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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
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.
- 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.
- Complete the exercise “Addition and Subtraction Word Problems .” You will do 12 questions.
- Complete the exercise “Negative Number Word Problems.”
Multiplication and Division with Positive and Negative Numbers
- 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.
- 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!
- 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…)
- Complete the exercise “Comparing Absolute Values.”
- 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.
Factors and Multiples
- 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.
- 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.
- Complete the “LCM and GCD word problems..” Pause the video. Read the problem and solve. Then watch the solution. Repeat for each problem.
- 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.
- Read about finding the least common multiple and answer the questions.
- Complete the exercise to subtract fractions.
- Choose Subtract Fractions and click on Go.
- Complete the exercise, “Fraction Word Problems.”
- Complete the exercise “Fractions on a Number Line 1.”
- Complete the exercise “Fractions on a Number Line 2.”
- Complete the exercise “Fractions on a Number Line 3.”
- 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.
Fractions, Decimals and Percents
- Complete the exercise “Adding Decimals with Hundredths.”
- Complete the exercise “Adding Decimals with Thousandths.”
- Complete the exercise “Subtracting Decimals with Hundredths.”
- 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.
Ratios and Proportions
- Complete the ratio word problems.
- 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.
- 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.
- 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.)
- 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.
- 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.
- Converting Gallons to quarts pints and cups
- Make a chart for gallons, quarts, pints, and cups that shows how many are in each other.
- Converting pounds to ounces
- Find out how much you weighed when you were born. Figure out how much you weighed in ounces.
- 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.
- Converting Farenheit to Celsius
- Take today’s temperature in Fahrenheit and figure out today’s temperature in Celsius.
SUMMER SCHOOL – Make sure you know those facts! Use flashcards, our facts practice workbooks, or online games and programs like xtramath.