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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 137 videos and exercises (with links) to complete Khan Academy arithmetic and prealgebra. (This is the same course that it was before Khan Academy aligned with Common Core. I was able to update Khan Academy’s links without changing the teaching. Where they have eliminated exercises, I just found alternatives on other sites.) 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 onto 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. 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. According to Khan Academy that’s the first one correct or five correct in a row. I suggest getting the first one wrong on purpose! 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.
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Addition and Subtraction with Positive and Negative Numbers
 Basic Addition Complete the exercise.
 Basic Subtraction Complete the exercise.
 Addition 2 Complete the exercise.
 Subtraction 2 Complete the exercise.
 Addition 3 Complete the exercise.
 Subtraction 3: Introduction to Borrowing or Regrouping Complete the exercise. You don’t have to finish the whole exercise before moving onto #7.
 Why borrowing works & Alternate mental subtraction method Finish the subtraction exercise from #6.
 Addition 4 Complete the exercise “3 digit addition with carrying.”
 Level 4 Subtraction Complete the exercise.
 Complete the exercise “Addition and Subtraction Word Problems .” If this site is giving you problems, making a free account seems to fix that.
 Negative Numbers Introduction Complete the exercise.
 Ordering Negative Numbers Complete the exercise.
 Adding Negative Numbers and Adding integers with different signs Complete the exercise.
 Adding/Subtracting negative numbers Complete the exercise “Adding and Subtracting Negative Numbers.”
 Complete the exercise “Negative Number Word Problems.”
Multiplication and Division with Positive and Negative Numbers
 Basic Multiplication and Multiplication 2: The Multiplication Tables Complete the exercise.
 Multiplication 3: 10,11,12 times tables Click on the 11 and then test. Then go again and click on 12 and then test.
 Multiplying by multiples of ten Complete the exercise.
 Division 1 and Division 2 Complete the exercise.
 Dividing Whole Numbers and Applications 1 Complete the exercise “Division without Remainders.”
 Multiplication : 3digit times 1digit number example and Multiplication 5: 2digit times a 2digit number Complete the exercise.
 Multiplication 6: multiple digit numbers. Begin the exercise. You don’t have to finish all of them before you go on to #8.
 Lattice Multiplication and Why Lattice Multiplication Works Finish the exercise “Multiplying 3 Digits by 2 Digits.”
 More long division and remainder examples Complete the exercise.
 Multiplication word problems and Division word problems Complete the exercise.
 Level 4 division Begin the exercise. You don’t have to finish the exercise before moving onto #12.
 Partial Quotient Division and Partial Quotient Method of Division 2 Finish “Multi Digit Division.”
 Answer the addition and subtraction word problems. (review)
 Place Value 1 and Place Value 2 and Place Value 3 Complete the exercise.
 Rounding Whole Numbers 1 and Rounding Whole Numbers 2 and Rounding Whole Numbers 3 Complete the exercise.
 Multiplying Positive and Negative Numbers and Why a Negative Times a Negative is a Positive and Dividing Positive and Negative Numbers Complete the exercise.
 Learn about basic exponents. Here’s the video lesson. Practice.
Number Properties
 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…)
 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 the questions 1 through 4 at the bottom of the page.
 The Distributive Property and The Distributive Property 2 and The Distributive Property Exercise Complete the exercise “Distributive Property.”
 The number line and absolute value. Complete the exercise “Finding Absolute Value.”
 Complete the exercise “Comparing Absolute Values.”
 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).
 Inverse Property of Addition and Inverse Property of Multiplication Can you identify the number property? (Click on review for any you got wrong.)
 Why Dividing by Zero is Undefined and Why Zero Divided by Zero is Undefined/Indeterminate and Undefined and Indeterminate Explain this concept to your mother.
 Answer the multiplication and division word problems. (review)
 Introduction to Order of Operations and More Complicated Order of Operations Example Complete the exercise. If you want to go for it, here’s a harder version with negative numbers.
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. Example 69: 6 + 9 = 15 You can divide 15 by 3 so you can divide 69 by 3.
 Recognizing Prime Numbers Complete the exercise.
 Recognizing Divisibility Common Divisibility Examples Complete the exercise “Divisibility Tests.”
 Divisibility Intuition Complete the exercise.
 Finding Factors of a Number Complete the exercise “Divisibility.”
 Prime Factorization and Prime Factorization Exercise Complete the exercise.
 Least Common Multiple (LCM) Do NOT do the exercise on the video page. Complete the exercise “Least Common Multiple.”
 Greatest Common Divisor Do NOT do the exercise on the video page. Complete the exercise “Greatest Common Divisor.”
 Complete the “LCM and GCD word problems..” Pause the video. Read the problem and solve. Then watch the solution. Repeat for each problem.
 The fundamental theorem of arithmetic Complete the exercise.
Fractions
 Numerator and Denominator of a Fraction Complete the exercise.
 Identifying Fraction Parts Complete these two exercises. one two
 Equivalent fractions Complete the exercise “Equivalent Fractions.”
 Equivalent Fractions Example Read the page and answer the questions.
 Comparing Fractions Complete the exercise “Equivalent Fractions 2.”
 Fractions in lowest terms Read the page and answer the questions.
 Comparing Fractions 2 Complete the exercise.
 Ordering Fractions Complete the exercise. (When I looked at this, it seemed to be having a weird technical issue. Just look at the fraction and ignore any gobbledy gook.)
 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.
 Converting Mixed Numbers to Improper Fractions Answer the questions.
 Changing an Improper Fraction to a Mixed Number Complete the exercise.
 Changing a Mixed Number to an Improper Fraction Complete the exercise “Comparing Fractions 2.”
 Comparing improper fractions and mixed numbers Complete the exercise “Comparing Improper Fractions and Mixed Numbers.”
 Adding Fractions with Like Denominators Complete the exercise.
 Subtracting Fractions Do NOT do the exercise on the video. Complete the exercise “Subtracting Fractions with Common Denominators.”
 Read about finding the least common multiple and answer the questions.
 Finding Common Denominators Read the page and answer the questions. Here’s a calculator for finding the least common multiple.
 Adding Fractions with Unlike Denominators and Adding fractions (ex 1) Complete the exercise.
 Complete the exercise “Subtracting Fractions.”
 Adding and subtracting fractions and Adding fractions with different signs Complete the exercise.
 Complete the exercise, “Fraction Word Problems 1.”
 Adding Mixed Numbers and Subtracting Mixed Numbers and Adding Mixed Numbers with Unlike Denominators Read the page and answer the questions.
 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.”
 Adding subtracting mixed numbers0.5 (ex1) and Adding subtracting mixed numbers0.5 (ex2) Complete the exercise “Adding Subtracting Mixed Numbers 0.5.”
 Adding subtracting mixed numbers1 (ex1) and Adding Subtracting Mixed Numbers1 (ex2) Complete the exercise “Adding Subtracting Mixed Numbers 1.”
 Adding Mixed Numbers Word Problem and Subtracting Mixed Numbers Word Problem Complete the exercises: one two.
 Multiplying Fractions Complete the exercise.
 Multiplying Mixed Numbers Complete the exercise.
 Multiplying Fractions and Mixed Numbers Complete the exercise “Multiplying Mixed Numbers.”
 Multiplying Fractions Word Problem Complete the exercise.

and Dividing Fractions Example Complete the exercise.
 Dividing Fractions Word Problem Complete the exercise.
 Reciprocal of a Mixed Number Read this lesson and answer the “Your Turn” questions at the bottom of the page.
 Dividing Mixed Numbers and Dividing Mixed Numbers and Fractions (This has some negative numbers. That’s just the same as dividing 4 by 2. The rules for multiplying and dividing negative numbers still apply even though they are mixed numbers instead of whole numbers.) Solve: 2 and 4/9 divided by 1 and 1/8. Convert the mixed numbers to improper fractions. Then multiply the first by the reciprocal of the second.
Fractions, Decimals and Percents
 Decimal Place Value and Decimal Place Value 2 Complete the exercises “Decimal Place Value” and “Decimals in Written Form.”
 Decimals on a Number Line Complete the exercise.
 Rounding Decimals Complete the exercise.
 Estimation with Decimals Complete the exercise. (on CK12)
 Comparing Decimals Complete the exercise “Decimals on a Number Line 2.”
 Adding Decimals Complete the exercise.
 Complete the exercise “Adding Decimals.”
 Complete the exercise “Adding Decimals 2.”
 Subtracting Decimals Complete the exercise.
 Complete the exercise “Subtracting Decimals.”
 Subtracting Decimals Word Problem Do NOT do the exercise on the video. Complete the exercise “Adding and Subtracting Decimal Word Problems.“
 Multiplying a Decimal by a Power of 10 and Dividing a Decimal by a Power of 10 Complete the exercise.
 Multiplying Decimals and Mulitplyling Decimals 3 Complete the exercise.
 Dividing Decimals 2.1 Complete the exercise “Dividing Decimals by 10.” The answers are at the bottom of the page. You won’t learn anything if you copy them. Grow your brain instead of cheating.
 Dividing decimal Complete the exercise.
 Dividing Decimals Complete the exercise “Dividing Decimals.”
 Decimals and Fractions and Converting Fractions to Decimals Example Complete the exercise.
 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.
 Converting decimals to fractions 1 (ex 1) and Converting decimals to fractions 1 (ex 2) and Converting decimals to fractions 1 (ex 3) and 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.
 Converting Repeating Decimals to Fractions 1 Complete the exercise.
 Converting Repeating Decimals to Fractions 2 Complete the exercise “Converting Decimals to Fractions 2.”
 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.
 Ordering numeric expressions Go to the video. Then read about ordering decimals and complete the “Your Turn” exercises.
 Representing a number as a decimal, percent, and fraction and Representing a number as a decimal, percent, and fraction 2 Complete the exercise.
 Points on a number line Go to the video and complete the exercise.
 Converting decimals to percents (ex 1) and Converting decimals to percents (ex 2) Complete the exercise “Converting Decimals to Percents.”
 Read this lesson. Complete the exercise “Converting Percents to Decimals.”
 Identifying Percent Amount and Base Read this lesson and answer the “Your Turn” questions.
 Solving Percent Problems and Solving Percent Problems 2 Complete the first five problems.
 Solving Percent Problems 3 and Growing by a percentage Complete the exercise.
Ratios and Proportions
 Introduction to Ratios Now practice.
 Ratios as Fractions in Simplest Form Complete this review exercise of “Simplifying Fractions.”
 Simplifying Rates and Ratios Play to practice.
 Complete the ratio word problems.
 Understanding Proportions Read this lesson, finding an unknown in a proportion. Answer the questions.
 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.
 Finding an unknown in a proportion Complete the exercise. (Write your answers as fractions or mixed numbers.)
 Finding Unit Rates and Finding Unit Prices Complete the exercise on units.
 Take a notepad to the grocery store. Write the price and unit price as well as the measurements (eg. 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.
 Unit conversion Read the page on converting units and answer the questions.
 Converting units of length Read the page and answer the questions.
 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.
 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.
 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.
Exponents
 Understanding Exponents and Raising Numbers to the 1st and 0th Power. Complete the exercise.
 Patterns in Zeros Complete the exercise.
 Exponent Rules Part 1 and Exponent Rules Part 2 and Exponents involving Quotients Complete the exercise.
 Understanding Square Roots Complete the exercise.
SUMMER SCHOOL – Make sure you know those facts! Use flashcards, our facts practice workbooks, or online games and programs like xtramath.
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