Khan Academy Curriculum South Africa

Transcription

1 Khan Academy Curriculum South Africa

2 Table of Contents Introduction...3 Unit Targets for the Year: Addition & Subtraction Multiplication & Division Negative Numbers Number Properties Order of Operations Factors and Multiples Fractions...10 Fractions Continued Decimals Percents Ratios and Proportions Exponents Solving Linear Equations Graphing Linear Equations Exponents and Radicals Logarithms

3 Introduction The videos and exercises prescribed here are intended for learners anywhere between grade seven and grade nine. However, there is no reason that it should not be used for earlier grades or later grades. You can use your judgement as to where you would like to begin. While we use the terminology Quarter 1, Quarter 2, Quarter 3, Quarter 4, this does not imply that your pilot need commence at the start of the year. Whether you start in January or May or September, we recommend beginning at the material assigned for Quarter 1 and working through the units in sequential order. Unit Targets On the next page you will see Term 1-4 unit targets. This is to give you an idea of how much material you should aim to cover each term. This is a best estimate. You may move faster/slower some terms. You will soon get a feel for how fast you can move your class through the units. Key to Reading Curriculum: The curriculum is split into units and each unit is displayed on a new page. In some cases, for longer units, the units are displayed over two pages. Each unit is divided into two columns videos and exercises. These two columns contain ALL of the videos and ALL of the exercises available on the Khan Academy website. Because we do not intend cover all videos and exercises, only those shadowed in grey should be covered. Next to the video column is a column that indicates how long each video is. This will help you to budget your time if you plan to watch videos in class as in some classes you may wish to watch more than one video. The O/N in the columns headed O/N stand for Optional and Numeric. Again, this corresponds to videos/exercises that are part of the Numeric Curriculum and those that are optional. Faster learners may enjoy venturing into the optional material. 3

4 Unit Targets for the Year: Quarter 1: Addition and Subtraction Multiplication and Division Negative Numbers Quarter 2: Number Properties Order of Operations Factors and Multiples Fractions Quarter 3: Solving Linear Equations Percents Ratios and Proportions Exponents Quarter 4: Graphing Linear Equations Logarithms Exponents and Radicals 4

5 1. Addition & Subtraction O/N Addition and subtraction Time O Basic Addition 7:42 O Addition 2 12:26 O Basic Subtraction 8:32 N Subtraction 2 12:32 O Subtracting Whole Numbers 2:54 O Level 2 Addition 9:48 N Addition 3 8:57 N Subtraction 3: Introduction to Borrowing or Regrouping18:26 N Why borrowing works 8:33 N Addition 4 8:49 N Level 4 Subtraction 8:47 O Subtraction Word Problem 5:09 O Alternate mental subtraction method 5:10 N Negative Numbers Introduction 9:36 N Adding Negative Numbers 5:41 N Adding integers with different signs 5:32 N Adding/Subtracting negative numbers 9:15 O Adding Whole Numbers and Applications 1 1:32 O u09 l1 t2 we4 Adding Real Numbers Application 3:15 O/N List of Unit Exercises O Addition 1 O Addition 2 O Subtraction 1 N Subtraction 2 N Addition 3 N Subtraction 3 N Addition 4 N Subtraction 4 N Adding negative numbers N Adding and subtracting negative numbers O Negative number word problems 5

6 2. Multiplication & Division O/N Multiplication and division Time O Basic Multiplication 13:20 O Multiplication 2: The Multiplication Tables 15:27 O Multiplication 3: 10,11,12 times tables 12:11 O Division 1 17:02 N Division 2 11:39 O Dividing Whole Numbers and Applications 1 2:28 N Multiplication 4: 2-digit times 1-digit number 12:08 N Multiplication 5: 2-digit times a 2-digit number 11:15 O Multiplying Whole Numbers and Applications 2 3:18 O Lattice Multiplication 7:15 O Why Lattice Multiplication Works 8:21 O Multiplying Whole Numbers and Applications 4 1:51 N Multiplication 6: Multiple Digit Numbers 10:27 N Multiplication 7: Old video giving more examples 6:17 O Multiplying Whole Numbers and Applications 6 2:39 N Division 3: More long division and remainder examples 10:07 O Partial Quotient Division 8:27 O Level 4 division 9:35 O Partial Quotient Method of Division 2 7:56 O Multiplying Whole Numbers and Applications 1 3:03 N Multiplying and dividing negative numbers 8:28 N Place Value 1 2:25 N Place Value 2 4:09 N Place Value 3 5:20 N Rounding Whole Numbers 1 4:23 N Rounding Whole Numbers 2 2:28 N Rounding Whole Numbers 3 1:04 O/N List of Unit Exercises O Multiplication 0.5 O Multiplication 1 O Multiplication 1.5 O Division 0.5 O Division 1 O Division 1.5 N Multiplication 2 N Multiplication 3 O Arithmetic word problems 2 N Multiplication 4 N Division 3 O Division 4 N Multiplying and dividing negative numbers N Place value N Rounding numbers 6

7 3. Negative Numbers O/N Negative numbers Time N Negative Numbers Introduction 9:36 N Ordering Negative Numbers 2:47 N Adding Negative Numbers 5:41 N Adding integers with different signs 5:32 N Adding/Subtracting negative numbers 9:15 N Multiplying and dividing negative numbers 8:28 O/N N N N O N List of Unit Exercises Adding negative numbers Ordering negative numbers Adding and subtracting negative numbers Negative number word problems Multiplying and dividing negative numbers 7

8 4.1 Number Properties O/N Number properties Time N Commutative Law of Addition 1:40 N Commutative Law of Multiplication 1:48 N Associative Law of Addition 2:10 N Associative Law of Multiplication 2:15 N Commutative Property for Addition 3:23 N The Distributive Property 4:56 N The Distributive Property 2 2:11 N Distributive Property Example 1 5:39 O CA Algebra I: Number Properties and Absolute Value 12:02 O Identity Property of 1 1:24 O Identity property of 1 (second example) 1:55 O Identity property of 0 4:46 O Inverse Property of Addition 2:59 O Inverse Property of Multiplication 3:17 O/N List of Unit Exercises N Properties of numbers 1 N Distributive property N Number properties terminology 1 N Properties of numbers 2 O Distributive property with variables 4.2 Order of Operations O/N Order of operations Time N Introduction to Order of Operations 9:40 N More Complicated Order of Operations Example 5:20 N Order of Operations 4:27 N Order of Operations 1 4:36 O/N N List of Unit Exercises Order of operations 8

9 5. Factors and Multiples O/N Factors and multiples Time N Prime Numbers 8:13 N Recognizing Prime Numbers 4:40 N Recognizing Divisibility 6:26 O Common Divisibility Examples 7:55 N Finding Factors of a Number 9:53 N Prime Factorization 4:09 N Least Common Multiple 4:01 O Least Common Multiple (LCM) 5:24 N Greatest Common Divisor 6:18 N Algebraic Expression Least Common Multiple 4:40 O/N List of Unit Exercises N Prime numbers O Prime factorization N Composite numbers N Divisibility 0.5 O Divisibility N Least common multiple N Greatest common divisor 9

10 6. Fractions O/N Fractions Time N Numerator and Denominator of a Fraction 2:31 N Identifying Fraction Parts 2:47 N Equivalent fractions 5:49 O Equivalent Fractions Example 4:50 N Comparing Fractions 2:30 N Fractions in lowest terms 5:42 R Comparing Fractions 2 7:08 R Ordering Fractions 7:48 N Proper and Improper Fractions 1:41 N Mixed numbers and improper fractions 9:13 O Converting Mixed Numbers to Improper Fractions 4:26 N Changing a Mixed Number to an Improper Fraction 6:43 N Changing an Improper Fraction to a Mixed Number 4:02 N Adding Fractions with Like Denominators 3:18 N Subtracting Fractions 2:26 N Finding Common Denominators 4:42 N Adding Fractions with Unlike Denominators 4:06 N Adding and subtracting fractions 9:48 O Adding Mixed Numbers 2:06 O Adding Mixed Numbers with Unlike Denominators 5:16 O Subtracting Mixed Numbers 3:59 O Subtracting Mixed Numbers 2 4:54 O/N List of Unit Exercises N Recognizing fractions 0.5 N Recognizing fractions N Fraction word problems 1 N Simplifying fractions N Equivalent fractions N Equivalent fractions 2 N Comparing fractions 1 N Comparing fractions 2 O Ordering fractions O Ordering numbers N Converting mixed numbers and improper fractions O Comparing improper fractions and mixed numbers O Ordering improper fractions and mixed numbers N Adding fractions with common denominators N Adding fractions N Adding and subtracting fractions O Adding subtracting mixed numbers 0.5 O Adding subtracting mixed numbers 1 O Adding subtracting mixed numbers 1 N Multiplying fractions 0.5 N Multiplying fractions O Multiplying mixed numbers 1 10

11 Fractions Continued O Adding Mixed Numbers Word Problem 3:22 O Subtracting Mixed Numbers Word Problem 4:41 N Adding fractions with different signs 6:22 N Multiplying Fractions 2:26 O Multiplying Mixed Numbers 4:21 O Multiplying Fractions and Mixed Numbers 4:03 O Multiplying Fractions Word Problem 3:39 N Dividing fractions 8:58 N Dividing Fractions Example 3:36 O Dividing Fractions Word Problem 2:08 O Reciprocal of a Mixed Number 1:41 O Dividing Mixed Numbers 2:41 O Dividing Mixed Numbers and Fractions 3:22 O Converting Fractions to Decimals Example 2:17 N Converting fractions to decimals 9:22 N Decimals and Fractions 2:42 O Coverting Repeating Decimals to Fractions 1 4:03 O Coverting Repeating Decimals to Fractions 2 9:06 R Representing a number as a decimal, percent, and fract 5:25 R Representing a number as a decimal, percent, and fract 3:32 O Points on a number line 1:58 O Ordering numeric expressions 9:22 N Dividing Fractions 0.5 N Dividing Fractions O Dividing fractions word problems O Converting fractions to decimals N Converting decimals to fractions 1 O Converting decimals to fractions 2 O Converting repeating decimals to fractions 1 O Converting repeating decimals to fractions 2 N Converting decimals to percents R Converting percents to decimals 11

12 7. Decimals O/N Decimals Time O Subtracting decimals (old) 8:32 N Decimal Place Value 4:00 N Decimal Place Value 2 3:31 N Decimals on a Number Line 1:39 N Rounding Decimals 1:26 O Estimation with Decimals 3:01 O Comparing Decimals 1:29 N Adding Decimals 2:45 N Subtracting Decimals 2:08 O Subtracting Decimals Word Problem 2:19 N Multiplying a Decimal by a Power of 10 3:47 O Mulitplication 8: Multiplying decimals (Old video) 9:44 O Multiplying Decimals 2:52 N Dividing a Decimal by a Power of 10 3:18 O Dividing Decimals 2.1 1:51 O Dividing decimal 9:27 O Dividing Decimals 5:32 O Mulitplyling Decimals 3 2:32 O Decimals and Fractions 2:42 O Converting Fractions to Decimals Example 2:17 O Converting fractions to decimals 9:22 O Coverting Repeating Decimals to Fractions 1 4:03 O Coverting Repeating Decimals to Fractions 2 9:06 O Percent and decimals 10:26 O Representing a number as a decimal, percent, and fract 5:25 O Representing a number as a decimal, percent, and fract 3:32 O Points on a number line 1:58 O Ordering numeric expressions 9:22 O/N List of Unit Exercises N Decimals on the number line 1 N Decimals on the number line 2 N Rounding numbers O Estimation with decimals N Adding decimals 0.5 N Adding decimals O Adding decimals 2 N Subtracting decimals 0.5 N Subtracting decimals O Adding and subtracting decimals word problems N Understanding moving the decimal O Multiplying decimals O Dividing decimals 1 O Dividing decimals 2 O Dividing decimals N Converting decimals to fractions 1 O Converting decimals to fractions 2 O Converting fractions to decimals O Ordering numbers O Converting repeating decimals to fractions 1 O Converting repeating decimals to fractions 2 12

13 8.1 Percents O/N Percents Time N Describing the Meaning of Percent 3:01 N Describing the Meaning of Percent 2 2:22 O Identifying Percent Amount and Base 2:32 O Representing a number as a decimal, percent, and fract 3:32 R Solving Percent Problems 6:17 R Solving Percent Problems 2 4:37 R Solving Percent Problems 3 5:26 O Growing by a percentage 9:42 O Representing a number as a decimal, percent, and fract 5:25 O Ordering numeric expressions 9:22 O/N N N List of Unit Exercises Converting decimals to percents Converting percents to decimals 8.2 Ratios and Proportions O/N Ratios and proportions (basic) Time N Introduction to Ratios (new HD version) 14:13 N Understanding Proportions 1:25 N Ratios as Fractions in Simplest Form 1:19 N Simplifying Rates and Ratios 2:28 O Find an Unknown in a Proportion 2 5:48 O Finding Unit Rates 2:31 O Finding Unit Prices 2:01 R Unit conversion 9:16 O Converting units of length 8:04 O Conversion between metric units 5:16 O U.S. Customary and Metric units 5:10 O Converting within the metric system 4:42 O Converting Gallons to quarts pints and cups 5:17 O Converting pounds to ounces 1:34 O Comparing Celsius and Farenheit temperature scales 2:50 O Converting Farenheit to Celsius 2:58 O Speed translation 9:55 13 O/N N O O List of Unit Exercises Expressing ratios as fractions Ratio word problems Units

14 9. Exponents O/N Exponents (basic) Time N Understanding Exponents 1:55 N Understanding Exponents 2 1:15 N Level 1 Exponents 9:45 N Level 2 Exponents 6:25 N Level 3 exponents 9:11 N Exponent Rules Part 1 9:43 N Exponent Rules Part 2 7:43 O/N List of Unit Exercises N Exponents 1 N Exponents 2 R Exponents 3 O Exponents 4 N Exponent rules 14

15 10. Solving Linear Equations O/N Solving linear equations Time N Variables Expressions and Equations 6:55 N Variables and Expressions 1 2:00 N Evaluating Expressions with Two Variables 1:46 N Order of Operations Example 14:23 N Simple Equations 11:06 N Solving One-Step Equations 1:54 N Solving One-Step Equations 2 2:23 N Algebra: Linear Equations 1 7:27 N One Step Equations 12:30 N Evaluate a formula using substitution 1:15 N Example of Solving for a Variable 6:58 N Solving for a Variable 1:24 N Solving for a Variable 2 2:41 N Algebra: Linear Equations 2 6:05 N Equations 2 8:41 N Solving Equations 1 3:04 N Two-Step Equations 13:50 O New Operator Definitions 6:50 N Solving Equations 2 4:06 N Equations 3 8:53 N Equations with Variables on Both Sides 9:28 O Multi-Step Equations 15:01 O Multi-step equations 1 4:33 O Multi-step equations 2 5:46 N Solving Equations with the Distributive Property6:04 N Solving equations with the distributive property 4:50 O Algebra: Linear Equations 3 6:43 O Algebra: Linear Equations 4 7:38 O/N Exercise List N Evaluating expressions 1 N Evaluating expressions 2 N Writing expressions 1 N Writing expressions 2 N Linear equations 1 N One step equations 0.5 N One step equations O Solving for a variable N Linear equations 2 N New definitions 1 O New definitions 2 N Linear equations 3 N Linear equations 4 O Radical equations O Rate problems 0.5 O Average word problems O Percentage word problems 1 O Percentage word problems 2 O Direct and inverse variation O Age word problems O Converting repeating decimals to fractions 1 O Converting repeating decimals to fractions 2 O Absolute value equations 15

16 11. Graphing Linear Equations O/N Graphing linear equations and inequalities Time N Quadrants of Coordinate Plane 2:24 N The Coordinate Plane 6:50 N Exploring linear relationships 4:58 N Plotting (x,y) relationships 4:29 N Plot ordered pairs 2:08 N Ordered pair solutions of equations 1:29 N Application problem with graph 5:22 N Interpreting Linear Graphs 5:05 N X and Y intercepts 4:08 N X and Y intercepts 2 3:25 N Slope of a line 4:40 N Slope Example 4:03 N Slope and Rate of Change 13:42 N Slope and Y-intercept Intuition 5:54 N Algebra: Slope 8:27 N Algebra: Slope 2 9:46 N Algebra: Slope 3 6:21 N Graphical Slope of a Line 4:00 N Slope of a Line 2 7:12 N Slope of a Line 3 5:05 O Hairier Slope of Line 6:32 N Graphing a line in slope intercept form 3:01 N Algebra: Slope and Y-intercept intuition 8:35 N Algebra: Equation of a line 6:45 O CA Algebra I: Slope and Y-intercept 12:30 N Graphing Using Intercepts 12:18 N Graphing using X and Y intercepts 3:58 O/N Exercise List N Graphing points N Plugging in values N Graphing points 2 N Interpreting linear equations N Solving for the x-intercept N Slope of a line N Line graph intuition N Graphing linear equations N Line graph intuition N Solving for the y-intercept 16

17 12. Exponents and Radicals O/N Exponents and Radicals Time D Understanding Exponents 1:55 D Understanding Exponents 2 1:15 D Exponent Rules 1 2:29 D Exponent Rules 2 3:58 D Level 1 Exponents 9:45 D Level 2 Exponents 6:25 N Negative Exponent Intuition 4:38 N Zero, Negative, and Fractional Exponents 14:04 D Level 3 exponents 9:11 O Exponent Rules Part 1 9:43 O Exponent Rules Part 2 7:43 N Exponent Properties 1 2:36 N Exponent Properties 2 5:12 N Exponent Properties 3 2:35 N Exponent Properties 4 3:07 O Exponent Properties 5 2:50 O Exponent Properties 6 4:19 O Exponent Properties 7 4:51 O Exponent Properties Involving Products 14:00 O Negative and Positive Exponents 2:19 O Exponent Properties Involving Quotients 9:22 O/N Exercise List D Exponents 1 D Exponents 2 N Exponents 3 N Exponents 4 D Exponent rules 17

18 13. Logarithms O/N Logarithms Time N Introduction to Logarithms 9:47 N Logarithm of a Power 4:49 N Sum of Logarithms with Same Base 5:04 N Introduction to logarithm properties 9:14 N Introduction to logarithm properties (part 2) 10:04 N Using Multiple Logarithm Properties to Simplify 2:10 O Change of Base Formula 7:32 O Logarithmic Scale 11:15 O Richter Scale 11:19 O Logarithmic Equations 1:27 O Solving Logarithmic Equations 4:13 O Proof: log a + log b = log ab 7:08 O Proof: log_a (B) = (log_x (B))/(log_x (A)) 7:25 O Proof: A(log B) = log (B^A), log A - log B = log 7:57 O Natural Logarithm with a Calculator 3:37 O Calculator for Natural Logarithms 1:09 O Graphing Natural Logarithm Function 9:13 O/N Exercise List N Logarithms 1 N Logarithms 2 18