6(A) - Math 7 Plus - Pollina

6(A) - Math 7 Plus - Pollina - 2019

Course Modules

Unit 1: Measuring Circles

Unit 1: Measuring Circles Unit 1: Measuring Circles

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Overview | Unit 1: Measuring Circles Overview | Unit 1: Measuring Circles 1

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1 How Well Can You Measure? |Exploring Circles 1 How Well Can You Measure? |Exploring Circles 3

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2 Exploring Circumference 2 Exploring Circumference 4

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3 Applying Circumference 3 Applying Circumference 5

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4 Circumference and Wheels | Estimating Areas | Exploring the Area of a Circle 4 Circumference and Wheels | Estimating Areas | Exploring the Area of a Circle 6

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5 Relating Area to Circumference | Applying Areas of Circles 5 Relating Area to Circumference | Applying Areas of Circles 7

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6 Distinguishing Circumference and Area 6 Distinguishing Circumference and Area 8

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Unit 2: Expressions, Equations, and Inequalities

Unit 2: Expressions, Equations, and Inequalities Unit 2: Expressions, Equations, and Inequalities

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Overview | Unit 2: Expressions, Equations, and Inequalities Overview | Unit 2: Expressions, Equations, and Inequalities 1

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1 Reasoning about Contexts with Tape Diagrams (Part 1) 1 Reasoning about Contexts with Tape Diagrams (Part 1) 2

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2 Reasoning about Contexts with Tape Diagrams (Part 2) | Reasoning about Equations and Tape Diagrams (Part 1) 2 Reasoning about Contexts with Tape Diagrams (Part 2) | Reasoning about Equations and Tape Diagrams (Part 1) 3

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3 Reasoning about Equations and Tape Diagrams (Part 2) | Distinguishing Between Two Types of Situations 3 Reasoning about Equations and Tape Diagrams (Part 2) | Distinguishing Between Two Types of Situations 4

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4 Reasoning about Solving Equations (Part 1) | Reasoning about Solving Equations (Part 2) 4 Reasoning about Solving Equations (Part 1) | Reasoning about Solving Equations (Part 2) 5

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5 Dealing with Negative Numbers 5 Dealing with Negative Numbers 6

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6 Different Options for Solving One Equation 6 Different Options for Solving One Equation 7

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7 Using Equations to Solve Problems 7 Using Equations to Solve Problems 8

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8 Solving Problems about Percent Increase or Decrease 8 Solving Problems about Percent Increase or Decrease 9

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9 Reintroducing Inequalities 9 Reintroducing Inequalities 10

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10 Finding Solutions to Inequalities in Context 10 Finding Solutions to Inequalities in Context 11

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11 Efficiently Solving Inequalities 11 Efficiently Solving Inequalities 12

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12 Interpreting Inequalities 12 Interpreting Inequalities 13

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14 Subtraction in Equivalent Expressions | Expanding and Factoring 14 Subtraction in Equivalent Expressions | Expanding and Factoring 15

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15 Combining Like Terms (Part 1) 15 Combining Like Terms (Part 1) 16

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16 Combining Like Terms (Part 2) | Combining Like Terms (Part 3) 16 Combining Like Terms (Part 2) | Combining Like Terms (Part 3) 17

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13 Modeling with Inequalities 13 Modeling with Inequalities 18

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Unit 3: Angles, Triangles, and Prisms

Unit 3: Angles, Triangles, and Prisms Unit 3: Angles, Triangles, and Prisms

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Overview | Unit 3: Angles, Triangles, and Prisms Overview | Unit 3: Angles, Triangles, and Prisms 1

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1 Relationships of Angles | Adjacent Angles 1 Relationships of Angles | Adjacent Angles 2

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2 Nonadjacent Angles | Solving for Unknown Angles 2 Nonadjacent Angles | Solving for Unknown Angles 3

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3 Using Equations to Solve for Unknown Angles | Building Polygons (Part 1) 3 Using Equations to Solve for Unknown Angles | Building Polygons (Part 1) 4

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4 Building Polygons (Part 2) 4 Building Polygons (Part 2) 5

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5 Triangles with 3 Common Measures |Drawing Triangles (Part 1) 5 Triangles with 3 Common Measures |Drawing Triangles (Part 1) 6

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6 Drawing Triangles (Part 2) 6 Drawing Triangles (Part 2) 7

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7 Volume of Right Prisms 7 Volume of Right Prisms 8

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9 Surface Area of Right Prisms 9 Surface Area of Right Prisms 10

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10 Distinguishing Volume and Surface Area 10 Distinguishing Volume and Surface Area 11

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8 Decomposing Bases for Area 8 Decomposing Bases for Area 11

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11 Applying Volume and Surface Area 11 Applying Volume and Surface Area 12

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Unit 4: Rigid Transformations and Congruence

Unit 4: Rigid Transformations and Congruence Unit 4: Rigid Transformations and Congruence

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Overview | Unit 4: Rigid Transformations and Congruence Overview | Unit 4: Rigid Transformations and Congruence 1

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1 Naming the Moves 1 Naming the Moves 2

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2 Grid Moves | Making the Moves 2 Grid Moves | Making the Moves 3

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3 Coordinate Moves 3 Coordinate Moves 4

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4 Describing Transformations I No Bending or Stretching 4 Describing Transformations I No Bending or Stretching 5

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5 Rotation Patterns |Moves in Parallel 5 Rotation Patterns |Moves in Parallel 6

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6 Composing Figures 6 Composing Figures 7

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7 What is the Same? 7 What is the Same? 8

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8 Congruent Polygons 8 Congruent Polygons 9

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9 Congruence 9 Congruence 10

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10 Alternate Interior Angles 10 Alternate Interior Angles 11

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11 Adding the Angles in a Triangle 11 Adding the Angles in a Triangle 12

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12 Parallel Lines and the Angles in a Triangles 12 Parallel Lines and the Angles in a Triangles 13

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Unit 5: Dilations, Similarity and Introducing Slope

Unit 5: Dilations, Similarity and Introducing Slope Unit 5: Dilations, Similarity and Introducing Slope

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Overview | Unit 5: Dilations, Similarity and Introducing Slope Overview | Unit 5: Dilations, Similarity and Introducing Slope 1

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1 Projecting and Scaling |Circular Grid 1 Projecting and Scaling |Circular Grid 2

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2 Dilations with No Grid | Dilations on the Square Grid 2 Dilations with No Grid | Dilations on the Square Grid 3

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3 More Dilations | Similarity 3 More Dilations | Similarity 4

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4 Similar Polygons 4 Similar Polygons 5

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5 Side Length Quotients in Similar Triangles 5 Side Length Quotients in Similar Triangles 6

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6 Meet Slope 6 Meet Slope 7

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7 Writing Equations for Lines 7 Writing Equations for Lines 8

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8 Using Equations for Lines 8 Using Equations for Lines 9

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9 The Shadow Knows 9 The Shadow Knows 10

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Unit 6: Linear Relationships

Unit 6: Linear Relationships Unit 6: Linear Relationships

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Overview | Unit 6: Linear Relationships Overview | Unit 6: Linear Relationships 1

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1 Introduction to Linear Relationships 1 Introduction to Linear Relationships 2

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2 More Linear Relationships 2 More Linear Relationships 3

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3 Representations of Linear Relationships 3 Representations of Linear Relationships 4

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4 Translating to y = mx + b 4 Translating to y = mx + b 5

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5 Slopes Don't Have to be Positive 5 Slopes Don't Have to be Positive 6

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6 Calculating Slope I Equations of All Kinds of Lines 6 Calculating Slope I Equations of All Kinds of Lines 7

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7 Solutions to Linear Equations I More Solutions to Linear Equations 7 Solutions to Linear Equations I More Solutions to Linear Equations 8

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8 Using Linear Relations to Solve Problems I More Solutions to Linear Equations 8 Using Linear Relations to Solve Problems I More Solutions to Linear Equations 9

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Unit 7: Linear Equations and Linear Systems

Unit 7: Linear Equations and Linear Systems Unit 7: Linear Equations and Linear Systems

Page

Overview | Unit 7: Linear Equations and Linear Systems Overview | Unit 7: Linear Equations and Linear Systems 1

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1 Keeping the Equation Balanced | Balanced Moves 1 Keeping the Equation Balanced | Balanced Moves 2

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2 More Balanced Moves 2 More Balanced Moves 3

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3 Solving Any Linear Equation | Strategic Solving 3 Solving Any Linear Equation | Strategic Solving 4

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4 All, Some, or No Solutions | How Many Solutions? 4 All, Some, or No Solutions | How Many Solutions? 5

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5 When Are They the Same? I On or Off the Line? 5 When Are They the Same? I On or Off the Line? 6

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6 On Both of the Lines 6 On Both of the Lines 7

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7 Systems of Equations I Solving Systems of Equations 7 Systems of Equations I Solving Systems of Equations 8

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8 Solving More Systems I Writing Systems of Equations 8 Solving More Systems I Writing Systems of Equations 9

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9 Solving Problems with Systems of Equations 9 Solving Problems with Systems of Equations 10

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10 Is it True? I Inequalities 10 Is it True? I Inequalities 11

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Unit 8: Functions and Volume

Unit 8: Functions and Volume Unit 8: Functions and Volume

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Overview | Unit 8: Functions and Volume Overview | Unit 8: Functions and Volume 1

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1 Inputs and Outputs 1 Inputs and Outputs 2

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2 Introduction to Functions 2 Introduction to Functions 3

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3 Equations for Functions 3 Equations for Functions 4

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4 Tables, Equations, and Graphs of Functions 4 Tables, Equations, and Graphs of Functions 5

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5 More Graphs of Functions I Even More Graphs of Functions 5 More Graphs of Functions I Even More Graphs of Functions 6

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6 Connecting Representations of Functions 6 Connecting Representations of Functions 7

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7 Linear Functions 7 Linear Functions 8

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8 Linear Models I Piecewise Linear Functions 8 Linear Models I Piecewise Linear Functions 9

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9 Filling Containers I How Much will Fit? 9 Filling Containers I How Much will Fit? 10

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10 The Volume of a Cylinder | Finding Cylinder Dimensions 10 The Volume of a Cylinder | Finding Cylinder Dimensions 11

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11 The Volume of a Cone I Finding Cone Dimensions 11 The Volume of a Cone I Finding Cone Dimensions 12

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12 The Volume of a Sphere 12 The Volume of a Sphere 13

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13 Cylinders, Cones, Spheres I Volume as a Function of... 13 Cylinders, Cones, Spheres I Volume as a Function of... 14

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Unit 9: Exponents and Scientific Notation

Unit 9: Exponents and Scientific Notation Unit 9: Exponents and Scientific Notation

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Overview | Unit 9: Exponents and Scientific Notation Overview | Unit 9: Exponents and Scientific Notation 1

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1 Exponent Review | Multiplying Powers of Ten 1 Exponent Review | Multiplying Powers of Ten 2

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2 Powers of Powers of 10 | Dividing Powers of 10 2 Powers of Powers of 10 | Dividing Powers of 10 3

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3 Negative Exponents with Powers of 10 | What about Other Bases? 3 Negative Exponents with Powers of 10 | What about Other Bases? 4

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4 Practice with Rational Bases | Combining Bases 4 Practice with Rational Bases | Combining Bases 5

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5 Describing Large and Small Numbers Using Powers of 10 | Representing Large Numbers on the Number Line 5 Describing Large and Small Numbers Using Powers of 10 | Representing Large Numbers on the Number Line 6

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6 Representing Small Numbers on the Number Line 6 Representing Small Numbers on the Number Line 7

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7 Applications of Arithmetic with Powers of 10 | Definition of Scientific Notation 7 Applications of Arithmetic with Powers of 10 | Definition of Scientific Notation 8

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8 Multiplying, Dividing, and Estimating with Scientific Notation 8 Multiplying, Dividing, and Estimating with Scientific Notation 9

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Unit 10: Pythagorean Theorem and Irrational Numbers

Unit 10: Pythagorean Theorem and Irrational Numbers Unit 10: Pythagorean Theorem and Irrational Numbers

Page

Overview | Unit 10: Pythagorean Theorem and Irrational Numbers Overview | Unit 10: Pythagorean Theorem and Irrational Numbers 1

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1 The Areas of Squares and Their Side Lengths | Side Lengths and Areas 1 The Areas of Squares and Their Side Lengths | Side Lengths and Areas 2

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2 Rational and Irrational Numbers 2 Rational and Irrational Numbers 3

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3 Square Roots on the Number Line | Reasoning About Square Roots 3 Square Roots on the Number Line | Reasoning About Square Roots 4

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4 Finding Side Lengths of Triangles | A Proof of the Pythagorean Theorem 4 Finding Side Lengths of Triangles | A Proof of the Pythagorean Theorem 5

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5 Finding Unknown Side Lengths 5 Finding Unknown Side Lengths 6

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6 The Converse | Applications of the Pythagorean Theorem 6 The Converse | Applications of the Pythagorean Theorem 7

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7 Finding Distances in the Coordinate Plane | Edge Lengths and Volumes 7 Finding Distances in the Coordinate Plane | Edge Lengths and Volumes 8

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8 Cube Roots | Decimal Representations of Rational Numbers 8 Cube Roots | Decimal Representations of Rational Numbers 9

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9 Infinite Decimal Expansions 9 Infinite Decimal Expansions 10

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Unit 11: Probability and Sampling

Unit 11: Probability and Sampling Unit 11: Probability and Sampling

Page

Overview | Unit 11: Probability and Sampling Overview | Unit 11: Probability and Sampling 1

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1 Chance Experiments | What Are Probabilities? 1 Chance Experiments | What Are Probabilities? 2

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2 Estimating Probabilities Through Repeated Experiments | More Estimating Probabilities 2 Estimating Probabilities Through Repeated Experiments | More Estimating Probabilities 3

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3 More Estimating Probabilities I Estimating Probabilities Using Simulation 3 More Estimating Probabilities I Estimating Probabilities Using Simulation 4

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4 Simulating Multi-step Experiments | Keeping Track of All Possible Outcomes 4 Simulating Multi-step Experiments | Keeping Track of All Possible Outcomes 5

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5 Keeping Track of All Possible Outcomes I Multi-step Experiments 5 Keeping Track of All Possible Outcomes I Multi-step Experiments 6

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6 Multi-Step Experiments I Designing Simulations 6 Multi-Step Experiments I Designing Simulations 7

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7 Deviation from the Mean 7 Deviation from the Mean 8

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8 Using Mean and MAD to Make Comparisons 8 Using Mean and MAD to Make Comparisons 9

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9 Quartile and Interquartile Ranges | Using Box Plots 9 Quartile and Interquartile Ranges | Using Box Plots 10

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10 Comparing Groups I Larger Populations 10 Comparing Groups I Larger Populations 11

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11 Larger Populations | What Makes a Good Sample? 11 Larger Populations | What Makes a Good Sample? 12

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12 Sampling in a Fair Way 12 Sampling in a Fair Way 13

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13 Estimating Population Measures of Center | Estimating Population Proportions 13 Estimating Population Measures of Center | Estimating Population Proportions 14

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14 More about Sampling Variability 14 More about Sampling Variability 15

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15 Comparing Populations Using Samples 15 Comparing Populations Using Samples 16

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16 Comparing Populations With Friends | Using Data to Solve Problems 16 Comparing Populations With Friends | Using Data to Solve Problems 17

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17 Memory Test 17 Memory Test 18

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Unit 12: Associations in Data

Unit 12: Associations in Data Unit 12: Associations in Data

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Overview | Unit 12: Associations in Data Overview | Unit 12: Associations in Data 1

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1 Organizing Data | Plotting Data 1 Organizing Data | Plotting Data 2

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2 What a Point in a Scatter Plot Means | Fitting a Line to Data 2 What a Point in a Scatter Plot Means | Fitting a Line to Data 3

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3 Describing Trends in Scatter Plots | The Slope of a Fitted Line 3 Describing Trends in Scatter Plots | The Slope of a Fitted Line 4

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4 Observing More Patterns in Scatter Plots | Analyzing Bivariate Data 4 Observing More Patterns in Scatter Plots | Analyzing Bivariate Data 5

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5 Looking for Associations | Using Data Displays to Find Associations 5 Looking for Associations | Using Data Displays to Find Associations 6

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Unit 13: Putting It All Together

Unit 13: Putting It All Together Unit 13: Putting It All Together

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Overview | Unit 13: Putting It All Together Overview | Unit 13: Putting It All Together 1

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13.1 Planning Recipes 13.1 Planning Recipes 2

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13.2 | Costs of Running a Restaurant 13.2 | Costs of Running a Restaurant 3

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13.3| More Costs of Running a Restaurant 13.3| More Costs of Running a Restaurant 4

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13.4| Restaurant Floor Plan 13.4| Restaurant Floor Plan 5

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13.5| How Crowded Is this Neighborhood? 13.5| How Crowded Is this Neighborhood? 6

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13.6| Fermi Problems 13.6| Fermi Problems 7

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13.7| More Expressions and Equations 13.7| More Expressions and Equations 8

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13.8| Measurement Error (Part 1) 13.8| Measurement Error (Part 1) 9

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13.9| Measurement Error (Part 2) 13.9| Measurement Error (Part 2) 10

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13.10| Measuring Long Distances Over Uneven Terrain 13.10| Measuring Long Distances Over Uneven Terrain 11

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13.11| Building a Trundle Wheel 13.11| Building a Trundle Wheel 12

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13.12| Using a Trundle Wheel to Measure Distances 13.12| Using a Trundle Wheel to Measure Distances 13

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13.13| Designing a 5K Course 13.13| Designing a 5K Course 14

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