Algebra 1

Khan Academy Video Correlations
By SpringBoard Activity and Learning Target

 

SB Activity

Video(s)

Unit 1:  Equations and Inequalities

Activity 1

Investigating Patterns

1-1 Learning Targets:

    Identify patterns in data.

    Use tables, graphs, and expressions to model situations.

    Use expressions to make predictions.

1-2 Learning Targets:

       Use patterns to write expressions.

       Use tables, graphs, and expressions to model situations.

Algebraic Expressions

Treating units algebraically and dimensional analysis

Writing simple algebraic expressions

Writing algebraic expressions

Writing algebraic expressions word problem

Evaluating an expression example

Evaluating an expression using substitution

Expression terms, factors, and coefficients

 

Patterns and Expressions

 

Activity 2

Solving Equations

2-1 Learning Targets:

       Use the algebraic method to solve an equation.

       Write and solved an equation to model a real-world situation.

2-2 Learning Targets:

       Write and solve an equation to model a real-world situation.

       Interpret parts of an expression in terms of its context.

2-3 Learning Targets:

       Solve complex equations with variables on both sides and justify each step in the solution process.

       Write and solve an equation to model a real-world situation.

2-4 Learning Targets:

       Identify equations that have no solution.

       Identify equations that have infinitely many solutions.

2-5 Learning Targets:

       Solve literal equations for a specified variable.

       Use a formula that has been solved for a specified variable to determine an unknown quantity.

The Why of Algebra:  Equation Basics

Why we do the same thing to both sides: Simple equations

Why we do the same thing to both sides: Multi-step equations

Representing a relationship with a simple equation

One-step equation intuition

Simple Equations

Simple equations of the form ax = b

Simple equations of the from x/a = b

Simple equations of the form x + a = b

Simple equations: examples involving a variety of forms

Equations with Variable on Both Sides

Solving two-step equations                                                            

Example: two-step equations

Adding and subtracting from both sides of an equation

Dividing from both sides of an equation

Example: two-step equation with numerator x

More Complex Equations

Solving a more complicated equation

Variables on both sides

Example 1: Variables on both sides                                            

Example 2: Variables on both sides

Solving equations with the distributive property

Solving equations with the distributive property 2

Equations with No Solutions or Infinitely Many Solutions

Equation special cases

Number of solutions to linear equations

Number of solutions to linear equations ex 2

Number of solutions to linear equations ex 3

Rearrange formulas to isolate specific variables

Solving Literal Equations for a Variable

Solving for a variable

Solving for a variable 2

Example: Solving for a variable

Activity 3

Solving Inequalities

3-1 Learning Targets:

       Understand what is meant by a solution of an inequality.

       Graph solutions of inequalities on a number line.

3-2 Learning Targets:

       Write inequalities to represent real-world situations.

       Solve multi-step inequalities.

3-3 Learning Targets:

       Graph compound inequalities.

       Solve compound inequalities.

 

One-Step Inequalities

Constructing and solving a one-step inequality

One-step inequality involving addition

Inequalities using addition and subtraction

Multiplying and dividing with inequalities

Multiplying and dividing with inequalities example

Multi-Step Inequalities

Constructing and solving a two-step inequality

Constructing, solving a two-step inequality example

Solving a two-step inequality

Multi-step inequalities

Multi-step inequalities 2

Multi-step inequalities 3

Compound Inequalities

Compound inequalities

Compound inequalities

Compound inequalities 2

Compound inequalities 3

Compound inequalities 4

Activity 4

Absolute Value Equations and Inequalities

4-1 Learning Targets:

       Understand what is meant by a solution of an absolute value equation.

       Solve absolute value equations.

4-2 Learning Targets:

       Solve absolute value inequalities.

       Graph solutions of absolute value inequalities.

 

                                Absolute Value Equations

Absolute value equations

Absolute value equations

Absolute value equations 1

Absolute value equations example 1

Absolute value equation example 2

Absolute value equation example

Absolute value equation with no solution

Absolute Value Inequalities

Absolute value inequalities

Absolute value inequalities example 1

Absolute inequalities 2

Absolute value inequalities example 3

Unit 2:  Functions

Activity 5

Functions and Function Notation

5-1 Learning Targets:

       Represent relations and functions using tables, diagrams, and graphs.

       Identify relations that are functions.

5-2 Learning Targets:

       Describe the domain and range of a function.

       Find input-output pairs for a function.

5-3 Learning Targets:

       Use and interpret function notation.

       Evaluate a function for specific values of the domain.

Relations and Functions

What is a function?

Relations and functions

Recognizing functions (example 1)

Domain and Range

Domain and range of a relation

Domain and range of a function

Domain and range 1

Function Notation

Evaluating with function notation

Understanding function notation (example 1)

Understanding function notation (example 2)

Understanding function notation (example 3)

Activity 6

Graphs of Functions

6-1 Learning Targets:

       Relate the domain and range of a function to its graph.

       Identify and interpret key features of graphs.

6-2 Learning Targets:

       Relate the domain and range of a function to its graph and to its function rule.

       Identify and interpret key features of graphs.

6-3 Learning Targets:

       Identify and interpret key features of graphs.

       Determine the reasonable domain and range for a real-world situation.

Graphs of Functions

Functions as graphs

Domain and range from graphs

Graphical relations and functions

Testing if a relationship is a function

Interpreting a graph exercise example

Activity 7

Graphs of Functions

7-1 Learning Targets:

       Graph a function given a table.

       Write an equation for a function given a table or graph.

7-2 Learning Targets:

       Graph a function describing a real-world situation and identify and interpret key features of the graph.

7-3 Learning Targets:

       Given a verbal description of a function, make a table and a graph of the function.

       Graph a function and identify and interpret key features of the graph.

Graphs of Functions

Graphing exponential functions

Interpreting a graph exercise example

Activity 8

Transformations of Functions

8-1 Learning Targets:

       Identify the effect on the graph of replacing f(x) by f(x) + k.

       Identify the transformation used to produce one graph from another.

N/A

Activity 9

Rates of Change

9-1 Learning  Targets:

       Determine the slope of a line from a graph.

       Develop and use the formula for slope.

9-2 Learning  Targets:

       Calculate and interpret the rate of change for a function.

       Understand the connection between rate of change and slope.

9-3 Learning  Targets:

       Show that a linear function has a constant rate of change.

       Understand when the slope of a line is positive, negative, zero, or undefined.

       Identify functions that do not have a constant rate of change and understand that these functions are not linear.

Slope

Slope of a line

Slope of a line 2

Slope of a line 3

Graphical slope of a line

Slope example

Slope and Rate of Change

Slope and rate of change

 

Activity 10

Linear Models

10-1 Learning Targets:

       Write and graph direct variation.

       Identify the constant of variation.

10-2 Learning Targets:

       Write and graph indirect variations.

       Distinguish between direct and indirect variation.

10-3 Learning Targets:

       Write, graph, and analyze a linear model for a real-world situation.

       Interpret aspects of a model in terms of the real-world situation.

10-4 Learning Targets:

       Write the inverse function for a linear function.

       Determine the domain and range of an inverse function.

Variation

Direct and inverse variation

Recognizing direct and inverse variation

Proportionality constant for direct variation

Direct variation 1

Direct variation application

 

Inverse Functions

Introduction to function inverses

Function inverse example 1

Function inverses example 2

Function inverses example 3

 

Activity 11

Arithmetic Sequences

11-1 Learning Targets:

       Identify sequences that are arithmetic sequences.

       Use the common difference to determine a specified term of an arithmetic sequence.

11-2 Learning Targets:

       Develop an explicit formula for the nth term of an arithmetic sequence.

       Use an explicit formula to find any term of an arithmetic sequence.

       Write a formula for an arithmetic sequence given two terms or a graph.

11-3 Learning Targets:

       Use function notation to write a general formula for the nth term of an arithmetic sequence.

       Find any term of an arithmetic sequence written as a function.

11-4 Learning Targets:

       Write a recursive formula for a given arithmetic sequence.

       Use a recursive formula to find the terms of an arithmetic sequence.

Arithmetic Sequences

Arithmetic sequences

Explicit and recursive definitions of sequences

Activity 12

Forms of Linear Functions

12-1 Learning Targets:

       Write the equation of a line in slope-intercept form.

       Use slope-intercept form to solve problems.

12-2 Learning Targets:

       Write the equation of a line in point-slope form.

       Use point-slope form to solve problems.

12-3 Learning Targets:

       Write the equation of a line in standard form.

       Use the standard form of a linear equation to solve problems.

12-4 Learning Targets:

       Describe the relationship among the slopes of parallel lines and perpendicular lines.

       Write an equation of a line that contains a given point and is parallel or perpendicular to a given line.

Slope-Intercept Form

Constructing linear equations to solve word problems

Graphing a line in slope-intercept form

Converting to slope-intercept form

Multiple examples of constructing linear equations in slope-intercept form

Slope-intercept form from table

Constructing equations in slope-intercept form from graphs

Graphing using x- and y-intercepts

Graphing using intercepts

x- and y-intercepts

x- and y-intercepts 2

Finding x-intercept of a line

Finding intercepts for a linear function from a table

Interpreting intercepts of linear functions

Point-Slope Form

Linear equation from slope and a point

Finding a linear equation given a point and slope

Converting from point-slope to slope intercept form

Constructing the equation of a line given two points

Standard Form

Linear equations in standard form

Point-slope and standard form

Slopes of Parallel and Perpendicular Lines

Equations of parallel and perpendicular lines 

Parallel lines 3   geometry

Perpendicular lines  geoemtry

Perpendicular lines 2  geometry

Perpendicular line slope  geometry

Activity 13

Equations from Data

13-1 Learning Targets:

       Use collected data to make a scatter plot.

       Determine the equation of a trend line.

13-2 Learning Targets:

       Use a linear model to make predictions.

       Use technology to perform a linear regression.

13-3 Learning Targets:

       Use technology to perform quadratic and exponential regressions, and then make predictions.

       Compare and contrast linear, quadratic, and exponential regressions.

Scatter Plots

Constructing a scatter plot

Constructing scatter plot exercise example

Correlation and causality

Trend Lines

Fitting a line to data

Comparing models to fit data

Estimating the line of best fit exercise

Interpreting a trend line

Unit 3:  Extensions of Linear Concepts

Activity 14

Piecewise-Defined Linear Functions

14-1 Learning Targets

       Use function notation and interpret statements that use function notation in terms of a context.

       Calculate the rate of change of a linear function presented in multiple representation.

14-2 Learning Targets

       Write linear equations in two variables given a table of values, a graph, or a verbal description.

       Determine the domain and range of a linear function, determine their reasonableness, and represent them using inequalities.

14-3 Learning Targets

       Evaluate a function at specific inputs within the function's domain.

      Graph piecewise-defined functions.

 

N/A

Activity 15

Comparing Equations

15-1 Learning Targets:

       Write a linear equation given a graph or a table.

       Analyze key features of a function given its graph.

15-2 Learning Targets:

       Graph and analyze functions on the same coordinate plane.

       Write inequalities to represent real-world situations.

15-3 Learning Targets:

       Write a linear equation given a verbal description.

       Graph and analyze functions on the same coordinate plane.

Writing and Graphing Equations

Exploring linear relationships

Linear equation word problem

Graphs of linear equations

Interpreting linear graphs

Interpreting a graph exercise example

Application problem with graph

 

 

Activity 16

Inequalities in Two Variables

16-1 Learning Targets:

       Write linear inequalities in two variables.

       Read and interpret the graph of the solutions of a linear inequality in two variables.

16-2 Learning Targets:

       Graph on a coordinate plane the solutions of a linear inequality in two variables.

       Interpret the graph of the solutions of a linear inequality in two variables.

Graphing Linear Inequalities

Graphing inequalities

Graphing inequalities 1

Graphing inequalities 2

Solving and graphing linear inequalities in two variables 1

Graphing linear inequalities in two variables example 2

Graphing linear inequalities in two variables 3

Activity 17

Solving Systems of Linear Equations

17-1 Learning Targets:

       Solve a system of linear equations by graphing.

       Interpret the solution of a system of linear equations.

17-2 Learning Targets:

       Solve a system of linear equations using a table or the substitution method.

       Interpret the solution of a system of linear equations.

17-3 Learning Targets:

       Use the elimination method to solve a system of linear equations.

       Write a system of linear equations to model a situation.

17-4 Learning Targets:

       Explain when a system of linear equations has no solution.

       Explain when a system of linear equations has infinitely many solutions.

17-5 Learning Targets:

       Determine the number of solutions of a system of equations.

       Classify a system of linear equations as independent or dependent and as consistent or inconsistent.

Solving Systems by Graphing

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

Solving Systems with  Tables and Substitution

Example 1: Solving systems by substitution

Example 2: Solving systems by substitution

Example 3: Solving systems by substitution

The substitution method

Substitution method 2

Substitution method 3

Practice using substitution for systems

Solving Systems using the Elimination Method

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

Simple elimination practice

Systems with elimination practice

Systems Without a Unique Solution

Infinite solutions to systems

Constructing solutions to systems of equations

Practice thinking about number of solutions to systems

Classifying Systems of Equations

Consistent and inconsistent systems

Inconsistent systems of equations

Independent and dependent systems

Activity 18

Solving Systems of Linear Inequalities

18-1 Learning Targets:

       Determine whether an ordered pair is a solution of a system of linear inequalities.

       Graph the solutions of a system of linear inequalities.

18-2 Learning Targets:

       Identify solutions to systems of linear inequalities when the solution region is determined by parallel lines.

       Interpret solutions of systems of linear inequalities.

Solving Systems of Linear Inequalities

Testing solutions for a system of inequalities

Visualizing the solution set for a system of inequalities

Graphing systems of inequalities

Graphing systems of inequalities 2

Unit 4:  Exponents, Radicals, and Polynomials

Activity 19

Exponent Rules

19-1 Learning Targets:

       Develop basic exponent properties.

       Simplify expressions involving exponents.

19-2 Learning Targets:

       Understand what is meant by negative and zero powers.

       Simplify expressions involving exponents.

19-3 Learning Targets:

       Develop the Power of a Power, Power of a Product, and the Power of a Quotient Properties.

       Simplify expressions involving exponents.

Basic Exponent Properties

Exponent properties 1

Exponent properties 2

Negative and Zero Powers

Introduction to negative exponents                                              

Thinking more about negative exponents

More negative exponent intuition

Additional Properties of Exponents

Products and exponents raised to an exponent properties

Negative and positive exponents

Exponent properties 3

Exponent properties 4

Exponent properties 5

Exponent properties 6

Exponent properties 7

Activity 20

Operations with Radicals

20-1 Learning Targets:

       Write and simplify radical expressions.

       Understand what is meant by a rational exponent.

20-2 Learning Targets:

       Add radical expressions.

       Subtract radical expressions.

20-3 Learning Targets:

       Multiply and divide radical expressions.

       Rationalize the denominator of a radical expression.

Operations with Radicals

Radical equivalent to rational exponents

Radical equivalent to rational exponents 2

Multiply and simplify a radical expression 1

Simplifying square roots

Radical expressions with higher roots

Subtracting and simplifying radicals

Simplifying cube roots

Activity 21

Geometric Sequences

21-1 Learning Targets:

       Identify geometric sequences and the common ratio in a geometric sequence.

       Distinguish between arithmetic and geometric sequences.

21-2 Learning Targets:

       Write a recursive formula for a geometric sequence.

       Write an explicit formula for a geometric sequence.

       Use a formula to find a given term of a geometric sequence.

Geometric Sequences

Geometric sequences introduction

 

 

Activity 22

Exponential Functions

22-1 Learning Targets:

       Understand the definition of an exponential function.

       Graph and analyze exponential growth functions.

22-2 Learning Targets:

       Describe characteristics of exponential decay functions.

       Graph and analyze exponential decay functions.

22-3 Learning Targets:

       Describe key features of graphs of exponential functions.

       Compare graphs of exponential and linear functions.

Exponential Functions

Graphing exponential functions

Exponential growth functions

Understanding linear and exponential models

Constructing linear and exponential functions from data

 

 

Activity 23

Modeling with Exponential Functions

23-1 Learning Targets:

       Create an exponential function to model compound interest,

23-2 Learning Targets:

       Create an exponential function to fit population data.

       Interpret values in an exponential function.

Examples of Exponential Functions

Introduction to compound interest

Exponential growth and decay word problems

Decay of cesium 137 example

Modeling ticket fines with exponential function

 

 

Activity 24

Adding and Subtracting Polynomials

24-1 Learning Targets:

       Identify parts of a polynomial.

       Identify the degree of a polynomial.

24-2 Learning Targets:

       Use algebra tiles to add polynomials.

       Add polynomials algebraically.

24-3 Learning Targets:

       Subtract polynomials algebraically.

Adding and Subtracting Polynomials

Terms coefficients and exponents in a polynomial

Adding polynomials

Polynomials 2

Example: Adding polynomials with multiple variables

Subtracting polynomials

Subtracting polynomials with multiple variables

Addition and subtraction of polynomials

Adding and subtracting polynomials 1

Adding and subtracting polynomials 2

Adding and subtracting polynomials 3

Activity 25

Multiplying Polynomials

25-1 Learning Targets:

  • Use a graphic organizer to multiply expressions.
  • Use the Distributive Property to multiply expressions.

25-2 Learning Targets:

  • Multiply binomials.
  • Find special products of binomials.

25-3 Learning Targets:

  • Use a graphic organizer to multiply polynomials.
  • Use the Distributive Property to multiply polynomials.

Multiplying Polynomials

Multiplying binomials and polynomials

Multiplying binomials word problems

FOIL for multiplying binomials

FOIL method for multiplying binomials example 2

Special Products of Binomials

Square a binomial

Squaring a binomial

Squaring a binomial example 2

Special products of binomials

Multiplying binomials to get difference of squares

Activity 26

Factoring

26-1 Learning Targets:

  • Identify the GCF of the terms in a polynomial.
  • Factor the GCF from a polynomial.

26-2 Learning Targets:

  • Factor a perfect square trinomial.
  • Factor a difference of two squares.

Factoring by Greatest Common Factor

Factor expressions using the GCF

Factoring linear binomials

Factoring and the distributive property

Factoring and the distributive property 2

Factoring Special Products

Example: Factoring perfect square trinomials

Factoring special products

Example 1: Factoring difference of squares

Example 2: Factoring difference of squares

Activity 27

Factoring Trinomials

27-1 Learning Targets:

  • Use algebra tiles to factor trinomials of the form x2 + bx + c.
  • Factor trinomials of the form x2 + bx + c.

27-2 Learning Targets:

  • Factor trinomials of the form ax2 + bx + c when the GCF is 1.
  • Factor trinomials of the form ax2 + bx + c when the GCF is not 1.

Factoring Trinomials

Factoring quadratic expressions

Examples: Factoring simple quadratics

Example 1: Factoring quadratic expressions

Example 1: Factoring trinomials with a common factor

Activity 28

Simplifying Rational Expressions

28-1 Learning Targets:

  • Simplify a rational expression by dividing a polynomial by a monomial.
  • Simplify a rational expression by dividing out common factors.

28-2 Learning Targets:

  • Divide a polynomial of degree one or two by a polynomial of degree one or two.
  • Express the remainder of polynomial division as a rational expression.

28-3 Learning Targets:

  • Multiply rational expressions.
  • Divide rational expressions.

28-4 Learning Targets:

  • Identify the least common multiple (LCM) of algebraic expressions.
  • Add and subtract rational expressions.

Simplifying Rational Expressions

Simplifying rational expressions introduction

Simplifying rational expressions 1

Simplifying rational expressions 2

Simplifying rational expressions 3

 

Multiplying & Dividing Rational Expressions

Multiplying and simplifying rational expressions

Multiplying and dividing rational expressions 1

Multiplying and dividing rational expressions 2

Multiplying and dividing rational expressions 3

 

Adding & Subtracting Rational Expressions

Adding and subtracting rational expressions

Adding and subtracting rational expressions 2

Adding and subtracting rational expressions 3

Subtracting rational expressions

Simplifying first for subtracting rational expressions

 

Unit 5:  Quadratic Functions

Activity 29

Introduction to Quadratic Functions

29-1 Learning Targets:

  • Model a real-world situation with a quadratic function.
  • Identify quadratic functions.
  • Write a quadratic function in standard form.

29-2 Learning Targets:

  • Graph a quadratic function.
  • Interpret key features of the graph of a quadratic function.

Graphing Parabolas

Graphing a parabola with a table of values

Graphing a parabola by finding the roots and vertex

Graphing a parabola using roots and vertex

Graphing a parabola in vertex form

Vertex and Axis of Symmetry

Parabola vertex and axis of symmetry

Finding the vertex of a parabola example

Multiple examples graphing parabolas using roots and vertices

 

Activity 30

Graphing Quadratic Functions          

30-1 Learning Targets:

  • Graph translations of the quadratic parent function.
  • Identify and distinguish among transformations.

30-2 Learning Targets:

  • Graph vertical stretches and shrinks of the quadratic parent function.
  • Identify and distinguish among transformations.

30-3 Learning Targets:

  • Graph reflections of the quadratic parent function.
  • Identify and distinguish among transformations.
  • Compare functions represented in different ways.

N/A

Activity 31

Solving Quadratic Equations by Graphing and Factoring

31-1 Learning Targets:

  • Use a graph to solve a quadratic equation.
  • Use factoring to solve a quadratic equation.
  • Describe the connection between the zeros of a quadratic function and the x-intercepts of the function's graph.

31-2 Learning Targets:

  • Identify the axis of symmetry of the graph of a quadratic function.
  • Identify the vertex of the graph of a quadratic function.

31-3 Learning Targets:

  • Use the axis of symmetry, the vertex, and the zeros to graph a quadratic function.
  • Interpret the graph of a quadratic function.

Solving Quadratic Equations

 

Vertex and Axis of Symmetry

Parabola vertex and axis of symmetry

Finding the vertex of a parabola example

Multiple examples graphing parabolas using roots and vertices

 

Activity 32

Algebraic Methods of Solving Quadratic Equations

32-1 Learning Targets:

  • Solve quadratic equations by the square root method.
  • Provide examples of quadratic equations having a given number of real solutions.

32-2 Learning Targets:

  • Solve quadratic equations by completing the square.
  • Complete the square to analyze a quadratic function.

32-3 Learning Targets:

  • Derive the quadratic formula.
  • Solve quadratic equations using the quadratic formula.

32-4 Learning Targets:

  • Choose a method to solve a quadratic equation.
  • Use the discriminant to determine the number of real solutions of a quadratic equation.

32-5 Learning Targets:

  • Use the imaginary unit i to write complex numbers.
  • Solve a quadratic equation that has complex solutions.

The Square Root Method

Solving quadratic equations by square roots

Example: Solving simple quadratic

Completing the Square

Solving quadratic equations by completing the square

Example 1: Completing the square

Example 2: Completing the square

Example 3: Completing the square

The Quadratic Formula

How to use the quadratic formula

Example: Quadratics in standard form

Example 1: Using the quadratic formula

Example 2: Using the quadratic formula

Example 3: Using the quadratic formula

Example 4: Applying the quadratic formula

Example 5: Using the quadratic formula

Choosing a Method and Using the Discriminant

Discriminant of quadratic equations

Discriminant for types of solutions for a quadratic

 

Complex Solutions

Example: Complex roots for a quadratic

 

Activity 33

Applying Quadratic Equations

33-1 Learning Targets:

  • Write a quadratic function to fit data.
  • Use a quadratic model to solve problems.

33-2 Learning Targets:

  • Solve quadratic equations.
  • Interpret the solutions of a quadratic equation in a real-world context.

Fitting Data with Quadratic and Exponential Functions

Comparing models to fit data

Comparing exponential and quadratic models

 

 

Activity 34

Modeling with Functions

34-1 Learning Targets:

  • Construct linear, quadratic, and exponential models for data.
  • Graph and interpret linear, quadratic, and exponential functions.

34-2 Learning Targets:

  • Identify characteristics of linear, quadratic, and exponential functions.
  • Compare linear, quadratic, and exponential functions.

34-3 Learning Targets:

  • Compare piecewise-defined, linear, quadratic, and exponential functions.
  • Write a verbal description that matches a given graph.

Modeling with Functions

Comparing exponential and quadratic models

Constructing linear and exponential functions from data

Constructing linear and exponential functions from graph

 

 

 

Activity 35

Systems of Equations

35-1 Learning Targets:

  • Write a function to model a real-world situation.
  • Solve a system of equations by graphing.

35-2 Learning Targets:

  • Write a system of equations to model a real-world situation.
  • Solve a system of equations algebraically.

Solving Systems of Nonlinear Equations

Systems of nonlinear equations 1

Systems of nonlinear equations 2

Systems of nonlinear equations 3

Non-linear systems of equations 1

Non-linear systems of equations 2

Non-linear systems of equations 3

 

 

Unit 6:  Probability and Statistics

Activity 36

Measures of Center and Spread

36-1 Learning Targets:

  • Interpret differences in center and spread of data in context.
  • Compare center and spread of two or more data sets.
  • Determine the mean absolute deviation of a set of data.

36-2 Learning Targets:

  • Interpret differences in center and spread of data in context.
  • Compare center and spread of two or more data sets.
  • Determine the mean absolute deviation of a set of data.

Mean, Median, Mode

Statistics intro: Mean, median and mode

Finding mean, median and mode

Exploring the mean and median

Distribution

Comparing means of distributions

Means and medians of different distributions

Variance of a population

 

 

Activity 37

Dot and Box Plots and the Normal Distribution

37-1 Learning Targets:

  • Construct representations of univariate data in a real-world context.
  • Describe characteristics of a data distribution, such as center, shape, and spread, using graphs and numerical summaries.
  • Compare distributions, commenting on similarities and differences among them.

37-2 Learning Targets:

  • Use modified box plots to summarize data in a way that shows outliers.
  • Compare distributions, commenting on similarities and differences among them.

Box and Whisker

Box and whisker plot

Constructing a box and whisker plot

Range

Finding the range and mid-range

Introduction to the normal distribution

 

 

Activity 38

Correlation

38-1 Learning Targets:

  • Describe a linear relationship between two numerical variables in terms of direction and strength.
  • Use the correlation coefficient to describe the strength and direction of a linear relationship between two numerical variables.

38-2 Learning Targets:

  • Calculate correlation.
  • Distinguish between correlation and causation.

Correlation

Constructing a scatter plot

Correlation and causality

 

 

Activity 39

The Best-Fit Line

39-1 Learning Targets:

  • Describe the linear relationship between two numerical variables using the best-fit line.
  • Use the equation of the best-fit line to make predictions and compare the predictions to actual values.

39-2 Learning Targets:

  • Use technology to determine the equation of the best-fit line.
  • Describe the linear relationship between two numerical variables using the best-fit line.
  • Use residuals to investigate whether a given line is an appropriate model of the relationship between numerical variables.

39-3 Learning Targets:

  • Interpret the slope of the best-fit line in the context of the data.
  • Distinguish between scatter plots that show a linear relationship and those where the relationship is not linear.

39-4 Learning Targets:

  • Create a residual plot given a set of data and the equation of the best-fit line.
  • Use residuals to investigate whether a line is an appropriate description of the relationship between numerical variables.

Line of Best-fit

Fitting a line to data

Estimating the line of best fit exercise

Comparing models to fit data

Interpreting a trend line

 

 

Activity 40

Bivariate Data

40-1 Learning Targets:

  • Summarize bivariate categorical data in a two-way frequency table.
  • Interpret frequencies and relative frequencies in two-way tables.

40-2 Learning Targets:

  • Interpret frequencies and relative frequencies in two-way tables.
  • Recognize and describe patterns of association in two-way tables.

Two-way Frequency Tables

Two-way frequency tables and Venn diagrams

Two-way relative frequency tables

Interpreting two way tables

Categorical Date

Analyzing trends in categorical data