Advanced High School Courses
Table of Contents

Statistics

Chapter 1: Representing Data

Opening

 

Chapter 1 Opening

Section 1.1

1.1.1

Visualizing Information

 

1.1.2

Histograms and Stem-and-Leaf Plots

 

1.1.3

Types of Data and Variables

Section 1.2

1.2.1

Choosing Mean or Median

 

1.2.2

Variance and Standard Deviation

 

1.2.3

Sample Variance and Sample Standard Deviation

 

1.2.4

Variance and Standard Deviation

Section 1.3

1.3.2

Percentiles

 

1.3.2

Z-Scores

 

1.3.3

Linear Transformations of Data

Chapter 2: Two-Variable Quantitative Data

Opening

 

Chapter 2 Opening

Section 2.1

2.1.1

Scatterplots and Association

 

2.1.2

Line of Best Fit

 

2.1.3

Residuals

 

2.1.4

The Least Squares Regression Line

 

2.1.5

Using Technology to Find the LSRL

Section 2.2

2.2.1

The Correlation Coefficient

 

2.2.2

Behavior of Correlation and the LSRL

 

2.2.3

Residual Plots

 

2.2.4

Association is Not Causation

 

2.2.5

Interpreting Correlation in Context

Chapter 3: Multivariable Categorical Data

Opening

 

Chapter 3 Opening

Section 3.1

3.1.1

Probability and Two-Way Frequency Tables

 

3.1.2

Association and Conditional Relative Frequency Tables

 

3.1.3

Probability Notation

 

3.1.4

Relative Frequency Tables and Conditional Probabilities

 

3.1.5

Analyzing False Positives

Section 3.2

3.2.1

Probability Tree Diagrams

 

3.2.2

Problem Solving with Categorical Data

Chapter 4:Studies and Experiments

Opening

 

Chapter 4 Opening

Section 4.1

4.1.1

Survey Design I

 

4.1.2

Samples and the Role of Randomness

 

4.1.3

Sampling When Random is Not Possible

 

4.1.4

Observational Studies and Experiments

 

4.1.5

Survey Design II (optional)

Section 4.2

4.2.1

Cause and Effect with Experiments

 

4.2.2

Experimental Design I

 

4.2.3

Experimental Design II

Chapter 5: Density Functions and Normal Distributions

Opening

 

Chapter 5 Opening

Section 5.1

5.1.1

Relative Frequency Histograms and Random Variables

 

5.1.2

Introduction to Density Functions

 

5.1.3

The Normal Probability Density Function

Section 5.2

5.2.1

The Inverse Normal Function

 

5.2.2

The Standard Normal Distribution and z-Scores

 

5.2.3

Additional Practice Problems

Chapter 6: Discrete Probability Distributions

Opening

 

Chapter 6 Opening

Section 6.1

6.1.1

Mean and Variance of a Discrete Random Variable

 

6.1.2

Linear Combinations of Independent Random Variables

 

6.1.3

Exploring the Variability of X – X

Section 6.2

6.2.1

Introducing the Binomial Setting

 

6.2.2

Binomial Probability Density Function

 

6.2.3

Exploring Binomial pdf and cdf

 

6.2.4

Shape, Center, and Spread of the Binomial Distribution

 

6.2.5

Normal Approximation to the Binomial Distribution

Section 6.3

6.3.1

Introduction to the Geometric Distribution

 

6.3.2

Binomial and Geometric Practice

Chapter 7: Variability in Categorical Data Sampling

Opening

 

Chapter 7 Opening

Section 7.1

7.1.1

Introduction to Sampling Distributions

 

7.1.2

Simulating Sampling Distributions of Sample Proportions

 

7.1.3

Formulas for the Sampling Distributions of Sample Proportions

Section 7.2

7.2.1

Confidence Interval for a Population Proportion

 

7.2.2

Confidence Levels for Confidence Intervals

 

7.2.3

Changing the Margin of Error in Confidence Intervals

 

7.2.4

Evaluating Claims with Confidence Intervals

Chapter 8: Drawing Conclusions From Categorical Data

Opening

 

Chapter 8 Opening

Section 8.1

8.1.1

Introduction to Hypothesis Testing

 

8.1.2

Hypothesis Tests for Proportions

 

8.1.3

Alternative Hypotheses and Two-Tailed Tests

Section 8.2

8.2.1

Types of Errors in Hypothesis Testing

 

8.2.2

Power of a Test

Section 8.3

8.3.1

The Difference Between Two Proportions

 

8.3.2

Two-Sample Proportion Hypothesis Tests

 

8.3.3

More Proportion Inference

Chapter 9: Chi-Squared Inference Procedures

Opening

 

Chapter 9 Opening

Section 9.1

9.1.1

Introduction to the Chi-Squared Distribution

 

9.1.2

Chi-Squared Goodness of Fit

 

9.1.3

More Applications of Chi-Squared Goodness of Fit

Section 9.2

9.2.1

Chi-Squared Test for Independence

 

9.2.2

Chi-Squared Test for Homogeneity of Proportions

 

9.2.3

Practicing and Recognizing Chi-Squared Inference Procedures

Chapter 10: Drawing Conclusions From Quantitative Data

Opening

 

Chapter 10 Opening

Section 10.1

10.1.1

Quantitative Sampling Distributions

 

10.1.2

More Sampling Distributions

Section 10.2

10.2.1

The Central Limit Theorem

 

10.2.2

Using the Normal Distribution with Means

Section 10.3

10.3.1

Introducing the t-Distribution

 

10.3.2

Calculating Confidence Intervals for μ

 

10.3.3

z-Tests and t-Tests for Population Means

Chapter 11:Comparing Means and Identifying Tests

Opening

 

Chapter 11 Opening

Section 11.1

11.1.1

Paired and Independent Data from Surveys and Experiments

 

11.1.2

Paired Inference Procedures

 

11.1.3

Tests for the Difference of Two Means

 

11.1.4

Two-Sample Mean Inference with Experiments and Two-Sample Confidence Intervals

Section 11.2

11.2.1

Inference in Different Situations

 

11.2.2

Identifying and Implementing an Appropriate Test

Chapter 12: Inference for Regression

Opening

 

Chapter 12 Opening

Section 12.1

12.1.1

Sampling Distribution of the Slope of the Regression Line

 

12.1.2

Inference for the Slope of the Regression Line

Section 12.2

12.2.1

Transforming Data to Achieve Linearity

 

12.2.2

Using Logarithms to Achieve Linearity

Chapter 13: ANOVA and Beyond!

Opening

 

Chapter 13 Opening

Section 13.1

13.1.1

Modeling With the Chi-Squared Distribution

 

13.1.2

Introducing the F-Distribution

Section 13.2

13.2.1

One-Way ANOVA

Section 13.3

13.3.1

Sign Test: Introduction to Nonparametric Inference

 

13.3.2

Mood’s Median Test

JAVA

Chapter 1: Object Anatomy

Lesson 1.0

What Will I Learn?

Lesson 1.1

Using BlueJ and Submitting Programs

Lesson 1.2

Objects, Comments, and Identifiers

Lesson 1.3

Identifiers and Reserved Words

Lesson 1.4

Identifiers and More Data Types

Lesson 1.5

Writing Methods

Lesson 1.6

The Constructor

Lesson 1.7

Java Mathematics

Lesson 1.8

Four 4s
Writing Class

Lesson 1.9.1

Time Conversions

Lesson 1.9.2

DollarsNcents

Chapter 2:Using Objects

Lesson 2.1.1

Instantiating Objects

Lesson 2.1.2

Four 4s V2

Lesson 2.2

System.out

Lesson 2.3

Error Types
User Interface

Lesson 2.4.1

Scanner

Lesson 2.4.2

Box Object

Lesson 2.4.3

Converter

Lesson 2.5

Car Dealership

Chapter 3: Classes from Libraries

Lesson 3.1.1

Strings Methods

Lesson 3.1.2

Strings Indexes

Lesson 3.2

Rounding Numbers

Lesson 3.3 

Random Numbers

Lesson 3.4

Aliases and References

Lesson 3.5

Binary, Hexadecimal Conversions

Chapter 4: Iteration and Decisions

Lesson 4.1.1

Cascading if else

Lesson 4.1.2

Multiple && ||

Lesson 4.1.3

Truth Tables
The while Loop

Lesson 4.2.1

while Loop Math

Lesson 4.2.2

while Loop Strings
The for Loop

Lesson 4.3.1

Word Analysis

Lesson 4.3.2

Sentence Analysis

Lesson 4.4

Nested Loops

Lesson 4.5

Working with GUIs

Chapter 5: Arrays

Lesson 5.1

Arrays of Primitives
Array of Objects

Lesson 5.2.1

Library of Books

Lesson 5.2.2

Deck of Cards

Lesson 5.3

StuffMart Parking Lot

Chapter 6: Two-Dimensional Arrays

Lesson 6.1.1

Introduction to Two-Dimensional Arrays

Lesson 6.1.2

Matrix Objects
Two-Dimensional Arrays of Strings

Lesson 6.2.1

Seating Chart

Lesson 6.2.2

Flags R Fun

Chapter 7: The ArrayList and Sorting

Lesson 7.1

ArrayLists of Objects

Lesson 7.2

ArrayLists of Wrapped Primitives

Lesson 7.3

Box of Chocolates

Lesson 7.4

Sorting Activity

Lesson 7.5

Sorting ArrayLists

Lesson 7.6

Sorting Arrays

Chapter 8: Inheritance and Polymorphism

Lesson 8.1

ArrayLists of Objects

Lesson 8.2

ArrayLists of Wrapped Primitives

Lesson 8.3

Box of Chocolates

Lesson 8.4

Sorting Activity

Lesson 8.5

Interfaces

Chapter 9: Recursion

Lesson 9.1

Recursive Methods

Lesson 9.2

Stack Overflow
Recursive Applications

Lesson 9.3.1

Merge Sort

Lesson 9.3.2

Binary Search

Chapter 10: Additional Projects and Review

Lesson 10.1

Craps

Lesson 10.2

StuffMart Parking Lot V2

Lesson 10.3

Tic Tac Toe

Lesson 10.4

Recursive Rectangles

Inspiring Connections
Course 1

Prelude

0.1.1 What do they have in common?
0.1.2 How can I effectively communicate with my team?
0.1.3 Is there another perspective?
0.1.4 How can I persevere through struggle?
0.1.5 How can I see this happening?
0.1.6 What patterns can I recognize?
0.1.7 What is the best strategy?
0.1.8 How does respect look?

Chapter 1

1.1 Proportions and Proportional Relationships
1.1.1 How can I determine the length?
1.1.2 How big is a million?
1.1.3 How can I predict the outcome?
1.1.4 What is your fair share?
1.1.5 How can I prove two ratios form a proportion?
1.1.6 What is the relationship between the numbers?
1.2 Integer Operations
1.2.1 How can I change temperatures?
1.2.2 How can I show my thinking?
1.2.3 How can adding zero help?
1.2.4 How can I multiply integers?
1.2.5 How can I divide integers?
1.2.6 How can I compose numbers?
1.2.7 What is My Number?
1.3 Proportions and Graphs
1.3.1 How can a graph tell a story?
1.3.2 How do graphs, scale, and proportions connect?

Chapter 2

2.1 Fraction and Decimal Conversions
2.1.1 How can I rewrite it?
2.1.2 How do I write it?
2.1.3 Which representations are equivalent?
2.2 Probability
2.2.1 Is it likely or unlikely?
2.2.2 How can I represent probability as a fraction, decimal, and percent?
2.2.3 How does probability work in real-world situations?
2.2.4 How can I predict the theoretical probability using experimental data?
2.3 Scale Drawings
2.3.1 How can I determine the distance?
2.3.2 How can I enlarge a shape?
2.3.3 Does that look right?
2.3.4 Is it a scaled copy?
2.3.5 What is the best scale?
2.4 Cross Sections
2.4.1 What do I see when I slice a three-dimensional object?
2.4.2 How are cross sections and volume related?

Chapter 3

3.1 Proportional Relationships
3.1.1 How does it grow?
3.1.2 How does the money grow?
3.1.3 Is this a proportional relationship?
3.1.4 How can I create a graph?
3.1.5 What do the points mean?
3.1.6 What connections can I make?
3.2 Data and Statistics: Using Samples to Make Predictions
3.2.1 What connections can I make?
3.2.2 Which sample is more accurate?
3.2.3 Does the sample represent the population?
3.2.4 How close is my sample?
3.2.5 How are the problems related?

Chapter 4

4.1 Multiple Representations of Proportional Relationships
4.1.1 How fast can I click?
4.1.2 How can I determine which grows faster?
4.1.3 How do I see the unit rate?
4.1.4 How can I write an equation?
4.1.5 What is the better deal?
4.1.6 What impact do I have?
4.1.7 How can I calculate values more efficiently?
4.1.8 How can I convert between different units of measurement?
4.1.9 How can I make the connections?
4.2 Circumference and Area of a Circle
4.2.1 How are they proportional?
4.2.2 How much space is inside?
4.2.3 What is the formula for the area of a circle?
4.2.4 How can the formula for the area of a circle help me?

Chapter 5

5.1 Probability
5.1.1 What are the chances?
5.1.2 How can I calculate the probability of more than one event?
5.1.3 What if there is more than one event?
5.1.4 What if there are more than two events?
5.1.5 How can I determine all of the outcomes?
5.1.6 What if it is more complicated?
5.2 Integer Operations Continued
5.2.1 How does each operation move points on a number line?
5.2.2 How can I show division?
5.2.3 How can I calculate it?
5.2.4 How can I check my guess?

Chapter 6

6.1 Data Distributions
6.1.1 Who is steadier?
6.1.2 How different are they?
6.1.3 How do they compare?
6.1.4 Who is more efficient?
6.1.5 How can I simulate a sample?
6.2 Numerical and Algebraic Expressions
6.2.1 How can I combine them?
6.2.2 How can I rewrite an expression?
6.2.3 How can I write an expression with negatives?
6.2.4 What does zero look like?
6.2.5 How does it move?
6.3 Equivalent Expressions
6.3.1 How can I group them?
6.3.2 Are they equivalent?
6.3.3 What are the connections?

Chapter 7

7.1 Operations With Rational Numbers
7.1.1 Will the amount increase or decrease?
7.1.2 Are differences and distance the same?
7.1.3 Can I add these?
7.2 Percent Change
7.2.1 Does this represent an increase or a decrease?
7.2.2 How does this change the total?
7.2.3 How is the money split?
7.2.4 Do I pay more?
7.3 Percents in the Real World
7.3.1 Is this good for business?
7.3.2 How much did it change?
7.3.3 Is this acceptable?
7.3.4 How are percents represented in expressions?
7.3.5 Which is easier, calculating with fractions or decimals?

Chapter 8

8.1 Multiplication and Division of Rational Numbers
8.1.1 Is the product positive or negative?
8.1.2 How are multiplication and division connected?
8.1.3 What is the relationship?
8.1.4 How can I divide?
8.1.5 How do I solve it?
8.2 Working With Expressions
8.2.1 Which is greater?
8.2.2 How can I record my work?
8.2.3 What happens when the comparison depends on x?

Chapter 9

9.1 Angle Relationships
9.1.1 How can I draw an angle?
9.1.2 How can I combine angles?
9.1.3 How can I calculate the measure of a missing angle?
9.2 Triangle Creation
9.2.1 How can I put angles and lengths together?
9.2.2 Will these lengths make a triangle?
9.2.3 How many triangles? 9.2.4 Can I construct it?
9.3 Volume and Surface Area
9.3.1 How much material do I need?
9.3.2 How do I calculate the surface area and volume?
9.3.3 How much will it hold?
9.3.4 What am I measuring?

Chapter 10

10.1: Explorations and Investigations
10.1.1 How can I make 0?
10.1.2 What number properties pair well?
10.1.3 How can you place algebraic expressions on the number line?
10.1.4 How can I solve it?
10.1.5 What can you say about the sums of consecutive numbers?
10.2: Restaurant Math
10.2.1 How can you draw it to scale?
10.2.2 How can you calculate the cost?
10.2.3 What do portions have to do with proportions?
10.2.4 What markdown undoes a markup?

Inspiring Connections
Course 2

Prelude

0.1.1

Who are my classmates?

0.1.2

How do I work collaboratively?

0.1.3

What questions can I ask?

0.1.4

How can I categorize my words?

0.1.5

How can I communicate my ideas?

0.1.6

How can the team build this together?

0.1.7

What do we need to work togethe

 

Chapter 1

1.1 Numbers and Data

1.1.1 How should data be placed on this line?

1.1.2 Where do these numbers belong on this line?

1.1.3 How can I use two lines to solve problems?

1.1.4 How can data be used to answer a question?

1.1.5 How are histograms helpful?

1.1.6 How else can data be displayed?

1.2 Shapes and Area,

1.2.1 How can I write equivalent expressions in area and perimeter?

1.2.2 What shapes make up the polygon?

1.2.3 How can I make it a rectangle?

1.3 Expressions

1.3.1 How can I describe it using symbols?

1.3.2 What are the parts of an expression?

1.3.3 How do I work with decimals?

1.3.4 How do I multiply multi-digit decimals?

1.3.5 How can I represent the arrangement?

Chapter 2

2.1 Ratio Language

2.1.1 How can I compare two quantities? 

2.1.2 How can I write ratios?

2.1.3 How can I see ratios in data representations?

2.2 Equivalent Ratios

2.2.1 How can I visualize ratios?

2.2.2 How can I see equivalent ratios in a table?

2.2.3 How can I see equivalent ratios in a double number line?

2.2.4 How can I see equivalent ratios in tape diagrams?

2.2.5  How can I use equivalent ratios?

2.2.6 What do these represent?

2.3 Measurement

2.3.1 What are the measurements?

2.3.2 What are the units?

2.3.3 How can I convert units

Chapter 3

3.1 Measures of Center 

3.1.1 How can I measure the center?

3.1.2 How else can I measure the center?

3.1.3 Which is the better measure of center?

3.1.4 What happens when I change the data?

3.2 Integers

3.2.1 What numbers do I see?

3.2.2 What number is this?

3.2.3 What does a number line say about a number?

3.2.4 How do I compare different types of numbers?

3.3 Absolute Value

3.3.1 How do I describe the location?

3.3.2 How far do I walk?

3.3.3 Which one is greater?

3.3.4 How do I communicate mathematically?

 

3.4 Coordinate Plane

3.4.1 How can you precisely indicate a location?

3.4.2 What is the correct order?

3.4.3bWhat symbol represents me?

Chapter 4

4.1 Fractions, Decimals, and Percents
4.1.1 How can I tell if the ratios are equal?
4.1.2 What does “percent” mean?
4.1.3 How can I convert a fraction?
4.1.4 How can I convert a percent?
4.1.5 How can I convert a decimal?

4.2 Percents 4.2.1 How can I show it?
4.2.2 What can I learn from the label?
4.2.3 Are the percents fair?
4.3 Unit Rates in Tables and Graphs 4.3.1 How can I compare rates?
4.3.2 Which rate is better?
4.3.3 Which deal is best?
4.3.4 What is the unit rate?
4.3.5 How can I use different data representations?

Chapter 5

5.1 Variation in Data
5.1.1 How do I ask a statistical question?
5.1.2 What does each representation say about the data?
5.1.3 What does the box in a box plot represent?
5.1.4 How else can I describe data?

5.2 Area
5.2.1 What is the height?
5.2.2 Can I reconfigure a parallelogram into a rectangle?
5.2.3 How do I calculate the area?
5.2.4 How many triangles do I need?
5.2.5 What is my perspective?
5.2.6 Is it fair to play by the rules?
5.2.7 What shapes do I see?

5.3 Fractions
5.3.1 How can I represent fraction multiplication?
5.3.2 How can I multiply fractions?
5.3.3 How can I multiply mixed numbers?

Chapter 6

6.1 Rules of Operations
6.1.1 What does it mean?
6.1.2 What do mathematicians call this?
6.1.3 How much should I ask for?
6.1.4 How can I write mathematical expressions?
6.1.5 How do mathematicians abbreviate?
6.1.6 In what order should I evaluate?

6.2 Multiples and Factors
6.2.1 When will they be the same?
6.2.2 What are multiples?
6.2.3 What do they have in common?
6.2.4 Who is your secret valentine?
6.2.5 How can I understand products?
6.2.6 How can I rewrite expressions?
6.2.7 Which method do I use?

Chapter 7

7.1 Whole Number and Decimal Division
7.1.1 How can I share equally?
7.1.2 Which strategy is the most efficient?
7.1.3 How can I write the number sentence?
7.1.4 How can I divide decimals?
7.1.5 How should the problem be arranged?

7.2 Fraction Division
7.2.1 What if the divisor is a fraction?
7.2.2 How many fit?
7.2.3 How can I visualize this?
7.2.4 What is common about this?
7.2.5 How can I use a Giant One?
7.2.6 Which method is most efficient?

Chapter 8

8.1. Algebra Tiles
8.1.1 What do these shapes represent?
8.1.2 What does a group of tiles represent?
8.1.3 What is an equivalent expression?
8.1.4 Which terms can be combined?
8.1.5 What do the numbers mean?
8.1.6 What can a variable represent?

8.2 Expressions
8.2.1 How can I count it?
8.2.2 What if the size of the pool is unknown?
8.2.3 How can I use an algebraic expression?

8.3 Equations and Inequalities
8.3.1 Which values make the equation true?
8.3.2 How can patterns be represented?
8.3.3 What is the equation?
8.3.4 How many could there be?

Chapter 9

9.1 Equations and Inequalities Continued
9.1.1 When is the statement true?
9.1.2 How do I undo that?
9.1.3 How can I visualize an equation?
9.1.4 How can I solve an equation?
9.1.5 How can I make the unknown known?
9.1.6 How can I include all the solutions?
9.1.7 Which method should I use?
9.2 Rate Problems
9.2.1 How much does rice cost?
9.2.2 How long will it take?
9.2.3 How can I compare them?
9.2.4 How long will the race take?
9.2.5 How can I represent the rate?

Chapter 10

10.1: Explorations and Investigations
10.1.1 How can I make 0?
10.1.2 What number properties pair well?
10.1.3 How can you place algebraic expressions on the number line?
10.1.4 How can I solve it?
10.1.5 What can you say about the sums of consecutive numbers?
10.2: Restaurant Math
10.2.1 How can you draw it to scale?
10.2.2 How can you calculate the cost?
10.2.3 What do portions have to do with proportions?
10.2.4 What markdown undoes a markup?

Chapter 11

11.1: Ratios and Proportions
11.1.1 How much food is there?
11.1.2 How much do we need?
11.1.3 How much is that?
11.1.4 How can I redesign the classroom?
11.2: The Number System
11.2.1 Can I determine all the right measurements?
11.2.2 How can I show my understanding?

Inspiring Connections
Course 3

Prelude

0.1.1 What can I learn from my classmates?
0.1.2 How can shapes move?
0.1.3 What does respect mean to me?
0.1.4 What story might this represent?
0.1.5 Do all cities value parks the same?
0.1.6 How can I contribute to my team?

Chapter 1

1.1 Data and Graphs
1.1.1 How can I represent data?
1.1.2 How can I use data to solve a problem?
1.1.3 Is the roller coaster safe?
1.1.4 Is there a relationship?
1.1.5 What is the relationship?

1.2 Introduction to Transformations
1.2.1 How can I move a figure on the coordinate plane?
1.2.2 How can I describe the steps precisely?
1.2.3 Is there another way?
1.3 Linear Relationships
1.3.1 How can I graph a proportional relationship?
1.3.2 How do they compare?
1.3.3 Can I graph myself?
1.3.4 How can I represent this with a graph?
1.3.5 How can I graph a linear relationship?

Chapter 2

2.1 Rigid Transformations
2.1.1 How can I describe it?
2.1.2 How does reflection affect coordinates?
2.1.3 What can I create?
2.2 Similarity
2.2.1 What if I multiply?
2.2.2 How do shapes change?
2.2.3 What can I say about dilated shapes?
2.2.4 Are they similar?
2.2.5 How can I move a shape on a coordinate plane?
2.3 Graphing Systems of Equations
2.3.1 Where do the lines cross?
2.3.2 Will different tile patterns ever have the same number of tiles?

Chapter 3

3.1 Trend Lines
3.1.1 Are these variables related?
3.1.2 Which line fits the data well?
3.1.3 How can this association be explained?
3.2 Solving Equations with Algebra Tiles
3.2.1 How can I represent an expression?
3.2.2 How can I rewrite an expression?
3.2.3 How can I compare two expressions?
3.2.4 How can I solve the equation?
3.3 Graphing Linear Equations
3.3.1 What is the rule?
3.3.2 How can I make a prediction?
3.3.3 What is a graph and how is it useful?
3.3.4 How should I graph?
3.3.5 What observations can I make about a graph?

Chapter 4

4.1 Exponents, Part 1
4.1.1 What is exponential growth?
4.1.2 How can you (re)write it?
4.1.3 How can notation help you make sense of exponential expressions?
4.1.4 Are there other exponent properties?
4.1.5 How can I prevent common exponential expression errors?
4.2 Solving Equations
4.2.1 How can I check my answer?
4.2.2 Is there always a solution?
4.2.3 How many solutions are there?
4.2.4 How can I solve complicated equations?
4.2.5 How can I write an equation to meet the criteria?
4.3 Exponents, Part 2
4.3.1 What if the exponent is not positive?
4.3.2 How do you know which exponent properties to use?

Chapter 5

5.1 Representations of a Line
5.1.1 What is the connection?
5.1.2 How can you show it?
5.1.3 How does it grow?
5.1.4 How is the growth represented?
5.1.5 How can I write the rule?
5.1.6 How can you make connections?
5.1.7 How can you use growth?
5.1.8 What are the connections?
5.2 Graphs & Equations of Systems
5.2.1 How can I change it to y = mx + b form?
5.2.2 How can I eliminate fractions and decimals in equations?
5.2.3 How do I change the line?
5.2.4 Is the intersection significant?
5.2.5 What is the equation?

Chapter 6

6.1 Solving Systems Algebraically
6.1.1 Where do the lines intersect?
6.1.2 When are they the same?
6.1.3 What if the equations are not in y = mx + b form?
6.1.4 How many solutions are there?
6.2 Slope & Rate of Change
6.2.1 What is the equation of the line?
6.2.2 How does y change with respect to x?
6.2.3 When is it the same?
6.2.4 What’s the point?
6.2.5 Can I connect rates to slopes?
6.3 Associations
6.3.1 What is the equation for a trend line?
6.3.2 How can I use an equation?
6.3.3 What if the data is not numerical?
6.3.4 Is there an association?

Chapter 7

7.1 Angles
7.1.1 How are the angles related?
7.1.2 Are there other congruent angles?
7.1.3 What about the angles in a triangle?
7.1.4 What if the angle is on the outside?
7.1.5 Can angles show similarity?
7.2 Right Triangle Theorem
7.2.1 Can I make a right triangle?
7.2.2 What is special about a right triangle?
7.2.3 How can I calculate the side length?
7.2.4 What kind of number is it?
7.2.5 How can I use the Right Triangle Theorem to Solve Problems?
7.2.6 How can I determine lengths in three dimensions?
7.2.7 How can I prove it?

Chapter 8

8.1Introduction to Functions

 

8.1.1

How can you (de)code the message?

 

8.1.2

How can a graph tell a story?

 

8.1.3

What can you predict?

 

8.1.4

Which prediction is best?

 

8.1.5

How does the output change based on the input?

 

8.1.6

How do you see the relationship?

8.2

 Characteristics of Functions

 

8.2.1

What is a function?

 

8.2.2

How can you describe the relationship?

 

8.2.3

How do I sketch it?

 

8.2.4

How many relationships are there?

8.3

Linear and Nonlinear Functions

 

8.3.1

Is it linear or nonlinear?

 

8.3.2

What clues do ordered pairs reveal about a relationship?

 

8.3.3

What other functions might you encounter?

Chapter 9

9.1Volume

 

9.1.1

Given the volume of a cube, how long is the side?

 

9.1.2

What if the base is not a polygon?

 

9.1.3

What if the layers are not the same?

 

9.1.4

What if it is oblique?

 

9.1.5

What if it is a three-dimensional circle?

9.2

Scientific Notation

 

9.2.1

How can I write very large or very small numbers?

 

9.2.2

How do I compare very large numbers?

 

9.2.3

How do I multiply and divide numbers written in scientific notation?

 

9.2.4

How do I add and subtract numbers written in scientific notation?

 

9.2.5

How do I compute it?

9.3

Applications of Volume

 

9.3.1

What does a volume function look like?

 

9.3.2

What is the biggest cone?

 

9.3.3

How do all the items fit together?

Chapter 10

10.1Explorations and Investigations

 

10.1.1

How close can I get?

 

10.1.2

Can you make them all?

 

10.1.3

How many triangles will there be?

 

10.1.4

What’s my angle?

 

10.1.5

Function-function, what’s your function?

 

10.1.6

Is it always true?

 

10.1.7

What’s right?

 

10.1.8

What’s your story?

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Algebra Tiles Blue Icon

Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.