# Course Description

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

## Class Overview

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

### Credit

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

## Prerequisites

You should have successfully completed 8th grade math.

## Supplies needed

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

## Organization of Secondary Math Level 1

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

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

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

## This Quarter Class

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

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

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

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

## Proctored Final

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

### Information about the Final Exam

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

## Final Grade

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

## Grading Scale

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

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

### 00.01 Curriculum Standards (Math Level 1)

 Utah Math I Standardshttp://www.uen.org/commoncore/downloads/MathSecondaryI.pdf

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. ### 00.03 Basic Skills (Math Level 1) Just like learning to use the English or Spanish language, you learn the language of mathematics by acquiring its vocabulary and grammar and by practicing until you can "think" fluently in the language. This pre-requisite lesson helps you verify you have a basic understanding of integers, fractions, and simplifying expressions, some of the basic building blocks of the "mathematics language."  Define: Integerhttp://www.google.com/search?q=define%3AintegerDefine: Fractionhttp://www.google.com/search?q=define%3AfractionDefine: Simplifying Expressionshttp://www.google.com/search?q=define%3Asimplifying+expressi... ### 00.03.01 Basic Skills - Integers (Math Level 1)  computer-scored 20 points possible 15 minutes Activity for this lesson Take the quiz 00.03.01 Basic Skills Integers If you don't pass the quiz on the first attempt, search the internet for adding, subtracting, multiplying and dividing integers. Review the material and try again. Pacing: complete this by the end of Week 1 of your enrollment date for this class. ### 00.03.02 Basic Skills - Fractions (Math Level 1)  computer-scored 20 points possible 20 minutes Activity for this lesson 1. Take the quiz listed as 00.03.02 Basic Skills - Fractions Quiz If you don't pass the quiz on the first attempt, search the internet for adding, subtracting, multiplying and dividing fractions. Review the material and try again. Pacing: complete this by the end of Week 1 of your enrollment date for this class. ### 00.03.03 Basic Skills - Simplifying Expressions (Math Level 1)  computer-scored 20 points possible 20 minutes Activity for this lesson 1. Take the quiz 00.03.03 Basic Skills - Simplifying Expressions Quiz If you don't pass the quiz on the first attempt, search the internet for simplifying expressions. Review the material and try again. Pacing: complete this by the end of Week 1 of your enrollment date for this class. ### 01.00 Solving Equations and Inequalities Overview (Math Level 1)  By the end of eighth grade students have had a variety of experiences working with expressions and creating equations. In this first unit, students continue this work by using quantities to model and analyze situations, to interpret expressions, and by creating equations to describe situations. By the end of the unit, students will be able to: Write expressions and equations to model real-life situations. Identify algebraic properties. Solve two-step equations, justify the steps involved and verify the solutions. Solve multi-step equations, justify the steps involved and verify the solutions. Solve multi-step inequalities, justify the steps involved and verify the solutions. Use the skills for solving equations to solve literal equations. Evaluate solutions of equations and inequalities. ### 01.01 Expressions and Formulas (Math Level 1)  Identify and explain the different parts of expressions, equations, inequalities and formulas and identify the variables, coefficients, constants, bases and exponents. Something to Ponder What is the difference between an expression and an equation? Mathematics Vocabulary Variable: a symbol, usually a letter, that represents one or more numbers; for example: x is a variable in the equation $\fn_jvn&space;3x&space;=&space;6$ Term: a number, or a variable or numbers and variables multiplied together; for example: $\fn_jvn&space;6x^{2}$$\fn_jvn&space;2xy^{3}z^{5}$ and $\fn_jvn&space;-5$ are terms Expression: mathematical phrase that can include numbers, variables and operation symbols; for example: $\fn_jvn&space;n&space;+&space;7$, $\fn_jvn&space;-7x^{2}$ and $\fn_jvn&space;4x^{2}+10y+8$ are expressions Polynomial: an expression with one or more monomials, which is combined using addition and/or subtraction; for example: $\fn_jvn&space;7x^{3}+6x^{2}+x-2$ Monomial: a polynomial with one term; for example: $\fn_jvn&space;-8z^{3}$ Binomial: a polynomial with two terms, for example: $\fn_jvn&space;2x^{3}&space;-&space;x$ Trinomial: a polynomial with three terms; for example: $\fn_jvn&space;8x^{3}&space;-&space;2x&space;+&space;9$ Coefficient: the numerical factor when a term has a variable; for example: in the expression $\fn_jvn&space;6x^{3}&space;-&space;8x^{2}&space;+&space;7x&space;-&space;9$; 6, -8 and 7 are the coefficients Constant: a fixed value, a term that does not have a variable; for example: in the expression $\fn_jvn&space;6x^{3}&space;-&space;8x^{2}&space;+&space;7x&space;-&space;9$; -9 is the constant Base: a number that is multiplied repeatedly; for example: $\fn_jvn&space;7^{3}$, 7 is the base Exponent: a number that shows how many times the base is to be multiplied; for example: $\fn_jvn&space;7^{3}$, 3 is the exponent, therefore, 7 · 7 · 7 Learning these concepts Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language." $\fn_phv {\color{Red}SCROLL }$ $\fn_phv {\color{Red}DOWN }$ $\fn_phv {\color{Red}TO }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}GUIDED }$ $\fn_phv {\color{Red}PRACTICE }$ $\fn_phv {\color{Red}SECTION }$ $\fn_phv {\color{Red}AND }$ $\fn_phv {\color{Red}WORK }$ $\fn_phv {\color{Red}THROUGH }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}EXAMPLES }$ $\fn_phv {\color{Red}BEFORE }$ $\fn_phv {\color{Red}SUBMITTING }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}ASSIGNMENT!!! }$ ### 01.01 Expressions and Formulas - Explanation Video Links (Math Level 1)  View Explanation Video 01.01-1http://www.youtube.com/embed/WVJrO6MdPAY?wmode=transparent&r...View Explanation Video 01.01-2http://www.youtube.com/embed/3GliJP2AUi0?wmode=transparent&r... ### 01.01 Expressions and Formulas - Explanation Videos (Math Level 1) ### 01.01 Expressions and Formulas - Extra Link (Math Level 1)  NROC Developmental Math: Variables and Expressionshttp://www.montereyinstitute.org/courses/DevelopmentalMath/U... I highly recommend that you click on the link above before continuing. You can watch the video that is under the PRESENTATION tab or work through the entire lesson. Guided Practice After watching the video try these problems. The worked solutions follow. Example 1: For each of the following polynomials, state the number of terms, name the polynomial and identify the variables, coefficients, constants, bases and exponents. a) 8x3- 3x2 + 2x - 10 b) 4x - 2 c) 8x2y3z d) 2y - 3x + 2z​​ Example 2: For each of the following formulas identify what each number and letter represents: a) Formula for Area of a circle: A = $\dpi{150} \fn_phv \pi$r2 b) Formula for Perimeter of a rectangle: P = 2l + 2w c) Formula for the Area of a trapezoid: $\dpi{120} \fn_phv A= \frac{h(a+b)}{2}$ d) Formula for finding the cost of a cell phone with a startup charge: C = 42m + 35 Answers Example 1: For each of the following polynomials, state the number of terms, name the polynomial and identify the variables, coefficients, constants, bases and exponents. a) $\fn_phv {\color{DarkOrange} 8} {\color{Blue} x^{{\color{Red} 3}}}-{\color{DarkOrange}3 }{\color{Blue} x}^{{\color{Red} 2}}+{\color{DarkOrange} 2}{\color{Blue}x }{\color{Green}-10 }$ Number of terms: 4 Name of polynomial: Polynomial Variables: x Coefficients: $\fn_phv {\color{DarkOrange} 8, -3, 2}$ Constants: $\fn_phv {\color{Green} -10}$ Bases: $\fn_phv {\color{Blue} x}$ Exponents: $\fn_phv {\color{Red} 3, 2, 1}$ (the 1 is not written but it is technically the exponent on the term 2x) b) $\fn_phv {\color{DarkOrange} 4} {\color{Blue} x}{\color{Green}-2}$ Number of terms: 2 Name of polynomial: binomial Variables: x Coefficients: $\fn_phv {\color{DarkOrange} 8}$ Constants: $\fn_phv {\color{Green} -2}$ Bases: $\fn_phv {\color{Blue} x}$ Exponents: $\fn_phv {\color{Red} 1}$ (technically the exponent is 1 on the term 4x) c) $\fn_phv {\color{DarkOrange} 8}{\color{Blue} x^{{\color{Red} 2}}}{\color{Blue} y^{{\color{Red} 3}}}{\color{Blue} z}$ Number of terms: 1 Name of polynomial: monomial Variables: x, y, z Coefficients: $\fn_phv {\color{DarkOrange} 8}$ Constants: none Bases: $\fn_phv {\color{Blue} x, y, z}$ Exponents: $\fn_phv {\color{Red} 2, 3, 1}$ (technically the exponent is 1 on z) d) $\fn_phv {\color{DarkOrange} 2}{\color{Blue} y}{\color{DarkOrange} -3}{\color{Blue} x}{\color{DarkOrange}+2 }{\color{Blue}z }$ Number of terms: 3 Name of polynomial: trinomial Variables: y, x, z Coefficients: $\fn_phv {\color{DarkOrange} 2, -3, 2}$ Constants: none Bases: $\fn_phv {\color{Blue} y, x, z}$ Exponents: $\fn_phv {\color{Red} 1, 1, 1}$ (technically the exponent is 1 on all three terms) Example 2: For each of the following formulas identify what each number and letter represents: a) Formula for Area of a circle: A = $\fn_phv \pi r^{}2$ A represents the area of a given circle $\fn_phv \pi$ is a constant $\fn_phv \approx$ 3.14 r represents the radius of a given circle b) Formula for Perimeter of a rectangle: P = 2l + 2w P represents the perimeter of a given rectangle l represents the length of a given rectangle w represents the width of a given rectangle 2 represents the fact that there are two lengths and two widths in every rectangle c) Formula for the Area of a trapezoid: $\fn_phv A=\frac{h(a+b)}{2}$ A represents the area of a trapezoid h represents the height of a given trapezoid a represents one of the bases of a given trapezoid b represents the other base of a given trapezoid 2 represents the fact that the average of the two bases is being used so the sum must be divided by 2 d) Formula for finding the cost of a cell phone with a startup charge: C = 42m + 35 C represents the cost of a cell phone with a startup charge m represents the number of minutes of use 42 represent the number of minutes in this specific instant 35 represents the startup charge ### 01.01 Expressions and Formulas - Worksheet (Math Level 1)  teacher-scored 20 points possible 20 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. ### 01.02 Writing Expressions (Math Level 1)  Write expressions and equations to model real-life situations. 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 Think about words used to represent these mathematical symbols. $\LARGE&space;\fn_jvn&space;+$ $\LARGE&space;\fn_jvn&space;-$ x (or $\LARGE&space;\fn_jvn&space;\cdot$ or $\LARGE&space;\fn_jvn&space;\ast$ ) $\LARGE&space;\fn_jvn&space;\div$ or / Learning these concepts Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language." $\fn_phv {\color{Red}SCROLL }$ $\fn_phv {\color{Red}DOWN }$ $\fn_phv {\color{Red}TO }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}GUIDED }$ $\fn_phv {\color{Red}PRACTICE }$ $\fn_phv {\color{Red}SECTION }$ $\fn_phv {\color{Red}AND }$ $\fn_phv {\color{Red}WORK }$ $\fn_phv {\color{Red}THROUGH }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}EXAMPLES }$ $\fn_phv {\color{Red}BEFORE }$ $\fn_phv {\color{Red}SUBMITTING }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}ASSIGNMENT!!! }$ ### 01.02 Writing Expressions - Explanation Video Links (Math Level 1)  Explanation Video 01.02-1http://www.youtube.com/embed/zqRnAklVmH8?wmode=transparent&r...Explanation Video 01.02-2http://www.youtube.com/embed/x1wt2i3R5_g?wmode=transparent&r... ### 01.02 Writing Expressions - Explanation Videos (Math Level 1) ### 01.02 Writing Expressions - Extra Link (Math Level 1)  Purplemath: Translating Word Problems: Exampleshttp://www.purplemath.com/modules/translat2.htm I highly recommend that you click on the link above and work through the material before continuing. Guided Practice After watching the video try these problems. The worked solutions follow. Example 1: Write an algebraic expression for each phrase: a) nine more than n b) the difference of n and twelve c) the product of n and four d) the quotient of n and two e) the sum of fourteen and n f) n less than fifteen g) three times a number plus ten h) nine less than six times a number Example 2: Write a word expression for each of the following algebraic expressions: a) 3x + 1 b) h - 6 c) 5(x + 4) d) $\fn_phv \frac{9}{y}$ e) 4y - 6 f) 45 + x g) 12n h) $\fn_phv \frac{6}{y}$ Example 3: Define a variable, write an equation, and solve: a) A number increased by 5 is equal to 34. Find the number. b) Six times a number is -96. Find the number. c) Negative twelve times a number is -156. What is the number? d) Twelve decreased by twice a number is -7. e) One fifth of a number plus five times that number is equal to seven times the number less 18. Find the number. Answers Example 1: Write an algebraic expression for each phrase: a) nine more than n: n + 9 b) the difference of n and twelve: n – 12 c) the product of n and four: n x 4 or $\fn_phv n\cdot 4$ d) the quotient of n and two: n $\fn_phv \div$ 2 or $\fn_phv \frac{n}{2}$ e) the sum of fourteen and n: 14 + n f) n less than fifteen: 15 – n g) three times a number plus ten: 3x + 10 h) nine less than six times a number: 6x – 9 Example 2: Write a word expression for each of the following algebraic expressions: a) 3x + 1: the sum of 3 times a number and 1 b) h - 6: 6 less than h c) 5(x + 4): the product of 5 and x + 4 d) $\fn_phv \frac{9}{y}$: the quotients of 9 and y e) 4y – 6: the difference between 4 times a number and 6 f) 45 + x: the sum of 45 and x g) 12n: the product of 12 and n h) $\fn_phv \frac{6}{y}$: the quotient of 6 and y Example 3: Define a variable, write an equation, and solve: a) A number increased by 5 is equal to 34. Find the number. Let x = a number x + 5 = 34 x = 29 b) Six times a number is -96. Find the number. Let x = a number 6x = –96 x = –16 c) Negative twelve times a number is –156. What is the number? Let x = a number –12x = –156 x = 13 d) Twelve decreased by twice a number is –7. Let n = a number 12 – 2n = –7 19 = 2n 9.5 = n e) One fifth of a number plus five times that number is equal to seven times the number less 18. Find the number. Let x = a number $\fn_phv \frac{1}{5}$x + 5x = 7x – 18 Multiply each term by 5: x + 25x = 35x – 90 25x = 35x – 90 –10x = –90 x = 9 ### 01.02 Writing Expressions - Worksheet (Math Level 1)  teacher-scored 53 points possible 20 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. ### 01.03 Algebraic Properties (Math Level 1)  Identify algebraic properties. Something to Ponder If asked, how would you compare and contrast two properties? Mathematics Vocabulary Algebraic Properties: Commutative Property of Addition: a + b = b + a Commutative Property Multiplication: a · b = b · a Associative Property of Addition: (a + b) + c = a + (b + c) Associative Property of Multiplication: (a · b) · c = a · ( b · c) Distributive Property: a(b + c) = ab + ac (b + c)a = ba + ca a(b – c) = ab – ac (b – c)a = ba - ca Additive Identity: n + 0 = n Multiplicative Identity: n ·1 = n Additive Inverse: there is an additive inverse –a such that a + (-a) = 0 Multiplicative Inverse: there is a multiplicative inverse $\dpi{100} \fn_phv \dpi{100} \fn_phv \fn_jvn \frac{1}{a}$, such that $\dpi{100} \fn_phv \frac{1}{a}$ x a = 1 Substitution: if a = b, then b can be substituted for a in any expression Properties of Equality and Inequality: Addition: if a = b, then a + c=b + c Subtraction: if a = b, then a - c=b - c Multiplication: if a = b, then ac = bc Division: if a=b then $\dpi{100} \fn_phv \frac{a}{c}$ = $\dpi{100} \fn_phv \frac{b}{c}$ Properties of Inequality Addition: if a<b, then a+c<b+c and if a>b, then a+c>b+c; applies to ≤ and ≥ Subtraction: if a<b, then a–c<b–c and if a>b, then a–c>b–c; applies to ≤ and ≥ Multiplication: when c is positive: if a<b, then ac<bc and if a>b, then ac>bc; applies to ≤ and ≥ when c is negative: if a<b, then ac>bc and if a>b, then ac<bc; applies to ≤ and ≥ Division: • when c is positive: if a<b, then $\dpi{100} \fn_phv \frac{a}{c}$$\dpi{100} \fn_phv \frac{b}{c}$ and if a>b, then $\dpi{100} \fn_phv \frac{a}{c}$ < $\dpi{100} \fn_phv \frac{b}{c}$; applies to ≤ and ≥ • when c is negative: if a<b, then $\dpi{100} \fn_phv \frac{a}{c}$ >$\dpi{100} \fn_phv \frac{b}{c}$ and if a>b, then $\dpi{100} \fn_phv \frac{a}{c}$ > $\dpi{100} \fn_phv \frac{b}{c}$; applies to ≤ and ≥ Learning these concepts $\fn_phv {\color{Red}SCROLL }$ $\fn_phv {\color{Red}DOWN }$ $\fn_phv {\color{Red}TO }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}GUIDED }$ $\fn_phv {\color{Red}PRACTICE }$ $\fn_phv {\color{Red}SECTION }$ $\fn_phv {\color{Red}AND }$ $\fn_phv {\color{Red}WORK }$ $\fn_phv {\color{Red}THROUGH }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}EXAMPLES }$ $\fn_phv {\color{Red}BEFORE }$ $\fn_phv {\color{Red}SUBMITTING }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}ASSIGNMENT!!! }$ Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language." ### 01.03 Algebraic Properties - Explanation Video Links (Math Level 1)  Explanation Video 01.03-1http://www.youtube.com/embed/52p9XdmGT8w?wmode=transparent&r... ### 01.03 Algebraic Properties - Explanation Videos (Math Level 1) ### 01.03 Algebraic Properties - Extra Links (Math Level 1)  NROC Developmental Math: Associative, Commutative, and Distributive Propertieshttp://www.montereyinstitute.org/courses/DevelopmentalMath/U...Coolmath.com: Properites of Arithmetichttp://www.coolmath.com/prealgebra/06-properties/index.html I highly recommend that you click on the link above before continuing. You can watch the video that is under the PRESENTATION tab or work through the entire lesson. Guided Practice After watching the video try these problems. The worked solutions follow. Example 1: Write the correct property for each of the following: a) 3 + 7 = 7 + 3 b) 9 + 0 = 9 c) 6 x 1=6 or $\fn_phv 6\cdot 1=6$ d) (6 x 4) x 5 = 6 x (4 x 5) or $\fn_phv 4\cdot (6\cdot 4)\cdot 5=6\cdot (4\cdot 5)$ e) (6 + 4) + 5 = 6 + (4 + 5) f) 5 + (-5)=0 g) 3 x 7 = 7 x 3 or $\fn_phv 3\cdot 7=7\cdot 3$ h) 2(x + 6)=2x + 12 i) 2 x $\dpi{100} \fn_phv \frac{1}{2}$ = 1 Answers Example 1: Write the correct property for each of the following:  Expression Property a) 3 + 7 = 7 + 3 Commutative property of addition b) 9 + 0 = 9 Additive identity c) 6 x 1=6 or $\fn_phv 6\cdot 1 = 6$ Multiplicative identity d) (6 x 4) x 5 = 6 x (4 x 5) or $\dpi{100} \fn_phv 4\cdot (6\cdot 4)\cdot 5=6\cdot (4\cdot 5)$ Associative property of multiplication e) (6 + 4) + 5 = 6 + (4 + 5) Associative property of addition f) 5 + (-5)=0 Additive inverse g) 3 x 7 = 7 x 3 or $\fn_phv 3\cdot 7=7\cdot 3$ Commutative property of multiplication h) 2(x + 6)=2x + 12 Distributive property i) 2 x $\dpi{100} \fn_phv \frac{1}{2}$= 1 Multiplicative inverse ### 01.03 Algebraic Properties - Quiz (Math Level 1)  computer-scored 23 points possible 20 minutes Activity for this lesson You have three attempts at the quiz and must score 16 or higher to meet the minimum requirements of the quiz. Pacing: complete this by the end of Week 2 of your enrollment date for this class. ### 01.04 Solving Two-Step Equations (Math Level 1)  Solve two-step equations, justify the steps involved and verify the solutions. Something to Ponder When solving two-step equations what is your strategy for deciding how to begin? Mathematics Vocabulary Solution: any value or values that make an equation true Inverse Operation: operations that reverse the effect of another operation; for example: addition is an inverse operation of subtraction, multiplication is an inverse operation of division Verify: check the answer by substituting the solution into the original equation. For example: $\fn_phv x + 2 = 7$. The answer is 5. To verify substitute in 5 for x: $\fn_phv x + 2 = 7$ $\fn_phv 5 + 2 = 7$ $\fn_phv 7 = 7 %u221A$ Learning these concepts $\fn_phv {\color{Red}SCROLL }$ $\fn_phv {\color{Red}DOWN }$ $\fn_phv {\color{Red}TO }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}GUIDED }$ $\fn_phv {\color{Red}PRACTICE }$ $\fn_phv {\color{Red}SECTION }$ $\fn_phv {\color{Red}AND }$ $\fn_phv {\color{Red}WORK }$ $\fn_phv {\color{Red}THROUGH }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}EXAMPLES }$ $\fn_phv {\color{Red}BEFORE }$ $\fn_phv {\color{Red}SUBMITTING }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}ASSIGNMENT!!! }$ Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language." ### 01.04 Solving Two-Step Equations - Explanation Video Links (Math Level 1)  Explanation Video 01.04-1http://www.youtube.com/embed/u40CTsVZ0TM?wmode=transparent&r...Explanation Video 01.04-2http://www.youtube.com/embed/Il_Gn1jU1tM?wmode=transparent&r... ### 01.04 Solving Two-Step Equations - Explanation Videos (Math Level 1) ### 01.04 Solving Two-Step Equations - Extra Links (Math Level 1)  mathispower4u: Solving Two Step Equations: The Basics http://www.youtube.com/embed/9ITsXICV2u0?wmode=transparent&r...mathispower4u: Ex 1: Solving Two-Step Equations Using Integers http://www.youtube.com/embed/HyUiYeLee3g?wmode=transparent&r...mathispower4u: Ex: Solve To Two Step Linear Equations in One Variable (Mixed Review)http://youtu.be/Hn1HdEL84_cmathispower4u: Solving Two Step Equations Involving Fractionshttp://www.youtube.com/embed/t-RfBljqlRg?wmode=transparent&r...mathispower4u: Ex 1: Solving a Two Step Equation with Fractions - NOT Clearing the Fractions http://youtu.be/fuS0H66cDcYmathispower4u: Ex 1: Solving a Two Step Equation with Fractions - Clearing the Fractions http://youtu.be/uFptwRC6eXEmathispower4u: Solving Two Step Equations Involving Decimals http://www.youtube.com/embed/MHACBubIBIY?wmode=transparent&r...mathispower4u: Solving Two Step Equations: Summaryhttp://www.youtube.com/embed/AvZpCcjAFsY?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 each of the following, justify the steps involved and verify the solutions. a) -3x - 15 = 6 b) 10 = $\dpi{100} \fn_phv \frac{m}{4}$ + 2 Answers Example 1: Solve each of the following, justify the steps involved and verify the solutions. a) –3x – 15 = 6 Step 1: Add 15 to both sides: -3x = 21 Step 2: Divide both sides by -3 x = -7 Verification: –3x – 15 = 6 –3(–7) – 15 = 6 21 – 15 = 6 6 = 6 √ b) 10 = $\fn_phv \frac{m}{4}$ + 2 Step 1: Subtract 2 from both sides: 8 = $\fn_phv \frac{m}{4}$ Step 2: Multiply both sides by 4: 32 = m Verification: 10 = $\fn_phv \frac{m}{4}$ + 2 10 = $\fn_phv \frac{32}{4}$ + 2 10 = 8 + 2 10 = 10 √ ### 01.04 Solving Two-Step Equations - 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 3 of your enrollment date for this class. ### 01.05 Solving Multi-step Expressions (Math Level 1)  Solve multi-step equations. Justify the steps involved and verify the solutions. Something to Ponder What is the difference between combining like terms and solving equations with variables on both sides? Mathematics Vocabulary Multi-step equation: equation or inequality that requires more than one step to solve Verify: check the answer by substituting the solution into the original equation. For example: x + 2 = 7. The answer is 5. To verify, substitute in 5 for x: x + 2 = 7 5 + 2 = 7 7 = 7 √ Learning these concepts Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language." $\fn_phv {\color{Red}SCROLL }$ $\fn_phv {\color{Red}DOWN }$ $\fn_phv {\color{Red}TO }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}GUIDED }$ $\fn_phv {\color{Red}PRACTICE }$ $\fn_phv {\color{Red}SECTION }$ $\fn_phv {\color{Red}AND }$ $\fn_phv {\color{Red}WORK }$ $\fn_phv {\color{Red}THROUGH }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}EXAMPLES }$ $\fn_phv {\color{Red}BEFORE }$ $\fn_phv {\color{Red}SUBMITTING }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}ASSIGNMENT!!! }$ ### 01.05 Solving Multi-step Expressions - Explanation Video Links (Math Level 1)  Explanation Video 01.05-1http://www.youtube.com/embed/uRil5t37lcg?wmode=transparent&r...Explanation Video 01.05-2http://www.youtube.com/embed/odAs7jJ9xW4?wmode=transparent&r... ### 01.05 Solving Multi-step Expressions - Explanation Videos (Math Level 1) ### 01.05.01 Solving Multi-step Equations - Extra Video (Math Level 1)  mathispower4u: Solving Multiple Step Equations http://www.youtube.com/embed/_PsDFffvBsI?wmode=transparent&r...mathispower4u: Ex 1: Solve an Equation with Parentheses http://www.youtube.com/embed/cHW7NmawYdc?wmode=transparent&r...mathispower4u: Ex: Solve an Equation with Variable Terms on Both Sides http://www.youtube.com/embed/xfXGgqgJyDE?wmode=transparent&r...mathispower4u: Ex 1: Solve an Equation with Variables and Parentheses on Both Sides http://www.youtube.com/embed/zYx4QtAguXc?wmode=transparent&r...mathispower4u: Ex: Solving a Multi-Step Linear Equation in One Variable http://www.youtube.com/embed/E5JE4DcYx2U?wmode=transparent&r...mathispower4u: Ex1A : Solve To Multi-Step Linear Equations in One Variable http://youtu.be/UNqu0Ghb3wQmathispower4u:Ex2A : Solve To Multi-Step Linear Equations in One Variable http://youtu.be/zxT4pQJzmVwmathispower4u: Ex 1: Solve an Equation with Fractions with Variable Terms on Both Sides http://www.youtube.com/embed/G5R9jySFMpw?wmode=transparent&r...mathispower4u: Ex: Solve a Linear Equation in One Variable that Requires Simplifying http://youtu.be/zNtqneXTSWMmathispower4u: Solving Multiple Step Equations Involving Decimalshttp://www.youtube.com/embed/rVMctO1xroE?wmode=transparent&r...mathispower4u: Ex: Solve a Linear Equation With Decimals and Variables on Both Sides http://www.youtube.com/embed/pZWTJvua-P8?wmode=transparent&r...mathispower4u: Ex: Solve an Equation with Decimals and Parentheseshttp://www.youtube.com/embed/te-Pzkdw3P0?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 each of the following, justify and verify. 3a + 6 + a = 90 Example 2: Solve each of the following, justify and verify. 2(x - 3) = 8 Example 3: Solve each of the following, justify and verify. (3x/2) + x/5 = 17 Example 4: Solve each of the following, justify and verify. 5x - 3 = 2x + 12 Answers Example 1: Solve each of the following, justify and verify. 3a + 6 + a = 90 Step 1: Collect like terms: 4a + 6 = 90 Subtract 6 from both sides: 4a = 84 Divide both sides by 4: a = 21 Verification 3a + 6 + a = 90 3(21) + 6 + 21 = 90 63 + 6 + 21 = 90 90 = 90 √ Example 2: Solve each of the following, justify and verify. 2(x - 3) = 8 Step 1: Clear the parentheses: 2x - 6 = 8 Add 6 to both sides: 2x = 14 Divide both sides by 2: x = 7 Verification 2(x - 3) = 8 2(7 - 3) = 8 2(4) = 8 8 = 8 √ Example 3: Solve each of the following, justify and verify. (3x/2) + x/5 = 17 Step 1: Multiply each term by the common denominator which is 10: 15x + 2x = 170 Step 2: Collect like terms: 17x = 170 Step 3: Divide both sides by 17: x = 10 Verification [3(10)/2] + 10/5 = 17 30/2 + 2 = 17 15 + 2 = 17 17 = 17 √ Example 4: Solve the following, justify and verify. 5x – 3 = 2x + 12 Step 1: Add 3 to both sides: 5x = 2x + 15 Step 2: Subtract 2x from both sides: 3x = 15 Step 3: Divide both sides by 3: x = 5 Verification 5x – 3 = 2x + 12 5(5) – 3 = 2(5) + 12 25 – 3 = 10 + 12 22 = 22 √ ### 01.05.02 Solving Multi-step Expressions - 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 3 of your enrollment date for this class. ### 01.06 Solving Multi-Step Inequalities (Math Level 1)  Solve multi-step inequalities and justify the steps involved. 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 Inequality: an expression with an inequality sign (like < , ≤ , > or ≥) instead of an equals sign Solve linear inequalities: perform the same operation on both sides of the inequality. Note: When $\fn_phv {\color{Red}multiplying }$ or $\fn_phv {\color{Red}dividing }$ both sides of an inequality by a $\fn_phv {\color{Red}negative }$ number, $\fn_phv {\color{Red}reverse }$ the $\fn_phv {\color{Red}inequality }$ $\fn_phv {\color{Red}symbol }$. An inequality remains unchanged if: • the same number is added to both sides of the inequatily • the same number is subtracted from both sides of the inequality • both sides of the inequality are multiplied or divided by a positive number Learning these concepts Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language." $\fn_phv {\color{Red}SCROLL }$ $\fn_phv {\color{Red}DOWN }$ $\fn_phv {\color{Red}TO }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}GUIDED }$ $\fn_phv {\color{Red}PRACTICE }$ $\fn_phv {\color{Red}SECTION }$ $\fn_phv {\color{Red}AND }$ $\fn_phv {\color{Red}WORK }$ $\fn_phv {\color{Red}THROUGH }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}EXAMPLES }$ $\fn_phv {\color{Red}BEFORE }$ $\fn_phv {\color{Red}SUBMITTING }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}ASSIGNMENT!!! }$ ### 01.06 Solving Multi-Step Inequalities - Explanation Video Link (Math Level 1)  Explanation Video 01.06-1http://www.youtube.com/embed/HSk45oWSjvc?wmode=transparent&r... ### 01.06 Solving Multi-Step Inequalities - Explanation Videos (Math Level 1) ### 01.06 Solving Multi-step Inequalities - Extra Video (Math Level 1)  NROC Developmental Math Multi-Step Inequalitieshttp://www.montereyinstitute.org/courses/DevelopmentalMath/U... I highly recommend that you click on the link above before continuing. You can watch the video that is under the PRESENTATION tab or work through the entire lesson. Guided Practice After watching the video try these problems. The worked solutions follow. Solve the following and graph each solution: Example 1: 5 + 4b < 21 Example 2: 3x + 4(6 - x) < 2 Example 3: 8z - 6 < 3z + 12 Example 4: 5(-3 + d) ≤ 3(3d - 2) Answers Solve the following and graph each solution: Example 1: 5 + 4b < 21 Step 1: Subtract 5 from both sides: 4b < 16 Step 2: Divide both sides by 4: b < 4 Example 2: 3x + 4(6 - x) < 2 Step 1: Clear the parentheses: 3x + 24 - 4x < 2 Step 2: Collect like terms: -x + 24 < 2 Subtract 24 from both sides: -x < -22 Step 3: Multiply each side by -1: Example 3: 8z - 6 < 3z + 12 Step 1: Add 6 to both sides: 8z < 3z + 18 Step 2: Subtract 3z from both sides: 5z < 18 Step 3: Divide both sides by 5: z < $\dpi{100} \fn_phv \fn_phv \frac{18}{5}$ Example 4: 5(-3 + d) ≤ 3(3d - 2) Step 1: Clear the parentheses: -15 + 5d ≤ 9d - 6 Step 2: Add 15 to both sides: 5d ≤ 9d + 9 Step 3: Subtract 9d from both sides: -4d ≤ 9 Step 4: Divide both sides by -4: d ≥ $\dpi{100} \fn_phv -\frac{9}{4}$ ### 01.06.01 Solving Multi-Step Inequalities - Worksheet (Math Level 1)  teacher-scored 54 points possible 30 minutes Activity for this lesson. 1. Please print the worksheet. 2. Complete each problem showing all your work and highlighting your answer. 3. Digitize (scan or take digital photo) and upload your assignment. Pacing: complete this by the end of Week 4 of your enrollment date for this class. ### 01.06.02 Quiz Check Point (Math Level 1)  computer-scored 20 points possible 20 minutes Quiz Check Point You are given 3 attempts at this check point quiz. You must earn at least 16 points in order to pass the quiz. You may use all of your attempts to earn the score you are happy with. Pacing: complete this by the end of Week 4 of your enrollment date for this class. ### 01.07 Justifying the Steps in Solving Equations (Math Level 1)  Justify the steps in solving linear equations and inequalities by applying and naming the properties of equality, inverse, and identity. Now that you have mastered solving linear equations and inequalities and verifying your answers, it is time to justify each step taken. For example: Solve: n + 1 + n = 3  Step Justification 1. n + 1 + n = 3 1. Given 2. 2n + 1 = 3 2. Combine like terms 3. 2n + 1 – 1 = 3 – 1 3. Subtraction Property of Equality 4. 2n + 0 = 2 4. Additive Inverse Property (1 + –1 = 0 5. 2n = 2 5. Additive Identity 6. $\dpi{100} \fn_phv \frac{2}{2}$n = $\dpi{100} \fn_phv \frac{2}{2}$ 6. Division Property of Equality 7. 1n = 1 7. Multiplicative Inverse 8. n = 1 8. Multiplicative Identity I know. This seems like a great deal of extra work! But it is important to recognize that there are reasons for the steps taken when solving equations and inequalities. Now, complete the following: Solve: 5(2 + 4m) = –90  Step Justification 1. 5(2 + 4m) = –90 1. 2. 2. Distributive Property 3. 10 – 10 + 20m = –90 –10 3. 4. 4. Additive Inverse Property 5. 20m = –100 5. Additive Identity 6. $\dpi{100} \fn_phv \frac{20}{20}$m = $\dpi{100} \fn_phv \frac{-100}{ 20}$ 6. 7. 7. Multiplicative Inverse 8. m = – 5 8. Please try to do these without looking at the answers!!! ANSWERS:  Steps Justification 1. 5(2 + 4m) = –90 $\dpi{100} \fn_phv {\color{Red} 1. Given}$ $\dpi{100} \fn_phv {\color{Red} 2.}$ $\dpi{100} \fn_phv {\color{Red} 10 + 20m =}$ $\dpi{100} \fn_phv {\color{Red} -100}$ 2. Distributive Property 3. 10 – 10 + 20m = –90 – 10 $\dpi{100} \fn_phv {\color{Red} 3. Subtraction}$ $\dpi{100} \fn_phv {\color{Red} Property}$ $\dpi{100} \fn_phv {\color{Red} 4.}$ $\dpi{100} \fn_phv {\color{Red} 0 + 20m =}$ $\dpi{100} \fn_phv {\color{Red} -100}$ 4. Additive Inverse Property 5. 20m = – 100 5. Additive Indentity 6. $\dpi{100} \fn_phv \frac{20}{20}$m = $\dpi{100} \fn_phv \frac{-100}{ 20}$ $\dpi{100} \fn_phv {\color{Red} 6. }{\color{Red} Division }$ $\dpi{100} \fn_phv {\color{Red} Property }$ $\dpi{100} \fn_phv {\color{Red} of }$ $\dpi{100} \fn_phv {\color{Red} Equality }$ $\dpi{100} \fn_phv {\color{Red} 7. }$ $\dpi{100} \fn_phv {\color{Red} 1m = }$ $\dpi{100} \fn_phv {\color{Red} -5}$ 7. Multiplicative Inverse 8. m = –5 $\dpi{100} \fn_phv {\color{Red} 8. }$ $\dpi{100} \fn_phv {\color{Red} Multiplicative }$ $\dpi{100} \fn_phv {\color{Red} Identity }$ Good luck with the assignment!! ### 01.07.01 Justifying the Steps in Solving Equations 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 5 of your enrollment date for this class. Pacing: complete this by the end of Week 5 of your enrollment date for this class. ### 01.08 Literal Equations (Math Level 1)  Use the skills for solving equations to solve literal equations. Something to Ponder What's a personal example of when the skill of solving literal equations for a specific variable would be useful? In other words, why should you care about being able to solve a literal equation for a specific variable? Mathematics Vocabulary Literal equation: an equation with two or more variables. It is also an equation where variables represent known values. Literal equations represent things like distance, time, interest, and slope as one of the variables in an equation. Learning these concepts Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language." $\fn_phv {\color{Red}SCROLL }$ $\fn_phv {\color{Red}DOWN }$ $\fn_phv {\color{Red}TO }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}GUIDED }$ $\fn_phv {\color{Red}PRACTICE }$ $\fn_phv {\color{Red}SECTION }$ $\fn_phv {\color{Red}AND }$ $\fn_phv {\color{Red}WORK }$ $\fn_phv {\color{Red}THROUGH }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}EXAMPLES }$ $\fn_phv {\color{Red}BEFORE }$ $\fn_phv {\color{Red}SUBMITTING }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}ASSIGNMENT!!! }$ ### 01.08 Literal Equations - Explanation Video Link (Math Level 1)  Explanation Video 01.08-1http://www.youtube.com/embed/FJH5z5NwSXI?wmode=transparent&r... Optionally: use the link above to view the explanatory math video. ### 01.08 Literal Equations - Explanation Videos (Math Level 1) ### 01.08.01 Literal Equations - Extra Links (Math Level 1)  mathispower4u: Solving Literal Equations - Part 1 (L7.1)http://youtu.be/OgEg5Rfp5cwmathispower4u: Solving Literal Equations - Part 2 (L7.1)http://youtu.be/Kjn1QP5saUgmathispower4u: Examples 1: Solving a Formula for a Variable http://www.youtube.com/embed/38Jq30ZA2L4?wmode=transparent&r...mathispower4u: Examples 2: Solving a Formula for a Variablehttp://www.youtube.com/embed/BUVJlJXfuFo?wmode=transparent&r...mathispower4u: Ex 1: Solve a Literal Equation for a Variable (Basic) http://youtu.be/DorYar-GjC0mathispower4u: Ex 2: Solve a Literal Equation for a Variablehttp://youtu.be/ecEUUbRLDQsmathispower4u: Ex 3: Solve a Literal Equation for a Variablehttp://youtu.be/bbi5FxfPn20mathispower4u: Ex: Literal Equation Application - Perimeter of a Rectanglehttp://youtu.be/NgyxDfkLWjQ 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 for h: A= $\dpi{100} \fn_phv \frac{1}{2}$Bh Example 2: Solve for l: P = 2l + 2w Example 2: Solve for b: ab - d = c Example 3: Solve the following for y: 2x - 3y = 6 Answers Example 1: Solve for h: A= $\fn_phv \frac{1}{2}$Bh Step 1: Multiply both sides by 2: 2A = Bh Step 2: Divide both sides by h: $\dpi{100} \fn_phv \fn_phv \frac{2A}{B}=\frac{Bh}{B}$ Step 3: Cancel the B's on the right sides $\dpi{100} \fn_phv \frac{Bh}{B} = h$ Example 2: Solve for l: P = 2l + 2w Step 1: Subtract 2w from both sides: P – 2w = 2l Step 2: Divide both sides by 2: $\dpi{100} \fn_phv \frac{P-2w}{2} = \frac{2l}{l}$ Step 3: Cancel the l's on the right side: $\dpi{100} \fn_phv \frac{P-2w}{2} = l$ Example 3: Solve for b: ab - d = c Step 1: Add d to both sides: ab = c + d Step 2: Divide both sides by a: $\dpi{100} \fn_phv \frac{ab}{a} = \frac{c+d}{a}$ Step 3: Cancel the a's on the left side: $\dpi{100} \fn_phv b = \frac{c+d}{a}$ Example 4: Solve the following for y: 2x - 3y = 6 Step 1: Subtract 2x from both sides: – 3y = 6 – 2x Step 2: Divide both sides by – 3: $\dpi{100} \fn_phv \frac{-3y}{-3} = \frac{6-2x}{-3}$ Step 3: Cancel the -3's from the left side: $\dpi{100} \fn_phv y = \frac{6-2x}{-3}$ or if you multiply each term on the right by – 1 and reordering the numerator: $\dpi{100} \fn_phv y = \frac{2x-6}{3}$ ### 01.08.02 Literal Equations - 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 5 of your enrollment date for this class. ### 01.09 Solutions to Equations and Inequalities (Math Level 1)  Evaluate solutions of equations and inequalities. Something to Ponder How can you know if a solution is really a solution? Mathematics Vocabulary Evaluate solution (or verify): Plugging a solution into the variable in an equation or inequality Learning these concepts $\fn_phv {\color{Red}SCROLL }$ $\fn_phv {\color{Red}DOWN }$ $\fn_phv {\color{Red}TO }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}GUIDED }$ $\fn_phv {\color{Red}PRACTICE }$ $\fn_phv {\color{Red}SECTION }$ $\fn_phv {\color{Red}AND }$ $\fn_phv {\color{Red}WORK }$ $\fn_phv {\color{Red}THROUGH }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}EXAMPLES }$ $\fn_phv {\color{Red}BEFORE }$ $\fn_phv {\color{Red}SUBMITTING }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}ASSIGNMENT!!! }$ Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language." ### 01.09 Solutions to Equations and Inequalities - Explanation Video Link (Math Level 1)  Explanation Video 01.09-1http://www.youtube.com/embed/DPdd40AMXQE?wmode=transparent&r... ### 01.09 Solutions to Equations and Inequalities - Explanation Videos (Math Level 1)  Guided Practice After watching the video try these problems. The worked solutions follow. Example 1: Is -7 a solution to 4x - 8 = 2x - 6? Example 2: Is x > - 4 a solution to 3(x + 2) > 2(x - 5)? Example 3: Solve: 3x - 6 = 3x + 2. Example 4: Solve: 4(x - 5) = 2(x - 10) + 2x. Answers Example 1: Is -7 a solution to 4x - 8 = 2x - 6? To make the determination, substitute -7 in for x: 4(–7) – 8 = 2(–7) – 6 –28 – 8 = –14 – 6 –36 = –20 NO! Example 2: Is x > - 4 a solution to 3(x + 2) > 2(x - 5)? To make this determination, solve the inequality: Step 1: Use the distributive property to simplify the inequality: 3x + 6 > 2x – 10 Step 2: Subtract 2x from both sides: x + 6 > – 10 Step 3: Subtract 2 from both sides: x > – 16 As you can see from the graph, x > – 4 is part of the solution but not THE solution. NO. Example 3: Solve: 3x - 6 = 3x + 2. Step 1: Add 6 to both sides: 3x = 3x + 8 Step 2: Subtract 3x from both sides: 0 = 8 Since this is false, there is no solution to this equation. Example 4: Solve: 4(x - 5) = 2(x - 10) + 2x. Step 1: Clear the parentheses: 4x - 20 = 2x - 20 + 2x Step 2: Collect like terms: 4x - 20 = 4x - 20 Step 3: Add 20 to both sides: 4x = 4x Step 3: Subtract 4x from both sides: 0 = 0 Since this is true but the value of x is not found, any value of x would work. There is an infinite number of solutions. ### 01.09 Solutions to Equations and Inequalities - 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 5 of your enrollment date for this class. ### 01.09 Unit 01 Review Quiz (Math Level 1)  teacher-scored 93 points possible 30 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 5 of your enrollment date for this class. ### 02.00 Writing Expressions, Equations and Inequalities Overview (Math Level 1)  In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They move beyond viewing functions as processes that take inputs and yield outputs and start viewing functions as objects in their own right. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that, depending upon the context, these representations are likely to be approximate and incomplete. Their work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions. By the end of the unit, students will be able to: Understand and apply the steps for solving problems. Write linear inequalities to model real-life situations. Write equations for solving problems involving travel. Write equations for solving problems involving proportions. Write equations for solving problems involving percent. Use equations to solve real-world problems. ### 02.01 Problem Solving (Math Level 1)  Understand and apply the steps for solving problems. 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 Steps for Problem Solving: 1. Identify the information given and relationships 2. Interpret what is to be found 3. Write an equation or choose another problem solving method 4. Solve the equation or formula and justify and verify the solution Strategies for Problem Solving: 1. Draw a Diagram 2. Try, Check and Revise 3. Look for a Pattern 4. Make a Table 5. Make an Organized list 6. Write an Equation Learning these concepts Click each mathematician image OR click the links below to launch the video to help you better understand this "mathematical language." $\fn_phv {\color{Red}SCROLL }$ $\fn_phv {\color{Red}DOWN }$ $\fn_phv {\color{Red}TO }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}GUIDED }$ $\fn_phv {\color{Red}PRACTICE }$ $\fn_phv {\color{Red}SECTION }$ $\fn_phv {\color{Red}AND }$ $\fn_phv {\color{Red}WORK }$ $\fn_phv {\color{Red}THROUGH }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}EXAMPLES }$ $\fn_phv {\color{Red}BEFORE }$ $\fn_phv {\color{Red}SUBMITTING }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}ASSIGNMENT!!! }$ ### 02.01 Problem Solving - Explanation Video Links (Math Level 1)  Explanation Video 02.01-1http://www.youtube.com/embed/6KGf44Fe6eQ?wmode=transparent&r...Explanation Video 02.01-2http://www.youtube.com/embed/O75mxhJnRfs?wmode=transparent&r... ### 02.01 Problem Solving - Explanation Videos (Math Level 1) ### 02.01 Problem Solving with Equations - Extra Video (Math Level 1)  Art of Problem Solving: Word Problems Part 1http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Word Problems Part 2http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Word Problems Part 3http://www.artofproblemsolving.com/Videos/external.php?video...mathispower4u: Writing Linear Equations to Solve Applications (L6.1)http://youtu.be/dE6Zd_J3Qr4 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: There are eight teams in a tennis tournament. If it is single elimination, how many sets will be played in all? Example 2: Find two consecutive integers whose sum is 75. Example 3: Seventy-two students are separated into two groups. The first group is 5 times as large as the second. How many students are in each group? Answers Example 1: There are eight teams in a tennis tournament. If it is single elimination, how many sets will be played in all? Sometimes, a problem lends itself to an equation and sometimes it doesn’t. For me, the easiest way to solve this problem is by creating the following: There will be 7 matches. Example 2: Find two consecutive integers whose sum is 75. Let x = the first number x + x + 1 = 75 2x = 74 x = 37 x + 1 = 38 The two numbers are 37 and 38. Example 3: Seventy-two students are separated into two groups. The first group is 5 times as large as the second. How many students are in each group? Let x = the number of students in the first group The other group = 5x x + 5x = 72 6x = 72 x = 12 The first group has 12 students and the second group has 60 students. ### 02.01.01 Problem Solving - 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 6 of your enrollment date for this class. ### 02.02 Writing Linear Inequalities (Math Level 1)  Write linear inequalities to model real-life situations. Something to Ponder Explain the meaning of "at most" and "at least" and how you write each of them with inequality symbols. Mathematics Vocabulary Model real-life situations: Sometimes students who study mathematics learn the rote-steps for solving tidy worksheet problems, but are unable to apply the learned skills to solve problems in real-life settings. Students fail to understand the variable "x" used extensively in algebra problems is actually related to real-life phenomena. For that student, the learning of rote-steps remains disconnected from real-world contexts. To remedy this huge gulf between discrete skill and real understanding of the fundamental language of mathematics, look for ways to create story problems that require application of a new mathematics skill. This kind of deep thinking helps the mind connect the skill to underlying concepts and leads to fluency in the language of mathematics. Learning these concepts Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language." $\fn_phv {\color{Red}SCROLL }$ $\fn_phv {\color{Red}DOWN }$ $\fn_phv {\color{Red}TO }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}GUIDED }$ $\fn_phv {\color{Red}PRACTICE }$ $\fn_phv {\color{Red}SECTION }$ $\fn_phv {\color{Red}AND }$ $\fn_phv {\color{Red}WORK }$ $\fn_phv {\color{Red}THROUGH }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}EXAMPLES }$ $\fn_phv {\color{Red}BEFORE }$ $\fn_phv {\color{Red}SUBMITTING }$ $\fn_phv {\color{Red}THE }$ $\fn_phv {\color{Red}ASSIGNMENT!!! }$ ### 02.02 Writing Linear Inequalities - Explanation Video Link (Math Level 1)  Explanation Video 02.02-1http://www.youtube.com/embed/unSBFwK881s?wmode=transparent&r... [video content from Khan Academy (CC) BY-NC-SA] ### 02.02 Writing Linear Inequalities - Explanation Videos (Math Level 1) ### 02.02 Writing Linear Inequalities - Extra Video (Math Level 1)  mathispower4u: Introduction to Basic Inequalities in One Variable (L7.2)http://youtu.be/a1OTyEsdYFcmathispower4u: Solving Linear Inequalities in One Variable (L7.3)http://youtu.be/iklg78Nmc5Mmathispower4u: Solving One-Step Linear Inequalities in One Variable http://www.youtube.com/embed/U4Soj7MhSfk?wmode=transparent&r...mathispower4u: Ex: Solving One Step Inequalities by Adding and Subtracting (Variable Left Side) http://www.youtube.com/embed/1Z22Xh66VFM?wmode=transparent&r...mathispower4u: Ex: Solving One Step Inequalities by Adding and Subtracting (Variable Right Side) http://www.youtube.com/embed/RBonYKvTCLU?wmode=transparent&r...mathispower4u: Ex: Solve One Step Linear Inequality by Dividing (Variable Left) http://www.youtube.com/embed/IajiD3R7U-0?wmode=transparent&r...mathispower4u: Ex: Solve One Step Linear Inequality by Dividing (Variable Right) http://www.youtube.com/embed/s9fJOnVTHhs?wmode=transparent&r...mathispower4u: Ex: Solving a One Step Linear Inequality by Multiplying http://www.youtube.com/embed/mBHQB5XlSks?wmode=transparent&r...mathispower4u: Solving Two-Step Linear Inequalities in One Variable http://www.youtube.com/embed/SXrxEmmfp7A?wmode=transparent&r...mathispower4u: Ex: Solve a Two Step Linear Inequality (Variable Left) http://www.youtube.com/embed/RB9wvIogoEM?wmode=transparent&r...mathispower4u: Ex: Solve a Two Step Linear Inequality (Variable Right) http://www.youtube.com/embed/9D2g_FaNBkY?wmode=transparent&r...mathispower4u: Solving Linear Inequalities in One Variable http://www.youtube.com/embed/MJ4dCBmYwvU?wmode=transparent&r...mathispower4u: Ex: Solve a Linear Inequality in One Variable (axb+c(dx+e)) http://youtu.be/FGTROofodZ4mathispower4u: Ex: Solve a Linear Inequality in One Variable (ax+b 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: Define a variable and write an inequality for each situation: a) A car dealership sells at least 45 cars each week. b) No more than 350 tickets to a concert will be sold. Example 2: Write and solve an inequality for each situation: a) Suppose you are trying to increase your butterfly collection to at least 200 specimens. How many more butterflies do you need if you already have a collection of 125 butterflies? b) The football team with 45 players is holding a fund-raiser to support their team activities. Their goal is to raise at least$300. On average, how much money does each student need to contribute to meet or exceed the goal?

Answers

Example 1: Define a variable and write an inequality for each situation:

a) A car dealership sells at least 45 cars each week.

Let c = the number of cars sold each week

c ≥ 45

b) No more than 350 tickets to a concert will be sold.

Let t = the number of tickets to be sold

t ≤ 350

Example 2: Write and solve an inequality for each situation:

a) Suppose you are trying to increase your butterfly collection to at least 200 specimens. How many more butterflies do you need if you already have a collection of 125 butterflies?

Let b = the number of butterfly specimens you will add to your collection

125 + b ≥ 200

Subtract 125 from both sides:

b ≥ 75

b) The football team with 45 players is holding a fund-raiser to support their team activities. Their goal is to raise at least $300. On average, how much money does each student need to contribute to meet or exceed the goal? m = the amount of money each student needs to contribute 45m ≥ 300 m ≥ 6.67 rounded to the nearest hundredth. Each student must contribute at least$6.67

### 02.02 Writing Linear Inequalities - 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 6 of your enrollment date for this class.

### 02.03 Problem Solving – Travel (Math Level 1)

 Write equations for solving problems involving travel.

Something to Ponder

What things need to be considered as you set up problems about distance?

Mathematics Vocabulary

Formula for Distance: $\fn_jvn&space;D&space;=&space;rt$, where D = distance, r = rate, and t = time.

Learning these concepts

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

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

### 02.03 Problem Solving – Travel - Explanation Video Link (Math Level 1)

 Explanation Video 02.03-1http://www.youtube.com/embed/OHeArsdBITw?wmode=transparent&r...

### 02.03 Problem Solving - Travel - Extra Video (Math Level 1)

 mathispower4u: Distance = Rate x Time Application Problemhttp://youtu.be/fIT8mShPr00Tyler Wallace: Distance Problemshttps://new.edu/nodes/rational-expressions-and-equations--3/...Khan Academy: Basic Rate Problem https://www.khanacademy.org/math/algebra/solving-linear-equa...

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:

If you drive at 75 miles per hour for 2 hours, how far did you travel?

Example 2:

You ride your bike 12 miles in 45 minutes. What rate are you traveling at?

Example 3:

If Michael rides his bicycle at 8 miles per hour, how far does he travel in 30 minutes? How long does it take him to ride 18 miles?

Example 4:

Jason drives at 40 miles per hour. It takes him 4 hours to get to his destination. How far did he travel? If he drives 15 miles per hour faster, how long will it take him to get there?

Answers

Example 1:

If you drive at 75 miles per hour for 2 hours, how far did you travel?

D = rt = 75 x 2 = 150 miles

Example 2:

You ride your bike 12 miles in 45 minutes. What rate are you traveling at?

45 minutes = 0.75 hours

D = rt

12 = r(0.75)

16 = r

You are traveling at 16 miles per hour.

Example 3:

If Michael rides his bicycle at 8 miles per hour, how far does he travel in 30 minutes? How long does it take him to ride 18 miles?

30 minutes = 0.5 hours

D = rt

D = 8(0.5) = 4 miles

D = rt

18 = 8t

2.25 = t

It will take Michael 2.25 hours or 2 hours and 15 minutes.

Example 4:

Jason drives at 40 miles per hour. It takes him 4 hours to get to his destination. How far did he travel? If he drives 15 miles per hour faster, how long will it take him to get there?

Jason drives at 40 miles per hour. It takes him 4 hours to get to his destination. How far did he travel? If he drives 15 miles per hour faster, how long will it take him to get there?

D = rt

D = 40(4) = 160

Jason drove 160 miles

D = rt

160 = 55(t)

2.9 rounded to the nearest tenth.

It will take Jason 2.9 hours to get there if he drives 55 miles per hour.

### 02.03.01 Problem Solving – Travel - 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 7 of your enrollment date for this class.

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

 teacher-scored 64 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.

### 02.04 Problem Solving – Proportions (Math Level 1)

 Write equations for solving problems involving proportions.

Something to Ponder

Explain why using "cross products" to solve proportions works in all cases.

Mathematics Vocabulary

Proportion: a statement that two ratios are equal (can be written as equivalent fractions or equal ratios)

Cross products: the resulting value of multiplying across the equal sign (a/b = c/d has cross products of ad = bc)

Similar figures: have the same shape but not necessarily the same size (corresponding angles are congruent and corresponding sides are proportional)

Indirect measurement: a way of measuring things that are too difficult to measure directly a drawing in which all lengths are proportional to the original

Scale drawing: a drawing in which all lengths are proportional to the original

Learning these concepts

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

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

### 02.04 Problem Solving – Proportions - Explanation Video Links (Math Level 1)

 Explanation Video 02.04-1http://www.youtube.com/embed/PKhSDQd_ifw?wmode=transparent&r...Explanation Video 02.04-2http://www.youtube.com/embed/X3Ip2m2AJsI?wmode=transparent&r...Explanation Video 02.04-3http://www.youtube.com/embed/Iie7Sslmijs?wmode=transparent&r...

### 02.04.01 Problem Solving - Proportions - Extra Video (Math Level 1)

 Art of Problem Solving: Ratio Problem Solvinghttp://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Conversion Factors - Part 1http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Conversion Factors - Part 2 http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Conversion Factors - Part 3http://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: Solve the following:

a) $\dpi{100} \fn_phv \fn_phv \frac{2}{7}=\frac{y}{14}$

b) $\dpi{100} \fn_phv \frac{x}{9}=\frac{4}{6}$

Example 2:

Write a proportion that could be used to solve for each variable and then solve. 3 pounds for $1.50 and x pounds for$4.50.

Example 3:

On a scale drawing of a room, 1 inch represents 2 feet. In the scale drawing, the room is 11 inches long. How long is the actual room?

Example 4:

A recipe for 3-1⁄2 dozen muffins requires 700 g of flour. How many dozens of muffins can be made using 800 g of flour?

Example 5:

ABCD ~ Parallelogram EFGH. Find the value of x.

Example 6:

A tree casts a shadow 10 ft long. A 5-ft woman casts a shadow 4 ft long. Use similar triangles to find the height of the tree.

Example 7:

A map scale is 1 in:24 mi. About how far is it between two cities that are 3 in apart on the map?

Answers

Example 1: Solve the following:

a) $\dpi{100} \fn_phv \frac{2}{7}=\frac{7}{14}$

7y = 28

y = 4

b) $\dpi{100} \fn_phv \frac{x}{9}=\frac{4}{6}$

6x = 36

x = 6

Example 2:

Write a proportion that could be used to solve for each variable. Then solve. 3 pounds for $1.50 and x pounds for$4.50

$\dpi{100} \fn_phv \frac{3}{1.50}=\frac{x}{4.50}$

13.50 = 1.50x

9 = x

There will be 9 pounds

Example 3:

On a scale drawing of a room, 1 inch represents 2 feet. In the scale drawing, the room is 11 inches long. How long is the actual room?

$\dpi{100} \fn_phv \frac{1 in}{2 ft}=\frac{11 in}{x }$

x = 22 ft

Example 4:

A recipe for 3 1⁄2 dozen muffins requires 700 g of flour. How many dozens of muffins can be made using 800 g of flour?

$\dpi{100} \fn_phv \frac{3.5}{700}=\frac{x}{800}$

Cross multiply:

2800 = 700x

Divide by 700 on both sides:

4 = x

There will be four dozen muffins made.

Example 5:

ABCD ~ Parallelogram EFGH. Find the value of x.

$\dpi{100} \fn_phv \frac{16}{4}=\frac{20}{x}$

Cross multiply:

16x = 80

Divide both sides by 16:

x = 5

Example 6:

A tree casts a shadow 10 ft long. A 5-ft woman casts a shadow 4 ft long. Use similar triangles to find the height of the tree.

$\dpi{100} \fn_phv \frac{x}{10}=\frac{5}{4}$

Cross multiply:

4x = 50

Divide both sides by 4:

x = 12.5 feet

Example 7:

A map scale is 1 in:24 mi. About how far is it between two cities that are 3 inches apart on the map?

$\dpi{100} \fn_phv \frac{1}{24}=\frac{3}{x}$

Cross multiply:

x = 72 miles

### 02.04.02 Problem Solving – Proportions - Worksheet (Math Level 1)

 teacher-scored 54 points possible 30 minutes

Activity for this lesson

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

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

### 02.05 Problem Solving – Percent (Math Level 1)

 Write equations for solving problems involving percent.

Something to Ponder

How can the percent proportion be used to find percents and other related numbers?

Mathematics Vocabulary

Percent: a number or ratio as a fraction of 100

Learning these concepts

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

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

### 02.05 Problem Solving – Percent - Explanation Video Links (Math Level 1)

 Explanation Video 02.05-1http://www.youtube.com/embed/DN_1zKDSVW8?wmode=transparent&r...Explanation Video 02.05-2http://www.youtube.com/embed/UMy34sHvMow?wmode=transparent&r...

### 02.05.01 Problem Solving - Percent - Extra Video (Math Level 1)

 Art of Problem Solving: Percent Introductionhttp://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Basic Percent Problemshttp://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Percent Increase and Decrease Part 1http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Percent Word Problems Part 1http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Percent Word Problems Part 2http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Percent Increase and Decrease Part 2 http://www.artofproblemsolving.com/Videos/external.php?video...Art of Problem Solving: Percent Problem Solving http://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:

a) What percent is 55 of 75?

b) 35% of what number is 40?

c) 18% of 360 is what number?

Example 2:

Find the percent of increase from 8 to 9.

Example 3:

Find the percent of decrease from 1,250 to 1,120

Example 4:

A grocery store has a 20% markup on a can of soup. The can of soup costs the store $1.25. The tax is 6%. What is the selling price for the soup? Example 5: A camera that regularly sells for$210 is on sale for 30% off. The tax is 6.5%. Find the selling price for the camera.

Answers

Example 1:

a) What percent is 55 of 75?

$\dpi{100} \fn_phv \fn_phv \frac{percent}{100}=\frac{part}{original}$

$\dpi{100} \fn_phv \frac{x}{100} = \frac{55}{75}$

Cross multiply: 75 = 5500

Divide both sides by 100:

x =  73.3

b) 35% of what number is 40?

$\dpi{100} \fn_phv \frac{percent}{100}=\frac{part}{original}$

$\dpi{100} \fn_phv \frac{35}{100}=\frac{40}{x}$

Cross multiply: 35x = 4000

Divide both sides by 35:

x = 114.29

c) 18% of 360 is what number?

$\dpi{100} \fn_phv \frac{percent}{100}=\frac{part}{original}$

$\dpi{100} \fn_phv \frac{18}{100}=\frac{x}{360}$

Cross multiply: 100x = 6480

Divide both sides by 100:

x = 64.8

Example 2:

Find the percent of increase from 8 to 9.

Increase = 9 - 8 = 1

$\dpi{100} \fn_phv \frac{percent}{100}=\frac{part}{original}$

$\dpi{100} \fn_phv \frac{x}{100}=\frac{1}{8}$

Cross multiply: 8x = 100

Divide both sides by 8:

x = 12.5%

Example 3:

Find the percent of decrease from 1,250 to 1,120

Decrease = 1250 - 1120 = 130

$\dpi{100} \fn_phv \frac{percent}{100}=\frac{part}{original}$

$\dpi{100} \fn_phv \frac{x}{100}=\frac{130}{1250}$

Cross multiply: 1250x = 13,000

Divide both sides by 1250:

x = 10.4% decrease

Example 4:

A grocery store has a 20% markup on a can of soup. The can of soup costs the store $1.25. The tax is 6%. What is the selling price for the soup? $\dpi{100} \fn_phv \frac{percent}{100}=\frac{part}{original}$ $\dpi{100} \fn_phv \frac{20}{100}=\frac{x}{1.25}$ Cross multiply: 100x = 25 Divide both sides by 100: x = .25 or 25¢ markup Price for the soup = 1.25 + 0.25 =$1.50

The tax is 6%

$\dpi{100} \fn_phv \frac{percent}{100}=\frac{part}{original}$

$\dpi{100} \fn_phv \frac{6}{100}=\frac{x}{1.50}$

Cross multiply: 100x = 9

Divide both sides by 100:

x = 0.09 or 9¢

Total cost of soup = 1.50 + 0.09 = $1.59 Example 5: A camera that regularly sells for$210 is on sale for 30% off. The tax is 6.5%. Find the selling price for the camera.

$\dpi{100} \fn_phv \frac{percent}{100}=\frac{part}{original}$

$\dpi{100} \fn_phv \frac{30}{100}=\frac{x}{210}$

Cross multiply: 100x = 6300

Divide both sides by 100:

x = 63

The markdown is $63 The sale price is 210 - 63 =$147

The sales tax is 6.5%

$\dpi{100} \fn_phv \frac{percent}{100}=\frac{part}{original}$

$\dpi{100} \fn_phv \frac{6.5}{100}=\frac{x}{147}$

Cross multiply: 100x = 955.5

Divide both sides by 100:

x = 9.56 or $9.56 Total cost of the camera is$147 + $9.56 =$156.56

### 02.05.02 Problem Solving – Percent - 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 8 of your enrollment date for this class.

### 02.06 Project (Math Level 1)

 Students can integrate writing into the math curriculum.

Connecting Skill to the Real World

At the end of this quarter, you have the opportunity to demonstrate that you have gained an understanding of all the concepts in a unique way. Every high school course is required to making writing part of the curriculum.

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.

### 02.06 Writing Assignment (Math Level 1)

 teacher-scored 30 points possible 45 minutes

Writing Assignment

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 Nice summary statement(s) 6

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

### 02.06 Unit 02 Review Quiz (Math Level 1)

 both teacher- and computer-scored 20 points possible 30 minutes

Unit 2 Review Quiz

You are allowed three attempts at the quiz

The quiz is worth 20 points and you must score 16 or higher to meet the minimum requirements.

1. Work all problems.

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