that opens when you click to submit this assignment.

************************************************************************************************

1. What is your full name, what name do you prefer to go by, your parent's/guardian's names, and contact information for both you and your parents? (email addresses and phone numbers.)

2. What high school do you attend and what grade are you in? What is the name of the last math class you completed?

3. Why have you chosen to take this math class with EHS?

4. What is your counselor's full name and contact information?

5. Have you read the EHS Honor Code and do you commit to following it? EHS Honor Code "As a student of the Electronic High School, I agree to turn in my assignments in a timely manner, do my own work, not share my work with others, and treat all students, teachers, and staff with respect."

6. Are you committed to finishing the class within the 10 week time frame, completing your final exam in week 9?

7. Now tell me about you! What are your likes/dislikes etc. Please be sure to include anything you think I need to know as your teacher.

************************************************************************************************

I am excited to learn more about you!

Grading criteria:

1. All requested information is included.

2. Complete sentences, correct punctuation and correct grammar are used.

Pacing: complete this by the end of Week 1 of your enrollment date for this class.


00.03 Basic Skills (Math Level 1)

Just like learning to use the English or Spanish language, you learn the language of mathematics by acquiring its vocabulary and grammar and by practicing until you can "think" fluently in the language.

This pre-requisite lesson helps you verify you have a basic understanding of integers, fractions, and simplifying expressions, some of the basic building blocks of the "mathematics language."

00.03.01 Basic Skills - Integers (Math Level 1)

computer-scored 20 points possible 15 minutes

Activity for this lesson

Take the quiz 00.03.01 Basic Skills Integers

If you don't pass the quiz on the first attempt, search the internet for adding, subtracting, multiplying and dividing integers. Review the material and try again.

Pacing: complete this by the end of Week 1 of your enrollment date for this class.


00.03.02 Basic Skills - Fractions (Math Level 1)

computer-scored 20 points possible 20 minutes

Activity for this lesson

  1. Take the quiz listed as 00.03.02 Basic Skills - Fractions Quiz

If you don't pass the quiz on the first attempt, search the internet for adding, subtracting, multiplying and dividing fractions. Review the material and try again.

Pacing: complete this by the end of Week 1 of your enrollment date for this class.


00.03.03 Basic Skills - Simplifying Expressions (Math Level 1)

computer-scored 20 points possible 20 minutes

Activity for this lesson

  1. Take the quiz 00.03.03 Basic Skills - Simplifying Expressions Quiz

If you don't pass the quiz on the first attempt, search the internet for simplifying expressions. Review the material and try again.

Pacing: complete this by the end of Week 1 of your enrollment date for this class.


03.00 Functions Overview (Math Level 1)

In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students learn function notation and develop the concepts of domain and range. They move beyond viewing functions as processes that take inputs and yield outputs and start viewing functions as objects in their own right. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that, depending upon the context, these representations are likely to be approximate and incomplete. Student work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. By the end of the unit, students will be able to:

  • Understand the definition of a function and identify its parts and write a relation in function notation.
  • Perform operations on and evaluate linear functions.
  • Identify linear functions represented in equations, tables, graphs or situations.
  • Graph linear functions using input-output pairs.
  • Define slope as the rate of change of a function and calculate slope given the coordinates of two points.
  • Use the slope and y-intercepts to graph and write functions.
  • Write linear functions in function notation to describe what is happening in a table.
  • write linear functions in function notation to describe what is happening in a graph.
  • Use x- and y-intercepts to graph linear functions.
  • Identify the relationships of and write equations for parallel and perpendicular lines.

03.01 Functions (Math Level 1)

Understand the definition of a function and identify its parts and write a relation in function notation.

Something to Ponder

How would you describe a function for someone younger than you who is learning mathematics?

Mathematics Vocabulary

Element: an item in a set

Set: a well-defined collection of elements

Relation: any set of ordered pairs

Domain: the possible values for the input of a function, usually the x values

Range: the possible values for the output of a function, usually the y values

Function: a relation that assigns exactly one value in the range to one value in the domain

Input/Output: input is the value that you substitute in the function and output is the solution

Function Notation: to write a rule in function notation, you use the symbol f(x) in place of y; for example: f(x) = 3x - 6 is written using function notation

Learning these concepts

Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

03.01 Functions - Explanation Video Links (Math Level 1)

03.01 Functions - Explanation Videos (Math Level 1)

See video
See video


03.01 Functions - Extra Videos (Math Level 1)

I highly recommend that you click on the links above and watch the videos before continuing.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Example 1: For the following relation, plot the points, state the domain and range, and determine if the relation is a function: {(1,3), (-2,5), (4,3), (0,-1), (-1,-1)}.

Answers

Example 1:

{A(1,3), B(-2,5), C(4,3), D(0,-1), E(-1,-1)}

Domain (x-values of the points usually written in numerical order): {-2, -1, 0, 1, 4}

Range (y-values of the points usually written in numerical order): {-1, -1, 3, 3, 5}

Function: Using the vertical line test, this is a function.

03.01 Functions - Worksheet (Math Level 1)

teacher-scored 64 points possible 30 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 1 of your enrollment date for this class.


03.02 Linear Function Operations (Math Level 1)

Perform operations on and evaluate linear functions.

Something to Ponder

How would you explain the process for composing a function?

Mathematics Vocabulary

Composite Function: a function whose values are found by applying one function to a given value and then applying the second function to the result of the first function

Learning these concepts

Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

03.02 Linear Function Operations - Explanation Video Links (Math Level 1)

03.02 Linear Function Operations - Explanation Videos (Math Level 1)

See video
See video
See video


 

03.02.01 Linear Function Operations - Extra Video (Math Level 1)

I highly recommend that you click on the links above and watch the videos before continuing.

NROC Links: You can just watch the video by click on the PRESENTATION tab or work through the sections.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Example 1: Find f(2) and f(y + 2) for the function f(x) = -3x-5

Example 2: Let f(x) = -2x + 6 and g(x) = 5x - 7. Find f(x) + g(x) and (f - g)(x).

Example 3: f(x) = x + 1 and g(x) = 2x. Find \large f(x)\cdot g(x).

Example 4: Let f(x) = 2x - 5 and g(x) = 3x + 2. Find \fn_phv \left ( \frac{f}{g} \right )(x).

Example 5: Let f(x) = x + 1 and g(x) = x - 5. Find \large (f\cdot g)(2).

Answers

Example 1: Find f(2) and f(y + 2) for the function f(x) = -3x-5

  • f(2) = -3(2) - 5 = -6 - 5 = -11
  • f(y + 2) = -3(y + 2) - 5 = -3y - 6 - 5 = -3y - 11

Example 2: Let f(x) = -2x + 6 and g(x) = 5x - 7. Find f(x) + g(x) and (f - g)(x).

  • f(x) + g(x) = -2x + 6 + 5x - 7 = 3x - 1
  • (f-g)(x) = (-2x + 6) - (5x - 7) = -2x + 6 - 5x + 7 = -7x + 13

Example 3: f(x) = x + 1 and g(x) = 2x. Find (f\cdot g)(2).

(f\cdot g)(2) = f(x)\cdot g(x) = (x + 1)(2x) = 2x2 + 2x

Example 4: Let f(x) = 2x - 5 and g(x) = 3x + 2. Find \left ( \frac{f}{g} \right )(x).

\left ( \frac{f}{g} \right )(x)=\frac{f(x)}{g(x)}=\frac{2x-5}{3x+2}

Example 5: Let f(x) = x + 1 and g(x) = x - 5. Find  (f\cdot g)(2).

First find g(2): g(2) = 2 – 5 = –3

Then find f(–3): f(–3) = –3 + 1 = –2

Answer: \small (f\cdot g(2))= – 2

03.02.02 Linear Function Operations Quiz (3 parts) (Math Level 1)

computer-scored 20 points possible 60 minutes

Activity for this lesson

1. Take the 03.02 Linear Function Operations - Evaluating Functions Part 1 Quiz

  • You need to score 16 or higher.

2. Take the  03.02 Linear Function Operations - Operations on Functions Part 2 Quiz

  • You need to score 16 or higher.

3. Take the 03.02 Linear Function Operations - Compositions of Functions Part 3 Quiz

  • You need to score 16 or higher

Pacing: complete this by the end of Week 2 of your enrollment date for this class.


03.02.03 Check Point Quiz 1 (Math Level 1)

teacher-scored 62 points possible 30 minutes

Quiz Check Point

  1. Print the quiz. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your quiz.

Pacing: complete this by the end of Week 2 of your enrollment date for this class.


03.03 Identifying Linear Functions (Math Level 1)

Identify linear functions represented in equations, tables, graphs or situations.

Something to Ponder

How would you describe a linear function and how it relates to tables, graphs and functions?

Mathematics Vocabulary

Linear Function: a function that can be represented on a graph as a straight line

Learning these concepts

Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

03.03 Identifying Linear Functions - Explanation Video Links (Math Level 1)

03.03 Identifying Linear Functions - Explanation Videos (Math Level 1)

See video


03.03.01 Identifiying Linear Functions - Extra Video (Math Level 1)

I highly recommend that you click on the links above before continuing.

You can watch the videos by clicking on the PRESENTATION tab or work through all sections.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Identify 3 points and graph them. Make a table and record the coordinates of each point. Write the domain and range of the set of points.

Example 1:

f(x) = \dpi{100} \fn_phv \frac{2}{3}x - 4

Example 2:

f(x) = -3x + 5

Example 3: Fill in the following table given the function and domain

Function Domain Range Ordered Pairs
f(x) = 3 – 4x –3, 0, 5    
f(x) = x – \frac{1}{3} 2, –4, 3    
f(x) = –5x –2, –1, 0    

 

Analyze the scenario, create a table and list the domain and range and ordered pairs.

Example 4:

The Spanish club is having a fund-raiser by selling piñatas that they have made. They will sell them for $15 each. The cost of all of the supplies to make them is $125. Their profit can be modeled with the function f(p) = 15p – 125 where p is the number of piñatas sold. What will their profit be if they sell 25? 50? 100?

Answers

Identify 3 points and graph them. Make a table and record the coordinates of each point. Write the domain and range of the set of points.

Example 1:

f(x) = \frac{2}{3}x - 4

x f(x)
-3 -6
0 -4
3 -2

 

Domain: {-3, 0, 3} if you just use the points or all real numbers if you consider all points.

Range: {-6, -4, -2} if you just use the points or all real numbers if you consider all points.

Example 2:

f(x) = -3x + 5

x f(x)
-2 11
0 5
-2 -1

 

D: {-2, 0, 2} if you just use the points or all real numbers if you consider all points.

R: {11, 5, -} if you just use the points or all real numbers if you consider all points.

Example 3: Fill in the following table given the function and domain.

Function Domain Range Ordered Pairs
f(x)=3-4x {-3 ,0, 5} {15, 3, -17} (-3,15), (3, 0), (5, -17)
f(x)=x-\frac{1}{3} {2, -4, 3} \left \{ \frac{5}{3},\frac{-13}{3},\frac{7}{3} \right \} \left ( \frac{5}{3},2\right),\left (\frac{-13}{5},-1 \right ), \left ( \frac7{}{3},3 \right )
f(x)=-5x {-2, -1, 0} {10, 5, 0} (-2,10), (5, -1), (0,0)

 

Analyze the scenario, create a table and list the domain and range and ordered pairs.

Example 4:

The Spanish club is having a fund-raiser by selling piñatas that they have made. They will sell them for $15 each. The cost of all of the supplies to make them is $125. Their profit can be modeled with the function f(p) = 15p – 125 where p is the number of piñatas sold. What will their profit be if they sell 25? 50? 100?

f(25) = 15(25) - 125 = 375 – 125 = 250

f(50) = 15(50) – 125 = 750 – 125 = 625

f(100) = 15(100) – 125 = 1375

x f(x)
25 250
50 625
100 1375

 

Domain: {25, 50, 100}

Range: {250, 625, 1375}

03.03.02 Identifying Linear Functions - Worksheet (Math Level 1)

teacher-scored 20 points possible 45 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 3 of your enrollment date for this class.


03.04 Graphing Linear Functions (Math Level 1)

Graph linear functions using input/output pairs.

Something to Ponder

How does the graph of a linear function relate to its input/output pairs?

Mathematics Vocabulary

Linear Function: a function that satisfies the following two properties:

  1. \fn_jvn f(x+y)= f(x) + f(y)
  2. \fn_jvn f(ax)= af(x)

Input/Output Pair: the input and output of a function is an "ordered pair", such as (4,16). This pair is an "ordered pair" because the input always comes first, and the output second. So (4,16) means that the function takes in "4" and gives out "16."

Learning these concepts

Click the mathematician image to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

03.04 Graphing Linear Functions - Explanation Video Link (Math Level 1)

03.04 Graphing Linear Functions - Explanation Videos (Math Level 1)

See video


03.04 Graphing Linear Functions - Extra Video (Math Level 1)

I highly recommend that you click on the link above.

You can just watch the video by clicking on PRESENTATION or work through each section.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Example 1:

Make a table and graph the function represented by the following ordered pairs:

{(-6,-3), (-3,-1), (0,1), (3,3), (6,5)}

           
           

Example 2:

Make a table and graph the function represented by the following domain and function.

Domain: {-2,-1,0,1,2} f(x)=2x–1

Example 3:

Make a table and graph the function:

f(x) = -2x + 5

Example 1:

Make a table and graph the function represented by the following ordered pairs:

{(-6,-3), (-3,-1), (0,1), (3,3), (6,5)}

x f(x)
-6 -3
-3 -1
0 1
3 3
6 5

 

When you graph a function with discrete points, you do not connect them.

Example 2:

Make a table and graph the function represented by the following domain and function.

Domain: {-2,-1,0,1,2} f(x) = 2x–1

x f(x)
-2 -5
-1 -3
0 -1
1 1
2 3

 

Example 3:

Make a table and graph the function:

f(x) = -2x + 5

x f(x)
-2 9
-1 7
0 5
1 3
2 1

 

03.04 Graphing Linear Functions - Worksheet (Math Level 1)

teacher-scored 48 points possible 45 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 3 of your enrollment date for this class.


03.05 Rate of Change and Slope (Math Level 1)

Define slope as the rate of change of a function and calculate slope given the coordinates of two points.

Something to Ponder

How is slope related to the rate of change of a function?

Mathematics Vocabulary

Rate of change: the relationship between two quantities that are changing, also referred to as slope

Slope: the ratio of the vertical change to the horizontal change; for example:

 x}=\frac{\Delta y}{\Delta x}=\frac{y_{2} - y_{1}}{x_{2} - x_{1}}

Learning these concepts

Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

03.05 Rate of Change and Slope - Explanation Video Links (Math Level 1)

03.05 Rate of Change and Slope - Explanation Videos (Math Level 1)

See video
See video


03.05 Rate of Change and Slope - Extra Video (Math Level 1)

I highly recommend that you click on the links above.

You can just watch the videos by clicking on PRESENTATION or work through each section.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Example 1:

For the data in the table, is the rate of change for each pair of consecutive mileage amounts the same?

miles fee
100 $30
150 $42
200 $54
250 $66

 

Example 2:

For the data in the table, is the rate of change for each pair the same?

Number of days Rental charge
1 $60
2 $75
3 $90
4 $115
5 $130

 

Example 3: Find the rate of change of the data in the graph:

Example 4:

Find the slope of each line and state if the slope is positive, negative, zero or undefined:

a)
b)
c)
d)

Example 5:

Find the slope of the line through each pair of points:

a) T(-4,-2) and U(9,-3)

b) A(6,-4) and B(7,-4)

c. C(3,8) and D(3,6)

Answers

Example 1: For the data in the table, is the rate of change for each pair of consecutive mileage amounts the same?

miles fee
100 $30
150 $42
200 $54
250 $66

 

  • 42-30 = 12
  • 54-42 = 12
  • 66-54 = 12

Yes, the rate of change is the same.

Example 2: For the data in the table, is the rate of change for each pair the same?

Number of days Rental charge
1 $60
2 $75
3 $90
4 $115
5 $130

 

  • 75-60 = 15
  • 90-75 = 15
  • 115-90 = 25
  • 130-115 = 15

No, the rate of change is not the same.

Example 3: Find the rate of change of the data in the graph:

Time (sec) Distance (meters
0 0
10 200
20 400
30 600
40 800

 

The difference between each y-value is 200. This is the rate of change of the data.

Example 4:

Find the slope of each line and state if the slope is positive, negative, zero or undefined:

a)

Step 1: Find two points on the graph.

(1, 0) and (2, 3)

Step 2: Find the slope.

\fn_phv m=\frac{(y{_2}-y{_1})}{(x{_2}-x{_1})} = \frac{(3-0)}{(2-1)} = \frac{3}{1} = 3

Step 3: State if the slope is positive, negative, zero or undefined

The slope is positive.

b)

Step 1: Find two points on the graph.

(-4, 0) and (1, -3)

Step 2: Find the slope.

m=\frac{(y{_2}-y{_1})}{(x{_2}-x{_1})} = \frac{(-3-0)}{(1- -4)} = \frac{-3}{5}

Step 3: State if the slope is positive, negative, zero or undefined

The slope is negative.

c)

Step 1: Find two points on the graph.

(-3, 0), (-3, 1)

Step 2: Find the slope.

m=\frac{(y{_2}-y{_1})}{(x{_2}-x{_1})} = \frac{(1-0)}{(-3--3)} = \frac{1}{0}

Step 3: State if the slope is positive, negative, zero or undefined

The slope is undefined because division by zero is not defined.

d)

Step 1: Find two points on the graph.

(0, -2) and (1, -2)

Step 2: Find the slope.

m=\frac{(y{_2}-y{_1})}{(x{_2}-x{_1})} = \frac{(-2--2)}{(1-0)} = \frac{0}{1} =0

(All horizontal lines have a slope of 0)

Step 3: State if the slope is positive, negative, zero or undefined.

The slope is zero.

Example 5:

Find the slope of the line through each pair of points:

a) T(-4,-2) and U(9,-3)

m=\frac{(y{_2}-y{_1})}{(x{_2}-x{_1})} = \frac{(-3--2)}{(9--4)} = \frac{-1}{13}

b) A(6,-4) and B(7,-4)

m=\frac{(y{_2}-y{_1})}{(x{_2}-x{_1})} = \frac{(-4--4)}{(7-6)} = \frac{0}{1}=0

c) C(3,8) and D(3,6)

m=\frac{(y{_2}-y{_1})}{(x{_2}-x{_1})} = \frac{(6--8)}{(3-3)} = \frac{14}{0}

The slope is undefined.

03.05.01 Rate of Change and Slope - Worksheet (Math Level 1)

teacher-scored 50 points possible 45 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 3 of your enrollment date for this class.


03.05.02 Check Point Quiz 2 (Math Level 1)

teacher-scored 52 points possible 45 minutes

Quiz Check Point

  1. Print the quiz. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your corrected quiz.

Pacing: complete this by the end of Week 3 of your enrollment date for this class.


03.06 Slope-Intercept Form (Math Level 1)

Use the slope and y-intercepts to graph and write functions.

Something to Ponder

How would you explain the parts of the Slope-Intercept form and how they relate to the graph of an equation?

Mathematics Vocabulary

Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept of the line

Learning these concepts

Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

03.06 Slope-Intercept Form - Explanation Video Link (Math Level 1)

03.06 Slope-Intercept Form - Explanation Videos (Math Level 1)

See video


03.06 Slope-Intercept Form - Extra Video (Math Level 1)

I highly recommend that you click on the links above.

NROC links: You can just watch the videos by clicking on PRESENTATION or work through each section.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Example 1:

What are the slope (m) and y-intercept (b) of the following:

a. y = 2x - 3

b. y=-\fn_phv \frac{2}{3}x + 6

c. 4x - 2y = -8

Example 2:

Write an equation in slope-intercept form with slope \frac{2}{5} and y-intercept 4.

Example 3:

Graph the following equations:

a. y = \frac{1}{3}x - 2

b. y = -2x + 1

c. y=-\frac{3}{2}x

Answers

Example 1: What are the slope and y-intercept (b) of the following?

a)  y={\color{Red} 2}x{\color{Blue} -3}

{\color{Red} m = 2} and {\color{Blue} b = -3}

b) y={\color{Red} \frac{2}{3}}x {\color{Blue} + 6}

{\color{Red} m=\frac{2}{3}}

{\color{Blue} b=6}

c) 4x - 2y = -8

Step 1: Write the equation in slope-intercept form.

4x - 2y = -8

Subtract 4x from both sides:

-2y = -4x - 8

Divide all three terms by -2:

y={\color{Red}2 }x{\color{Blue}+4 }

Step 2: Identify m and b.

{\color{Red} m=2} and {\color{Blue} b=4}

Example 2: Write an equation in slope-intercept form with slope {\color{Red} \frac{2}{5}} and y-intercept {\color{Blue} 4}.

y={\color{Red} m}x {\color{Blue} + b}={\color{Red} \frac{2}{5}}x {\color{Blue} +4}

Example 3: Graph the following equations:

a) y={\color{Red} \frac{1}{3}}x {\color{Blue} -2}

b) y=\color{Red}-2x {\color{Blue} +1}

c) y=-{\color{Red} \frac{3}{2}}x

03.06 Slope-Intercept Form - Worksheet (Math Level 1)

teacher-scored 20 points possible 60 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 4 of your enrollment date for this class.


03.07 Writing Functions from Tables (Math Level 1)

Write linear functions in function notation to describe what is happening in a table.

Something to Ponder

How would you describe the process for writing a linear function rule from a table?

Mathematics Vocabulary

Function Rule: an equation that describes a function

Rate of Change: the relationship between two quantities that are changing, also referred to as slope

y-Intercept: the y coordinate of the point where a line crosses the y axis

Growth Factor: the number b in an exponential growth function of the form \fn_jvn y = b^{x} + k, where b > 1

Decay Factor: the number b in an exponential decay function of the form y = b^{x} + k, where 0 < b < 1

Constant: the number k in an exponential function of the form y = b^{x} + k, also the horizontal asymptote

Asymptote: a line that continually approaches a given curve but does not meet it at any finite distance.

Learning these concepts

Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

 

03.07 Writing Functions from Tables - Explanation Video Link (Math Level 1)

See video

03.07 Writing Functions from Tables - Extra Video (Math Level 1)

I highly recommend that you click on the link above and watch the video before continuing.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Find the rate of change (m) and y-intercept (b). Write a function rule for each table:

Example 1:

x f(x)
0 -2
1 -1
2 0
3 1
8 2

 

Example 2:

x f(x)
0 0
1 2
2 4
3 6
4 8

 

Example 3:

x f(x)
0 -3
1 0
2 3
3 6
8 9

Answers

Find the rate of change (m) and y-intercept (b). Write a function rule for each table:

Example 1:

Step 1: Find the rate of change (m)

Using the first two points: (0, -2) and (1, -1):

\fn_phv m=\frac{-1--2}{1-0}=\frac{-1+2}{1}=\frac{1}{1}=1

Step 2: Find the y-intercept (b)

When x = 0, y = -2 so the y-intercept is -2

Step 3: Write a function rule:

f(x) = mx + b = x - 2

Example 2:

Step 1: Find the rate of change (m)

Using the first two points: (0, 0) and (1, 2):

m=\frac{1-0}{2-0}=\frac{1}{2}

Step 2: Find the y-intercept (b)

When x = 0, y = -3 so the y-intercept is -3

Step 3: Write a function rule:

f(x) = mx + b = \frac{1}{2}x + 0 = \frac{1}{2}x

Example 3:

Step 1: Find the rate of change (m)

Using the first two points: (0, -3) and (1, 0):

m=\frac{0--3}{1-0}=\frac{0+3}{1}=\frac{3}{1}=3

Step 2: Find the y-intercept (b)

When x = 0, y = -3 so the y-intercept is -3

Step 3: Write a function rule:

f(x) = mx + b = 3x + -3

03.07 Writing Functions from Tables - Worksheet (Math Level 1)

teacher-scored 20 points possible 45 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 4 of your enrollment date for this class.


03.08 Writing Functions from Graphs (Math Level 1)

Write linear functions in function notation to describe what is happening in a graph.

Something to Ponder

How would you describe the process for writing a linear function rule from a graph?

Mathematics Vocabulary

Function notation: A function \fn_jvn f with domain X and codomain Y is commonly denoted by

\fn_jvn f: X\rightarrow Y

or

X\overset{f}{\rightarrow}Y

The elements of x are called arguments of \fn_jvn f. For each argument x, the corresponding unique y in the codomain is called the function value at x or the image of x under \fn_jvn f. It is written as f(x). One says that \fn_jvn f associates y with x or maps x to y. This is abbreviated by

y=f(x)

A general function is often denoted by \fn_jvn f.

[definition from http://en.wikipedia.org/wiki/Function_notation#Notation ]

 

Learning these concepts

Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

 

03.08 Writing Functions from Graphs - Explanation Video Link (Math Level 1)

03.08 Writing Functions from Graphs - Explanation Videos (Math Level 1)

See video


03.08 Writing Functions from Graphs - Extra Video (Math Level 1)

I highly recommend that you click on the links above and watch the videos before continuing.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Write a function rule from each graph:

Example 1:

 

 

 

 

 

 

 

Example 2:

 

 

 

 

 

 

 

Example 3:

Example 4:

 

Answers

Write a function rule from each graph:

Example 1:

Step 1: Find two points – (0, 3) and (2, 0)

Step 2: Calculate the slope:

m=\frac{0-3}{2-0}=\frac{3}{2}

Step 3: Find the y-intercept using the point where x = 0 – (0, 3)

y-intercept (b) = 3

Step 4: Write the function rule:

f(x) = mx + b = \frac{3}{2}x + 3

Example 2:

Step 1: Find two points – (1, 2) and (0, –2)

Step 2: Calculate the slope:

m=\frac{-2-2}{0-1}=\frac{-4}{-1}=4

Step 3: Find the y-intercept using the point where x = 0 = (0, –2)

y-intercept (b) = –2

Step 4: Write the function rule:

f(x) = mx + b = 4x – 2

Example 3:

Step 1: Find two points – (2, 0) and (6, 3)

Step 2: Calculate the slope:

m=\frac{3-0}{6-2}=\frac{3}{4}

Step 3: Find the y-intercept by using the point (2, 0) as follows:

y = mx + b

0=\frac{3}{4}\cdot 2+b = \frac{3}{2}+b

Subtract \frac{3}{2} from both sides:

-\frac{3}{2} = b

Step 4: Write the function rule:

y = mx + b

y=\frac{3}{4}x-\frac{3}{2}

Example 4:

Step 1: Find two points – (1, 0) and (0, 2)

Step 2: Calculate the slope:

m=\frac{2-0}{0-1}=\frac{2}{-1}=-2

Step 3: Find the y-intercept using the point where x = 0 – (0, –2)

y-intercept = –2

Step 4: Write the function rule:

f(x) = mx + b = –2x + 2

03.08.01 Writing Functions from Graphs - Worksheet (Math Level 1)

teacher-scored 20 points possible 30 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 4 of your enrollment date for this class.


03.08.02 Check Point Quiz 3 (Math Level 1)

teacher-scored 40 points possible 30 minutes

Quiz Check Point

  1. Print the quiz. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your quiz.

Pacing: complete this by the end of Week 4 of your enrollment date for this class.


03.09 Standard Form and Intercepts (Math Level 1)

Use x- and y-intercepts to graph functions.

Something to Ponder

How would you describe the process of graphing an equation in Standard form?

Mathematics Vocabulary

Standard form: \fn_jvn Ax + By = C

y-intercept: the y coordinate of the point where the line crosses the y axis

x-intercept: the x coordinate of the point where the line crosses the x axis

Learning these concepts

Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

03.09 Standard Form and Intercepts - Explanation Video Links (Math Level 1)

03.09 Standard Form and Intercepts - Explanation Videos (Math Level 1)

See video
See video
See video


03.09 Standard Form and Intercepts - Extra Video (Math Level 1)

I highly recommend that you click on the links above and watch the videos before continuing.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Example 1:

Find the coordinates of the x- and y-intercepts of 2x + 5y = 6.

Example 2:

Graph 3x + 5y = 15 using intercepts.

Example 3:

Graph each function:

a) y = 4

b) x = -3

Example 4:

Convert the following functions in standard form to slope-intercept form:

a) 3x + y = -15

b) 2x + 7y = 14

c) -6x -3y = 9

Example 5:

Convert the following equations in slope-intercept form to standard form:

a) y=3x - 8

b) y=-\fn_phv \frac{2}{3}x + 4

c) y = 4x

Answers

Example 1:

Find the coordinates of the x- and y-intercepts of 2x + 5y = 6.

The x-intercept is where y = 0:

2x + 0 = 6; 2x = 6; x = 3

(3, 0)

The y-intercept is where x = 0:

0 + 5y = 6; 5y = 6; y = \frac{6}{5}

\left ( 0, \frac{6}{5} \right )

Example 2:

Graph 3x + 5y = 15 using intercepts.

x-intercept: 3x = 15; x = 5; (5, 0)

y-intercept: 5y = 15; y = 3; (0, 3)

Example 3:

Graph each function:

a) y = 4

b) x = -3

Example 4:

Convert the following functions in standard form to slope-intercept form:

a) 3x + y = -15

Subtract 3x from both sides:

y = -3x - 15

b) 2x + 7y = 14

Subtract 2x from both sides:

7y = -2x + 14

Divide ALL terms by 7:

y=-\frac{2}{7}x + 2

c) -6x -3y = 9

Add 6x to both sides:

-3y = 6x + 9

Divide ALL terms by -3:

y = 2x - 3

Example 5:

Convert the following equations in slope-intercept form to standard form:

a) y=3x - 8

Subtract 3x from both sides:

-3x + y = -8

Multiply ALL terms by -1:

3x - y = 8

b) y=-\frac{2}{3}x + 4

Add \frac{2}{3} to both sides:

\frac{2}{3}x + y = 4

Multiply ALL terms by 3:

2x + 3y = 12

c) y = 4x

Subtract 4x from both sides:

-4x + y = 0

Multiply ALL terms by -1

4x - y = 0

03.09 Standard Form and Intercepts - Worksheet (Math Level 1)

teacher-scored 92 points possible 45 minutes

Activity for this lesson

  1. Print each worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 5 of your enrollment date for this class.


03.10 Point-Slope Form (Math Level 1)

Write functions using the point-slope form.

Something to Ponder

What is the main purpose of the point-slope form?  How would you describe how to use it for this purpose?

Mathematics Vocabulary

Point-slope form: \fn_jvn y - y_{1} = m(x - x_{1}), where m is the slope and (x_{1} , y_{1}) is a point on the line
 

Learning these concepts

Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

 

03.10 Point-Slope Form - Explanation Video Links (Math Level 1)

03.10 Point-Slope Form - Explanation Videos (Math Level 1)

See video
See video


03.10 Point-Slope Form - Extra Video (Math Level 1)

I highly recommend that you click on the links above and watch the videos before continuing.

For the NROC lesson, you can just watch the video by clicking on PRESENTATION or work through each section.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Example 1:

Write the equation of the line, in point-slope form and in slope-intercept form, with slope -2 that passes through the point (3,-3)

Example 2:

Write equations for the line, in point-slope form and in slope-intercept form, that passes through points (-1,4) and (2,3).

Answers

Example 1:

Write the equation of the line, in point-slope form and in slope-intercept form, with slope -2 that passes through the point (3, -3)

Point-slope form: \fn_phv y-{y{_1}}=m(x-{x{_1}})

y - - 3 = -2(x – 3)

y + 3 = -2(x – 3)

Slope-intercept form: y = mx + b

y = -2x + b

-3 = -2(3) + b

-3 = -6 + b

3 = b

y = -2x + 3

Example 2:

Write equations for the line, in point-slope form and in slope-intercept form, that passes through points (-1,4) and (2,3).

Step 1: Calculate the slope:

m=\frac{3-4}{2--1} = \frac{-1}{3}

Step 2: Write the point-slope form:

Point-slope form: y-{y{_1}}=m(x-{x{_1}})

y-3=-\frac{1}{3}(x-2)

Step 3: Calculate the y-intercept (b):

Slope-intercept form: y = mx + b

3=-\frac{1}{3}\cdot 2 + b=-\frac{2}{3}+b

Add \frac{2}{3} to both sides:

\frac{11}{3}=b

Step 4: Write the slope-intercept form:

y= -\frac{1}{3}x+\frac{11}{3}

03.10.01 Point-Slope Form - Worksheet (Math Level 1)

teacher-scored 72 points possible 45 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 5 of your enrollment date for this class.


03.10.02 Check Point Quiz 4 (Math Level 1)

teacher-scored 56 points possible 45 minutes

Quiz Check Point

  1. Print the quiz. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your quiz.

Pacing: complete this by the end of Week 5 of your enrollment date for this class.


03.11 Parallel and Perpendicular Lines (Math Level 1)

Identify the relationships of and write equations for parallel and perpendicular lines.

Something to Ponder

How would you describe the slopes of parallel and perpendicular lines?

Mathematics Vocabulary

Parallel line: two lines in a plane that do not intersect or touch at a point

Perpendicular line: a line is perpendicular to another line if the two lines intersect at a right angle

Learning these concepts

Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

 

03.11 Parallel and Perpendicular Lines - Explanation Video Links (Math Level 1)

03.11 Parallel and Perpendicular Lines - Explanation Videos (Math Level 1)

See video
See video


03.11 Parallel and Perpendicular LInes - Extra Video (Math Level 1)

I highly recommend that you click on the links above and watch the videos before continuing.

NROC links: You can just watch the videos by clicking on PRESENTATION or work through each section.

Guided Practice:
After watching the video try these problems. The worked solutions follow.

Example 1:

Write an equation in slope-intercept form for the line parallel to y = 2x - 3 that contains (-5,-8).

Example 2:

Write an equation in standard form for a line perpendicular to y = \fn_phv \frac{1}{4}x + 1 that contains (10,0).

Answers

Example 1:

Write an equation in slope-intercept form for the line parallel to y = {\color{Red} 2}x - 3 that contains (-5,-8).

A line parallel to another line has the same slope which in this case is {\color{Red} 2}.

Slope-intercept form: y = {\color{Red} m}x + b = {\color{Red} 2}x + b

-8 = 2(-5) + b

-8 = -10 + b

{\color{Blue} 2=b}

y = {\color{Red} 2}x + {\color{Blue} 2}

Example 2:

Write an equation in standard form for a line perpendicular to y = {\color{Red} \frac{1}{4}}x + 1 that contains (10,0).

A line perpendicular to another line has a slope that is the negative inverse of the first line’s slope which in this case is {\color{Red} -4}.

Slope-intercept form: y = {\color{Red} m}x + b

0 = {\color{Red} -4}(10) + b

0 = -40 +b

{\color{Blue} 40 = b}

y = {\color{Red} -4}x + {\color{Blue} 40}

Add 4x to both sides: 4x + y = 40.

03.11 Unit 03 Review Quiz (Math Level 1)

teacher-scored 132 points possible 60 minutes

Unit Review Quiz

  1. Print both part 1 and part 2 of the quiz. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload both part 1 and part 2 of the quiz.

Pacing: complete this by the end of Week 6 of your enrollment date for this class.


03.11.01 Parallel and Perpendicular Lines - Worksheet (Math Level 1)

teacher-scored 68 points possible 45 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 6 of your enrollment date for this class.


04.00 Exponential Functions Overview (Math Level 1)

Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions. By the end of the unit, students will be able to:

  • Evaluate exponential functions.
  • Identify exponential functions represented in equations, tables, graphs or situations.
  • Graph exponential functions using input-output pairs.
  • Write exponential equations in function notation to describe what is happening in a table.
  • Write exponential equations in function notation to describe what is happening in a graph.
  • Graph parent functions and transformations of exponential functions.

04.01 Evaluating Exponential Functions (Math Level 1)

Evaluate exponential functions.

Something to Ponder

How would you define and describe an exponential function?

Mathematics Vocabulary

Exponential Function: a function that repeatedly multiplies by the same positive number

Growth factor: the amount >1 by which the parent function increases

Decay factor: the amount between 0 and 1 by which the parent function decreases

Learning these concepts

Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

 

04.01 Evaluating Exponential Functions - Explanation Video Links (Math Level 1)

04.01 Evaluating Exponential Functions - Explanation Videos (Math Level 1)

See video
See video


04.01 Evaluating Exponential Functions - Extra Video (Math Level 1)

I highly recommend that you click on the links above and watch the video or work through the material before continuing.

Guided Practice
After watching the video try these problems. The worked solutions follow.

Example 1:

Find f(2) for each function:

a) \fn_phv f(x)=2^{x}

b) f(x) = (\frac{1}{4})^{x}+2

c) f(x)=3^{x} - 4

Example 2:

Find f(2) for each function:

a) f(x)=x^{2}

b) f(x) = (\frac{1}{4})^{2}+2

c) f(x) = (\frac{1}{3})^{2}-4

Example 3:

Let f(x) =2 ^{x} and g(x) =3 ^{x} - 5

Find (f\cdot g)(2)

Example 4:

Let f(x) =3 ^{x} - 2 and g(x) =2^{x}

Find (g\cdot f)(5)

Example 5:

Let f(x) =4 ^{x} + 2 and g(x) =3 ^{x} -5

Find (f◦g)(3) or f(g(3)

Answers

Example 1:

Find f(2) for each function:

a) f(x) = 2x; f(2) = 22 = 2x2 = 4

b) f(x) = (\frac{1}{4})^{x}+ 2 ;f(2) = (\frac{1}{4})^{2} + 2= \frac{1}{4}\cdot \frac{1}{4} + 2=\frac{1}{16} + 2 = \frac{33}{16}

c) f(x) = 3x - 4; f(2) = 32 - 4 = 3x3 - 4 = 9 - 4 = 5

Example 2:

Find f(-3) for each function:

a) f(x) = 2x; f(-3) = 2-3 = \frac{1}{2^{3}} = \frac{1}{2\cdot 2\cdot 2} = \frac{1}{8}

b) f(x) = (\frac{1}{4})^{x}+ 2; f(-3) = (\frac{1}{4})^{-3}+ 2 =(\frac{1}{\frac{1}{4}})^{3}+ 2 = 4(\frac{1}{\frac{1}{4}})^{3}3+3 = 4x4x4 + 2 = 64 + 2 = 66

c) f(x) = (\frac{1}{3})^{x}- 4; f(-3) = (\frac{1}{\frac{1}{3}})^{3}- 4 = 33 - 4 = 3x3x3 - 4 = 27 - 4 = 23

Example 3:

Let f(x) = 2x and g(x) = 3x - 5

Find (f\cdot g)(2)) = f(2)\cdot g(2)=2^{2}\cdot (3^{2}-5)=4(9-5)=4\cdot 4=16

Example 4:

Let f(x) = 3x + 2 and g(x) = 2x

Find (f^{\circ}g)(3))

g(3) = 2^3 = 8

f(8) = 3^8 + 2 = 6561+2 = 6563

Example 5:

Let f(x) =4 ^{x} + 2 and g(x) =3 ^{x} -5

Find (f◦g)(3) or f(g(3)

Step 1: Find g(3)

g(3) = 33 + 2 = 27 + 2 = 22

Step 2: Find f(22)

f(22) = 222 + 2= 4,194,304 + 4 = 4,194,308

04.01 Evaluating Exponential Functions - Worksheet (Math Level 1)

teacher-scored 72 points possible 45 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 6 of your enrollment date for this class.


04.02 Identifying Exponential Functions (Math Level 1)

Write linear and exponential equations in function notation to describe what is happening in a graph.

Something to Ponder

How would you describe an exponential function and how it relates to a table, equation and graph?

Mathematics Vocabulary

Exponential function: a function whose value is a constant raised to the power of the argument.

Learning these concepts

Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

04.02 Identifying Exponential Functions - Explanation Video Links (Math Level 1)

04.02 Identifying Exponential Functions - Explanation Videos (Math Level 1)

See video
See video
See video


Guided Practice
After watching the video try these problems. The worked solutions follow.

For the following functions, identify 3 points on the graphs. Make a table and record the coordinates of each point. Write the domain and range of the set of points.

Example 1:

\fn_jvn f(x) = 3^{x}

x f(x)
   
   
   

 

Example 2:

\fn_jvn f(x) = 2^{x} - 3

x f(x)
   
   
   

 

Complete the table of values for each function:

Example 3:

\fn_jvn f(x) = 4^{x}

x f(x)
0  
1  
2  
3  
4  

 

Example 4:

\fn_jvn f(x) = 3^{x} + 2

x f(x)
0  
1  
2  
3  
4  

For each of the following analyze the scenario, create a table and list the domain and range and ordered pairs.

 

Example 5:

A new car that sells for $16,000 depreciates at a rate of 22% each year. This can be modeled with the function f(x) = \fn_jvn f(x) = 16000(0.78)^{x}. How much will the car be worth after 2 years? 5 years? 10 years?

Answers

Example 1:

f(x) = 3x

x f(x)
0 1
-1 \fn_phv \frac{1}{3}
1 3

 

D: {all real numbers or the three specific x-values you wrote in the table}

R: {all real numbers > 0 or the three specific y-values you wrote in the table}

Example 2:

f(x) = 2x - 3

x f(x)
-1 -\frac{5}{2}
0 -2
1 -1

 

D: {all real numbers or the three specific x-values you wrote in the table}

R: (all real numbers > -3 or the three specific y-values you wrote in the table}

Example 3:

f(x) = 4x

x f(x)
0 1
1 4
2 16
3 64
4 256

 

Example 4:

f(x) = 3x+2

x f(x)
0 3
1 5
2 11
3 29
4 83

 

Example 5:

A new car that sells for $16,000 depreciates at a rate of 22% each year. This can be modeled with the function f(x) = 16000(0.78)x. How much will the car be worth after 2 years? 5 years? 10 years?

f(2) = 16000(0.78)2 = 16000(0.6084) = $9734.40 (Remember the order of operations – exponents before multiplication!)

f(5) = 16000(0.78)5 = 16000(0.2887) = $4619.48 rounded to the nearest hundredth

f(10) = 16000(0.78)10 = 16000(0.0833) = $1333.72 rounded to the nearest hundredth

04.02 Identifying Exponential Functions - Worksheets (Math Level 1)

teacher-scored 37 points possible 30 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 7 of your enrollment date for this class.


04.03 Graphing Exponential Functions (Math Level 1)

Graph exponential functions using input-output pairs.

Something to Ponder

How would you describe an exponential function and how it relates to a table, equation and graph?

Mathematics Vocabulary

Exponential: change by a given proportion over a set interval. An example of exponential behavior is a medical isotope decaying to half the previous amount every twenty minutes and a bacteria culture tripling every day each, because, in a given set amount of time (in these examples - twenty minutes or one day), the quantity has changed by a constant proportion (one-half as much and three times as much.

Exponential function graph: points on a graph are either too close to one fixed value or else to too large to be conveniently graphed. There will generally be only a few points that are "reasonable" to use for drawing the curve; picking sensible points require that a good grasp of the general behavior of an exponential, so the curve can be approximated.[defintion derived from http://www.purplemath.com/modules/graphexp.htm ]

Learning these concepts

Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

04.03 Graphing Exponential Functions - Explanation Video Links (Math Level 1)

04.03 Graphing Exponential Functions - Explanation Videos (Math Level 1)

See video


 

04.03 Graphing Exponential Functions - Extra Video (Math Level 1)

I highly recommend that you click on the links above and watch the videos before continuing.

Guided Practice:
After watching the video try these problems. The worked solutions follow.

Example 1:

Make a table and graph the function represented by the following ordered pairs:

{(0, 1), (1, \small \frac{1}{2}), (-1,2), (-2,4), (-3,8)}

Example 2:

Make a table and graph the function represented by the following domain and equation:

Domain: {-2,-1,0,1,2}; f(x)=3x^+4

Example 3:

Make a table and graph the function:

\small f(x) = (\frac{1}{3})^{x}-2

Answers

Example 1:

Make a table and graph the function represented by the following ordered pairs:

{(0, 1), (1, ½), (-1, 2), (-2, 4), (-3, 8)}

x f(x)
0 1
1 \small \frac{1}{2}
-1 2
-2 4
-3 8

 

Example 2:

Make a table and graph the function represented by the following domain and equation:

Domain: {-2, -1, 0, 1, 2}; f(x) = 3x + 4

x f(x)
-2 \small \frac{37}{9}
-1 \small \frac{13}{3}
0 5
1 7
2 13

 

Example 3:

Make a table and graph the function:

\small f(x)= (\frac{1}{3})^{x}-2

x f(x)
-2 7
-1 1
0 -1
1 \small -\frac{5}{3}
2 \small -\frac{17}{9}

 

04.03.01 Graphing Exponential Functions - Worksheet (Math Level 1)

teacher-scored 20 points possible 60 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 7 of your enrollment date for this class.


04.03.02 Check Point Quiz (Math Level 1)

teacher-scored 56 points possible 30 minutes

Quiz Check Point

  1. Print the quiz. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your quiz.

Pacing: complete this by the end of Week 7 of your enrollment date for this class.


04.04 Writing Functions from Tables (Math Level 1)

Write exponential equations in function notation to describe what is happening in a table.

Something to Ponder

How would you describe the process of writing exponential function rules from tables?

Mathematics Vocabulary

y-Intercept: the y coordinate of the point where the function crosses the y-axis

Growth/Decay Factor: the b value in \fn_jvn y = b^{x} + c

Constant/Shift: the c value in y = b^{x} + c

Learning these concepts

Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

 

04.04 Writing Functions from Tables - Explanation Video Links (Math Level 1)

04.04 Writing Functions from Tables - Extra Video (Math Level 1)

I highly recommend that you click on the link above and watch the video before continuing.

Guided Practice:
After watching the video try these problems. The worked solutions follow.

Example 1:

Find the growth/decay factor and constant. Write a function rule for each table:

a)

x f(x)
0 1
1 2
2 4
a b
c d

 

b)

x f(x)
0 4
1 5
2 7
a b
c d

 

c)

x f(x)
0 0
-1 2
-2 8
a b
c d

 

Answers

Example 1:

Find the growth/decay factor and constant. Write a function rule for each table:

a)

x f(x)
0 1
1 2
2 4
{\color{Red}3 } {\color{Red}8 }
{\color{Red}4 } {\color{Red}16 }

 

Vertical shift = 1 – 1 = 0

Growth Factor = 2

f(x) = 2x

b)

x f(x)
0 4
1 5
2 7
{\color{Red}3 } {\color{Red}11 }
{\color{Red}4 } {\color{Red}19 }

 

Vertical shift = 4 – 1 = 3

Growth Factor = 2

f(x) = 2x + 3

c)

x f(x)
0 0
-1 2
-2 8
{\color{Red}-3 } {\color{Red}24 }
{\color{Red}-4 } {\color{Red}78 }

 

Vertical shift = 0 – 1 = – 1

Decay Factor = 3

f(x)=(\frac{1}{3})^{x}-1

04.04 Writing Functions from Tables - Worksheet (Math Level 1)

teacher-scored 66 points possible 60 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 8 of your enrollment date for this class.


04.05 Writing Functions from Graphs (Math Level 1)

Write exponential equations in function notation to describe what is happening in a graph.

Something to Ponder

How would you describe the process of writing exponential function rules from graphs?

Mathematics Vocabulary

Vertical Shift: the movement along the y-axis / change from parent function

Asymptote: the boundary that a function approaches but does not cross

Learning these concepts

Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

04.05 Writing Functions from Graphs - Explanation Video Link (Math Level 1)

See video

 

04.05 Writing Functions From Graphs - Extra Video (Math Level 1)

I highly recommend that you click on the links above and watch the videos before continuing.

Guided Practice:
After watching the video try these problems. The worked solutions follow.

Example 1:

Write a function rule from each graph:

a)

b)

c)

Answers

Example 1:

Write a function rule from each graph:

a)

Vertical shift = (0, 1) to (0, -2) = - 3

Asymptote: y = - 3

Growth Factor = 3 – 1 = 2 (see blue line)

f(x) = 2x - 3

b)

Vertical shift = (1, 0) to (2, 0) = 1

Asymptote: y = 1

Decay Factor = 3 – 1 = 2 (see blue line)

\fn_phv f(x)=(\frac{1}{2})^{x}+1

c)

Vertical shift = (0, 1) to (0, 3) = 3 – 1 = 2

Asymptote: y = 2

Growth Factor = 4 – 2 = 2

f(x) = 2x + 2

04.05 Writing Functions from Graphs - Worksheet (Math Level 1)

teacher-scored 20 points possible 40 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity.

Pacing: complete this by the end of Week 8 of your enrollment date for this class.


04.06 Translating Functions (Math Level 1)

Graph parent functions and transformations of exponential functions.

Something to Ponder

How would you explain the meaning of vertical shift and how it is used to graph exponential functions?

Mathematics Vocabulary

Parent Function: the most basic equation of a function, before any shifts or alterations

Translation: a transformation that shifts a function horizontally, vertically or both

Vertical Shift: a transformation up or down

Learning these concepts

Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language."

{\color{Red}SCROLL } {\color{Red}DOWN } {\color{Red}TO } {\color{Red}THE } {\color{Red}GUIDED } {\color{Red}PRACTICE } {\color{Red}SECTION } {\color{Red}AND } {\color{Red}WORK } {\color{Red}THROUGH } {\color{Red}THE } {\color{Red}EXAMPLES } {\color{Red}BEFORE } {\color{Red}SUBMITTING } {\color{Red}THE } {\color{Red}ASSIGNMENT!!! }

 

04.06 Translating Functions - Explanation Video Link (Math Level 1)

04.06 Translating Functions - Explanation Videos (Math Level 1)

See video


04.06 Translating Functions - Extra Link (Math Level 1)

I highly recommend that you click on the link above and work through the material before continuing.

Guided Practice:
After watching the video try these problems. The worked solutions follow.

Example 1:

Write the parent function and the vertical shift for each of the following functions:

a) \fn_phv f(x)=3^{x}+2

b) f(x)=(\frac{1}{2})^{x}-6

Example 2:

Write the parent function and the vertical shift for each of the following functions:

a)

b)

Answers

Example 1:

Write the parent function and the vertical shift for each of the following functions:

a) f(x) = 3x + 2

Parent function: 3x

Vertical shift: 2

b) f(x)=(\frac{1}{2})^{x}-6

Parent function: f(x)=(\frac{1}{2})^{x}

Vertical shift: – 6

Example 2:

a)

Parent function: 2x

Vertical shift: 3 – 1 = 2 (see the blue line)

b)

Parent function: f(x)=(\frac{1}{2})^{x}

Vertical shift: -1 – 1 = – 2

04.06.01 Translating Functions - Worksheet (Math Level 1)

teacher-scored 20 points possible 40 minutes

Activity for this lesson

  1. Print the worksheet. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your worksheet activity

Pacing: complete this by the end of Week 8 of your enrollment date for this class.


04.06.02 Writing Assignment (Math Level 1)

teacher-scored 30 points possible 45 minutes

As a mathematics teacher, I often hear the question, “When am I ever going to use this?” from students who fail to understand the practical worth of mathematical competency.

Write an essay (at least 3 paragraphs and at least 100 words) answering that question regarding specific topics presented this quarter.

If necessary, research possible occupations you are considering. If you can’t think of any possible way you will use this, research possible reasons for studying this type of math.

Rubric

Criteria Description Points
Introduction (one paragraph) Stage is set for the body of the essay 6
Sentence Structure Complete and correct sentences; sentence variation – simple, compound, complex 5
Mechanics Proper punctuation, capitalization, grammar, and spelling 5
Organization Clear and logical order; smooth transitions among sentences, ideas, and paragraphs 8
Conclusion (one paragraph) Nice summary statement(s) 6

 

Pacing: complete this by the end of Week 8 of your enrollment date for this class.


04.06.03 Unit 04 Review Quiz (Math Level 1)

teacher-scored 53 points possible 45 minutes

Unit Review Quiz

  1. Print the quiz. Work all the problems showing ALL your steps.
  2. Digitize (scan or take digital photo) and upload your quiz.

Pacing: complete this by the end of Week 8 of your enrollment date for this class.