Ms. Lisa’s favorite Pre-Algebra & Algebra math videos for Farm School Students

Pre-algebra: Statistics and Displaying Data

McD chp 11 & 9.2

Art of Problem Solving Prealgebra Chapter 13

  1. Mean, median and mode: watch either this Math Antics video about mean, median, mode or this Art of Problem Solving video about the same topic Intro to Average (mean), Median & Mode (6 minutes)

  2. AoPs video another way to think about Averages (8 minutes)

  3. BONUS: AoPs video on the limits of basic statistics (part 2)—(11 minutes) sometimes the question is impossible!

  4. BONUS: AoPs video on the limits of basic statistics part 3 (9 minutes)

  5. AoPs video on Bar Charts and Pie Charts

  6. AoPs video on Line Graphs

  7. Box and Whisker Plot by Mash Up Math: how to construct a box and whisker plot using a table of data AND how to analyze the box and whisker plot

  8. Stem and Leaf Plot McD chp 11.1

  9. Scatter Plots (math 8 chp 9.1 & 9.2)

  10. McD Chp 9.2 Scatter Plots and Line of Best Fit

Pre-algebra: All about Lines (Graphing Linear Equations)

McD chp 8

Graphing calculator on the web: play with this equation graphing website https://www.desmos.com/calculator

  1. Graphing on a Coordinate Plane Math Antics Video about Graphing on a Coordinate Plane (McD chp 1)

  2. McD 8.1 RELATIONS & FUNCTIONS:

  3. McD 8.2 Does a given ordered pair represent a solution to this linear equation? (Math 8 Section 2.1) Is a given ordered pair a solution of a linear equation?

  4. McD 8.3 & 8.4 Slope of a line & Slope-intercept form y=mx + b

  5. Horizontal & vertical line slopes:

  6. How to find the x & y intercepts of a line?

  7. Point-Slope Form (Math 8 chp 8.4)

  8. Parallel and Perpendicular lines: what’s the relationship between the slopes of these lines?

  9. McD 8.7 Function Notation

Pre-algebra: Percents

McD Chp 7 - Print out percent formulas review notes

  1. Converting fractions to percents and vice versa Introduction to percent with Richard from AoPs converting fractions into percents and percents into fractions without a calculator

  2. There are three basic types of percent problems - watch Richard of AoPs review how to solve these three basic problems.

    • What is this percent of that? Example What is 30% of 120?

    • What percent of this is that? What percent is 88 of 33?

    • This is that percent of what number? 42 is 150% of what number?

  3. If you are struggling with these three types of percent problems, watch these two good but long summaries of how to use proportions and translate sentences to equations to solve percent word problems with Dr. Dan

  4. AoPs percent word problems part 1

  5. AoPs percent word problems part 2 (This is a PENTAGON level video. These are harder problems and show mistakes commonly made by students and adults.)

  6. Percent of Change (McD 7.5 or 7.6)

    WATCH this Math Antics Percent Change video 

  7. Percent Increase or Decrease (McD 7.6)

    WATCH this Art of Problem Solving Percent Change or Increase or Decrease video part 1

  8. Simple Interest (McD 7.7)

    • Calculating Simple Interest: Interest = Prt video by Mario on simple interest and

    • Solving for the account balance (A) or R or T or P. The first 7:30 minutes of this video are also good —> organic chemistry tutor do several simple interest problems including ones where you are solving for the rate (r) or t (time in years to earn a certain amount of interest). Note you can stop watching after around 7:30 as the last 3 minutes is an advertisement for an algebra course)

  9. Interest Compounded Annually (McD 7.7)

Pre-algebra: Rates, Ratios & Proportions

McD Chp 6

  1. Conversion Factors 6 minute video Ketzbook

  2. GAME: Equivalent ratios - space invaders equivalent ratio game from MathGameTime.com

  3. Get a preview of rates and ratios with this Math Antics video: https://www.youtube.com/watch?v=RQ2nYUBVvqI

  4. Introduction to Ratios (What Are Ratios?) | Ratio Examples and Answers - Math with Mr. J

  5. Required Video: Watch

  6. Introducing ratios by Richard of AoPs https://www.youtube.com/watch?v=6ItURzd64WE&list=PLqiSsHAcyf9cJfapnn3i5nuMFIu4JXfrW

  7. Ratios- Parts & Wholes by Richard of AoPs https://www.youtube.com/watch?v=z7aYEexTb7Q&list=PLqiSsHAcyf9cJfapnn3i5nuMFIu4JXfrW&index=2

  8. Ratios - Multi part ratios by Richard of AoPs https://www.youtube.com/watch?v=Lkw4Slh4uRg&list=PLqiSsHAcyf9cJfapnn3i5nuMFIu4JXfrW&index=3

  9. Proportions:

    • Intro to solving proportions with cross products? Watch this Math Antics Proportions video (10 minutes)

    • Word Problems with proportions. How to set up a proportions when reading word problems? Watch Richard from AoPs set up proportion (equal ratios are called proportions) (Note at minute 6 he “clears” the fraction by multiplying by 2 so he doesn’t have to have a fraction in the numerator.) He calls method 1 finding an equivalent ratio “scaling it up by a factor of _____”

Pre-algebra: Probability

McD 6.7

  1. Theoretical and Experimental Probability Math Antics Probability

  2. Odds in favor and odds against: What are odds?

  3. Counting principle video needed/ combinations

  4. Review of probabilty up to this point Review of probability concepts including compound events (independent events only) with Magic of Math (all 7thg grade math probability)

  5. Compound Probability: Independent events and dependent events (McD 11.9, Alg PH 4.6, Math 7?)

    4 minute Video from Joann’s School - Dependent vs. Independent Compound events

    Compound Probability both independent and dependent events with Organic Chemistry tutor (the dependent event part is at the very end)

    AoPs has 80 advanced videos on Counting and Probability (it’s a year long advanced math course!)— if this is interesting to you, you can start here to start watching those videos here https://www.youtube.com/watch?v=3u5wGmU6A1U&list=PLiNDnWouRxbnh0R71E3YtaOezk8f-DNo8

Pre-Algebra: Fractions

McD Chp 5

Fractions

  1. Introduction to fractions - Art of Problem Solving (AoPs) Prealgebra Chapter 4.1

  2. Multiplying Fractions

  3. Dividing by a Fraction

  4. Simplifying fractions

  5. Equivalent fractions

  6. Comparing Fractions using number lines

  7. Easiest Common Denominator - Math Antics https://www.youtube.com/watch?v=N-Y0Kvcnw8g&list=PLr7qXmZNC_A-i6B7zBWsi7IkqVzd2Ed-I&index=4

  8. Lowest Common Denominator - Math Antics https://www.youtube.com/watch?v=pZEmFSP3Z0I&list=PLr7qXmZNC_A-i6B7zBWsi7IkqVzd2Ed-I&index=3

  9. Adding & Subtracting Like Fractions - with same denominator

    • Same Denominator or “Like Fractions”: This is a proof from AoPs explains why you can just add the numerators (tops) when the denominators are the same (bottom) Same Denominator

  10. Adding & Subtracting Unlike Fractions - with Different Denominator —Adding fractions with different denominators from AoPs

  11. Adding Mixed numbers

  12. Subtracting Mixed numbers

    • Simple way—> turn everything into IMPROPER NUMBERS Math Antics https://www.youtube.com/watch?v=RqUPSZLwHH0

    • Clever way (FASTER) if you can handle the distributive property to deal with subtraction and negative numbers and mixed numbers, a.k.a how to separate out the integers and fraction separately. There’s a trick to this— use the distributive property to distribute the negative when subtracting. If you master this it’s a faster way to subtract mixed numbers! Mixed number Subtraction with Richard of AoPs

  13. Using Multiplicative Inverses (aka reciprocals) to solve equations with fractions faster

  14. Clearing Fractions from an equation by multiplying by a common denominator or by the reciprocal

  15. Using cross products aka cross multiplication (looks like a butterfly) to solve proportions Start at minute 10 of the video with Prof. Rob Bob https://www.youtube.com/watch?v=De5ghpLlkUQ&list=PLGbL7EvScmU7ZqJW4HumYdDYv12Wt3yOk&index=32

Pre-algebra: Order of operations (PEMDAS or GEMDAS)

McD chp 1

Order of Operations review problems

  1. PEMDAS/GEMDAS 10 MINUTE Math Antics video on order of operations

  2. She calls it GEMDAS (Grouping symbols instead of parentheses) https://www.youtube.com/watch?v=kQp1ZpvBVVo

Pre-algebra: Geometry - triangles, perimeter, area, volume, surface area

McD chp 9 & 10

Mostly Algebra Videos

Algebraic Fractions (Algebra 1 chp 6)

  1. Simplifying fractions with rational expressions and restricting the variables (Algebra 6.1) 14 minute video with Nancy Pi and take notes https://www.youtube.com/watch?v=i7w_aRlVagU then try to do one of the problems before she does so pause the video.

  2. Dividing fractions that have quadratic expressions in them which requires factoring with Brian M. dividing fractions with quadratic expressions (aka dividing rational expressions) Brian also shows you the educated guess and check method of factoring a quadratic expression

  3. Fractional Equations method #2 solve as proportion —> cross multiplication (Algebra chp 7.4) Prof Rob Bob video (but he doesn’t go into fractions that need to be factored first as in example 3. You’ll need to read the book for that. https://www.youtube.com/watch?v=De5ghpLlkUQ&list=PLGbL7EvScmU7ZqJW4HumYdDYv12Wt3yOk&index=32

  4. Polynomial Long Division (Algebra chp 6.7)

Factoring Polynomials

Algebra - Big Al Textbook chp 5 (Polynomials are monomials added together)

Factoring Techniques videos from Prof. Rob Bob

Factoring Overview

Factoring Monomials from a Polynomial

Factoring Polynomials Difference of Squares

Factoring Polynomials Sum Difference of Cubes

Factoring Quadratic Trinomial x^2+bx+c Polynomial

Factoring Quadratic Trinomial ax^2+bx+c

Factoring by Grouping

Solving Quadratic Functions

Solving quadratic equations by completing the square (Algebra 12.2)

Solving quadratic equations using quadratic formula (Algebra 12.3)

The Discriminant = what’s under the radical sign in the quadratic equation = b-squared - 4ac (Algebra 12.4)

Imaginary Numbers

Solving Systems of equations (two variables, two equations— classic dimes and nickels problems Algebra 1 chp 9)

  1. Substitution Method

  2. Elimination Method



Distance x Rate = Time Problems

(Algebra chp 4)

  1. Motion in Opposite Directions (Either moving toward or away from each other- aka meet or pass each other as heading towards each other or flying away from each other.)

  2. Motion in Same Direction (a.k.a. overtaking problems)

  3. Motion Round Trip Problems

    • A - Video from My Math Source

    • B - this is a totally different way of solving the problem when you have two variables, called system of equations method. We’ll get to this later in our book. Traveling round trip with Mario - similar to example 3 on page 169

Geometry: Similar Figures

  1. What does similar mean? How is that different from congruent? Video Similar v. congruent (Math 8 chp 4.3)

  2. Using proportions to find missing measurements in similar figures short video. Here’s a longer one (11 minutes) if you need more examples from Organic Chemistry Tutor (Math 8 chp 4.3)

  3. Corresponding parts in congruent polygons- 9 minute video on corresponding parts in congruent polygons: https://www.youtube.com/watch?v=aG7KcNNoe5I )

Geometry: Transformations

  1. Overview of three transformations (reflections, translation, rotation) which don’t change the size so these will be congruent (5 minutes): https://www.youtube.com/watch?v=7cduccqwguM

  2. Dialation— does change the size!

  3. Rotation

  4. Overview of translation, rotation but LOOONG (45 minutes) from Organic Chem Tutor

  5. Transformations (reflections, rotations) Math 8 Chp 5.6 Read examples on page 226-228. Do #7-25 odds

  6. Determining if a shape is similar or congruent: If you need a video review on how to decide if you’re looking at a similar tranformation (same shape (same angles and side proportions) but not the same size) or if you’re looking at a congruent shape (exactly the same but in a different position or orientation), here’s a helpful video: https://www.youtube.com/watch?v=V80UfaC8syg


Geometry: Angles

  1. Angle basics from Math Antics and Angle Review (vertical, complementary, supplementary etc ) w/ Ms. Merkins https://www.youtube.com/watch?v=M7ToxgRvKx0&list=PLJM2N9UmkFqhRi05TkVVWbGTNMYLQvide&index=5

  2. Lines & Angles Rap 3 minutes by Go Noodle & Angle Names by Tutoring hour 5 minutes

  3. Richard from AoPs explain straight angles (a.k.a. a straight line) https://www.youtube.com/watch?v=EjTaOODJTVg

    • After Richard writes the supplementary angles problem on the board, pause the video and try to draw a picture of the problem. Unpause. Then try to write an equation before he does. Then once he’s written the equation, pause the video and YOU solve for “c” and then figure out the measurement of each angle before he does. Then watch him and correct your work.

    • Do the same when he writes the vertical angle problem on the board.

  4. Supplementary & complementary angles from Mr. J

  5. Angles & Parallel lines: Richard from AoPs solve problems involving angles and parallel lines Try pausing the video when he starts to do a problem and and see if you can draw it out, write the equation and solve it. Unpause after you do each step to see if you are on the right track.

  6. Harder supplementary angle problems with variables and equations

  7. Much more complicated angles when there are parallel lines with a transversal cutting across two parallel lines with Mario

  8. Another sample of finding angles when parallel lines are cut by a transversal https://www.youtube.com/watch?v=uOrXWJQ8vWA&list=PLCqwggKH0w8b3J9_iGeax3huTLTBxl-iS&index=2

Square Roots

Algebra chp 11

  1. Square Root introduction part 1 by Art of Problem Solving

  2. Square Root intro part 2 by Art of Problem Solving

  3. Square Roots - non-integer square roots (such as what is the square root of 2?)

  4. Square Root of a product by Art of Problem Solving

  5. Sum of Square Roots — beware common errors! sums and products are different! by Art of Problem Solving

  6. Simplifying Square Roots Part 1 by Art of Problem Solving

  7. Simplifying Square Roots Part 2 by Art of Problem Solving before you watch this video, review divisibility rules

  8. Simplifying radical expressions by Mario’s Math Tutoring A different method for evaluating radical expressions by breaking down the radican into it’s prime factors Simplifying Radicals Easy Method by Mario’s Math Tutoring

Word Problems— translating word problems into linear equations

  1. Words to equations with Mario Translating Sentences into Equations - YouTube 2 minutes

  2. Translating words to equations with Mash up Math TRANSLATING WORDS INTO ALGEBRAIC EXPRESSIONS! - YouTube 8 minutes

  3. Translating words into inequalities Translating Words to Inequalities - YouTube 6 minutes by Victoria Miles

  4. Translating words into symbols and numbers with Richard at Art of Problem Solving: (Word Problems Part 1: https://www.youtube.com/watch?v=mSg1mgCHmX0&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=10)

  5. Translating words into symbols and numbers with Richard at Art of Problem Solving: (Word Problems Part 2: https://www.youtube.com/watch?v=mSg1mgCHmX0&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=10)

  6. Translating words into symbols and numbers with Richard at Art of Problem Solving: (Word Problems Part 3: https://www.youtube.com/watch?v=vNPWFe3zL4w&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=12)

  7. Setting up equations from word problems AND equations with fractions with Prof Rob Bob (46 minutes— lots of sample problems) https://www.youtube.com/watch?v=ROGk0lJBipU


Linear Functions

(Algebra 1 chp 8)

  1. How to determine if an equation or set of data represents a function? Four ways to determine if an equation or set of ordered pairs represents a FUNCTION here

  2. Input & Output Tables Math Antics Video about functions inputs & output table

Function Notation

(Algebra 1 chp 8)

  1. Overview of function notation 10 minute video by Kevin Dorey https://www.youtube.com/watch?v=lVUeWKIiypM )

  2. 4 minute Mario math tutor video https://www.youtube.com/watch?v=_e0EdFGpcvc and do problem 2 before he does them. Example four is like problem 29 on page 381

  3. More advanced examples f(g+2)=blah blah https://www.youtube.com/watch?v=8wYVB7Jgo40 by Math WOEs

  4. How to determine if an equation or set of data represents a function? Four ways to determine if an equation or set of ordered pairs represents a FUNCTION here

Basic Linear equations & Graphing

(Algebra 1 chp 8)

Graphing calculator on the web: play with this equation graphing website https://www.desmos.com/calculator

  1. Graphing on a Coordinate Plane Math Antics Video about Graphing on a Coordinate Plane

  2. Rate of Change How to figure out what the rate of change is from a table of x’s and y’s. Rate of change video from Brian: 2 minutes https://www.youtube.com/watch?v=vFXXStHpfaQ & optional 4 minute video https://www.youtube.com/watch?v=6cqQzI3RrqQ&list=PL0G-Nd0V5ZMrdoj-MFw0FR7CSAAON0gU0&index=3

  3. Does a given ordered pair represent a solution to this linear equation? (Math 8 Section 2.1) Is a given ordered pair a solution of a linear equation?

  4. Slope of a line & Slope-intercept form y=mx + b

  5. Horizontal & vertical line slopes:

  6. How to find the x & y intercepts of a line?

  7. Point-Slope Form (Math 8 chp 8.4)

  8. Parallel and Perpendicular lines: what’s the relationship between the slopes of these lines?

  9. Direct Variation y=kx straight line through the origin (Math 8 chp 8.5, Algebra 1 chp 8.9)

  10. Inverse Variation —> Hyperbolas! xy=k (Algebra 1 chp 8.10)

  11. Longer Summary (30 minutes) of Linear equations (formats, slope, ) with Organic Chemistry Tutor https://www.youtube.com/watch?v=Ft2_QtXAnh8

Simple interest & Interest compounded annually (Interest Rates & Balance of Account)

  1. Calculating Simple Interest: Interest = Prt video by Mario on simple interest and

  2. Solving for the account balance (A) or R or T or P. The first 7:30 minutes of this video are also good —> organic chemistry tutor do several simple interest problems including ones where you are solving for the rate (r) or t (time in years to earn a certain amount of interest). Note you can stop watching after around 7:30 as the last 3 minutes is an advertisement for an algebra course)

Percent

Print out percent formulas review notes

Percent of Change (Percent increase or percent decrease)

  1. Introduction to percent with Richard from AoPs converting fractions into percents and percents into fractions without a calculator

  2. There are three basic types of percent problems - watch Richard of AoPs review how to solve these three basic problems.

    • What is this percent of that? Example What is 30% of 120?

    • What percent of this is that? What percent is 88 of 33?

    • This is that percent of what number? 42 is 150% of what number?

  3. If you are struggling, watch these two good but long summaries of how to use proportions and translate sentences to equations to solve percent word problems with Dr. Dan

    1. Dr. Dan video #50 : How to translate the sentence into an equation https://www.youtube.com/watch?v=hYv63oei9Vo (28 minutes)

    2. Dr. Dan video #51:  https://www.youtube.com/watch?v=50cCWoIKon8 (28 minutes)

  4. AoPs percent word problems part 1

  5. AoPs percent word problems part 2 (This is a PENTAGON level video. These are harder problems and show mistakes commonly made by students and adults.)

  6. WATCH this Math Antics Percent Change video 

  7. WATCH this Art of Problem Solving Percent Change or Increase or Decrease video part 1

Probability

  1. Theoretical and Experimental Probability Math Antics Probability

  2. Odds in favor and odds against: What are odds?

  3. Counting principle video needed/ combinations

  4. More fun with Richard of AoPs — this is very advanced and not part of pre-algebra  probability games https://www.youtube.com/watch?v=cvE7w1tFj7M

  5. Richard has 80 advanced videos on Counting and Probability (it’s a year long advanced math course!)— if this is interesting to you, you can start here to start watching those videos here https://www.youtube.com/watch?v=3u5wGmU6A1U&list=PLiNDnWouRxbnh0R71E3YtaOezk8f-DNo8

Rates, Ratios, and Proportions

  1. GAME: Equivalent ratios - space invaders equivalent ratio game from MathGameTime.com

  2. Get a preview of rates and ratios with this Math Antics video: https://www.youtube.com/watch?v=RQ2nYUBVvqI

  3. Introducing ratios by Richard of AoPs https://www.youtube.com/watch?v=6ItURzd64WE&list=PLqiSsHAcyf9cJfapnn3i5nuMFIu4JXfrW

  4. Ratios- Parts & Wholes by Richard of AoPs https://www.youtube.com/watch?v=z7aYEexTb7Q&list=PLqiSsHAcyf9cJfapnn3i5nuMFIu4JXfrW&index=2

  5. Ratios - Multi part ratios by Richard of AoPs https://www.youtube.com/watch?v=Lkw4Slh4uRg&list=PLqiSsHAcyf9cJfapnn3i5nuMFIu4JXfrW&index=3

  6. Proportions:

    • Intro to solving proportions with cross products? Watch this Math Antics Proportions video (10 minutes)

    • Word Problems with proportions. How to set up a proportions when reading word problems? Watch Richard from AoPs set up proportion (equal ratios are called proportions) (Note at minute 6 he “clears” the fraction by multiplying by 2 so he doesn’t have to have a fraction in the numerator.) He calls method 1 finding an equivalent ratio “scaling it up by a factor of _____”

Graphing and Solving Inequalities (Pre-algebra chp 3 & Algebra Chp 10.7)

  1. Optional review video by Mr. J “Multiplication or Division Inequalities One -step”

  2. Explanation of why we flip the inequality sign when multiplying or dividing by a negative by Mr. J

  3. Intro to graphing inequalities on coordinate plane - how to shade the half-open plane - 7 minute video by Organic Chem Tutor https://www.youtube.com/watch?v=cskHdgwB5k8

  4. Intro to graphing inequalities on a number line — includes clearing fractions: https://www.youtube.com/watch?v=EE2qWIyjKD0 12 minute video by Mike Devor

  5. Art of Problem Solving Pre-algebra Chp 5.5 Basics of Inequalities Part 1

  6. Art of Problem Solving Pre-algebra Chp 5.5 Basics of Inequalities Part 2

  7. Art of Problem Solving Pre-algebra Chp 5.5 Solving Linear Equalities

  8. Art of Problem Solving Pre-algebra Chp 5.5. Solving Linear Equalities Word Problem

  9. 30 how to solve multistep inequalities by Organic Chemistry Tutor https://www.youtube.com/watch?v=rIl2USa8XPY

  10. Graphing

Fractions

  1. Introduction to fractions - Art of Problem Solving (AoPs) Prealgebra Chapter 4.1 :

  2. Multiplying Fractions

  3. Dividing by a Fraction

  4. Simplifying fractions

  5. Equivalent fractions

  6. Comparing Fractions using number lines

  7. Easiest Common Denominator - Math Antics https://www.youtube.com/watch?v=N-Y0Kvcnw8g&list=PLr7qXmZNC_A-i6B7zBWsi7IkqVzd2Ed-I&index=4

  8. Lowest Common Denominator - Math Antics https://www.youtube.com/watch?v=pZEmFSP3Z0I&list=PLr7qXmZNC_A-i6B7zBWsi7IkqVzd2Ed-I&index=3

  9. Adding & Subtracting Like Fractions - with same denominator

    • Same Denominator or “Like Fractions”: This is a proof from AoPs explains why you can just add the numerators (tops) when the denominators are the same (bottom) Same Denominator

  10. Adding & Subtracting Unlike Fractions - with Different Denominator —Adding fractions with different denominators from AoPs

  11. Adding Mixed numbers

  12. Subtracting Mixed numbers

    • Simple way—> turn everything into IMPROPER NUMBERS Math Antics https://www.youtube.com/watch?v=RqUPSZLwHH0

    • Clever way (FASTER) if you can handle the distributive property to deal with subtraction and negative numbers and mixed numbers, a.k.a how to separate out the integers and fraction separately. There’s a trick to this— use the distributive property to distribute the negative when subtracting. If you master this it’s a faster way to subtract mixed numbers! Mixed number Subtraction with Richard of AoPs

  13. Using Multiplicative Inverses (aka reciprocals) to solve equations with fractions faster

  14. Clearing Fractions from an equation by multiplying by a common denominator or by the reciprocal

  15. Using cross products aka cross multiplication (looks like a butterfly) to solve proportions Start at minute 10 of the video with Prof. Rob Bob https://www.youtube.com/watch?v=De5ghpLlkUQ&list=PLGbL7EvScmU7ZqJW4HumYdDYv12Wt3yOk&index=32

Solving Linear Equations and Simplifying Expressions

  1. Simplifying expressions (combining like terms) with Richard on this AoPs video (simplifying expressions)

  2. Adding and Subtracting Polynomials: Watch video on how to do problems like this (4x + 6) - ( 2x + y - 10). Adding and Subtracting Polynomials by Organic Chem Tutor Pay attention to what he does at minute 1:40

  3. Solving linear expressions such as x + 8 = 13 with addition and subtraction (inverse operations)

  4. How to solve equations like this 3x = 21 or 7 = w/9 ( inverse operations of multiplication and division)

  5. Solving two-step linear equations such as 4x + 8 = 13 with Richard from AoPs (solving linear equations part 3)

  6. Solving linear equations with fractions part 1 with Richard from AoPs (includes clearing fractions method): https://www.youtube.com/watch?v=BtWX9kSNWrc&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=7

  7. Solving linear equations with fractions part 2 with Richard from AoPs (also includes clearing fractions method to knock out the fractions): https://www.youtube.com/watch?v=aW4fKupD0eQ&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=8

  8. Solving linear equations - special cases with Richard from AoPs: https://www.youtube.com/watch?v=yPWu02VnGxM&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=9

Perimeter, Area & Volume

Review Area of Triangle Math Antics video https://www.youtube.com/watch?v=xCdxURXMdFY

Factorization- Multiples - Divisibility

Art of Problem Solving Prealgebra Chapter 3

Exponent Laws

McD chp 1

  1. Introduction to exponents — 10-minute video to review how exponents work: Intro to Exponents by Math Antics

Art of Problem Solving Prealgebra Chapter 2

  1. Summary: Laws of Exponents from Math Antics: https://www.youtube.com/watch?v=LkhPRz7Hocg Write these rules down (again— you should already have them in your notes) NOTE- broken link was fixed on 1/19/21

  2. Division and Exponents— here’s a simple video on dividing with variables https://www.youtube.com/watch?v=_DQ7vs5tdUQ

  3. Math Antics video explains patterns: x to 0 power is? and how to “undo” exponents and roots https://www.youtube.com/watch?v=S3IEeCyUWWA

  4. AoPs Multiplying squares— “Product of Squares”

  5. AoPs Dividing squares - “Quotient of Squares”

  6. AoPs how to find the next perfect square when you know the one before it “Square of a Sum” ( = a² + 2a +1 draw a square and add another column, row and one more square)

  7. How to estimate an non-perfect square like square root of 61 WITHOUT a calculator: Magic of Math https://www.youtube.com/watch?v=bxRT-byKd90&list=PLIa7w81Zp_7wQivt4auzylmrZUlE7UrE2&index=55 How to Approximate Square Roots WITHOUT a Calculator -Grade 8 Math from The Magic of Math

  8. AoPs What are the exponent rules? Deriving the exponent rules. Then, can we use exponent rules to make a problem easier to solve? “Same Base Exponent Rules” at 5:10 try to solve the problem, then watch Richard the math wiz solve it.

  9. AoPs Sample Exponent Rule problem. Stop the video at 0:15, write down the problem and use your exponent rules (aka Laws of Exponents) to solve the problem. Hint: write these in terms of the same base. Then watch Richard the math wiz solve it. Then look at problems 2.19a,b,c in AoPs Prealgebra text p. 71. Do those problems and check your answers.

  10. AoPs What does 3 to the zero power mean? “Zero as an Exponent”

  11. AoPs “Negative exponents Introduction” After watching this video, turn to page 78-9 in AoPs Prealgebra text and do problems 2.28-2.30. Check your answers in the text on pages 80-82

  12. Scientific Notation What is it? Math Magic video: https://www.youtube.com/watch?v=7Mi3cZwixIA&list=PLIa7w81Zp_7wQivt4auzylmrZUlE7UrE2&index=28

  13. Scientific Notation - how to add, subtract, multiply and divide in scientific notation Math Magic “How to Perform Operations in Scientific Notation . . . How to Add, Subtract, Multpliy & Divide”

  14. Bonus: AoPs “Reciprocals and negative exponents” Pause the video at 1:38 and do the problem then watch Richard’s solution. (Reciprocal of a reciprocal returns the original number)

  15. Bonus: AoPs “Exponent Rules with Negative Exponents” Pause the video at 0:20 and try to simplify the expressions so you can compare them. Afterwards, watch Richard solve the problem. After watching this video, turn to page 79 in AoPs Prealgebra text and do problems 2.31-2.35 then check your answers on pages 82-86

  16. Bonus: Fractional exponents

Reciprocals and Division including dividing Fractions

Art of Problem Solving Prealgebra Chapter 1 Properties of Arithmetic

  1. Short 2 minute video about reciprocals.

  2. This Math Antics video shows you how you can use reciprocals to divide fractions: https://www.youtube.com/watch?v=4lkq3DgvmJo

  3. AoPs “What is a Reciprocal?” #10

  4. AoPs division is multiplying by a reciprocal “Introducing Division” #11

  5. AoPs “Dividing a Sum by a Number” #12 — using the distributive property to rewrite division problems as multiplication problems. Pause the video at 2:45 and try to solve the problem by dividing a sum by a number before math wiz, Richard does it. (He uses “hangman division”).

Negation and Adding & Subtracting Positive & Negative Integers

  1. AoPs Definition of subtraction is adding a negative: “Subtractions with Negatives Part 1”

  2. Another version of this by Math and Science 16 minutes “Rethink subtraction as adding a negative”

  3. AoPs Prealgebra Video “Subtractions with Negatives Part 2” Prealgebra Video

  4. Math Antics review of adding + and - numbers: review of adding and subtracting positive and negative integers

  5. Using our addition super power (commutative property) and the idea that subtraction is adding a negative to move numbers around to make problems easier to solve: AoPs “Subtraction Problems” Pause the video at 1:00 and do the problem before Richard does it. Do that again at minute 3:00. Hint: add a negative and pair up the numbers in a way that makes it easy to add.

Absolute Value

  • MathAntics video demonstrating how absolute value is distance between a number and zero or sometimes distance between two numbers. Watch Math Antics’ 13 minute video here. It also addresses order of operations and absolute value.

Multiplication

Distributive Property in Arithmetic

  1. MathAntics: https://www.youtube.com/watch?v=VZ0jG3W53nE how to do the distributive property and WHY the distributive property helps you do hard problems more easily. Note: in this video, to show multiplication they use “x” not “ · ” In your homework use “ · "

  2. AoPs Introduction to “Distributive Property” Prealgebra Video At minute 3:10, pause the video and do the problem on the screen before Richard, AofP math wiz, does.

  3. Why is repeated addition called multiplication? AofP “Repeated Addition” Prealgebra Video

  4. AoPs “Distributive Property and Subtraction” Prealgebra Video At minute 2:16, pause the video and do the problem on the screen before Richard, AofP math wiz, does. Add again pause the problem at minute 3:22 and attempt the problem before Richard does. Hint: can you write the big number as 1,000,000 minus something?

Multiply and Dividing Positive & Negative Integers

5. Math Antics video on multiplying and dividing positive and negative integers (10 minutes)

Addition Properties

  1. AoPs “Commutative Property of Addition” Prealgebra Video

  2. AoPs “Associative Property of Addition” Prealgebra Video

  3. AoPs using these super powers of addition to rearrange big/scary looking problems so they are easier to solve: “Sum of numbers from 1 to 100” Pause the video at minute 1:45 and use your super powers to pair up addends (numbers in an addition problem) to add them up quickly. Prealgebra Video

Algebra Tiles & Expressions with variables and constants such as 3x² + 4x + 7

What are Polynomials?

  1. What are Polynomials? by MathAntics: https://www.youtube.com/watch?v=ffLLmV4mZwU This video reviews what monomials, binomials, trinomials and polynomials

Distributive Property in Algebra

2. Watch this video on the Distributive Property in Algebra by MathAntics: https://www.youtube.com/watch?v=v-6MShC82ow

3. Watch this harder algebra video about the distributive property  https://www.youtube.com/watch?v=T0a92gEDukY Pause the video and try one of the hard problems when the teacher tells you to do so. Then correct your answer. (These problems are from Integrated Math 1, i.e. 9th grade math. Pat yourself on the back if you’re starting to get this. Don’t sweat it if these challenge problems are challenging.)

Simplifying Expressions with Like Terms

4. AoPs “Combining Like Terms with Multiple Variables”

Perfect Square Numbers

  1. Basic 3 minute video “Square Numbers Explained” by Minity Math

  2. More advanced 6-minute video: What is a Perfect Squares and a Square Root? by MathMashUp

  3. 4 minute video “Perfect Squares” by Simplify the Middle

Introduction to Exponents and Roots

Math antics video which explains what exponents are and how they work. We’ll be working with exponents in Week 1 https://www.youtube.com/watch?v=B4zejSI8zho

REVIEW OF ALL OF ALGEBRA 1