2014c Course 3

Khan Academy Video Correlations

By SpringBoard Activity

 

SB Activity

Video(s)

Unit 1:  Numerical Relationships

 

Patterns

Activity 1

Investigating Patterns

1-1 Learning Targets:

·           Analyze simple sequences.

·           Describe patterns in simple sequences and give the next terms in a sequence.

1-2 Learning Targets:

·           Analyze more complex sequences.

·           Describe patterns in sequences and develop methods for predicting any term in a sequence

1-3 Learning Targets:

·           Understand increasing and decreasing sequences.

·           Analyze sequences containing mathematical operations and those based on other patterns.

Number patterns: Seeing relationships

Number patterns: interpreting relationships

Math patterns example 1

Math patterns example 2

Activity 2

Operations with Fractions

2-1  Learning Targets:

·           Represent a real-world context with fractions.

·           Simplify expressions involving fractions by adding and subtracting

2-2  Learning Targets:

·           Represent a real-world context with fractions.

·           Simplify expressions involving fractions by multiplying and dividing.

·           Write the reciprocal of a number.

Adding and Subtracting Fractions

Adding, subtracting fractions

Multiplying and Dividing Fractions

Multiplying negative and positive fractions

Activity 3

Powers and Roots

3-1 Learning Targets:

·           Interpret and simplify the square of a number.

·           Determine the square root of a perfect square

3-2 Learning Targets:

·           Interpret and simplify the cube of a number.

·       Determine the cube root of a perfect cube

3-3 Learning Targets:

·           Simplify expressions with powers and roots.

·           Follow the order of operations to simplify expressions

Exponents

Introduction to exponents

Exponent example 1

Exponent example 2

Roots

Understanding square roots

Finding cube roots

Order of Operations

Introduction to order of operations

Order of operations example

Order of operations example: putting it all together

Activity 4

Rational Numbers

4-1 Learning Targets:

·           Model fractions graphically.

·           Convert between fractions, decimals, and percents.

4-2 Learning Targets:

·           Define and recognize rational numbers.

·           Represent repeating decimals using bar notation.

·           Convert a repeating decimal to a fraction.

4-3 Learning Targets:

·           Compare rational numbers in different forms.

·           Represent repeating decimals using bar notation.

·           Utilize various forms of rational numbers.

Converting Between Forms of Rational Numbers

Converting percent to decimal and fraction

Fraction to decimal

Converting fractions to decimals

Converting a fraction to a repeating decimal

Converting repeating decimals to fractions 1

Converting repeating decimals to fractions 2

Converting decimals to fractions 2 (ex 1)

Converting decimals to fractions 2 (ex 2)

Converting decimals to percents

Converting decimals to percents example 2

Converting percents to decimals

Converting percents to decimals example 2

Activity 5

Rational and Irrational Numbers

5-1 Learning Targets:

·           Differentiate between rational and irrational numbers.

·           Approximate an irrational number in terms of a rational number

5-2 Learning Targets:

·           Approximate an irrational number in terms of a rational number.

·           Compare and order irrational and rational numbers.

Irrational Numbers

Introduction to rational and irrational numbers

Recognizing irrational numbers

Approximating irrational number exercise example

Activity 6

Properties of Exponents

6-1  Learning Targets:

·           Understand and apply properties of integer exponents.

·           Simplify multiplication expressions with integer exponents.

·           Simplify division expressions with integer exponents.

6-2  Learning Targets:

·           Understand and apply properties of integer exponents.

·           Simplify expressions with negative exponents.

6-3  Learning Targets:

·           Understand and apply properties of integer exponents.

·           Simplify expressions with zero as the exponent.

·           Simplify expressions with exponents raised to a power.

Properties of Positive Exponents

Exponent properties involving products

Exponent properties involving quotients

Products and exponents raised to an exponent properties

Exponent rules part 1

Exponent rules part 2

Properties of Zero, Fractional, and Negative Exponents

Negative exponents

Zero, negative, and fractional exponents

Activity 7

Scientific Notation

7-1 Learning Targets:

·           Express numbers in scientific notation.

·           Convert numbers in scientific notation to standard form.

·           Use scientific notation to write estimates of quantities.

7-2 Learning Targets:

·           Express numbers in scientific notation.

·           Convert numbers in scientific notation to standard form.

·           Compare and order numbers in scientific notation.

·           Use scientific notation to write estimates of quantities.

Scientific Notation

Introduction to scientific notation

Scientific notation

Scientific notation examples

Scientific notation example 1

Scientific notation example 2

Activity 8

Operations with Scientific Notation

8-1 Learning Targets:

·           Multiply numbers expressed in scientific notation.

·           Divide numbers expressed in scientific notation

8-2 Learning Targets:

·           Add numbers expressed in scientific notation.

·           Subtract numbers expressed in scientific notation.

Multiplying and Dividing in  Scientific Notation

Multiplying and dividing in scientific notation

Multiplying in scientific notation

Multiplying in scientific notation example

Dividing in scientific notation example

Unit 2:  Equations

Activity 9

Writing Expressions

9-1 Learning Targets:

·           Identify and represent patterns using models, tables, and expressions.

·           Write and evaluate algebraic expressions that represent patterns with constant differences.

9-2 Learning Targets:

·           Identify patterns that do not have a constant difference.

·           Write and evaluate algebraic expressions that represent patterns that do not have a constant difference.

Algebraic Expressions

What is a variable?

Expression terms, factors, and coefficients

Representing Patterns

Number patterns: Seeing relationships

Number patterns: interpreting relationships

Math patterns example 1

Math patterns example 2

Writing Algebraic Expressions

Writing simple algebraic expressions

Writing algebraic expressions

Writing algebraic expressions word problem

Evaluating Algebraic Expressions

Evaluating an expression example

Evaluating an expression using substitution

Activity 10

Solving Equations

10-1 Learning Targets:

·           Solve linear equations with rational number coefficients.

·           Solve linear equations by using the Distributive Property and collecting like terms.

10-2 Learning Targets:

·           Use linear equations with one variable to model and solve real-world and mathematical problems.

·           Solve linear equations with variables on both sides of the equation by using the Distributive Property and collecting like terms.

Solving Linear Equations with Variables on Both Sides

Variables on both sides

Example 1: Variables on both sides

Example 2: Variables on both sides

Equation special cases

Ex 2: Multi-step equation

Solving Equations Using the Distributive Property

Solving equations with the distributive property

Solving equations with the distributive property 2

Ex 1: Distributive property to simplify

Ex 2: Distributive property to simplify

Ex 3: Distributive property to simplify

Number of Solutions to a Linear Equation

Number of solutions to linear equations

Number of solutions to linear equations ex 2

Number of solutions to linear equations ex 3

Activity 11

Exploring Slope

11-1 Learning Targets:

·           Understand the concept of slope as the ratio  between any two points on a line.

·       Graph proportional relationships; interpret the slope and the y-intercept (0, 0) of the graph.

·           Use similar right triangles to develop an understanding of slope,

11-2 Learning Targets:

·           Understand the connections among proportional relationships, lines, and linear equations.

·           Graph proportional relationships; interpret the slope and the y-intercept (0, y) of graphs.

·       Examine linear relationships as graphs and as equations to solve real-world problems.

Slope

Slope of a line

Slope of a line 2

Slope of a line 3

Graphical slope of a line

Slope example

y-intercepts

Interpreting intercepts of linear functions

Interpreting linear functions example

Activity 12

Slope-Intercept Form

12-1 Learning Targets:

·           Graph linear relationships represented in different forms.

·           Write an equation in the form y = mx + b to model a linear relationship between two quantities.

·           Interpret the meaning of slope and y-intercept in a problem context.

12-2 Learning Targets:

·           Compare different proportional relationships represented in different ways.

·           Graph linear relationships and identify and interpret the meaning of slope in graphs.

12-3 Learning Targets:

·           Derive equations of the form y = mx and y = mx + b from their graphs.

·           Graph linear relationships and identify and interpret the meaning of slope and y-intercept in graphs.

Graphing Linear Equations

Graphing a line in slope intercept form

Writing Linear Equations

Multiple examples of constructing linear equations in slope-intercept form

 

 

Interpreting Key Characteristics of Linear Functions

Interpreting linear functions example

Interpreting intercepts of linear functions

Activity 13

Proportional Relationships

13-1 Learning Targets:

·           Represent linear proportional situations with tables, graphs, and equations.

·           Identify slope and y-intercept in these representations and interpret their meaning in real-life contexts.

13-2 Learning Targets:

·           Solve problems involving direct variation.

·           Distinguish between proportional and nonproportional situations using tables, graphs, and equations

Linear Proportional Relationships

Graphing proportional relationships example

Graphing proportional relationships example 2

Graphing proportional relationships example 3

Constructing an equation for a proportional relationship

Directly Proportional Relationships

Analyzing proportional relationships from a table

Comparing proportional relationships

Activity 14

Graphing Systems of Linear Equations

14-1        Learning Targets:

·           Understand that solutions to systems of linear equations correspond to the points of intersection of their graphs.

·       Solve systems of linear equations numerically and by graphing.

·       Use systems of linear equations to solve real-world and mathematical problems.

14-2 Learning Targets:

·           Convert linear equations into slope-intercept form.

·           Solve systems of linear equations by graphing.

·           Solve simple systems of linear equations by inspection.

Solving Systems of Linear Equations Graphically

Solving linear systems by graphing

Solving systems graphically

Graphing systems of equations

Graphical systems application problem

Example 2: Graphically solving systems

Example 3: Graphically solving systems

Testing a solution for a system of equations

Activity 15

Solving Systems of Linear Equations Algebraically

15-1 Learning Targets:

·           Connect solutions to systems of linear equations to the points of intersection of their graphs.

·           Solve systems of linear equations algebraically

15-2 Learning Targets:

·           Write linear systems to solve real-world and mathematical problems.

·           Solve systems of linear equations algebraically.

Solving Linear Systems Algebraically: Substitution

The substitution method

Substitution method 2                                                  

Substitution method 3

Example 1: Solving systems by substitution

Example 2: Solving systems by substitution

Example 3: Solving systems by substitution

Practice using substitution for systems

Solving Linear Systems Algebraically: Elimination

Example 1: Solving systems by elimination

Example 2: Solving systems by elimination

Example 3: Solving systems by elimination

Addition elimination method 1

Addition elimination method 2

Addition elimination method 3

Addition elimination method 4

Applications of Linear Systems

Using a system of equations to find the price of apples and oranges

Linear systems word problem with substitution

Systems of equation to realize you are getting ripped off

Thinking about multiple solutions to a system of equations

Unit 3:  Geometry

Activity 16

Angle-Pair Relationships

16-1 Learning Targets:

·           Identify and determine the measure of complementary angles.

·           Identify and determine the measure of supplementary angles.

16-2 Learning Targets:

·           Determine the measure of angles formed by parallel lines and transversals.

·           Identify angle pairs formed by parallel lines and transversals.

Complementary and Supplementary Angles

Complementary and supplementary angles

Find measure of complementary angles

Find measure of supplementary angles

Angles formed by Parallel Lines and Transversals

Angles formed by parallel lines and transversals

Figuring out angles between transversal and parallel lines

Using algebra to find measures of angles formed from transversal

Activity 17

Angles of Triangles and Quadrilaterals

17-1 Learning Targets:

·           Describe the relationship among the angles of a triangle.

·           Write and solve equations involving angles of a triangle.

17-2 Learning Targets:

·           Describe and apply the relationship between an exterior angle of a triangle and its remote interior angles.

·           Describe and apply the relationship among the angles of a quadrilateral.

Angles in Triangles

Proof: Sum of measures of angles in a triangle are 180

Triangle angle example 1

Triangle angle example 2

Triangle angle example 3

Challenging triangle angle problem

Finding more angles

Activity 18

Introduction to Transformations

18-1 Learning Targets:

·           Recognize rotations, reflections, and translations in physical models.

·           Explore rigid transformations of figures.

18-2 Learning Targets:

·           Determine the effect of translations on two-dimensional figures using coordinates.

·           Represent and interpret translations involving words, coordinates, and symbols.

18-3 Learning Targets:

·           Determine the effect of reflections on two-dimensional figures using coordinates.

·           Represent and interpret reflections involving words, coordinates, and symbols.

18-4 Learning Targets:

·           Determine the effect of rotations on two-dimensional figures using coordinates.

·           Represent and interpret rotations involving words, coordinates, and symbols.

Translations and Coordinates

Translations of polygons

Determining a translation for a shape

Reflections and Coordinates

Reflection and mapping points example

Rotations and Coordinates

Rotation of polygons example

Performing a rotation to match figures

Rotating segment about origin example

Activity 19

Rigid Transformations and Compositions

19-1 Learning Targets:

·           Explore properties of translations, rotations, and reflections on two-dimensional figures.

·           Explore congruency of transformed figures.

19-2 Learning Targets:

·           Explore composition of transformations.

·           Describe the effect of composition of translations, rotations, and reflections on two-dimensional figures using coordinates.

Congruence and Transformations

Testing congruence by transformations example

Another congruence by transformation example

Activity 20

Similar Triangles

20-1 Learning Targets:

·           Identify similar triangles.

·           Identify corresponding sides and angles in similar triangles.

20-2 Learning Targets:

·           Determine whether triangles are similar given side lengths or angle measures.

·           Calculate unknown side lengths in similar triangles.

Exploring Similar Triangles

Testing similarity through transformations

Similar triangles

Activity 21

Dilations

21-1 Learning Targets:

·           Investigate the effect of dilations on two-dimensional figures.

·           Explore the relationship of dilated figures on the coordinate plane.

21-2 Learning Targets:

·           Determine the effect of the value of the scale factor on a dilation.

·           Explore how scale factor affects two-dimensional figures on a coordinate plane.

Dilations

Thinking about dilations

Scaling down a triangle by half

Activity 22

The Pythagorean Theorem

22-1 Learning Targets:

·           Investigate the Pythagorean Theorem.

·           Understand and apply the Pythagorean Theorem.

22-2 Learning Targets:

·           Investigate the Pythagorean Theorem.

·           Find missing side lengths of right triangles using the Pythagorean Theorem.

Pythagorean Theorem Basics

The Pythagorean theorem intro

Pythagorean theorem

Pythagorean theorem 2

Activity 23

Applying the Pythagorean Theorem

23-1 Learning Targets:

·           Apply the Pythagorean Theorem to solve problems in two dimensions.

·           Apply the Pythagorean Theorem to solve problems in three dimensions.

23-2 Learning Targets:

·           Apply the Pythagorean Theorem to right triangles on the coordinate plane.

·           Find the distance between points on the coordinate plane.

Applications of the Pythagorean Theorem

Pythagorean theorem 1

Pythagorean theorem 3

Thiago asks: How much time does a goalkeeper have to react to a penalty kick?

Pythagorean theorem in 3D

Activity 24

Converse of the Pythagorean Theorem

24-1 Learning Targets:

·           Explain the converse of the Pythagorean Theorem.

·           Verify whether a triangle with given side lengths is a right triangle.

24-2 Learning Targets:

·           Verify whether a set of whole numbers is a Pythagorean triple.

·           Use a Pythagorean triple to generate a new Pythagorean triple.

 

N/A

Activity 25

Surface Area

25-1 Learning Targets:

·           Find the lateral and surface areas of rectangular prisms.

·           Find the lateral and surface areas of triangular prisms.

25-2 Learning Targets:

·           Find the lateral area of cylinders.

·           Find the surface area of cylinders.

Surface Area

Nets of polyhedra

Finding surface area: nets of polyhedra

Activity 26

Volumes of Solids

26-1 Learning Targets:

·           Apply the formula for the volume of a prism.

·           Apply the formula for the volume of a pyramid.

26-2 Learning Targets:

·           Apply the formula for the volume of a cone.

·           Apply the formula for the volume of a cylinder.

·           Apply the formula for the volume of a sphere.

26-3 Learning Targets:

·           Decompose composite solids into simpler three-dimensional figures.

·           Find the volume of composite solids.

Volume

Find the volume of a triangular prism and cube

Cylinder volume and surface area

Volume of a cone

Volume of a sphere

Unit 4:  Functions

Activity 27

Introduction to Functions

27-1 Learning Targets:

·           Define relation and function.

·           Evaluate functions.

27-2 Learning Targets:

·           Understand that a function is a rule that assigns exactly one output to each input.

·           Identify functions using ordered pairs, tables, and mappings.

27-3 Learning Targets:

·           Define domain and range.

·           Determine the domain and range of a relation.

27-4 Learning Targets:

·           Identify functions using graphs.

·           Understand the difference between discrete and continuous data.

What is a Function

What is a function?

Difference between equations and functions

Evaluating with function notation

Understanding function notation (example 1)

Understanding function notation (example 2)

Understanding function notation (example 3)

Mapping Inputs and Outputs

Relations and functions

Testing if a relationship is a function

Identifying Functions

Domain and range of a relation

Domain and range of a function

Domain and range 1

Graphs of Functions

Graphical relations and functions

Domain and range from graphs

Activity 28

Comparing Functions

28-1 Learning Targets:

·           Represent functions algebraically, graphically, tabularly, or verbally.

·           Compare properties of two or more functions.

28-2 Learning Targets:

·           Compare properties of two or more functions, each represented in a different way.

·           Identify examples of proportional and nonproportional functions.

Comparing Linear Functions

Comparing linear functions

Comparing linear functions 1

Comparing linear functions 2

Comparing linear functions 3

Activity 29

Constructing Functions

29-1 Learning Targets:

·           Construct a function to model a linear relationship between two quantities.

·           Graph functions that model linear relationships.

29-2 Learning Targets:

·           Determine the rate of change and initial value of a function.

·           Interpret the rate of change and initial value of a linear function in terms of the situation it models.

·           Identify examples of proportional and nonproportional functions that arise from mathematical and real-world problems.

Constructing Functions

 

Activity 30

Linear Functions

30-1 Learning Targets:

·           Model linear relationships between quantities using functions.

·           Identify and represent linear functions with tables, graphs, and equations.

30-2 Learning Targets:

·           Identify linear and non-linear functions from tables, graphs, and equations.

·           Graph a linear function from a verbal description.

·           Understand that y = mx + b defines a linear equation.

Rate of Change

Slope and rate of change

Activity 31

Linear and Non-Linear Functions

31-1 Learning Targets:

·           Determine if a function is linear or non-linear.

·           Represent functions with tables, graphs, and equations.

·           Find a trend line to represent data.

31-2 Learning Targets:

·           Define, evaluate, and compare functions.

·           Recognize patterns in non-linear functions.

·           Represent functions with tables, graphs, and equations.

31-3 Learning Targets:

·           Recognize the relationship between verbal descriptions and graphs of linear and non-linear functions.

·           Use a trend line to make predictions.

Linear and Non-Linear Functions

Recognizing linear functions

Linear and nonlinear functions (example 1)

Linear and nonlinear functions (example 2)

Linear and nonlinear functions (example 3)

Unit 5:  Probability and Statistics

Activity 32

Scatter Plots and Association

32-1 Learning Targets:

·           Make a scatter plot.

·           Recognize patterns in scatter plots.

32-2 Learning Targets:

·           Recognize patterns in scatter plots.

·           Describe association between two numerical variables in terms of direction, form and strength.

Scatter Plots

Constructing a scatter plot

Activity 33

Bivariate Data

33-1 Learning Targets:

·           Collect bivariate data from an experiment.

·           Summarize bivariate data in a scatter plot.

33-2 Learning Targets:

·           Informally fit a line to bivariate data.

·           Use a trend line to make a prediction.

33-3 Learning Targets:

·           Interpret scatter plots.

·           Use a trend line to make predictions.

Trend Lines

Interpreting a trend line

Estimating the line of best fit exercise

Activity 34

Median-Median Line

34-1 Learning Targets:

·           Determine if a linear model is a good fit for a scatter plot.

·           Find the median-median line for bivariate numerical data.

34-2 Learning Targets:

·           Find the median-median line for bivariate numerical data.

·           Use the median-median line to make predictions.

N/A

Activity 35

Two-Way Tables and Association

35-1 Learning Targets:

·           Analyze two-way tables and find relative frequencies.

·           Construct segmented bar graphs to display association.

35-2 Learning Targets:

·           Understand association between two categorical variables.

·           Describe association between two categorical variables.

Two-Way Frequency Tables

Two-way frequency tables and Venn diagrams

Two-way relative frequency tables

Interpreting two way tables

Investigating Association

Analyzing trends in categorical data

Unit 6:  Personal Financial Literacy

Activity 36

Managing Money

N/A