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**Course Description: **Students will work through basic operations with integers, fractions and decimals. Students will progress through the study of number properties as well proportions, rates, exponents and radicals.

DIRECTIONS: This is an ordered list of 139 videos and exercises.

(This courses uses many links, especially teaching videos, from Khan Academy. It’s the same course that it was *before* Khan Academy aligned with Common Core. We don’t solely use Khan Academy. There are other sites and much of our own materials as well. This course had a major update in 2022.)

You will start at the top of the page with Addition and Subtraction and work your way down in order. Make sure you read the directions ** every **time. The first link on each line is to the video, unless marked differently. You can move on to the exercise as soon as you know the material. That means you can do the exercise without watching the video if you already know how to do it. IT WILL START AT THE BEGINNING! The point is for you to fill any gaps in your learning and then progress forward with that solid foundation. At some point, you should probably be watching all of the videos. When you do, write the problems down and work through them with the teacher to help you stay focused and to make sure you can do it too. Some days you will be doing more than one exercise. Some days you won’t make it through one whole exercise. You will stay on an exercise until you are proficient. You should be able to do

**five in a row correct**before you move on. One suggestion is to set aside 20 – 30 minutes for math each day. When you stop in the middle of an exercise, it should remember how many problems you’ve done.

**Addition and Subtraction with Positive and Negative Numbers**

**Lesson 1**

Welcome to your first day of school! I wanted to give you one **important reminder** before you begin. Many of your lessons below have an internet link for you to click on. When you go to the different internet pages for your lessons, please **DO NOT click on anything else on that page** except what the directions tell you to. DO NOT click on any advertisements or games. DO NOT click on anything that takes you to a different website. Just stay focused on your lesson and then close that window and you should be right back here for the next lesson. Okay?

- If you didn’t get here through My EP Assignments, I suggest you go there and create an account. There is an offline version of this course if you are interested in a workbook. Go to the top of the course page for the link.
- Read the directions for this course.
- You do NOT need to watch this if you can add 2 + 2, but here’s a video, Basic Addition.
- Complete the exercise.
**(YES, this is correct for this level. This course starts at the beginning and will emphasize any holes in your math knowledge. PLEASE read the course description if you are confused by how easy this seems starting out.)** - Here’s a second video. This is for adding two-digit numbers without regrouping.
- Add two-digit numbers without regrouping.
- This is the end of Lesson 1. Did you set a timer for 20 or 30 minutes? If you still have time left, move on to Lesson 2. You get to move at your pace for this course. Feel free to move quickly through these early lessons.

**Lesson 2**

- Basic Subtraction (You only need to watch the lesson videos if you can’t do a good job on the exercise.)
- Complete the exercise.

**Lesson 3 **

- Adding 2-digit numbers with regrouping
- Complete the exercise.

**Lesson 4 **

- Subtracting two-digit numbers with regrouping (Remember, the video is only if you need it. If you “got this,” then you don’t need this video.)
- Complete the exercise.

**Lesson 5 **

- Addition 3 (Remember, the video is only if you need it. If you “got this,” then you don’t need this video.)
- Complete the exercise.

**Lesson 6 **

- Subtracting Three-Digit Numbers Borrowing or Regrouping (Remember, the video is only if you need it. If you “got this,” then you don’t need this video.)
- Complete the exercise.

**Lesson 7 **

- Why borrowing works & Alternate mental subtraction method
- Try the subtraction exercise with the new method. It’s a good habit to have a math notebook where you write out your math work. You don’t have to do it in your head.

**Lesson 8 **

- Addition 4 – adding up to four digits
- Complete the exercise.

**Lesson 9 **

- Subtracting Across Zeroes
- Complete the exercise.

**Lesson 10 **

- Complete the exercise “Addition and Subtraction Word Problems .” You will do 12 questions.

**Lesson 11 **

- This lesson introduces negative numbers. This is new!
- Negative Numbers Introduction
- Complete the exercise.

**Lesson 12 **

- Please watch the videos for these lessons on negative numbers.
- Ordering Negative Numbers
- Play the game. Choose Math Options, Compare, and Yes. Click on the card that has the greatest value. Here’s an alternative practice.

**Lesson 13 **

- These are new lessons on adding and subtracting negative numbers.
- Adding Negative Numbers and Adding Integers with Different Signs
- Add integers. Their signs are the same.
- Add integers. Their signs are different.

**Lesson 14 **

- Adding/Subtracting Negative Numbers
- Complete the exercise “Adding and Subtracting Negative Numbers.”
- Play the game. Choose Math Options, Arithmetic, Subtract, Yes. Pay attention!

**Lesson 15 **

- Complete the exercise “Negative Number Word Problems.”

**Lesson 16**

- Add integers. Play the game. Choose Math Options, Arithmetic, Add, Yes. Pay attention!
- Subtract integers. Play the game. Choose Math Options, Arithmetic, Subtract, Yes. Pay attention! (Or, here’s an alternative if you want a faster pace.)

**Multiplication and Division with Positive and Negative Numbers**

**Lesson 17**

- Basic Multiplication and Multiplication 2: The Multiplication Tables and Multiplication 3: 10,11,12 Times Tables The videos in these easy lessons are just if you need them.
- Multiply.
- Click on the 11 and fill in the answers.

**Lesson 18**

- Multiplying by Multiples of Ten
- The video only shows zeros in one number.
- 40 x 60 is the same thing. 6×4=24 and two zeros, 2400.
- 20 x 100 is two and three zeros, 2000.
- 400 x 5 does not have two zeros in the answer! It is 4×5=20 and two zeros, 2000.

- Multiply with zeros.

**Lesson 19**

- Division 1 and Division 2
- Complete the exercise.

**Lesson 20**

- Watch at least the first part of this video about the different ways we can express division problems.
- Divide without remainders.

**Lesson 21**

- Multiplication : 3-digit Times a 1-digit Number Example and Multiplication 5: 2-digit Times a 2-digit Number
- Complete the exercise.
- Complete the exercise.

**Lesson 22**

- Multiplication 6: Multiple Digit Numbers.
- Complete the exercise. You can do half today. Get five correct.

**Lesson 23**

- Lattice Multiplication and Why Lattice Multiplication Works
- Finish the exercise, “Multiplying 3 Digits by 2 Digits.” Do the other half. Get five correct. Try the new method. Use your math notebook.

**Lesson 24**

- Long division with remainder examples
- Complete the exercise.

**Lesson 25**

- Multiplication Word Problems and Division Word Problems
- Complete the exercise.

**Lesson 26**

- Dividing four digits by two digits
- Begin the exercise. Do half today. Get five correct.

**Lesson 27 **

- Partial Quotient Division and Partial Quotient Method of Division 2
- Finish “Multi Digit Division.” Do the other half. Get five correct. Use your math notebook and try the partial quotient method.

**Lesson 28**

- Answer the addition and subtraction word problems. (review)
- Answer the multiplication and division word problems. (review)

**Lesson 29**

- Place Value 1 and Place Value 2 and Place Value 3
- Complete the exercise.

**Lesson 30**

- Rounding Whole Numbers 1 and Rounding Whole Numbers 2 and Rounding Whole Numbers 3
- Complete the exercise. Choose nearest 100.

**Lesson 31**

- This lesson is on multiplying and dividing with negative numbers. This is new! Please watch the videos.
- Multiplying Positive and Negative Numbers and Why a Negative Times a Negative is a Positive and Dividing Positive and Negative Numbers
- Complete the exercise.
- Complete the exercise.
- Play the game. Choose Math Options, Arithmetic, Multiply, Yes. Pay attention!

**Lesson 32**

- Learn about basic exponents. Here’s the video lesson.
- Practice.

**Number Properties**

**Lesson 33**

- Commutative Law of Addition and Commutative Law of Multiplication
- Explain and demonstrate the commutative law to a younger sibling (or someone else) using toys. (If I give you one car and one plane, you have a car and a plane. If I give you one plane and one car… If I give you a toy car two times, you have… If I give you two toy cars one time, you have…)

**Lesson 34 **

- Associative Law of Addition and Associative Law of Multiplication
- If you need any more help on these, you can look at the first two sections on the page about the commutative and associative laws. Complete questions 1 through 4 at the bottom of the page.

**Lesson 35**

- The Distributive Property and The Distributive Property 2 and The Distributive Property Exercise
- Complete the exercise “Distributive Property.”

**Lesson 36**

- The Number Line and Absolute Value.
- Complete the exercise “Finding Absolute Value.”

**Lesson 37**

- Complete the exercise “Comparing Absolute Values.”

**Lesson 38**

- Identity Property of 1 and Identity Property of 1 (second example) and Identity Property of 0
- Demonstrate with toys and explain the identity property to a younger sibling (or someone else).

**Lesson 39**

- Inverse Property of Addition and Inverse Property of Multiplication
- Can you identify the number property? (Click on “review” for any you got wrong.)

**Lesson 40**

- Why Dividing by Zero is Undefined and Why Zero Divided by Zero is Undefined/Indeterminate and Undefined and Indeterminate
- Explain this concept to your parent or homeschool teacher.

**Lesson 41**

- Review.
- Adding integers 3 + 5 = 8 but 3 + (-5) = 3 – 5 or -(5 – 3)= -2
- Subtracting integers 3 – 5 = -2 but 3 – (-5) = 3 + 5 = 8
- Multiplying integers 3 x -5 = -15 but -3 x -5 = 15
- Dividing integers 15 / -5 = -3 but -15 / -5 = 3

**Lesson 42**

**Factors and Multiples**

**Lesson 43**

- Prime Numbers
- Read my notes below.
- A prime number can’t be divided evenly (no remainder) by any number except itself and the number 1. Example: 7/7=1, 7/1=7 You can’t divide 7 evenly by any number other than itself and 1.
- If it is even, then you can divide it by 2.
- If it ends in 5 or 0, then you can divide it by 5.
- If you can add up the digits and divide the sum by 3 or 9, then you can divide the whole number by 3 or 9. For example 69: 6 + 9 = 15. You can divide 15 by 3, so you can divide 69 by 3.

**Lesson 44**

- Recognizing Prime Numbers
- Complete the exercise.

**Lesson 45**

- Recognizing Divisibility
- Common Divisibility Examples
- Complete the exercise “Divisibility Tests.”
- An even number (0, 2, 4, 6, 8) is divisible by 2.
- A number ending 0 or 5 is divisible by 5.
- A number whose digits add to 9 are divisible by 3. 126 is divisible by 3 because 1 + 2 + 6 = 9 and 9 is divisible by 3. By the way, 126 is also divisible by 6! Why? Because any even number that you can divide evenly by 3 will automatically be divisible by 6.

**Lesson 46**

- Read about how to find factor pairs. Then find them.
- Check your answers.

**Lesson 47**

- Finding Factors of a Number
- Complete the exercise.

**Lesson 48**

- Prime Factorization and Prime Factorization Exercise
- Complete the exercise.

**Lesson 49**

- Least Common Multiple (LCM) Do NOT do the exercise on the video page.
- Complete the exercise “Least Common Multiple.”

**Lesson 50**

- Greatest Common Divisor Do NOT do the exercise on the video page.
- Complete the exercise “Greatest Common Divisor.”

**Lesson 51**

- Complete the “LCM and GCD word problems..” Pause the video. Read the problem and solve. Then watch the solution. Repeat for each problem.

**Lesson 52**

- Here’s the same video, Introduction to Order of Operations, on order of operations from before. The second example had parentheses. That’s what you’re adding in today. You solve what’s inside the parentheses first.
- Complete the exercise. If you are on a mobile device and it wants you to get the app, try this link instead.

**Fractions**

**Lesson 53**

- Numerator and Denominator of a Fraction
- Complete the exercise.

**Lesson 54**

- Identifying Fraction Parts
- Complete these two exercises. one two

**Lesson 55**

- Equivalent fractions
- Complete the exercise “Equivalent Fractions.”

**Lesson 56**

- Equivalent Fractions Example
- Read the page and answer the questions.

**Lesson 57**

**Lesson 58**

- Comparing Fractions
- Compare the fractions by finding a common denominator. Then the numerator will let you know which one is bigger.
- Get out your math notebook and write these down. Write down the equivalent fractions with their common denominators.

**Lesson 59**

- Fractions in lowest terms
- Read the page and answer the questions.

**Lesson 60**

- Ordering Fractions
- Complete the exercise.

**Lesson 61**

- Proper and Improper Fractions and Mixed numbers and improper fractions
- Read about proper and improper fractions as well as mixed numbers. Tell someone what each of those are and when you use them.

**Lesson 62**

**Lesson 63**

- Changing an Improper Fraction to a Mixed Number
- Complete the exercise.

**Lesson 64**

- Comparing mixed numbers
- Complete the exercise “Comparing Mixed Numbers.”

**Lesson 65**

- Comparing improper fractions and mixed numbers
- Complete the exercise “Comparing Improper Fractions and Mixed Numbers.”

**Lesson 66**

- Adding Fractions with Like Denominators
- Complete the exercise.

**Lesson 67**

- Subtracting Fractions Do NOT do the exercise on the video.
- Complete the exercise “Subtracting Fractions with Common Denominators.”

**Lesson 68**

- Read about finding the least common multiple and answer the questions.

**Lesson 69**

- Finding Common Denominators
- Read the page and answer the questions. Here’s a calculator for finding the least common multiple.

**Lesson 70**

- Adding Fractions with Unlike Denominators and Adding fractions Example
- Complete the exercise. Choose Add Fractions and click on Go.

**Lesson 71**

- Complete the exercise to subtract fractions.
- Choose Subtract Fractions and click on Go.

**Lesson 72**

- Complete the exercise, “Fraction Word Problems.”

**Lesson 73**

- Adding fractions with different signs.
- Complete the exercise.

**Lesson 74**

- Subtracting Negative Fractions
- Subtract some negative fractions.

**Lesson 75**

- Complete the exercise “Fractions on a Number Line 1.”

**Lesson 76**

- Complete the exercise “Fractions on a Number Line 2.”

**Lesson 77**

- Complete the exercise “Fractions on a Number Line 3.”

**Lesson 78**

- Adding mixed numbers with regrouping
- Get at least five correct, adding mixed numbers with like denominators.
- Get at least five correct, adding mixed numbers with unlike denominators.

**Lesson 79**

- Subtracting mixed numbers with regrouping
- Get at least five correct, subtracting mixed numbers with like denominators.
- Get at least five correct, subtracting mixed numbers with unlike denominators.

**Lesson 80**

- Adding Mixed Numbers Word Problem and Subtracting Mixed Numbers Word Problem
- Complete the exercises: one two.

**Lesson 81**

- Multiplying Fractions
- Complete the exercise.

**Lesson 82**

- Multiplying Mixed Numbers
- Complete the exercise.

**Lesson 83**

- Multiplying Fractions and Mixed Numbers
- Make sure you realize how to turn a whole number into a fraction. You can jump to 50 seconds into the video.
- Get five correct of the exercise, Multiplying Fractions and Whole Numbers.
- Get five correct of the exercise “Multiplying Fractions and Mixed Numbers.”

**Lesson 84**

- Multiplying Fractions Word Problem
- Complete the exercise.

**Lesson 85**

- Dividing fractions and Dividing Fractions Example
- Complete the exercise.

**Lesson 86**

- Dividing Fractions Word Problem
- Complete the exercise.

**Lesson 87**

- Reciprocal of a Mixed Number
- Read this lesson and answer the “Your Turn” questions at the bottom of the page.

**Lesson 88**

- Dividing Mixed Numbers
- Remember, if you are using a whole number, you need to think of it as a fraction. You can jump a minute into the video.
- Do the exercise. Get five correct.
- Do the exercise. Get five correct.

**Fractions, Decimals and Percents**

**Lesson 89**

- Decimal Place Value and Decimal Place Value 2
- Complete the exercises “Decimal Place Value” and “Decimals in Written Form.”

**Lesson 90**

- Decimals on a Number Line
- Complete the exercise.

**Lesson 91**

- Rounding Decimals
- Complete the exercise.

**Lesson 92**

- Estimation with Decimals
- Complete the exercise.

**Lesson 93**

- Comparing Decimals
- Complete the exercise on comparing decimals. Choose level 6.

**Lesson 94**

- Adding Decimals
- Get confetti twice (or get at least ten correct). Choose Addition and then click on the Decimals box and choose the first level with numbers 1 – 10. Go to Figure It!

**Lesson 95**

- Complete the exercise “Adding Decimals with Hundredths.”

**Lesson 96**

- Complete the exercise “Adding Decimals with Thousandths.”

**Lesson 97**

- Subtracting Decimals
- Get confetti twice (or get at least ten correct). Choose Subtraction and then click on the Decimals box and choose the first level with numbers 1 – 10. Go to Figure It!

**Lesson 98**

- Complete the exercise “Subtracting Decimals with Hundredths.”

**Lesson 99**

- Subtracting Decimals Word Problem Do NOT do the exercise on the video.
- Complete the exercise “Adding and Subtracting Decimal Word Problems.“

**Lesson 100**

- Multiplying a Decimal by a Power of 10
- Complete the exercise.

**Lesson 101**

- Multiplying Decimals and Multiplying Decimals
- Complete the exercise.

**Lesson 102**

- Dividing Decimals by a power of ten
- Complete the exercise.

**Lesson 103**

- Dividing decimal
- Complete the exercise.

**Lesson 104**

- Dividing Decimals
- Complete the exercise “Dividing Decimals.”

**Lesson 105**

- Decimals and Fractions and Converting Fractions to Decimals Example
- Complete the exercise.

**Lesson 106**

- Converting fractions to decimals (ex1) and Converting fractions to decimals (ex2)
- Go to this lesson and complete the “Your Turn” questions at the bottom of the page.

**Lesson 107**

- Converting decimals to fractions 1 (ex 1) and Converting decimals to fractions 1 (ex 2) and Converting decimals to fractions 1 (ex 3)
- Practice writing decimals as fractions. Get five correct.
- Practice writing decimals as mixed numbers. Get five correct.

**Lesson 108**

- Converting decimals to fractions 2 (ex 1) and Converting decimals to fractions 2 (ex 2)
- Go to this lesson and complete the “Your Turn” questions at the bottom of the page.

**Lesson 109**

- Converting Fractions to Repeating Decimals
- Complete the exercise.

**Lesson 110**

- Describing the Meaning of Percent and Describing the Meaning of Percent 2
- Do NOT do the exercise on the videos. Go to this lesson and answer the review questions at the bottom of the page.

**Lesson 111**

- Converting decimals to percents (ex 1) and Converting decimals to percents (ex 2)
- Complete the exercise “Converting Decimals to Percents.”

**Lesson 112**

- Read this lesson.
- Complete the exercise “Converting Percents to Decimals.”

**Lesson 113**

- Points on a number line
- Complete the exercise.

**Lesson 114**

- Ordering numeric expressions Go to the video.
- Then read about ordering decimals and then play the game.

**Lesson 115 **

- Representing a number as a decimal, percent, and fraction and Representing a number as a decimal, percent, and fraction 2
- Convert fractions to percents. Hint: turn them into decimals first.

**Lesson 116**

- Read about percent problems.
- Read this lesson. Then look at the “Your Turn” questions at the bottom of the page. You will NOT be finding the answers. Today, for each question, just identify the part, whole, and percent. One will be unknown, ?, the thing you are needing to find.

**Lesson 117**

- Learn more about solving with percents.
- Use what you just learned to complete the problems.

**Lesson 118 **

- Learn more about solving with percents.
- Finish the page and solve 7 – 10.
- If you need more practice, you can work on solving the your turn questions.

**Ratios and Proportions**

**Lesson 119 **

**Lesson 120**

- Ratios as Fractions in Simplest Form
- Complete this review exercise of “Simplifying Fractions.” Choose Reduce Fractions.

**Lesson 121**

- Simplifying Rates and Ratios
- Play to practice.

**Lesson 122**

- Complete the ratio word problems.

**Lesson 123**

- Understanding Proportions – Do you see they are all equivalent fractions?
- Read the top of the page until it says “Working with Proportions” and then answer questions 1 – 5 by clicking on the questions at the bottom of this page: finding an unknown in a proportion. We’ll look at this page again in the next lesson.

**Lesson 124**

- Remember that you are supposed to work on each lesson until you are proficient, until you get it. Don’t move on if you are stuck. Give it another try the next day.
- Read the page on finding an unknown in a proportion.
- Practice with cross multiplication. You don’t have to race. You can take your time and try again.

**Lesson 125**

- Finding an unknown in a proportion (At 3 minutes it starts talking about cross multiplying, you can watch the whole thing, but I think cross multiplying is an easy trick that I use a lot, even in my adult non-school life. If another way makes more sense to you, it’s okay to use another method. You can STOP watching when he says, “You can stop watching.”)
- Complete the exercise. (Write your answers as fractions or mixed numbers.)

**Lesson 126**

- Finding Unit Rates and Finding Unit Prices
- Complete the exercise on units.

**Lesson 127**

- Take a notepad to the grocery store. Write the price and unit price as well as the measurements (e.g., 4 ounces) for five different products. You’ll find the info on the tag. The unit price is written small. At home, see if you can take the product price and come up with the same unit price as the store.

**Lesson 128**

- Unit conversion
- Read the page on converting units and answer the questions.

**Lesson 129**

- Converting units of length
- Read the page and answer the questions.

**Lesson 130 **

- Measure something in centimeters and inches. Write them as a proportion.
- Measure something just in inches and use the proportion to figure out what the measurement is in centimeters.
- Now measure it in centimeters and see if you were right. If you don’t know what U.S. Customary and Metric units are, then watch this.

**Lesson 131**

- Conversion between metric units and Converting within the metric system
- Make a chart for milliliters, liters, kiloliters; millimeters, centimeters, meters and kilometers; milligrams, grams, kilograms. Your chart should show how many of each are in the other.

**Lesson 132**

- Converting Gallons to quarts pints and cups
- Make a chart for gallons, quarts, pints, and cups that shows how many are in each other.

**Lesson 133**

- Converting pounds to ounces
- Find out how much you weighed when you were born. Figure out how much you weighed in ounces.

**Lesson 134**

- Comparing Celsius and Fahrenheit temperature scales 0 (zero) degrees Celsius is the same temperature as 32 degrees Fahrenheit. 100 degrees Celsius is the same temperature as 212 degrees Fahrenheit.
- Can you figure out how to get from one to the other? After you’ve thought about it, find the formula online or on the video. Plug in 0 and 100 and see if you get 32 and 212.

**Lesson 135**

- Converting Farenheit to Celsius
- Take today’s temperature in Fahrenheit and figure out today’s temperature in Celsius.

**Exponents**

**Lesson 136**

- Understanding Exponents and Using Exponents with Negative Numbers
- Complete the exercise.

**Lesson 137**

- Patterns in Zeros
- Complete the exercise.

**Lesson 138**

- More Complicated Order of Operations Example
- Practice order of operations with exponents and parentheses.
- Want more? Here’s another with negative numbers.

**Lesson 139**

- Understanding Square Roots
- Complete the exercise.
- Congratulations on finishing the course!

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