# 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

• 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.

## 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.
7. The exam is timed. You will have 2.0 hours to complete the exam. You must finish it in one attempt.

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

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.

 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 QuickTime for Chromehttps://support.google.com/chrome/answer/2445742?hl=enFirefox browserhttp://www.mozilla.org/en-US/firefox/new/ Recommended ### 00.02 About Me (Math Level 1)  teacher-scored 10 points possible 10 minutes $\fn_phv {\color{Red} CAREFULLY }$ $\fn_phv {\color{Red} FOLLOW }$ $\fn_phv {\color{Red} THE }$ $\fn_phv {\color{Red} DIRECTIONS }$ $\fn_phv {\color{Red} BELOW!! }$ 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 $\fn_phv {\color{Magenta}DIFFERENT }$ $\fn_phv {\color{Magenta}COLOR }$. 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. ### 05.00 Analyzing Algebraic Models Overview (Math Level 1)  Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. By the end of the unit, students will be able to: Write arithmetic sequences. Write geometric sequence. Compare and contrast linear and exponential functions. Use functions to model a situation. Draw conclusions and make inferences from graphs and use a graph to model a situation. ### 05.01 Sequences (Math Level 1)  Recognize arithmetic sequence as having a common difference between consecutive terms. Extend and graph arithmetic sequences. Recognize a geometric sequence as having a constant common ratio between consecutive terms. Extend and graph geometric sequences. Sequences This content is from: ©CK-12 Foundation Licensed under Terms of UseAttribution The Arcade On the way home from school on the day of the trip downtown, a bunch of students stopped off at the arcade. It was always fun to talk and get something to eat and play a video game or two. Sam and Henry began to play a favorite game of theirs with aliens. “That has a lot of math in it,” Sasha commented as Henry had his turn. “How do you figure?” Henry asked. “It just does,” Sasha said convincingly. “Think about it. In this video game, an alien splits into two aliens who then split into two more aliens every 10 minutes.” “Good point, how many aliens there would be after they split 10 times?” Henry asked. We can start by thinking about this as a number pattern. This lesson is all about patterns and sequences. Think about the video game and you will need to solve the sequence at the end of the lesson. Recognize an Arithmetic Sequence as Having a Common Difference Between Consecutive Terms Look at this example of a sequence. You probably saw a pattern right away. If there were another set of boxes, you’d probably guess at how many there would be. If you saw this same pattern in terms of numbers, it would look like this: 2, 4, 6, 8, 10 This set of numbers is called a sequence; it is a series of numbers that follow a pattern. If there was another set of boxes, you’d probably guess there would be 12, right? Just like if you added another number to the sequence, you’d write 12. You noticed that there was a difference of 2 between each two numbers, or terms, in the sequence. When we have a sequence with a fixed number between each of the terms, we call this sequence an arithmetic sequence. Example What is the common difference between each of the terms in the sequence? 7, 12, 17, 22, 27 Answer: The difference is 5 between each number. This is an example of an arithmetic sequence. You can see that you have to be a bit of a detective to figure out the number patterns in these examples. Extend and Graph Arithmetic Sequences Finding the difference between two terms in a sequence is one way to look at sequences. We have used tables of values for several types of equations and we have used those tables of values to create graphs. Graphs are helpful because they are visual representations of the same numbers. When values rise, we can see them rise on a graph. Let’s use the same ideas, then, to graph arithmetic sequences. Example Graph the sequence 2, 5, 8, 11, 14, 17, … First convert it into a table of values with independent values being the term number and the dependent values being the actual term. Use this table to create a graph. You can see the pattern clearly in the graph. That is one of the wonderful things about graphing arithmetic sequences. In the graph that we created in the example, each term was expressed as a single point. This is called discrete data—only the exact points are shown. This type of data is usually involves things that are counted in whole numbers like people or boxes. Depending on what type of situation you are graphing, you may choose to connect the points with a line. The line demonstrates that there are data points between the points that we have graphed. This is called continuous data and usually involves things like temperature or length that can change fractionally. So, we can graph sequences and classify them as either discrete or continuous data. Yet another possibility is continuing a sequence in either direction by adding terms that follow the same pattern. Recognize a Geometric Sequence as Having a Constant Common Ratio Between Consecutive Terms Arithmetic sequences are commonplace in the world of mathematics. There are other types of sequences, though, that follow other types of patterns. Look at the boxes below. Can you see a pattern? The boxes increase each time. Using numbers, the sequence could be written 1, 4, 16, 64. You might even guess at what would come next. Is there a common difference between them? Not really. There is a difference of 3 between the first two terms, 12 between the second and third terms, and 48 between the third and fourth terms. If you guessed that 256 would follow it’s because you figured out the pattern. You noticed that to get to the next term, you have to multiply by 4 instead of by adding a certain number. This is a geometric sequence; it’s a sequence in which the terms are found by multiplying by a fixed number called the common ratio. In the example above, the common ratio is 4. Once you know the common ratio, then you can figure out the next step in the pattern. Example What is the common ratio between each of the terms in the sequence? 5, 10, 20, 40, 80 The ratio is 2 between each number. You can see how knowing the common ratio helped us with our problem solving. Extend and Graph a Geometric Sequence Consider the following sequence: 8, 24, 72, 216, … Doesn’t your brain want to find the next number? You’ve probably figured out that the common ratio here is 3. So the next term in the sequence would be 216 x 3 or 648. You would continue the same process to find the term that follows. Or, you could divide by 3 to find the previous term. Just as we did with arithmetic sequences, it can be useful to graph geometric sequences. We’ll use the same method as before—create a table of values and then use a coordinate plane to plot the points. Example The amount of memory that computer chips can hold in the same amount of space doubles every year. In 1992, they could hold 1MB. Chart the next 15 years in a table of values and show the amount of memory on the same size chip in 2007.  Year Memory (MB) 1992 1 1993 2 1994 4 1995 8 1996 16 1997 32 1998 64 1999 128 2000 256 2001 1024 Now, graph these points. This is not a straight line like the arithmetic sequences. It is an exponential curve. Now let’s go back and solve the problem from the introduction. Real-Life Example Completed The Arcade Here is the problem from the introduction. Reread it and then solve figure out the solution. On the way home from school on the day of the trip downtown, a bunch of students stopped off at the arcade. It was always fun to talk and get something to eat and play a video game or two. Sam and Henry began to play a favorite game of theirs with aliens. “That has a lot of math in it,” Sasha commented as Henry had his turn. “How do you figure?” Henry asked. “It just does,” Sasha said convincingly. “Think about it. In this video game, an alien splits into two aliens who then split into two more aliens every 10 minutes.” “Good point, how many aliens there would be after they split 10 times?” Henry asked. Solution to Real – Life Example We can write a number pattern. 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 1024 aliens after 10 splits! This is the answer to our problem. Vocabulary Sequence – a series of numbers that follows a pattern. Arithmetic Sequence – a fixed number between each of the terms in a sequence. Discrete data – only the exact points are shown. Continuous data – data that changes continuously. Geometric Sequence – a sequence where you find terms by multiplying a fixed number by a common ratio. ### 05.01 Sequences Worksheet (Math Level 1)  teacher-scored 30 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. ### 05.02 Arithmetic Sequences (Math Level 1)  Write arithmetic sequences. Something to Ponder How would you explain the process for writing a recursive formula for an arithmetic sequence? Mathematics Vocabulary Arithmetic Sequence: a numerical sequence formed by adding a term in the sequence by a fixed number to find the next term. Common Difference: the fixed number that is added to each term of an arithmetic sequence. Arithmetic Sequence Formulas: • Recursive$\fn_phv a_{n} =a_{n-1}+d$ • Explicit: $\fn_phv a_{n} =a_{1}+d(n-1)$ which must be simplified once the values are plugged in!! Learning these concepts Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language." Then watch the two additional videos. Scroll down to the Guided Practice section and work through the examples before submitting the assignment. ### 05.02 Arithmetic Sequences - Explanation Video Link (Math Level 1)  Explanation Video 05.02-1http://www.youtube.com/embed/F5WFmkTKlwM?wmode=transparent&r... ### 05.02 Arithmetic Sequences - Explanation Videos (Math Level 1) ### 05.02 Arithmetic Sequences - Extra Video (Math Level 1)  Mathispower4u: Introduction to Sequenceshttps://www.youtube.com/watch?v=p-rc5mTDt9EMathispower4u: Arithmetic Sequenceshttps://www.youtube.com/watch?v=jExpsJTu9o8 I highly recommend that you click on the links above and watch the additional videos before continuing. Guided Practice After watching the video try these problems. The worked solutions follow. Example 1: Is the given sequence arithmetic? If so, identify the common difference. a) 2, 4, 8, 16... b) 5, 9, 13, 17, 21... Example 2: Find the next three terms of the sequence: 1100, 1135, 1170, ... Example 3: Given the explicit formula, write an arithmetic sequence for each of the following: an = -42+10n Example 4: Given the first four numbers in each arithmetic sequence write a recursive and explicit formula: 39, 42, 45, 48, ... Answers Example 1: a) 2, 4, 8, 16... Common difference: 4 – 2 = 2, 8 – 4 = 4… NO, it is not an arithmetic sequence! b) 5, 9, 13, 17, 21... Common difference: 9 – 5 = 4; 13 – 9 = 4… YES, it is an arithmetic sequence with d = 4 Example 2: Find the next three terms of the sequence: 1100, 1135, 1170… Common difference: 1135 – 1100 = 35 a4 = 1170 + 35 = 1205 a5 = 1205 + 35 = 1240 a6 = 1240 + 35 = 1275 Example 3: Given the explicit formula, write an arithmetic sequence for each of the following: an = –42+10n a1 = –42 + 10(1) = -42 + 10 = – 32 a2 = –42 + 10(2) = -22 a3 = –42 + 10(3) = -12 Sequence: –32, –22, –12, –2, 8, 18, … Example 4: Given the first four numbers in each arithmetic sequence write a recursive and explicit formula: 39, 42, 45, 48, ... a1 = 39, d = 3 E: an = a1 + d(n–1); an = 39 + 3(n-1) = 39 +3n – 3 = 36 + 3n R: an = a(n-1) + d = a(n-1) + 3 ### 05.02 Arithmetic Sequences - Worksheet (Math Level 1)  teacher-scored 70 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 1 of your enrollment date for this class. ### 05.03 Geometric Sequences (Math Level 1)  Write geometric sequences. Something to Ponder How would you compare and contrast Arithmetic and Geometric Sequences? Mathematics Vocabulary Geometric Sequence: a number sequence formed by multiplying a term in a sequence by a fixed number to find the next term Common Ratio: the fixed number that is multiplied to each term of an geometric sequence. Geometric Sequence Formulas: • Recursive: $\dpi{100} \fn_phv \fn_jvn a_{1} =$ _____ , $\dpi{100} \fn_phv a_{n} = a_{n-1} \cdot r$ • Explicit: $\dpi{100} \fn_phv a_{n} = a_{1} \cdot r^{n-1}$ Learning these concepts Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language." Scroll down to the Guided Practice section and work through the examples before submitting the assignment. ### 05.03 Geometric Sequences - Explanation Video Links (Math Level 1)  Explanation Video 05.03-1http://www.youtube.com/embed/20qZDfPxDSk?wmode=transparent&r...Explanation Video 05.03-2http://www.youtube.com/embed/rsQ5hXxSMX0?wmode=transparent&r... ### 05.03 Geometric Sequences - Explanation Videos (Math Level 1) ### 05.03 Geometric Sequences - Extra Video (Math Level 1)  Mathispower4u: Geometric Sequenceshttps://www.youtube.com/watch?v=XHyeLKZYb2w I highly recommend that you click on the link above and watch an additional video before continuing. Guided Practice After watching the video try these problems. The worked solutions follow. Example 1: Is the given sequence geometric? If so, identify the common ratio. a) 5, 15, 45, 135, ... b) 15, 30, 45, 60, ... Example 2: Find the next three terms of the following geometric sequences a) 2, 12, 72, 432, ... b) 4, 24, 144, 864, ... Example 3: Given the explicit formula, write a geometric sequence for each of the following: a) an = 2x2(n-1) b) an = 2x4(n-1) Example 4: Given the first four numbers in each geometric sequence write a recursive and explicit formula: a) -1, -3, -9, -27, ... b) 4, 12, 36, 108, ... Answers Example 1: Is the given sequence geometric? If so, identify the common ratio. a) 5, 15, 45, 135, ... 15 $\div$ 3 = 5; 45 $\div$ 15 = 3 r = $\dpi{100} \fn_phv \frac{1}{3}$, YES b) 15, 30, 45, 60, ... 30 $\div$ 15 = 3; 45 $\div$ 30 = 1.5 NO Example 2: Find the next three terms of the following geometric sequences: a) 2592, 15,552, 93,312 15,552 $\div$ 2592 = 6 = r a1 = 93,312 x 6 = 559,872 a2 = 559,872 x 6 = 3,359,232 a3 = 3,359,232 x 6 = 20,155,392 b) 5184, 31,104, 186,624 31,104 $\div$ 5184 = 6 = r a1 = 1,119,744 a2 = 6,718,464 a3 = 40,310,784 Example 3: Given the explicit formula, write a geometric sequence for each of the following: a) an = 2x2(n-1) an = a1xr(n-1) a1 = 2, r = 2 a1 = 2 a2 = 2x2(2-1)= 2x21 = 2x2 = 4 a3 = 2x2(3-1)= 2x22 = 2x4 = 8 Sequence: 2, 4, 8, 16, 32, … b) an = 2x4(n-1) an = a1xr(n-1) a1 = 2, r = 4 a1 = 2 a2 = 2x4(2-1) = 2x41 = 2x4 = 8 a3 = 2x4(3-1) = 2x42 = 2x16 = 32 Sequence: 2, 8, 32, 128, 512, … Example 4: Given the first four numbers in each geometric sequence write a recursive and explicit formula: a) – 1, – 3, – 9, – 27, … a1 = –1 r = $\dpi{100} \fn_phv \frac{-3}{-1}$ = –3 E: a1xr(n-1) = (– 1)(3)(n-1) R: an = a(n-1) x r = a(n-1) x 3, a1 = –1 b) 4, 12, 36, 108, ... a1 = 4 r = $\dpi{100} \fn_phv \dpi{100} \fn_phv \frac{12}{4}$ = 3 E: a1 x r(n-1) = (4)(3)(n-1) R: an = a(n-1) x r = a(n-1) x 3, a1 = 4 ### 05.03 Geometric Sequences - Worksheet (Math Level 1)  teacher-scored 70 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 1 of your enrollment date for this class. ### 05.04 Comparing Linear and Exponential Functions (Math Level 1)  Compare and contrast linear and exponential functions. Something to Ponder How would you compare and contrast Linear and Exponential functions? Mathematics Vocabulary Linear Function: a function that can be represented on a graph as a straight line; for example: $\dpi{100} \fn_phv \fn_jvn y=mx+b$ Exponential Function: a function that repeatedly multiplies the initial amount by the same positive number; for example: $\dpi{100} \fn_phv y=b^{x}+k$ Simple Interest: interest on an investment that is calculated once per period, usually annually, on the amount of the capital alone and not on any interest already earned. Formula: I = P x r x t where I = interest, P = principal or starting value, r = interest rate. Compound Interest: interest which is calculated not only on the initial principal but also the accumulated interest of prior periods. Formula: B = P(r + 1)t where B = Balance, P = principal or starting value, r = interest rate. Learning these concepts Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language." Scroll down to the Guided Practice section and work through the examples before submitting the assignment. ### 05.04 Comparing Linear and Exponential Functions - Explanation Video Links (Math Level 1)  Explanation Video 05.04-1http://www.youtube.com/embed/ZJ-yAemweP0?wmode=transparent&r...Explanation Video 05.04-2http://www.youtube.com/embed/01ASwIKyHeQ?wmode=transparent&r...Explanation Video 05.04-3http://www.youtube.com/embed/OZ1ayhXS3GI?wmode=transparent&r...Explanation Video 05.04-4http://www.youtube.com/embed/OqOzZmnTZtI?wmode=transparent&r... ### 05.04 Comparing Linear and Exponential Functions - Explanation Videos (Math Level 1) ### 05.04 Comparing Linear and Exponential Functions - Extra Video (Math Level 1)  mathispower4u: Determine if a Table Represents a Linear or Exponential Functionhttps://www.youtube.com/watch?v=x36yjjdtGjM&feature=youtu.bemathispower4u: Compare Simple Interest and Annual Compounded Interest https://www.youtube.com/watch?v=sGPMn6CZrDI&feature=youtu.be 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: Suppose you deposit$500 in a savings account. The interest rate is 4% per year. Find the simple interest earned in 10 years. How much money will you have? Make a table and graph of the first 10 years of interest and the resulting income.

Example 2:

Suppose you deposit $500 in a savings account. The interest rate is 4% compounded annually. Find the compound interest earned in 10 years. How much money will you have? Make a table and graph of the first 10 years of interest and the resulting income. Answers Example 1: I = P x r x t; P =$500, r = 0.04; t = 1 through 10

 Year Interest Income 1 I = 500x.04x1 = 20 500+20 = 520 2 I = 500x.04x2 = 40 500+40 = 540 3 I = 500x.04x3 = 60 500+60 = 560 4 I = 500x.04x4 = 80 500+80 = 580 5 I = 500x.04x5 = 100 500+100 = 600 6 I = 500x.04x6 = 120 500+100 = 620 7 I = 500x.04x7 = 140 500+100 = 640 8 I = 500x.04x8 = 160 500+100 = 660 9 I = 500x.04x9 = 180 500+100 = 680 10 I = 500x.04x10 = 200 500+100 = 700

Example 2:

### 05.05 Functions in the Real World - 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 2 of your enrollment date for this class.

### 05.06 Graphs of Functions in the Real World (Math Level 1)

 Draw conclusions and make inferences from graphs and use a graph to model a situation.

Something to Ponder

What are some things you need to consider as you write expressions or equations to model real-life situations and problems?

Mathematics Vocabulary

Independent Variable: a variable that provides the input values of a function

Dependent Variable: a variable that provides the output values of a function

Scale: a system of ordered marks at fixed intervals used as a reference standard in measurement. All x-axes and y-axes must use a fixed scale. For example, the x-axis may be numbered by 2's: the origin, then 2, 4, 6, 8 etc., on each tick mark. The y-axis on the same graph may by numbered by 5's: the origin, then 5, 10, 15, 20, etc., on each tick mark.

Learning these concepts

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

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 05.06 Graphs of Functions in the Real World - Explanation Videos (Math Level 1)

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

Example 1:

The graph below shows the number of live births per 10,000 of 23-year-old women in the United States between 1917 and 1975.

a)  What are the labels on the chart?

b)  What do they represent?

c)  What is the independent variable?

d)  What is the dependent variable?

e)  What is the scale for the dependent and independent variables?

f)  What conclusions can you draw from the graph?

g)  If the graph continues in the same way, what do you think the birthrate might have been in 1987?

Example 2:

The table shows the average salaries of CEOs by age. Make a graph and interpret what the graph is telling you. Based on the trend, what might the salary of a 30 year old be? A 70 year old?

 age average salary (in thousands) 35 40 45 50 55 60 65 281 340 382 426 553 590 640

Example 1:

a) What are the labels on the chart? Years and Birthrate
b) What do they represent? The years between 1917 and 1975; live births of 23-year old women
c) What is the independent variable? Year
d) What is the dependent variable? births
e) What is the scale for the dependent and independent variables? Year: 12; Birthrate: 40
f) What conclusions can you draw from the graph? Births were affected by wars with spikes in between the various wars.

If the graph continues, the birthrate in 1987 might be < 120.

Example 2:

a) Based on the trend, what might the salary of a 30 year old be? $150,000 b) A 70 year old?$700,000

### 05.06 Graphs of Functions in the Real World - 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 3 of your enrollment date for this class.

### 05.06 Unit 05 Review Quiz (Math Level 1)

 teacher-scored 58 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 corrected quiz.

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

### 06.00 Systems of Equations and Inequalities Overview (Math Level 1)

 By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation and to justify the process used in solving a system of equations. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. Students explore systems of equations and inequalities, and they find and interpret their solutions. All of this work is grounded on understanding quantities and on relationships between them. By the end of the unit, students will be able to: Solve systems of linear equations graphically and predict the number of solutions to a system of equations. Solve systems of linear equations by substitution. Solve systems of linear equations by elimination. Graph linear inequalities. graph systems of linear inequalities. Use systems of equations to solve real world problems.

### 06.01 Systems of Equations (Math Level 1)

 Solve systems of linear equations graphically and predict the number of solutions to a system of equations.

Something to Ponder

How would you explain the process for predicting the number of solutions to a system of equations without graphing?

Mathematics Vocabulary

Systems of Linear Equations: two or more linear equations that use the same variables (referring to a common scenario)

Solution of a System of Linear Equations: any ordered pair that makes all of the equations in a system true

Learning these concepts

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

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 06.01 Systems of Equations - Explanation Video Link (Math Level 1)

Optionally: use the link above to view the explanatory math video.

### 06.01 Systems of Equations - Extra Video (Math Level 1)

 NROC Algebra 1: Solving Systems of Equations by Graphinghttp://www.montereyinstitute.org/courses/Algebra1/U06L1T1_RE...mathispower4u: Solving Systems of Linear Equations by Graphing - Part 1 (L12.1A)http://youtu.be/wOQNBED5Yu8mathispower4u: Solving Systems of Linear Equations by Graphing - Part 2 (L12.1B)http://youtu.be/lN8LaXBLmsUmathispower4u: Solving Systems of Equations by Graphing http://www.youtube.com/embed/cauaqqwAWCE?wmode=transparent&r...mathispower4u: Ex: Determine Solutions to Systems of Linear Equations Graphically http://youtu.be/sTSKBzXdTJ4mathispower4u: Ex: Identify the Solution to a System of Equation Given a Graph, Then Verify http://www.youtube.com/embed/bd6Lm7uJ7VQ?wmode=transparent&r...mathispower4u: Ex 1: Solve a System of Equations by Graphing http://www.youtube.com/embed/uNuIxrHZTQs?wmode=transparent&r...mathispower4u: Ex 2: Solve a System of Equations by Graphing http://www.youtube.com/embed/Lv832rXAQ5k?wmode=transparent&r...mathispower4u: Ex: Solve a System of Equations by Graphing (Infinite Solutions)http://www.youtube.com/embed/KX2w-6EGWVA?wmode=transparent&r...mathispower4u: Ex: Solve a System of Equations by Graphing (No Solution)http://www.youtube.com/embed/EWxYkqWw07E?wmode=transparent&r...

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

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

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

Example 1:

Solve by graphing:

y = 2x + 1
y = 3x - 1

Example 2:

Solve by graphing:

y = 3x + 2
y = 3x - 2

Example 3:

Solve by graphing:

3x + 4y = 12
y = $\dpi{100} \fn_phv \dpi{100} \fn_phv -\frac{3}{4}$x + 3

Example 4:

Without graphing, predict the number of solutions for the following systems of equations.

a) 5x - 3y= 12
5x - 3y= -9

b) 2x - y   = -6
4x - 2y = -12

c) x + 4y = 12
5x -  4y  = 12

Example 5:

For the following determine if the given ordered pair is a solution to the system:

a) y =    x - 2, (3,1)
y = $\dpi{100} \fn_phv -\frac{2}{3}$x+ 3

b) y =  4x + 3, (1,-1)
y = -2x - 3

Example 1:

Solution: (2, 5)

Example 2:

No solution

Example 3:

Solution: (0, 3)

Example 4:

a) No solution – the coefficients of the x-values are the same; the coefficients of the y-value are the same. This means the lines are parallel.

b) Infinite solutions – the bottom equation equals the top equation by multiplied by 2. This means they are the same line.

c) One solution.

Example 5:

For the following determine if the given ordered pair is a solution to the system:

a) y =    x - 2, (3,1)
y = $\dpi{100} \fn_phv -\frac{2}{3}$ x+ 3

1st Equation:

2 = 3 - 2

2 ≠ 1

No, the ordered pair is not a solution.

b) y =  4x + 3, (1,-1)
y = -2x - 3

1st Equation:

-1 = 4(1) + 3

-1 = 4 + 3

No, the ordered pair is not a solution.

### 06.01 Systems of Equations - Worksheet (Math Level 1)

 teacher-scored 76 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 4 of your enrollment date for this class.

### 06.02 Solving Systems Using Substitution (Math Level 1)

 Solve systems of linear equations by substitution.

Something to Ponder

When should you choose to use the substitution method for solving a system of equations?

Mathematics Vocabulary

Substitution method: solution strategy in which a variable is replaced with a value or expression from another equation in the system

Learning these concepts

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

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 06.02 Solving Systems Using Substitution - Extra Video (Math Level 1)

 NROC Algebra 1: Solving Systems of Equations with Substitutionhttp://www.montereyinstitute.org/courses/Algebra1/U06L1T2_RE...mathispower4u: Solving Systems of Linear Equations Using Substitution (L12.2)http://youtu.be/RASOhKXTa5cmathispower4u: Solving Systems of Equations by Substitutionhttps://www.youtube.com/watch?v=HxhacvH49o8mathispower4u: Ex 1: Solve a System of Equations Using Substitutionhttp://www.youtube.com/embed/oUC931TcBuw?wmode=transparent&r...mathispower4u: Ex 2: Solve a System of Equations Using Substitution http://www.youtube.com/embed/MIXL35YRzRw?wmode=transparent&r...mathispower4u: Ex 3: Solve a System of Equations Using Substitutionhttp://www.youtube.com/embed/MT2afriULmU?wmode=transparent&r...mathispower4u: Ex 4: Solve a System of Equations Using Substitution http://www.youtube.com/embed/j_BsjiDF8_4?wmode=transparent&r...mathispower4u: Ex: Solve a System of Equations Using Substitution - Infinite Solutions http://www.youtube.com/embed/Pcqb109yK5Q?wmode=transparent&r...mathispower4u: Ex: Solve a System of Equations Using Substitution - No Solutionhttp://www.youtube.com/embed/kTtKfh5gFUc?wmode=transparent&r...Art of Problem Solving: Solving Systems of Linear Equations with Substitutionhttp://www.artofproblemsolving.com/Videos/external.php?video...

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

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

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

Example 1:

Solve using substitution:

a) -x - y = - 5
y = 3

b) y = - 3x
2x - 5y = 34

c) 4x + 2y = 1
y = -2x - 5

Example 1:

Solve using substitution:

a) -x - y = - 5
y = 3

Substitute y = 3 into the top equation:

-x - 3 = -5

Solve for x:

-x = -2

x = 2

You were given the value of y so now write your answer as an ordered pair: (2, 3)

b) y = - 3x
2x - 5y = 34

Substitute y = -3x into the bottom equation:

2x – 5(-3x) = 34

2x + 15x = 34

17x = 34

x = 2

Use this value of x to solve for y:

y = -3x = -3(2) = -6

Solution: (2, -6)

c) 4x + 2y = 1
y = -2x - 5

Substitute y = -2x - 5 into the top equation:

4x + 2(-2x – 5) = 1

4x – 4x – 10 = 1

-10 = 1

Since this makes no sense, there is no solution.

### 06.02 Solving Systems Using Substitution - Worksheet (Math Level 1)

 teacher-scored 60 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.

### 06.03 Solving Systems Using Elimination (Math Level 1)

 Solve systems of linear equations by elimination.

Something to Ponder

In solving a system of equations, why does it work to multiply an equation by a number?

Mathematics Vocabulary

Elimination method: solution strategy where a single variable is eliminated in every equation within a system

Learning these concepts

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

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 06.03 Solving Systems Using Elimination - Extra Video (Math Level 1)

 Art of Problem Solving: Solving Systems of Equations with Elimination, Part 1http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Solving Systems of Equations with Elimination, Part 2http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Solving Systems of Equations with No Solutionhttp://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Solving Systems of Equations with Many Solutionshttp://www.artofproblemsolving.com/Videos/external.php?video...mathispower4u: Solving Systems of Linear Equations Using Addition (Elimination) (L12.3)http://youtu.be/GqILa2JYDacmathispower4u: Solving Systems of Equations by Eliminationhttp://www.youtube.com/embed/ova8GSmPV4o?wmode=transparent&r...mathispower4u: Ex 1: Solve a System of Equations Using the Elimination Method http://www.youtube.com/embed/M4IEmwcqR3c?wmode=transparent&r...mathispower4u: Ex 2: Solve a System of Equations Using the Elimination Methodhttp://www.youtube.com/embed/_liDhKops2w?wmode=transparent&r...mathispower4u: Ex 3: Solve a System of Equations Using the Elimination Methodhttp://www.youtube.com/embed/YY9FbDbYVXU?wmode=transparent&r...mathispower4u: Ex: System of Equations Using Elimination (Infinite Solutions)http://www.youtube.com/embed/NRxh9Q16Ulk?wmode=transparent&r...mathispower4u: Ex: System of Equations Using Elimination (No Solution)http://www.youtube.com/embed/z5_ACYtzW98?wmode=transparent&r...

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:

Solve by elimination:

a)  2x + 3y = 11
-2x + 9y = 1

b)  3x - 2y = 3
3x +3y = 18

Example 2:

Solve by elimination:

a)  3x + 6y = -6
-5x -  2y = -14

b)  3x + 5y = 10
5x + 7y = 10

Example 1:

Solve by elimination:

a) 2x + 3y = 11
-2x + 9y = 1

12y = 12

Solve for y:

y = 1

Substitute this value of y into one of the equations:

2x + 3(1) = 11

2x + 3 = 11

2x = 8

x = 4

Solution: (4, 1)

b) 3x - 2y = 3
3x +3y = 18

Multiply the top equation by -1

-3x + 2y = -3

Add this to the bottom equation:

-3x + 2y = -3

3x + 3y = 18

5y = 15

y = 3

Substitute this value of y into the bottom equation:

3x – 2(3) = 3

3x – 6 = 3

3x = 9

x = 3

Solution: (3, 3)

Example 2:

Solve by elimination:

a)  3x + 6y = -6
-5x -  2y = -14

Multiply the bottom equation by 3:

-15x - 6y = -42

Add this to the top equation:

-15x - 6y = -42

3x + 6y = -6

-12x = -48

Divide both sides by -12:

x = 4

Now solve for y by substituting this value into the first equation:

3(4) + 6y = -6

12 + 6y = -6

Subtract 12 from both sides:

6y = -18

Divide both sides by 6:

y = -3

Solution: (4, -3)

b)  3x + 5y = 10
5x + 7y = 10

Multiply the top equation by -5 and the bottom equation by 3:

-15x - 25y = -50

15x + 21y = 30

-4y = -20

y = 5

Substitute this value for y into the first equation:

3x + 5(5) = 10

3x + 25 = 10

Subtract 25 from both sides:

3x = -15

Divide both sides by 3:

x = -5

Solution: (-5, 5)

### 06.03.01 Solving Systems Using Elimination - Worksheet (Math Level 1)

 teacher-scored 60 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.

### 06.03.02 Check Point Quiz (Math Level 1)

 teacher-scored 60 points possible 40 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 4 of your enrollment date for this class.

### 06.04 Linear Inequalities (Math Level 1)

 Graph linear inequalities.

Something to Ponder

How would you explain the process for graphing linear inequalities?

Mathematics Vocabulary

Linear inequality: a math sentence that represents all possible solutions

Solutions of an inequality: the shaded region bound by the inequality

Learning these concepts

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

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 06.04 Linear Inequalities - Extra Video (Math Level 1)

 mathispower4u: Ex 1: Graph a System of Linear Inequalitieshttp://www.youtube.com/embed/ACTxJv1h2_c?wmode=transparent&r...mathispower4u: Ex 2: Graph a System of Linear Inequalities http://www.youtube.com/embed/cclH2h1NurM?wmode=transparent&r...

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:

a) Graph: y > 2x + 1

b) Graph: y < -3x - 1

Example 1: Graph: y > 2x + 1

b) Graph: y < -3x - 1

### 06.04.01 Linear Inequalities - Worksheet (Math Level 1)

 teacher-scored 48 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 5 of your enrollment date for this class.

### 06.05 Systems of Linear Inequalities (Math Level 1)

 Graph systems of linear inequalities.

Something to Ponder

How would you describe what the solution to a system of linear inequalities represents?

Mathematics Vocabulary

System of linear inequalities: two or more linear inequalities that use the same variables (referring to a common scenario)

Solution of a system of linear inequalities: any ordered pair that makes all of the inequalities in the system true

Learning these concepts

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

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 06.05 Systems of Linear Inequalities - Extra Video (Math Level 1)

 NROC Algebra 1: Graphing Systems of Inequalitieshttp://www.montereyinstitute.org/courses/Algebra1/U06L3T1_RE...mathispower4u: Systems of Linear Inequalities http://www.youtube.com/embed/ZsmAF10e9Vo?wmode=transparent&r...

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

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

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

Example 1:

Solve by graphing:

a) y < -x + 3
y ≥ x

b) y ≥ -x + 2
y < x +1

Example 1:

a) y < -x + 3
y ≥ x

b) y ≥ -x + 2
y < x +1

### 06.05 Systems of Linear Inequalities - 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 5 of your enrollment date for this class.

### 06.05.01 Check Point Quiz 2 (Math Level 1)

 teacher-scored 50 points possible 25 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.

### 06.06 Systems of Equations in the Real World (Math Level 1)

 Use systems of equations to solve real world problems.

Something to Ponder

What are some examples from your personal life of systems of equations?

Mathematics Vocabulary

Real world problem solving steps:

1. Highlight the problem's important information.
2. Define the variables
3. Write two equations
4. Select the methods (elimination, substitution, etc.) to solve

Learning these concepts

Click the image or the link below to launch the video to help you better understand this "mathematical language."

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 06.06 Systems of Equations in the Real World - Extra Link (Math Level 1)

 Making Decisions with System of Equationshttp://www.sophia.org/using-systems-of-equations-to-make-dec...

### 06.06 Systems of Equations in the Real World - Extra Video (Math Level 1)

 Art of Problem Solving: Systems of Equations and Word Problems Part 1http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Systems of Equations and Word Problems Part 2http://www.artofproblemsolving.com/Videos/external.php?video...mathispower4u: Applications Involving Systems of Equations http://www.youtube.com/embed/GTolISAXveg?wmode=transparent&r...mathispower4u: Application Using a System of Linear Equations (L12.4)http://youtu.be/rb823rFmDVEmathispower4u: More Applications Involving Systems of Equations http://www.youtube.com/embed/8yw6ra--RDE?wmode=transparent&r...mathispower4u: Ex: System of Equations Application - Number Problem Using Substitution http://www.youtube.com/embed/VVkJTRMYoPY?wmode=transparent&r...mathispower4u: Ex: System of Equations Application - Number Problem Using Elimination http://www.youtube.com/embed/5XZagl_MSvQ?wmode=transparent&r...mathispower4u: Ex: System of Equations Application - Compare Phone Plans http://www.youtube.com/embed/7ikvixNSKEU?wmode=transparent&r...mathispower4u: Ex: System of Equations Application - Entrance Feeshttp://www.youtube.com/embed/uH4CgUhuDv0?wmode=transparent&r...mathispower4u: Ex: System of Equations Application - Coin Problemhttp://www.youtube.com/embed/GZYtSP-X_is?wmode=transparent&r...mathispower4u: Ex: System of Equations Application - Investment Accountshttp://www.youtube.com/embed/3hJeqNT5mrk?wmode=transparent&r...mathispower4u: Ex: System of Equations Application (Corral Perimeter) http://www.youtube.com/embed/z5E0x45bpZ4?wmode=transparent&r...mathispower4u: Ex: System of Linear Function Application - Median Home Priceshttp://youtu.be/jJ2mlQWV0Hk

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:

Jennifer and Jill are selling boxes of tangerines for the school fundraiser. Customers can buy either large or small boxes. Jennifer sold 7 small and 4 large boxes of tangerines for a total of $192. Jill sold 3 small and 4 large for a total of$128. What is the cost of each of the sizes of boxes?

Example 2:

The music department is selling tickets to the annual talent show. On the first day they sold 8 adult and 3 student tickets for a total of $136. On the second day they took in$106 by selling 7 adult and 1 student ticket. What is the cost of each adult and each student ticket?

Example 3:

Two high school senior classes are planning field trips to the state fair. High School A fills 6 vans and 6 busses with 390 students. High School B filled 8 vans and 4 buses with 312 students. How many students could ride on each van and each bus?

Example 4:

The sum of two numbers is 10 and their difference is 2. What are the numbers?

Example 1:

Let L = large box and S = small box

7S + 4L = $192 3S + 4L =$128

Multiply the top equation by -1 then add that to the bottom equation:

-7S – 4L = -$192 3S + 4L =$128

-4S = -$64 S =$16

Substitute this value of S into the top equation:

7S + 4L = $192 7(16) + 4L =$192

112 + 4L = $192 4L =$80

L = $20 The cost of the small boxes is$16 and the cost of the large boxes is $20. Example 2: Let a = adult tickets and s = student tickets 8a + 3s =$136

7a + s = $106 Multiply the bottom equation by -3 and then add it to the first equation: -21a – 3a = -318 8a + 3s = 136 -13a = -182 a =$14

Substitute this value of a into the bottom equation:

7(14) + s = 106

98 + s = 106

s = $8 The cost of an adult ticket is$14 and the cost of a student ticket is \$8.

Example 3:

Let v = cans and b = busses

6v + 6b = 390

8v + 4b = 312

Multiply the top equation by -2 and the bottom equation by 3 then add them together:

-12v – 12b = -780

24v + 12b = 936

12v = 156

v = 13

Substitute this value of v into the top equation:

6(13) + 6b = 390

78 + 6b = 390

6b = 312

b = 52

Each van can hold 13 students and each bus can hold 52 students.

Example 4:

Let the first number = x and the second number =y

x + y = 10

x – y = 2

x + y = 10

x – y = 2

2x = 12

x = 6

Substitute this value of x into the top equation:

6 + y = 10

y = 4

The two numbers are 4 and 6.

### 06.06 Systems of Equations in the Real World - Worksheet (Math Level 1)

 teacher-scored 60 points possible 60 minutes

Activity for this lesson

1. Print the worksheets. Work all the problems showing ALL your steps.
2. Digitize (scan or take digital photo) and upload your worksheet activity.
3. Turn in both assignments at the same time!

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

### 06.06 Unit 06 Review Quiz (Math Level 1)

 teacher-scored 108 points possible 40 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 corrected quiz.

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

### 07.00 Geometric Figures Overview (Math Level 1)

 In previous grades, students were asked to draw triangles based on given measurements. They also have prior experi- ence with rigid motions: translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work. By the end of the unit, students will be able to: Define, name and model geometric figures including points, lines, rays, segments, angles and planes. Find perimeter and area of geometric figures. Write equations for solving problems involving angle relationships. Find the lengths of segments using addition and midpoint properties. Find the measures of angles using addition and bisector properties. Explain and use the properties of triangles. Explain and use the properties of quadrilaterals and polygons. Find the measures of angles in circles and polygons.

### 07.01 Geometry Basics (Math Level 1)

 Define, name and model geometric figures including points, lines, rays, segments, angles and planes.

Something to Ponder

How would you describe the similarities and differences between lines, rays and segments?

Mathematics Vocabulary

Point: a location in space. Example:

Line: a series of points extending infinitely in two opposite directions. Example: $\fn_phv \overline{AC\E}$

Ray: a series of points having one terminal end and extending infinitely in one direction. Example: $\fn_phv \overrightarrow{BA}}$

Segment: a portion of a line, having two terminal ends. Example: $\fn_phv \overline{BE}$

Angle: two rays sharing a terminal end. Example: $\fn_phv \angle ABC}$

Arc: part of the perimeter of a given circle. Example:

Plane: a two dimensional surface that has no thickness and extends infinitely. Example: $\fn_phv \square }ABC$ or $\fn_phv \square ABCD$ (either is correct for the top of the cube above)

Parallel lines: lines on a single plane that do not intersect. Example: $\fn_phv \overline{AD} || \overline{BC}$

Skew lines: lines on separate planes that do not intersect. Example: $\fn_phv \overline{AB}$ and $\fn_phv \overline{FG}$

Parallel planes: two or more planes that do not intersect. Example: $\fn_phv \square }ABC$ and $\fn_phv \square }EFG$

Intersection: the location where two or more “things” meet (planes intersect in a line, lines intersect at a point)

Learning these concepts

Click the image or the link below to launch the video to help you better understand this "mathematical language."

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 07.01 Geometry Basics - Extra links (Math Level 1)

 mathispower4u: Points, Lines and Planeshttps://www.youtube.com/watch?v=VQ15ECqYDGsArt of Problem Solving: Introduction to Angleshttp://www.artofproblemsolving.com/Videos/external.php?video...rapidtables.com: Geometry Symbolshttp://www.rapidtables.com/math/symbols/Geometry_Symbols.htmmathispower4u: Parallel and Perpendicular Lines and Planeshttps://www.youtube.com/watch?v=LYh8jXhG7q8

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

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

Example 1:

Name each of the points, lines, rays, segments and angles in the figure in two ways using correct mathematical notation:

Example 2:

Using the box-like figure:

a. Name all labeled segments that are parallel to BF
b. Name all labeled segments that are skew to BF
c. Name all the planes
d. Name all the pairs of parallel planes
e. Name the intersection of segments DH and DA; segments CG and GF.
f. Name the intersection of the top and right planes; The back and bottom planes.

Example 3:

Draw and label the following:

a. Point B

d. line MN

b. segment XY

c. ray CK

e. angle GHI

f. plane QRST

Example 1:

 Points A B C D E Lines1 $\dpi{100} \fn_phv \fn_phv \overline{BC}$ $\dpi{100} \fn_phv \overline{CE}$ $\dpi{100} \fn_phv \overline{BE}$ Rays $\dpi{100} \fn_phv \overrightarrow{BC}$ $\dpi{100} \fn_phv \overrightarrow{CB}$ $\dpi{100} \fn_phv \overrightarrow{CE}$ $\dpi{100} \fn_phv \overrightarrow{EC}$ $\dpi{100} \fn_phv \overrightarrow{BE}$ $\dpi{100} \fn_phv \overrightarrow{EA}$ $\dpi{100} \fn_phv \overrightarrow{EB}$ $\dpi{100} \fn_phv \overrightarrow{BA}$ $\dpi{100} \fn_phv \overrightarrow{DC}$ Segments $\dpi{100} \fn_phv \overline{BC}$ $\dpi{100} \fn_phv \overline{AB}$ $\dpi{100} \fn_phv \overline{CE}$ $\dpi{100} \fn_phv \overline{BE}$ $\dpi{100} \fn_phv \overline{ED}$ $\dpi{100} \fn_phv \overline{EC}$ Angles $\dpi{100} \fn_phv \angle BCE$ $\dpi{100} \fn_phv \angle CBE$ $\dpi{100} \fn_phv \angle ECB$ $\dpi{100} \fn_phv \angle CBA$

1The line above each of these should have arrows on both ends.

Example 2:

a) Parallel to $\dpi{100} \fn_phv \overline{BF}$: $\dpi{100} \fn_phv \overline{CG}$ and $\dpi{100} \fn_phv \overline{EA}$

b) Skew to $\dpi{100} \fn_phv \overline{BF}$: $\dpi{100} \fn_phv \overline{AD}$, $\dpi{100} \fn_phv {\overline{CD}}$ and $\dpi{100} \fn_phv {\overline{GH}}$ (must be in the same plane as $\dpi{100} \fn_phv {\overline{BF}}$

c) Planes: $\dpi{100} \fn_phv \square ABC$, $\dpi{100} \fn_phv \square EFG$, $\dpi{100} \fn_phv \square BFG$, $\dpi{100} \fn_phv \square ADH$, $\dpi{100} \fn_phv \square ABF$, $\dpi{100} \fn_phv \square CDH$ (top, bottom, left right, back, front)

d) Pairs of parallel planes: $\dpi{100} \fn_phv \square ABC$ and $\dpi{100} \fn_phv \square EFG$ (top and bottom), $\dpi{100} \fn_phv \square ADG$ and $\dpi{100} \fn_phv \square EFG$ (left and right, $\dpi{100} \fn_phv \square ABF$ and $\dpi{100} \fn_phv \square DCG$ (back and front)

e) Intersection of $\dpi{100} \fn_phv \overline{DH}$ and $\dpi{100} \fn_phv \overline{DA}$: Point d; intersection of $\dpi{100} \fn_phv \overline{CG}$ and $\dpi{100} \fn_phv \overline{GF}$: Point G

f) Intersection of $\dpi{100} \fn_phv \square ABC$ (top) and $\dpi{100} \fn_phv \square BFG$ (right): $\dpi{100} \fn_phv \overline{BC}$; intersection of $\dpi{100} \fn_phv \square ABF$ (back) and $\dpi{100} \fn_phv \square EFG$ (bottom: $\dpi{100} \fn_phv \overline{EF}$

Example 3:

 Point B Segment XY Ray C Line MN Angle GHI Plane QRST

### 07.01 Geometry Basics - Worksheet (Math Level 1)

 teacher-scored 42 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 6 of your enrollment date for this class.

### 07.02 Perimeter and Area (Math Level 1)

 Find the perimeter and area of geometric figures.

Something to Ponder

How would you explain the differences between perimeter and area and tell how to find each?

Mathematics Vocabulary

Perimeter: the sum of the side lengths of a shape

Area: the number of square units enclosed by a plane figure

Formulas

Rectangle:

• Area = length x width or lw
• Perimeter = 2(base + width)

Triangle:

• Area = 1/2 x base x height or 1/2 x Bh

Parallelogram:

• Area = base x height or Bh

Trapezoid:

• Area$\dpi{100} \fn_phv \frac{b{_1\cdot b{_2}}}{2}$h where b1 and b2 are the bases and h is the height

Kite:

• Area = $\dpi{100} \fn_phv \frac{d_{1} \cdot d_{2}}{2}$; where d1 and d1 are the diagonals

Circle:

• Circumference: $\fn_jvn&space;2&space;\cdot&space;\pi&space;\cdot&space;radius$
• Area = $\fn_jvn&space;\pi&space;\cdot&space;radius^{2}$

Learning these concepts

Click the image or the link below to launch the video to help you better understand this "mathematical language."

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 07.02 Perimeter and Area - Extra Video (Math Level 1)

 NROC Developmental Math: Perimeter and Areahttp://www.montereyinstitute.org/courses/DevelopmentalMath/U...Art of Problem Solving: Area of a Circle part 1http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Area of a Circle part 2http://www.artofproblemsolving.com/Videos/external.php?video...Free Video Lectures: Circumference of a Circlehttp://freevideolectures.com/Course/2567/Geometry/11

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:

Use the formulas above to find the following:

a) the area of a kite with diagonals of 12 and 16

b) the circumference and area of a circle with a radius of 8

Example 2:

Use the formulas above to find the following:

a) the area of a triangle with a base of 6 and a height of 10

b) the area of a trapezoid with bases of 7 and 9 and a height of 4

c) the area and perimeter of a rectangle with a base of 20 and a height of 12

d) the area of a parallelogram with a base of 14.8 and a height of 6.2

Example 1:

a) The area of a kite with diagonals of 12 and 16

$\dpi{100} \fn_phv \fn_phv A=\frac{d_{1} \cdot d_{2}}{2} = \frac{12\cdot 16}{2}=\frac{192}{2}=96$

b) The circumference and area of a circle with a radius of 8

$\dpi{100} \fn_phv C=2\pi r=2\cdot \pi \cdot 8=16\pi=50.3$ rounded to the nearest tenth.

$\dpi{100} \fn_phv A=\pi r^{2}=\pi\cdot8 ^{2}=\pi 64=201.1$ rounded to the nearest tenth.

Example 2:

a) The area of a triangle with a base of 6 and a height of 10

$\dpi{100} \fn_phv A=\frac{1}{2}Bh=\frac{1}{2}\cdot6 \cdot 10=30$

b) The area of a trapezoid with bases of 7 and 9 and a height of 4

$\dpi{100} \fn_phv A=\frac{h(a+b)}{2}=\frac{4(7+9)}{2}=\frac{4\cdot 16}{2}=\frac{64}{2}=32$

c) The area and perimeter of a rectangle with a base of 20 and a height of 12

$\dpi{100} \fn_phv A=b\cdot h = 20\cdot 12 = 240$

d) The area of a parallelogram with a base of 14.8 and a height of 6.2

$\dpi{100} \fn_phv A=b\cdot h = 14.8\cdot 6.2 = 91.76$

### 07.02 Perimeter and Area - Worksheet (Math Level 1)

 teacher-scored 32 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 6 of your enrollment date for this class.

### 07.03 Angle Relationships (Math Level 1)

 Write equations for solving problems involving Angle Relationships.

Something to Ponder

What are some things you need to consider as you write expressions or equations to model real-life situations and problems?

Mathematics Vocabulary

Angle: two rays with a common terminal end

Complementary Angle: two angles whose sum is 90 degrees

Supplementary Angle: two angles whose sum is 180 degrees

Vertical Angle: congruent angles formed by intersecting lines

Linear pair: two angles that are adjacent and supplementary

Postulate: an accepted statement of fact

Theorem: a conjecture that is proven

Proof: a convincing argument that uses deductive reasoning

Parallel Lines: coplanar lines that with no common points

Transversal: a line that intersects two coplanar lines

Postulates and Theorems

Corresponding Angles Postulate: corresponding angles generated by parallel lines are congruent

Alternate Interior Angles Theorem: alternate interior angles generated by parallel lines are congruent

Same-side Interior Angles Theorem: same side interior angles generated by parallel lines are supplementary

Alternate Exterior Angles Theorem: alternate exterior angles generated by parallel lines are congruent

Same-side Exterior Angles Theorem: same side exterior angles generated by parallel lines are supplementary

Learning these concepts

Click the images or the links below to launch the videos to help you better understand this "mathematical language."

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 07.03 Angle Relationships - Extra Video (Math Level 1)

 mathispower4u: Complementary, Supplementary, and Vertical Angleshttp://www.youtube.com/embed/rjOjwcV79HM?wmode=transparent&r...Art of Problem Solving: Angles around a Pointhttp://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Straight and Vertical Angleshttp://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Angles and Parallel Lineshttp://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Angles in a Triangle Part 2http://www.artofproblemsolving.com/Videos/external.php?video...

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 value of x if  m$\angle$1 = 3x + 30 and m$\angle$2 = 2x + 45. Then find the measures of the two angles.

Example 2:

Find the value of x if m$\angle$2 = 2x + 10 and m$\angle$3 = x + 20. Then find the measure of the angles.

Example 3:

a) Identify which angle forms a pair of same-side interior angles with $\angle$1.

b) Identify which angle forms a pair of corresponding angles with $\angle$2.

Example 4:

Find the value of x.

Example 5:

Find the value of x.

Example 1:

Find the value of x if m$\angle$1 = 3x + 30 and m$\angle$2 = 2x + 45. Then find the measures of the two angles.

m$\angle$1 + m$\angle$2 = 180 = 3x + 30 + 2x + 45 = 5x + 75

105 = 5x

21 = x

m$\angle$1 = 3x + 30 = 3(21) + 30 = 63 + 30 = 93

m$\angle$2 = 2x + 45 = 2(21) + 45 =42 + 45 = 87

Example 2:

Find the value of x if m$\angle$2 = 2x + 10 and m$\angle$3 = x + 20. Then find the measure of the angles.

m$\angle$2 + m$\angle$3 = 180 = 2x + 10 + x + 20 = 3x + 30

Example 3:

a) Identify which angle forms a pair of same-side interior angles with $\angle$2.

$\dpi{100} \fn_phv \fn_phv \angle 2$ and $\dpi{100} \fn_phv {\color{Green} \angle 3}$ are same-side interior angles

b) Identify which angle forms a pair of corresponding angles with $\fn_phv \angle$2.

$\dpi{100} \fn_phv \angle$2 and $\dpi{100} \fn_phv {\color{Green} \angle 4}$ are same-side interior angles.

Example 4:

Find the value of x.

These two angles are alternate interior angles. We know that these are congruent:

3x – 20 = x + 8

2x = 28

x = 14

Example 5:

Find the value of x.

These two angles area consecutive interior angles which are supplementary.

3x + 40 + 2x + 60 = 180

5x + 100 = 180

5x = 80

x = 16

### 07.03 Angle Relationships - Worksheet (Math Level 1)

 teacher-scored 80 points possible 50 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 9 of your enrollment date for this class.

### 07.03 Check Point Quiz (Math Level 1)

 teacher-scored 83 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 corrected quiz.

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

### 07.04 Properties of Segments (Math Level 1)

 Find the lengths of segments using addition and midpoint properties.

Something to Ponder

How would you describe the segment addition postulate?

Mathematics Vocabulary

Midpoint: the point that divides a segment into two congruent parts

Congruent segments: segments of identical length

Segment addition: segment AB plus segment BC equals segment AC

Learning these concepts

Click the image or the link below to launch the video to help you better understand this "mathematical language."

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 07.04 Properties of Segments - Extra Video (Math Level 1)

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

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

Example 1: If AB = 24, AN = 3x – 5 and NB = 2x + 4, find the value of x. Then find AN and NB.

Example 2: If AB = 4x - 5, AN = 2x + 2 and NB = 9, find the value of x. Then find AB and AN.

Example 3: M is the midpoint of RT. If RT = 6x + 10 and 2x + 14 find x, RM, MT, and RT.

Example 4: If m ∠ 1 = 42 and m ∠ ABC = 88, find m∠ 2.

Example 1: If AB = 24, AN = 3x – 5 and NB = 2x + 4, find the value of x. Then find AN and NB.

We know that AN + NB = AB. We can then substitute in the values given:

3x–5 + 2x + 4 = 24. Now we can collect like terms:

5x–1 = 24

5x = 25

x = 5

Now we can find the values of AN and NB:

AN = 3x – 5 = 3(3) – 5 = 9 – 5 = 4

NB = 2x + 4 = 2(5) + 4 = 10 + 4 = 14

Example 2: If AB = 4x - 5, AN = 2x + 2 and NB = 9, find the value of x. Then find AB and AN.

We know that AN + NB = AB. We can then substitute in the values given:

2x + 2 + 9 = 4x – 5. Now we can collect like terms:

2x + 11 = 4x – 5

11 = 2x – 5

16 = 2x

8 = x

Now we can find the values of AN and NB:

AB = 4x – 5 = 4(8) – 5 = 32 – 5 = 27

AN = 2x + 2 = 2(8) + 2 = 18

Example 3: M is the midpoint of RT. If RT = 6x + 10 and 2x + 14 find x, RM, MT, and RT.

We know that RM + MT = RT and that RM = RT because M is the midpoint of RT. We can then substitute in the values given:

2x + 14 + 2x + 14 = 6x + 10

4x + 28 = 6x + 10

28 = 2x + 10

18 = 2x

9 = x

Now we can find the values of RT, RM and MT:

RT = 6(9) + 10 = 54 + 10 = 64

RM = 2x + 14 = 2(9) + 14 = 18 + 14 = 32

MT = 32

Example 4: If m ∠ 1 = 42 and m ∠ ABC = 88, find m∠ 2.

We know that the m$\fn_phv \angle$ABC = m$\fn_phv \angle$1 + m$\fn_phv \angle$2. We can then substitute in the values given:

88 = 42 + m$\fn_phv \angle$2

46 = m$\fn_phv \angle$2

### 07.04 Properties of Segments - 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 7 of your enrollment date for this class.

### 07.05 Properties of Angles (Math Level 1)

 Find the measures of angles using addition and bisector properties.

Something to Ponder

In your own words, how would you describe and then compare the segment and angle addition properties and the midpoint and angle bisector properties?

Mathematics Vocabulary

Angle bisector: a ray that divides an angle into two congruent angles

Congruent angles: angles with identical measures

Angle addition: angle 1 + angle 2 = angle 3 (which has the measure of angle 1 + angle 2)

Learning these concepts

Click the image or the link below to launch the video to help you better understand this "mathematical language."

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 07.05 Properties of Angles - 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:

If m$\angle$1 = 42 and m$\angle$ABC = 88, find m 2.

Example 2:

If m$\angle$1 = x + 3, m$\angle$2 = 3x – 7 and m$\angle$ABC = 6x – 12, find x, m$\angle$1, m$\angle$2 and m$\angle$ABC.

Example 3:

WR bisects AWB, m$\angle$AWR = x and m$\angle$BWR = 4x – 48.  Find x, m$\angle$AWB, m$\angle$AWR and m$\angle$BWR.

Example 1

If m$\angle$1 = 42 and m$\fn_phv \angle$ABC = 88, find m$\fn_phv \angle$2.

We know that the m$\fn_phv \angle$ABC = m$\fn_phv \angle ^{}$1 + m$\fn_phv \angle ^{}$2. We can then substitute in the values given:

88 = 42 + m$\fn_phv \angle ^{}$2

46 = m$\fn_phv \angle ^{}$2

Example 2

If m$\fn_phv \angle ^{}$1 = x + 3, m$\fn_phv \angle ^{}$2 = 3x – 7 and m$\fn_phv \angle ^{}$ABC = 6x – 12, find x, m$\fn_phv \angle ^{}$1, m$\fn_phv \angle ^{}$2 and m$\fn_phv \angle ^{}$ABC.

We know that the m$\fn_phv \angle ^{}$ABC = m$\fn_phv \angle ^{}$1 + m$\fn_phv \angle ^{}$2. We can then substitute in the values given:

6x - 12 = x + 3 + 3x - 7

6x - 12 = 4x - 4

2x - 12 = -4

2x = 8

x = 4

We can now solve for m$\fn_phv \angle ^{}$1, m$\fn_phv \angle ^{}$2 and m$\fn_phv \angle ^{}$ABC.

m$\fn_phv \angle ^{}$1 = x + 3 = 4 + 3 = 7

m$\fn_phv \angle ^{}$2 = 3x – 7 = 3(4) - 7 = 12 - 7 = 5

m$\fn_phv \angle ^{}$ABC = 6x – 12 = 6(4) - 12 = 24 - 12 = 12

Example 3

WR bisects AWB, m$\fn_phv \angle ^{}$AWR = x and m$\fn_phv \angle ^{}$BWR = 4x – 48.  Find x, m$\fn_phv \angle ^{}$AWB, m$\fn_phv \angle ^{}$AWR and m$\fn_phv \angle ^{}$BWR.

We know that m$\fn_phv \angle ^{}$AWR = m$\fn_phv \angle ^{}$BRW because of the bisection. We can then substitute in the values given:

x = 4x - 48

-3x = -48

x = 16

We can now solve for m$\fn_phv \angle ^{}$AWB, m$\fn_phv \angle ^{}$AWR and m$\fn_phv \angle ^{}$BWR.

m$\fn_phv \angle ^{}$AWB = m$\fn_phv \angle ^{}$AWR + m$\fn_phv \angle ^{}$BRW = x + 4x - 48 = 5x - 48 = 5(16) - 48 = 32

m$\fn_phv \angle ^{}$AWR = x = 16

m$\fn_phv \angle ^{}$BWR = 4x - 48 = 4(16) - 48 = 16

### 07.05 Properties of Angles - 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.

### 07.06 Properties of Triangles (Math Level 1)

 Explain and use the properties of triangles.

Something to Ponder

How would you explain the relation between the remote interior angles of a triangle and the exterior angle?

Mathematics Vocabulary

Acute triangle: an angle that measures less than 90 degrees

Obtuse triangle: an angle that measures more than 90 degrees but less than 180 degrees

Right triangle: an angle that measures exactly 90 degrees

Equiangular triangle: a triangle in which all angles have the same measure (60 degrees)

Isosceles triangle: a triangle that has two sides of equal length (2 congruent legs)

Scalene triangle: a triangle that has no sides of equal length (no congruent legs)

Equilateral triangle: a triangle that has all three sides of equal length

Exterior angle of a triangle: an angle formed by a side and an extension of an adjacent side

Remote interior angles: the 2 interior angles that are non-adjacent to the exterior angle

Theorems

Triangle Angle-Sum: the sum of the measures of the interior angles of a triangle is 180 degrees

Triangle Exterior Angle:  the measure of each exterior angle of a triangle equals the sum of the measures of its 2 remote interior angles:

$\fn_jvn&space;m\angle&space;1&space;=&space;m\angle&space;2&space;+&space;m\angle&space;3$

Learning these concepts

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

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 07.06 Properties of Triangles - Extra Videos (Math Level 1)

 Khan Academy: Classifying Triangleshttps://www.youtube.com/watch?v=7Mfcs8ZkS3Mmathispower4u: Angle Relationships and Types of Triangleshttps://www.youtube.com/watch?v=z_O2Knid2XADavitily: How to Find the Missing Angle in a Triangle Using the Triangle Sum Theoremhttps://www.youtube.com/watch?v=fIZGlZDxAHw&feature=youtu.beIntuitive Animations: Exterior Angles of a Triangle & Exterior Angle Theoremhttps://www.youtube.com/watch?v=NpVsF4St6eI

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:

Classify the following triangles by their sides and angles:

a)

b)

c)

d)

e)

f)

g)

h)

Example 2:

Find the values of x, y and z.

Example 3:

Find each missing angle measure:

a)

b)

Example 1:

 Triangle By Sides By Angles a) Scalene Acute b) Scalene Obtuse c) Equilateral Acute or Equilangular d) Isosceles Acute e) Isosceles Obtuse f) Isosceles Right g) Scalene Right h) Equilateral Equilangular

Example 2:

Find the values of x, y and z.

Step 1: The isosceles triangle tells us that m$\fn_phv \angle$w = $\fn_phv 70^{\circ}$.

Step 2: The angles of a triangle add to $\dpi{100} \fn_phv \fn_phv 180^{\circ}$ so $\dpi{100} \fn_phv 70^{\circ}$ + $\dpi{100} \fn_phv 70^{\circ}$ + m$\fn_phv \angle$x = $\dpi{100} \fn_phv 180^{\circ}$

$\dpi{100} \fn_phv 140^{\circ}$ + m$\fn_phv \angle$x = 180

m$\fn_phv \angle$x = $\dpi{100} \fn_phv 40^{\circ}$

Step 3: m$\fn_phv \angle$w + m$\fn_phv \angle$y = $\dpi{100} \fn_phv 180^{\circ}$

$\fn_phv 70^{\circ}$ + m$\fn_phv \angle$y = $\dpi{100} \fn_phv 180^{\circ}$

m$\fn_phv \angle$y = $\dpi{100} \fn_phv 110^{\circ}$

Step 4: $\fn_phv 25^{\circ}$ + m$\fn_phv \angle$y + m$\fn_phv \angle$z = $\dpi{100} \fn_phv 180^{\circ}$

$\fn_phv 25^{\circ}$ + $\fn_phv 110^{\circ}$ + m$\fn_phv \angle$z = $\dpi{100} \fn_phv 180^{\circ}$

$\fn_phv 135^{\circ}$ + m$\fn_phv \angle$z = $\dpi{100} \fn_phv 180^{\circ}$

m$\fn_phv \angle$z = $\dpi{100} \fn_phv 45^{\circ}$

Example 3

Find each missing angle measure:

a)

Using the Triangle Exterior Angle Theorem, we know that $\dpi{100} \fn_phv 65^{\circ}$ = $\dpi{100} \fn_phv 37^{\circ}$ + m$\fn_phv \angle$x

$\dpi{100} \fn_phv 28^{\circ}$ = m$\fn_phv \angle$x

b)

Using the Triangle Exterior Angle Theorem, we know that  m$\fn_phv \angle$x = $\dpi{100} \fn_phv 72^{\circ}$ + $\dpi{100} \fn_phv 44^{\circ}$ = $\dpi{100} \fn_phv 116^{\circ}$

### 07.06 Properties of Triangles - 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 8 of your enrollment date for this class.

### 07.07 Properties of Quadrilaterals and Polygons (Math Level 1)

 Explain and use the properties of quadrilaterals and polygons.

Something to Ponder

Could you describe the main categories of quadrilaterals and their characteristics?

Mathematics Vocabulary

Quadrilateral: a closed plane figure (polygon) that has 4 sides

Parallelogram: a quadrilateral with opposite sides parallel

Rectangle: a parallelogram with four right angles

Rhombus: a parallelogram with four congruent sides

Square: a parallelogram with all four congruent sides and four right angles (can also be classified as a quadrilateral, parallelogram, rectangle and a rhombus)

Trapezoid: a quadrilateral with exactly one pair of parallel sides

Iscosceles trapezoid: a trapezoid with two congruent legs

• Legs: the non-parallel sides
• Bases: the parallel sides
• Base angles: the angle connecting a base to a leg

Kite: a quadrilateral with 2 pair of congruent sides and no parallel sides

Polygon: a closed plane figure with at least 3 sides

Convex: a polygon wherein no diagonal contains points outside the polygon

Concave: a polygon wherein a diagonal contains points outside the polygon

Equilateral polygon: a polygon whose sides are all of equal measure

Equiangular polygon: a polygon whose angles are all of equal measure

Regular polygon:  a polygon that is both equilateral and equiangular

Learning these concepts

Click the images or the links below to launch the videos to help you better understand this "mathematical language."

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 07.07 Properties of Quadrilaterails and Polygons - Extra Videos (Math Level 1)

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

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

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

Example 1:

Example 2:

List the characteristics of each of the following and then draw it

b. parallelogram

c. rectangle

d. rhombus

e. square

f. trapezoid

g. kite

Example 3:

What is the name of each of the following polygons with the given number of sides?

a) 12  b) 8  c) 5  d) 9  e) 3  f) 7  g) 4  h) 6  i) 11  j) 15  k) 10

Example 4:

Classify each polygon by its sides. Identify each as convex or concave.

Example 1:

a) Rectangle

b) Parallelogram

d) Isosceles Trapezoid

e) Square

f) Trapezoid

g) Rhombus

h) Parallelogram

Example 2:

List the characteristics of each of the following and then draw it

 Quadrilateral Drawing Characteristics a) Quadrilateral 4 sides b) Parallelogram 2 pair of parallel sides 2 pair of congruent sides c) Rectangle 2 pair of parallel sides 2 pair of congruent sides 4 right angles d) Rhombus 2 pair of parallel sides 4 congruent sides e) Square 2 pair of parallel sides 4 congruent sides 4 right angles f) Trapezoid 1 pair of parallel sides g) Kite 2 pair of congruent sides

Example 3:

What is the name of each of the following polygons with the given number of sides?

a) 12 - dodecagon

b) 8 - octagon

c) 5 - pentagon

d) 9 - nonagon or enneagon

e) 3 - triangle

f) 7 - heptagon

h) 6 - hexagon

i) 11 - hendecagon or undecagon

k) 10 - decagon

Example 4:

Classify each polygon by its sides. Identify each as convex or concave.

a) hexagon, convex

b) octagon, concave

c) nonagon or enneagon, concave

f) pentagon, convex

g) heptagon, concave

### 07.07.01 Properties of Quadrilaterals and Polygons - 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 8 of your enrollment date for this class.

### 07.07.02 Check Point Quiz (Math Level 1)

 teacher-scored 20 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 corrected quiz.

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

### 07.08 Angles in Circles and Polygons (Math Level 1)

 Find the measures of angles in circles and polygons.

Something to Ponder

How do the central angles of circles and polygons compare?

Mathematics Vocabulary

Circle: the set of coplanar points equidistant from a given point

Center point: a point not on a circle from which all points on a circle are equidistant

Radius: the distance from the center point to any point on a circle

Diameter: the distance from one point on the circle to another point on the circle passing through the center point

Semi circle: half a circle

Central angle: an angle whose vertex is the centre poilnt of a circle

Arc: a portion of a circle's circumference

Arc addition: the sum of two or more arc lengths

Formulas

Polygon interior angle sum: the sum of the interior angles of any polygon can be found by (n-2) 180 where n is the number of sides of the polygon

Polygon exterior angle sum: the sum of the exterior angles (one at each vertex) of a polygon is always 360 degrees

Learning these concepts

Click the images or the links below to launch the videos to help you better understand this "mathematical language."

Scroll down to the Guided Practice section and work through the examples before submitting the assignment.

### 07.08 Angles in Circles and Polygons - Extra Video (Math Level 1)

 mathispower4u: Introductions to Circleshttps://www.youtube.com/watch?v=FwAcdhnphPMArt of Problem Solving: Angles in a Polygon Part 1http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Angles in a Polygon Part 2 http://www.artofproblemsolving.com/Videos/external.php?video...mathispower4u: Interior and Exterior Angles of a Polygonhttps://www.youtube.com/watch?v=Y0q7IKfoABo

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:

Identify the center, diameter, radii, chords, central angles and arcs in circle P.

Example 2:

Find the measures of the central angles in circle O if radius $\dpi{100} \fn_phv \dpi{120} \fn_phv \overline{CO}$ bisects DOB and m$\dpi{120} \fn_phv \angle$AOE = $\dpi{100} \fn_phv \large 130^{\circ}$

Example 3:

Find the sum of the measures of the interior angles of a hexagon. Find the sum of the exterior angles of a hexagon.

Example 4:

Find the measure of each interior and exterior angle of a regular octagon.

Example 5:

Find the measure of each angle of the regular hexagon below:

Example 1:

Identify the center, diameter, radii, chords, central angles and arcs in circle P.

Center: point P

Diameter: $\dpi{100} \fn_phv \overline{AC}$

Radii: $\dpi{100} \fn_phv \overline{AP}$, $\dpi{100} \fn_phv \overline{CP}$, $\dpi{100} \fn_phv \overline{BP}$

Chords: $\dpi{100} \fn_phv \overline{CD}$, $\dpi{100} \fn_phv {\overline{CB}}$

Central Angles: $\dpi{100} \fn_phv \angle APB$, $\dpi{100} \fn_phv \angle BPC$

Arcs: $\dpi{100} \fn_phv \widehat{AD}$, $\dpi{100} \fn_phv \widehat{AB}$, $\dpi{100} \fn_phv \widehat{BC}$, $\dpi{100} \fn_phv \widehat{CD}$

Example 2:

Find the measures of the central angles in circle O if radius $\fn_phv \overline{CO}$ bisects DOB and m$\fn_phv \angle$AOE or $\fn_phv \angle$4 = $\fn_phv 130^{\circ}$.

Step 1: m$\fn_phv \angle$1 = m$\fn_phv \angle$2 ($\dpi{100} \fn_phv \overline{CO}$ bisects $\fn_phv \angle$DOB)

Step 2: m$\fn_phv \angle$AOD = $\dpi{100} \fn_phv 180^{\circ}$ = m$\fn_phv \angle$4 + m$\fn_phv \angle$3 = $\dpi{100} \fn_phv 130^{\circ}$ + m$\fn_phv \angle$3

$\fn_phv 50^{\circ}$ = m$\fn_phv \angle$3

Step 3: m$\fn_phv \angle$1 + m$\fn_phv \angle$2 + m$\fn_phv \angle$3 = $\dpi{100} \fn_phv 180^{\circ}$

2m$\fn_phv \angle$1 + $\dpi{100} \fn_phv 50^{\circ}$ = $\dpi{100} \fn_phv 180^{\circ}$

2m$\fn_phv \angle$1 = $\dpi{100} \fn_phv 130^{\circ}}$

m$\fn_phv \angle$1 = $\dpi{100} \fn_phv 65^{\circ}$ = m$\fn_phv \angle$2

Step 4: m$\fn_phv \angle$5 + m$\fn_phv \angle$1 + m$\fn_phv \angle$2 = $\dpi{100} \fn_phv 180^{\circ}$

m$\fn_phv \angle }$5 + $\dpi{100} \fn_phv 65^{\circ}$$\dpi{100} \fn_phv 65^{\circ}$ = $\dpi{100} \fn_phv 180^{\circ}$

m$\fn_phv \angle$5 + $\dpi{100} \fn_phv 130^{\circ}$ = $\dpi{100} \fn_phv 180^{\circ}$

m$\fn_phv \angle$5 = $\dpi{100} \fn_phv 50^{\circ}$

Step 5: m$\fn_phv \angle$4 + m$\fn_phv \angle$3 = $\dpi{100} \fn_phv 180^{\circ}$

m$\fn_phv \angle$4 + $\fn_phv 50^{\circ}$ = $\dpi{100} \fn_phv 180^{\circ}$

m$\fn_phv \angle$4 = $\dpi{100} \fn_phv 130^{\circ}$

m$\fn_phv \angle$1 = $\dpi{100} \fn_phv 65^{\circ}$, m$\fn_phv \angle$2 = $\dpi{100} \fn_phv 65^{\circ}$, m$\fn_phv \angle$3 = $\dpi{100} \fn_phv 50^{\circ}$, m$\fn_phv \angle$4 = $\dpi{100} \fn_phv 130^{\circ}$, m$\fn_phv \angle$5 = $\dpi{100} \fn_phv 50^{\circ}$

Example 3:

Find the sum of the measures of the interior angles of a hexagon. Find the sum of the exterior angles of a hexagon.

Sum of interior angles of a polygon = 180(n - 2) where n = the number of sides.

Sum of interior angles of a hexagon = 180(6 - 2) = 180(4) = $\dpi{100} \fn_phv 720^{\circ}$

Sum of exterior angles of a polygon = $\dpi{100} \fn_phv 360^{\circ}$

Example 4:

Find the measure of each interior and exterior angle of a regular octagon.

Interior angle = $\dpi{100} \fn_phv \frac{180(5-2)}{5}=\frac{180(3))}{5}=\frac{540}{5}=108^{\circ}$

Exterior angle = $\dpi{100} \fn_phv \frac{360}{5}=72^{\circ}$

Example 5:

Find the measure of each angle of the regular hexagon below:

Step 1: Measure of an interior angle of a hexagon = $\dpi{100} \fn_phv \frac{180(6-2)}{6}=\frac{180(4))}{6}=\frac{720}{6}=120^{\circ}=m\angle 3$

Step 2: Measure of an interior angle of an equilateral triangle = $\dpi{100} \fn_phv \frac{180}{3}=60^{\circ}=m\angle 1, m\angle 2, m\angle 3$

Step 3: m$\fn_phv \angle$1 + m$\fn_phv \angle$4 = $\dpi{100} \fn_phv 180^{\circ}$

$\fn_phv 60^{\circ}$ + m$\fn_phv \angle$4 = $\dpi{100} \fn_phv 180^{\circ}$

m$\fn_phv \angle$4 = $\dpi{100} \fn_phv 120^{\circ}$

Therefore, m$\fn_phv \angle$1 = $\dpi{100} \fn_phv 60^{\circ}$ , m$\fn_phv \angle$2 = $\dpi{100} \fn_phv 60^{\circ}$ ; m$\fn_phv \angle$3 = $\dpi{100} \fn_phv 120^{\circ}$ ; m$\fn_phv \angle$4 = $\dpi{100} \fn_phv 120^{\circ}$ ; m$\fn_phv \angle$5 = $\dpi{100} \fn_phv 60^{\circ}$

### 07.08.01 Angles in Circles and Polygons - 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 9 of your enrollment date for this class.

### 07.08.02 Unit 07 Review Quiz (Math Level 1)

 teacher-scored 20 points possible 40 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 corrected quiz.

Pacing: complete this by the end of Week 9 of your enrollment date for this class.

### 07.08.03 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.