Foundational Skills in Mathematics 9-12   (#1200400)

Version for Academic Year:

Course Standards

General Course Information and Notes

Version Description

This course supports students who need additional instruction in foundational mathematics skills as it relates to core instruction. Instruction will use explicit, systematic, and sequential approaches to mathematics instruction addressing all strands including number sense & operations, algebraic reasoning, functions, geometric reasoning and data analysis & probability. Teachers will use the listed benchmarks that correspond to each students’ needs. 

Effective instruction matches instruction to the need of the students in the group and provides multiple opportunities to practice the skill and receive feedback. The additional time allotted for this course is in addition to core instruction. The intervention includes materials and strategies designed to supplement core instruction.

General Notes

Florida’s Benchmarks for Excellent Student Thinking (B.E.S.T.) Standards
This course includes Florida’s B.E.S.T. ELA Expectations (EE) and Mathematical Thinking and Reasoning Standards (MTRs) for students. Florida educators should intentionally embed these standards within the content and their instruction as applicable. For guidance on the implementation of the EEs and MTRs, please visit https://www.cpalms.org/Standards/BEST_Standards.aspx and select the appropriate B.E.S.T. Standards package.

English Language Development ELD Standards Special Notes Section:

Teachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL’s need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link: https://cpalmsmediaprod.blob.core.windows.net/uploads/docs/standards/eld/ma.pdf

General Information

Course Number: 1200400
Course Path:
Abbreviated Title: FDN SKILLS MATH 9-12
Number of Credits: Multiple Credit (more than 1 credit)
Course Length: Multiple (M) - Course length can vary
Course Type: Elective Course
Course Level: 2
Course Status: State Board Approved
Grade Level(s): 9,10,11,12

Educator Certifications

One of these educator certification options is required to teach this course.

State Adopted Instructional Materials

The following instructional materials have been adopted by the State of Florida as an option for this course.
MathXL for School
Author: Pearson - Company: Savvas Learning Company LLC - Edition: 1 - Copyright: 2009
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Student Resources

Vetted resources students can use to learn the concepts and skills in this course.

Original Student Tutorials

Adding Polynomials using Algebra Tiles:

Learn to use algebra tiles to model adding polynomial expressions with this interactive tutorial.

Type: Original Student Tutorial

Accessible Version:

Learn how to use a numberline to add integers in this interactive tutorial.

Type: Original Student Tutorial

Factoring Polynomials with Greatest Common Factor:

Learn how to factor polynomials by finding their greatest common factor in this interactive tutorial.

Type: Original Student Tutorial

Identifying and Interpreting Parts of Quadratic Equations in Vertex Form:

Identify parts of quadratic equations in vertex form and interpret them in terms of the context they represent in this interactive tutorial.

Type: Original Student Tutorial

Quadratic Function Part 2: Launches:

Learn about different formats of quadratic equations and their graphs with experiments involving launching and shooting of balls in this interactive tutorial.

This is part 2 of a two-part series: Click HERE to open part 1.

Type: Original Student Tutorial

Quadratic Functions Part 1: Ball Games:

Join us as we watch ball games and explore how the height of a ball bounce over time is represented by quadratic functions, which provides opportunities to interpret key features of the function in this interactive tutorial.

This is part 1 of a two-part series: Click HERE to open part 2.

Type: Original Student Tutorial

Objects in the Solar System: Interactive Science Research Page:

Explore and compare objects in the solar system, including planets, moons, the Sun, comets, and asteroids, with this interactive research page.

Type: Original Student Tutorial

Pnyx Hill: Government in the Open Air:

Explore how weathering and erosion may have affected Pnyx Hill, the ancient Greek democratic meeting place which influenced our modern government with this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Fractions:

Evaluate numerical expressions with fractions using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Decimals:

Evaluate numerical expressions with decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

How Text Sections Convey an Author’s Purpose:

Explore excerpts from the extraordinary autobiography Narrative of the Life of Frederick Douglass, as you examine the author's purpose for writing and his use of the problem and solution text structure. By the end of this interactive tutorial, you should be able to explain how Douglass uses the problem and solution text structure in these excerpts to convey his purpose for writing.

Type: Original Student Tutorial

Order of Operations with Whole Numbers: Part 2:

Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.

This is part 2 of a series on evaluating expressions with whole numbers.

Type: Original Student Tutorial

Order of Operations with Integers:

Evaluate numerical expressions with integers using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Identifying Rhetorical Appeals in "Eulogy of the Dog" (Part Two):

Continue to study George Vest's "Eulogy of the Dog" speech and his use of rhetorical appeals. In Part Two of this two-part series, you'll identify his use of ethos and pathos throughout his speech.

Make sure to complete Part One before beginning Part Two. Click HERE to launch Part One.

Type: Original Student Tutorial

Identifying Rhetorical Appeals in "Eulogy of the Dog" (Part One):

Read George Vest's "Eulogy of the Dog" speech in this two-part interactive tutorial. In this series, you'll identify and examine Vest's use of ethos, pathos, and logos in his speech. In Part One, you'll identify Vest's use of logos in the first part of his speech. In Part Two, you'll identify his use of ethos and pathos throughout his speech. 

Make sure to complete both part of this series! Click HERE to launch Part Two.

Type: Original Student Tutorial

Square Root Part 3: Simplifying Radicals:

Learn how to simplify radicals in this interactive tutorial.

Type: Original Student Tutorial

Square Root Part 2: Non-Perfect Squares:

Learn what non-perfect squares are and find the decimal approximation of their square roots in this interactive tutorial.

Type: Original Student Tutorial

Multistep Factoring: Quadratics:

Learn how to use multistep factoring to factor quadratics in this interactive tutorial.

This is part 5 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

That's So Epic: How Epic Similes Contribute to Mood (Part Two):

Continue to study epic similes in excerpts from The Iliad in Part Two of this two-part series. In Part Two, you'll learn about mood and how the language of an epic simile produces a specified mood in excerpts from The Iliad.

Make sure to complete Part One before beginning Part Two. Click HERE to view "That's So Epic: How Epic Similes Contribute to Mood (Part One)."

Type: Original Student Tutorial

That's So Epic: How Epic Similes Contribute to Mood (Part One):

Learn about how epic similes create mood in a text, specifically in excerpts from The Iliad, in this two-part series.

In Part One, you'll define epic simile, identify epic similes based on defined characteristics, and explain the comparison created in an epic simile.

In Part Two, you'll learn about mood and how the language of an epic simile produces a specified mood in excerpts from The Iliad. Make sure to complete both parts!

Click HERE to view "That's So Epic: How Epic Similes Contribute to Mood (Part Two)." 

Type: Original Student Tutorial

Risky Betting: Text Evidence and Inferences (Part Two):

Type: Original Student Tutorial

Risky Betting: Text Evidence and Inferences (Part One):

Read the famous short story “The Bet” by Anton Chekhov and explore the impact of a fifteen-year bet made between a lawyer and a banker in this three-part tutorial series.

In Part One, you’ll cite textual evidence that supports an analysis of what the text states explicitly, or directly, and make inferences and support them with textual evidence. By the end of Part One, you should be able to make three inferences about how the bet has transformed the lawyer by the middle of the story and support your inferences with textual evidence.

Make sure to complete all three parts!

Click HERE to launch "Risky Betting: Text Evidence and Inferences (Part Two)."

Click HERE to launch "Risky Betting: Analyzing a Universal Theme (Part Three)." 

Type: Original Student Tutorial

Analyzing Sound in Poe's "The Raven" :

Identify rhyme, alliteration, and repetition in Edgar Allan Poe's "The Raven" and analyze how he used these sound devices to affect the poem in this interactive tutorial.

Type: Original Student Tutorial

In the Driver's Seat: Character Interactions in Little Women:

Study excerpts from the classic American novel Little Women by Louisa May Alcott in this interactive English Language Arts tutorial. Using excerpts from chapter eight of Little Women, you'll identify key characters and their actions. You'll also explain how interactions between characters contributes to the development of the plot. 

Type: Original Student Tutorial

Factoring Polynomials when "a" Does Not Equal 1, Snowflake Method:

Learn to factor quadratic trinomials when the coefficient a does not equal 1 by using the Snowflake Method in this interactive tutorial.

This is part 4 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

What it Means to Give a Gift: How Allusions Contribute to Meaning in "The Gift of the Magi":

Examine how allusions contribute to meaning in excerpts from O. Henry's classic American short story “The Gift of the Magi." In this interactive tutorial, you'll determine how allusions in the text better develop the key story elements of setting, characters, and conflict and explain how the allusion to the Magi contributes to the story’s main message about what it means to give a gift.

Type: Original Student Tutorial

Analyzing Imagery in Shakespeare’s "Sonnet 18":

Type: Original Student Tutorial

Solving Systems of Linear Equations Part 6: Writing Systems from Context:

Learn how to create systems of linear equations to represent contextual situations in this interactive tutorial.

This part 6 in a 7-part series. Click below to explore the other tutorials in the series. 

Type: Original Student Tutorial

Comparing Universal Themes in Shakespeare’s "Sonnet 18":

Study William Shakespeare's "Sonnet 18" to determine and compare two universal themes and how they are developed throughout the sonnet. 

Type: Original Student Tutorial

How Form Contributes to Meaning in Shakespeare’s "Sonnet 18":

Explore the form and meaning of William Shakespeare's “Sonnet 18.”  In this interactive tutorial, you’ll examine how specific words and phrases contribute to meaning in the sonnet, select the features of a Shakespearean sonnet in the poem, identify the solution to a problem, and explain how the form of a Shakespearean sonnet contributes to the meaning of "Sonnet 18."

Type: Original Student Tutorial

Solving Systems of Linear Equations Part 5: Connecting Algebraic Methods to Graphing:

Learn to solve systems of linear equations by connecting algebraic and graphing methods in this interactive tutorial.

This part 5 in a 7-part series. Click below to explore the other tutorials in the series. 

Type: Original Student Tutorial

Analyzing Universal Themes in "The Gift of the Magi":

Analyze how O. Henry uses details to address the topics of value, sacrifice, and love in his famous short story, "The Gift of the Magi." In this interactive tutorial, you'll also determine two universal themes of the story.

Type: Original Student Tutorial

How Story Elements Interact in “The Gift of the Magi" – Part Two:

Explore key story elements in more excerpts from the classic American short story “The Gift of the Magi” by O. Henry.

In Part Two of this two-part series, you'll analyze how important information about two main characters is revealed through the context of the story’s setting and events in the plot. By the end of this tutorial, you should be able to explain how character development, setting, and plot interact in "The Gift of the Magi."

Make sure to complete Part One before beginning Part Two. Click HERE to launch Part One. 

Type: Original Student Tutorial

How Story Elements Interact in “The Gift of the Magi" -- Part One:

Explore key story elements in the classic American short story “The Gift of the Magi” by O. Henry. Throughout this two-part tutorial, you'll analyze how important information about two main characters is revealed through the context of the story’s setting and events in the plot. By the end of this tutorial series, you should be able to explain how character development, setting, and plot interact in excerpts from this short story.

Make sure to complete both parts! Click HERE to view "How Story Elements Interact in 'The Gift of the Magi' -- Part Two."

Type: Original Student Tutorial

Factoring Quadratics When the Coefficient a Does Not Equal 1: The Box Method:

Learn how to factor quadratic polynomials when the leading coefficient (a) is not 1 by using the box method in this interactive tutorial.

This is part 3 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

The Diamond Game: Factoring Quadratics when a = 1:

Learn how to factor quadratics when the coefficient a = 1 using the diamond method in this game show-themed, interactive tutorial.

This is part 1 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Solving Systems of Linear Equations Part 4: Advanced Elimination:

Learn to solve systems of linear equations using advanced elimination in this interactive tutorial.

This part 4 in a 7-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Solving Systems of Linear Equations Part 3: Basic Elimination:

Learn to solve systems of linear equations using basic elimination in this interactive tutorial.

This part 3 in a 7-part series. Click below to explore the other tutorials in the series.

Part 1: Solving Systems of Linear Equations Part 1: Using Graphs

Part 2: Solving Systems of Linear Equations Part 2: Substitution

Part 4: Solving Systems of Linear Equations Part 4: Advanced Elimination (Coming soon)
Part 5: Solving Systems of Linear Equations Part 5: Connecting Algebraic Methods to Graphing (Coming soon)
Part 6: Solving Systems of Linear Equations Part 6: Writing Systems from Context (Coming soon)
Part 7: Solving Systems of Linear Equations Part 7: Word Problems (Coming soon)

Type: Original Student Tutorial

Highs and Lows Part 2: Completing the Square:

Learn the process of completing the square of a quadratic function to find the maximum or minimum to discover how high a dolphin jumped in this interactive tutorial.

This is part 2 of a 2 part series. Click HERE to open part 1.

Type: Original Student Tutorial

Highs and Lows Part 1: Completing the Square:

Learn the process of completing the square of a quadratic function to find the maximum or minimum to discover how high a dolphin jumped in this interactive tutorial.

This is part 1 of a 2 part series. Click HERE to open Part 2.

Type: Original Student Tutorial

Action ‘Figures’ Unite! - Part 8:

Apply your understanding of the defining attributes of all 2-dimensional figures covered in this series to classify their relationships using Euler and Venn Diagrams.

This part 8 in a 8-part series. Click below to explore the other tutorials in the series.

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

Part 4: Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams

Part 5: Quadrilaterals

Part 6: Trapezoids

Part 7: More Quadrilaterals

Type: Original Student Tutorial

Identifying Parts of Linear Expressions:

Learn to identify and interpret parts of linear expressions in terms of mathematical or real-world contexts in this original tutorial.

Type: Original Student Tutorial

Movies Part 2: What’s the Spread?:

Follow Jake along as he relates box plots with other plots and identifies possible outliers in real-world data from surveys of moviegoers' ages in part 2 in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Archetypes – Part Two: Examining Archetypes in The Princess and the Goblin:

Read more from the fantasy novel The Princess and the Goblin by George MacDonald in Part Two of this three-part series. By the end of this tutorial, you should be able to compare and contrast the archetypes of two characters in the novel.

Make sure to complete all three parts of this series in order to compare and contrast the use of archetypes in two texts.

Click HERE to view "Archetypes -- Part One: Examining an Archetype in The Princess and the Goblin."

Click HERE to view "Archetypes -- Part Three: Comparing and Contrasting Archetypes in Two Fantasy Stories." 

Type: Original Student Tutorial

Archetypes – Part One: Examining an Archetype in The Princess and the Goblin:

Learn to determine the important traits of a main character named Princess Irene in excerpts from the fantasy novel The Princess and the Goblin by George MacDonald. In this interactive tutorial, you’ll also identify her archetype and explain how textual details about her character support her archetype.  

Make sure to complete all three parts of this series in order to compare and contrast the use of archetypes in two texts.

Click HERE to view "Archetypes -- Part Two: Examining Archetypes in The Princess and the Goblin."

Click HERE to view "Archetypes -- Part Three: Comparing and Contrasting Archetypes in Two Fantasy Stories." 

Type: Original Student Tutorial

Solving Systems of Linear Equations Part 2: Substitution:

Learn to solve systems of linear equations using substitution in this interactive tutorial.

This part 2 in a 7-part series. Click below to explore the other tutorials in the series.

Part 1: Solving Systems of Linear Equations Part 1: Using Graphs

Part 3: Solving Systems of Linear Equations Part 3: Basic Elimination (Coming soon)

Part 4: Solving Systems of Linear Equations Part 4: Advanced Elimination (Coming soon)

Part 5: Solving Systems of Linear Equations Part 5: Connecting Algebraic Methods to Graphing (Coming soon)

Part 6: Solving Systems of Linear Equations Part 6: Writing Systems from Context (Coming soon)

Part 7: Solving Systems of Linear Equations Part 7: Word Problems (Coming soon)

Type: Original Student Tutorial

More Quadrilaterals - Part 7:

By the end of this tutorial you should be able to identify examples of quadrilaterals and their defining attributes to classify them using diagrams. We will focus on kites and other quadrilaterals in this tutorial.

This part 7 in a 7-part series. Click below to explore the other tutorials in the series.

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

Part 4: Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams

Part 5: Quadrilaterals

Type: Original Student Tutorial

Movies Part 1: What's the Spread?:

Follow Jake as he displays real-world data by creating box plots showing the 5 number summary and compares the spread of the data from surveys of the ages of moviegoers in part 1 of this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

The Power to Cure or Impair: The Importance of Setting in "The Yellow Wallpaper" -- Part One:

Learn to identify aspects of setting and character as you analyze several excerpts from “The Yellow Wallpaper," a chilling short story by Charlotte Perkins Gilman that explores the impact on its narrator of being confined to mostly one room. You'll also determine how the narrator’s descriptions of the story’s setting better reveal her emotional and mental state.

This interactive tutorial is Part One in a two-part series. By the end of Part Two, you should be able to explain how the narrator changes through her interaction with the setting. Click below to launch Part Two.

The Power to Cure or Impair: The Importance of Setting in 'The Yellow Wallpaper' -- Part Two 

Type: Original Student Tutorial

Trapezoids Part 6:

Explore the defining attributes of trapezoids--a special type of quadrilateral--and classify them using diagrams in this interactive tutorial. You'll also learn how two different definitions for a trapezoid can change affect classifications of quadrilaterals. 

This part 6 in a 6-part series. Click below to explore the other tutorials in the series. 

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

Part 4: Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams

Part 5: Quadrilaterals

Type: Original Student Tutorial

The Power to Cure or Impair: The Importance of Setting in "The Yellow Wallpaper" -- Part Two:

Continue to examine several excerpts from the chilling short story “The Yellow Wallpaper” by Charlotte Perkins Gilman, which explores the impact on its narrator of being confined to mostly one room. In Part Two of this tutorial series, you'll determine how the narrator’s descriptions of the story’s setting reveal its impact on her emotional and mental state. By the end of this tutorial, you should be able to explain how the narrator changes through her interaction with the setting.

Make sure to complete Part One before beginning Part Two. Click HERE to launch "The Power to Cure or Impair: The Importance of Setting in 'The Yellow Wallpaper' -- Part One." 

Type: Original Student Tutorial

Exponential Functions Part 3: Decay:

Learn about exponential decay as you calculate the value of used cars by examining equations, graphs, and tables in this interactive tutorial.

Type: Original Student Tutorial

Quadrilaterals - Part 5:

Learn how to classify quadrilaterals--including parallelograms, rectangles, rhombi, and squares--based on their defining attributes using diagrams in this interactive tutorial.

This is part 5 in a 6-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

The Mystery of the Past: How the Form of a Villanelle Contributes to Meaning in "The House on the Hill":

Explore the mysterious poem “The House on the Hill” by Edwin Arlington Robinson in this interactive tutorial. As you explore the poem's message about the past, you’ll identify the features of a villanelle in the poem. By the end of this tutorial, you should be able to explain how the form of a villanelle contributes to the poem's meaning.

Type: Original Student Tutorial

Solving Systems of Linear Equations Part 1: Using Graphs:

Learn how to solve systems of linear equations graphically in this interactive tutorial.

Type: Original Student Tutorial

Linear Functions: Jobs:

Learn how to interpret key features of linear functions and translate between representations of linear functions through exploring jobs for teenagers in this interactive tutorial. 

Type: Original Student Tutorial

Exponential Functions Part 2: Growth:

Learn about exponential growth in the context of interest earned as money is put in a savings account by examining equations, graphs, and tables in this interactive tutorial.

Type: Original Student Tutorial

Exponential Functions Part 1:

Learn about exponential functions and how they are different from linear functions by examining real world situations, their graphs and their tables in this interactive tutorial.

Type: Original Student Tutorial

A Giant of Size and Power – Part Two: How the Form of a Sonnet Contributes to Meaning in "The New Colossus":

Continue to explore the significance of the famous poem “The New Colossus” by Emma Lazarus, lines from which are engraved on the pedestal of the Statue of Liberty. 

In Part Two of this two-part series, you’ll identify the features of a sonnet in the poem "The New Colossus." By the end of this tutorial, you should be able to explain how the form of a sonnet contributes to the poem's meaning. 

Make sure to complete Part One before beginning Part Two.

Click HERE to launch "A Giant of Size and Power -- Part One: Exploring the Significance of 'The New Colossus.'"

Type: Original Student Tutorial

Analyzing the Beginning of The Red Umbrella – Part Two: How Setting Influences Characters:

Continue to examine how setting influences characters in excerpts from The Red Umbrella by Christina Diaz Gonzalez with this interactive tutorial.

This is part 2 in a two-part series. Make sure to complete Part One first. Click HERE to launch "Analyzing the Beginning of The Red Umbrella -- Part One: How Setting Influences Events." 

Type: Original Student Tutorial

A Giant of Size and Power -- Part One: Exploring the Significance of "The New Colossus":

In Part One, explore the significance of the famous poem “The New Colossus” by Emma Lazarus, lines from which are engraved on the pedestal of the Statue of Liberty. 

This famous poem also happens to be in the form of a sonnet. In Part Two of this two-part series, you’ll identify the features of a sonnet in the poem. By the end of this tutorial series, you should be able to explain how the form of a sonnet contributes to the poem's meaning. Make sure to complete both parts!

Click HERE to launch "A Giant of Size and Power -- Part Two: How the Form of a Sonnet Contributes to Meaning in 'The New Colossus.'"

Type: Original Student Tutorial

Analyzing the Beginning of The Red Umbrella – Part One: How Setting Influences Events:

Explore excerpts from the beginning of the historical fiction novel The Red Umbrella by Christina Diaz Gonzalez in this two-part series. In Part One, you'll examine how setting influences events. In Part Two, you'll examine how setting influences characters.

Make sure to complete both parts! Click HERE to launch Part Two.

Type: Original Student Tutorial

Functions, Functions, Everywhere: Part 2:

Continue exploring how to determine if a relation is a function using graphs and story situations in this interactive tutorial. 

This is the second tutorial in a 2-part series. Click HERE to open Part 1.

Type: Original Student Tutorial

Travel with Functions:

Learn how to evaluate and interpret function notation by following Melissa and Jose on their travels in this interactive tutorial.

Type: Original Student Tutorial

Solving Rational Equations: Using Common Denominators:

Learn how to solve rational functions by getting common denominators in this interactive tutorial.

Type: Original Student Tutorial

Physical Science Unit: Water Beach Vacation Lesson 17 Video:

This SaM-1 video provides the students with the optional "twist" for Lesson 17 and the Model Eliciting Activity (MEA) they have been working on in the Grade 3 Physical Science Unit: Water Beach Vacation. 

 

To see all the lessons in the unit please visit https://www.cpalms.org/page818.aspx.

Type: Original Student Tutorial

Physical Science Unit: Water Beach Vacation Lesson 14 Video:

This video introduces the students to a Model Eliciting Activity (MEA) and concepts related to conducting experiments so they can apply what they learned about the changes water undergoes when it changes state.  This MEA provides students with an opportunity to develop a procedure based on evidence for selecting the most effective cooler.

This SaM-1 video is to be used with lesson 14 in the Grade 3 Physical Science Unit: Water Beach Vacation. To see all the lessons in the unit please visit https://www.cpalms.org/page818.aspx.

Type: Original Student Tutorial

Dilations...The Effect of k on a Graph:

Visualize the effect of using a value of k in both kf(x) or f(kx) when k is greater than zero in this interactive tutorial.

Type: Original Student Tutorial

Math Models and Social Distancing:

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Type: Original Student Tutorial

Solving Rational Equations: Cross Multiplying:

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Type: Original Student Tutorial

Solving Inequalities and Graphing Solutions Part 2:

Learn how to solve and graph compound inequalities and determine if solutions are viable in part 2 of this interactive tutorial series.

Click HERE to open Part 1.

Type: Original Student Tutorial

Writing Equations in Two Variables:

Learn how to write equations in two variables in this interactive tutorial. 

Type: Original Student Tutorial

Solving Inequalities and Graphing Solutions: Part 1:

Learn how to solve and graph one variable inequalities, including compound inequalities, in part 1 of this interactive tutorial series.

Click HERE to open Part 2.

Type: Original Student Tutorial

Reflections...The Effect of k on a Graph:

Learn how reflections of a function are created and tied to the value of k in the mapping of f(x) to -1f(x) in this interactive tutorial.

Type: Original Student Tutorial

Translations...The Effect of k on the Graph:

Explore translations of functions on a graph that are caused by k in this interactive tutorial. GeoGebra and interactive practice items are used to investigate linear, quadratic, and exponential functions and their graphs, and the effect of a translation on a table of values.

Type: Original Student Tutorial

Volume of Spherical Bubble Tea:

Learn how to calculate the volume of spheres while learning how they make Bubble Tea in this interactive tutorial.

Type: Original Student Tutorial

Angle UP: Player 1:

Explore the construction processes for constructing an angle bisector, copying an angle and constructing a line parallel to a given line through a point not on the line using a variety of tools in this interactive, retro video game-themed tutorial.

NOTE: This tutorial uses both the angle bisector construction and the construction to copy an angle as an extension opportunity to also construct a line parallel to a given line through a point not on the line. Students also learn to identify corresponding angles created when a transversal crosses parallel lines, and discover using Geogebra that these angles are congruent.

Type: Original Student Tutorial

Exploring Relationships with Venn & Euler Diagrams – Part 2:

Learn how to show relationships represented in Venn & Euler Diagrams as you complete this interactive geometry tutorial.

This is part two of four. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Reading into Words with Multiple Meanings:

Explore Robert Frost's poem "Mending Wall" and examine words, phrases, and lines with multiple meanings. In this interactive tutorial, you'll analyze how these multiple meanings can affect a reader’s interpretation of the poem.

Type: Original Student Tutorial

Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams – Part 4:

Learn how triangles can be sorted and classified using side lengths and angle measures in this interactive tutorial.

This is the final tutorial in a four-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Pennant Company Challenge: Inscribed Circles of Triangles:

Discover how easy it is for Katie to construct an inscribed circular logo on her company's triangular pennant template. If she completes the task first, she will win a $1000 bonus! Follow along with this interactive tutorial.

Type: Original Student Tutorial

Classifying Triangles by Angles using Euler Diagrams – Part 3:

Learn to classify triangles and use Euler diagrams to show relationships, in this interactive tutorial.

This is part-three of four. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

From Myth to Short Story: Drawing on Source Material – Part Two:

Examine the topics of transformation and perfection as you read excerpts from the “Myth of Pygmalion” by Ovid and the short story “The Birthmark” by Nathaniel Hawthorne. By the end of this two-part interactive tutorial series, you should be able to explain how the short story draws on and transforms source material from the original myth. 

This tutorial is the second in a two-part series. Click HERE to launch Part One.

Type: Original Student Tutorial

From Myth to Short Story: Drawing on Source Material – Part One:

Examine the topics of transformation and perfection as you read excerpts from the “Myth of Pygmalion” by Ovid and the short story “The Birthmark” by Nathaniel Hawthorne. By the end of this two-part interactive tutorial series, you should be able to explain how the short story draws on and transforms source material from the original myth.  

This tutorial is the first in a two-part series. Click HERE to launch Part Two.

Type: Original Student Tutorial

"Figuring Out" 2D Figures - Part 1:

Explore 2D (two-dimensional) figures and see how every 2D figure possesses unique attributes in this interactive tutorial.

This is part one of four. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Meet Me Half Way:

Plan a paddle board expedition by learning how to do basic geometric constructions including copying a segment, constructing a segment bisector, constructing a segment's perpendicular bisector and constructing perpendicular segments using a variety of tools in this interactive tutorial.

Type: Original Student Tutorial

A Square Peg in a Round Hole:

Learn how to construct an inscribed square in a circle and why certain constructions are used in this interactive tutorial.

Type: Original Student Tutorial

The Nightmare of Pouring Polygons: Quadrilateral Classification:

Overcome the nightmare of quadrilateral classification based on the presence of parallel, perpendicular, and congruent sides as you complete this interactive tutorial. Learn about parallelogram, rectangles, rhombi and squares and how they are related.

Type: Original Student Tutorial

Where IS that Cell Tower?:

Find the location and coverage area of cell towers to determine the center and radius of a circle given its equation, using a strategy completing the square in this interactive tutorial. 

Type: Original Student Tutorial

Designing with Hexagons:

Learn how to construct an inscribed regular hexagon and equilateral triangle in a circle in this interactive tutorial.

Type: Original Student Tutorial

Good as New:

Learn the steps to circumscribe a circle around a triangle in this interactive tutorial about constructions. Grab a compass, straightedge, pencil and paper to follow along!

Type: Original Student Tutorial

Don't Plagiarize: Cite Your Sources!:

Learn more about that dreaded word--plagiarism--in this interactive tutorial that's all about citing your sources, creating a Works Cited page, and avoiding academic dishonesty!

Type: Original Student Tutorial

High Tech Seesaw:

Learn how to find the point on a directed line segment that partitions it into a given ratio in this interactive tutorial.

Type: Original Student Tutorial

Avoiding Plagiarism and Citing Sources:

Learn more about that dreaded word--plagiarism--in this interactive tutorial that's all about citing your sources and avoiding academic dishonesty!

Type: Original Student Tutorial

Analyzing Word Choice in Emerson's "Self-Reliance": Part 2:

Explore excerpts from Ralph Waldo Emerson's essay "Self-Reliance" in this two-part series. This tutorial is Part Two. In this tutorial, you will continue to examine excerpts from Emerson's essay that focus on the topic of traveling. You'll examine word meanings and determine the connotations of specific words. You will also analyze the impact of specific word choices on the meaning of this portion of the essay.

Make sure to complete Part One first. Click HERE to launch Part One.

Type: Original Student Tutorial

MacCoder’s Farm Part 1: Declare Variables:

Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.

Type: Original Student Tutorial

Analyzing Word Choice in Emerson's "Self-Reliance": Part 1:

Explore excerpts from Ralph Waldo Emerson's essay "Self-Reliance" in this two-part interactive tutorial series. You will examine word meanings, examine subtle differences between words with similar meanings, and think about the emotions or associations that are connected to specific words. Finally, you will analyze the impact of specific word choices on the meaning of these excerpts.

Make sure to complete both parts! Click HERE to launch Part Two.

Type: Original Student Tutorial

Analyzing Figurative Meaning in Emerson's "Self-Reliance": Part 2:

Explore excerpts from Ralph Waldo Emerson's essay "Self-Reliance" in this interactive two-part tutorial. This tutorial is Part Two. In this two-part series, you will learn to enhance your experience of Emerson's essay by analyzing his use of the word "genius." You will analyze Emerson's figurative meaning of "genius" and how he develops and refines the meaning of this word over the course of the essay.

Make sure to complete Part One before beginning Part Two. Click HERE to view Part One.

Type: Original Student Tutorial

Analyzing Figurative Meaning in Emerson's "Self-Reliance": Part 1:

Explore excerpts from Ralph Waldo Emerson's essay "Self-Reliance" in this interactive two-part tutorial. In Part One, you’ll learn to enhance your experience of a text by analyzing its use of a word’s figurative meaning. Specifically, you'll examine Emerson's figurative meaning of the key term "genius." In Part Two, you’ll learn how to track the development of a word’s figurative meaning over the course of a text. 

Make sure to complete both parts of the tutorial! Click HERE to launch Part Two.

Type: Original Student Tutorial

Circle Up!:

Learn how to write the equation of a circle using Pythagorean Theorem given its center and radius using step-by-step instructions in this interactive tutorial.

Type: Original Student Tutorial

Finding the Zeros of Quadratic Functions:

Learn to find the zeros of a quadratic function and interpret their meaning in real-world contexts with this interactive tutorial.

Type: Original Student Tutorial

Introduction to Polynomials, Part 2 - Adding and Subtracting:

Learn how to add and subtract polynomials in this online tutorial. You will learn how to combine like terms and then use the distribute property to subtract polynomials.

This is part 2 of a two-part lesson. Click below to open part 1.

Type: Original Student Tutorial

Introduction to Polynomials: Part 1:

Learn how to identify monomials and polynomials and determine their degree in this interactive tutorial.

This is part 1 in a two-part series. Click here to open Part 2.

Type: Original Student Tutorial

Analyzing Word Choices in Poe's "The Raven" -- Part Two:

Practice analyzing word choices in "The Raven" by Edgar Allan Poe, including word meanings, subtle differences between words with similar meanings, and emotions connected to specific words. In this interactive tutorial, you will also analyze the impact of specific word choices on the meaning of the poem.

This is Part Two of a two-part series. Part One should be completed before beginning Part Two. Click HERE to open Part One.

Type: Original Student Tutorial

Analyzing Word Choices in Poe's "The Raven" -- Part One:

Practice analyzing word choices in "The Raven" by Edgar Allan Poe in this interactive tutorial. In this tutorial, you will examine word meanings, examine subtle differences between words with similar meanings, and think about emotions connected to specific words. You will also analyze the impact of specific word choices on the meaning of the poem.

This tutorial is Part One of a two-part series on Poe's "The Raven." Click HERE to open Part Two.

Type: Original Student Tutorial

A Poem in 2 Voices: Jekyll and Hyde:

Learn how to create a Poem in 2 Voices in this interactive tutorial. This tutorial is Part Three of a three-part series. In this tutorial, you will learn how to create a Poem in 2 Voices using evidence drawn from a literary text: The Strange Case of Dr. Jekyll and Mr. Hyde by Robert Louis Stevenson.

You should complete Part One and Part Two of this series before beginning Part Three.   

Click HERE to launch Part One. Click HERE to launch Part Two. 

Type: Original Student Tutorial

The Voices of Jekyll and Hyde, Part Two:

Get ready to travel back in time to London, England during the Victorian era in this interactive tutorial that uses text excerpts from The Strange Case of Dr. Jekyll and Mr. Hyde. This tutorial is Part Two of a three-part series. You should complete Part One before beginning this tutorial. In Part Two, you will read excerpts from the last half of the story and practice citing evidence to support analysis of a literary text. In the third tutorial in this series, you’ll learn how to create a Poem in 2 Voices using evidence from this story. 

Make sure to complete all three parts! Click to HERE launch Part One. Click HERE to launch Part Three. 

Type: Original Student Tutorial

Its all about Mood: Bradbury's "Zero Hour":

Learn how authors create mood in a story through this interactive tutorial. You'll read a science fiction short story by author Ray Bradbury and analyze how he uses images, sound, dialogue, setting, and characters' actions to create different moods. This tutorial is Part One in a two-part series. In Part Two, you'll use Bradbury's story to help you create a Found Poem that conveys multiple moods.

When you've completed Part One, click HERE to launch Part Two.

Type: Original Student Tutorial

Expository Writing: Eyes in the Sky (Part 4 of 4):

Practice writing different aspects of an expository essay about scientists using drones to research glaciers in Peru. This interactive tutorial is part four of a four-part series. In this final tutorial, you will learn about the elements of a body paragraph. You will also create a body paragraph with supporting evidence. Finally, you will learn about the elements of a conclusion and practice creating a “gift.” 

This tutorial is part four of a four-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

The Voices of Jekyll and Hyde, Part One:

Practice citing evidence to support analysis of a literary text as you read excerpts from one of the most famous works of horror fiction of all time, The Strange Case of Dr. Jekyll and Mr. Hyde. 

This tutorial is Part One of a three-part tutorial. In Part Two, you'll continue your analysis of the text. In Part Three, you'll learn how to create a Poem in 2 Voices using evidence from this story. Make sure to complete all three parts! 

Click HERE to launch Part Two. Click HERE to launch Part Three. 

Type: Original Student Tutorial

Expository Writing: Eyes in the Sky (Part 3 of 4):

Learn how to write an introduction for an expository essay in this interactive tutorial. This tutorial is the third part of a four-part series. In previous tutorials in this series, students analyzed an informational text and video about scientists using drones to explore glaciers in Peru. Students also determined the central idea and important details of the text and wrote an effective summary. In part three, you'll learn how to write an introduction for an expository essay about the scientists' research. 

This tutorial is part three of a four-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Drones and Glaciers: Eyes in the Sky (Part 2 of 4):

Learn how to identify the central idea and important details of a text, as well as how to write an effective summary in this interactive tutorial. This tutorial is the second tutorial in a four-part series that examines how scientists are using drones to explore glaciers in Peru. 

This tutorial is part two of a four-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Drones and Glaciers: Eyes in the Sky (Part 1 of 4):

Learn about how researchers are using drones, also called unmanned aerial vehicles or UAVs, to study glaciers in Peru. In this interactive tutorial, you will practice citing text evidence when answering questions about a text.

This tutorial is part one of a four-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Avoiding Plagiarism: It's Not Magic:

Learn how to avoid plagiarism in this interactive tutorial. You will also learn how to follow a standard format for citation and how to format your research paper using MLA style. Along the way, you will also learn about master magician Harry Houdini. This tutorial is Part Two of a two-part series on research writing.

Be sure to complete Part One first. Click to view Part One.

Type: Original Student Tutorial

Research Writing: It's Not Magic:

Learn about paraphrasing and the use of direct quotes in this interactive tutorial about research writing. Along the way, you'll also learn about master magician Harry Houdini. This tutorial is part one of a two-part series, so be sure to complete both parts.

Check out part two—Avoiding Plaigiarism: It's Not Magic here.

Type: Original Student Tutorial

It's all about Mood: Creating a Found Poem:

Learn how to create a Found Poem with changing moods in this interactive tutorial. This tutorial is Part Two of a two-part series. In Part One, students read “Zero Hour,” a science fiction short story by author Ray Bradbury and examined how he used various literary devices to create changing moods. In Part Two, students will use words and phrases from “Zero Hour” to create a Found Poem with two of the same moods from Bradbury's story.

Click HERE to launch Part One.

Type: Original Student Tutorial

Happy Halloween! Textual Evidence and Inferences:

Cite text evidence and make inferences about the "real" history of Halloween in this spooky interactive tutorial. 

Type: Original Student Tutorial

Long Division With Polynomials:

Use long division to rewrite a rational expression of the form a(x) divided by b(x) in the form q(x) plus the quantity r(x) divided by b(x), where a(x), b(x), q(x), and r(x) are polynomials with this interactive tutorial.

Type: Original Student Tutorial

Plagiarism: What Is It? How Can I Avoid It?:

Learn more about that dreaded word--plagiarism--in this interactive tutorial that's all about citing your sources and avoiding academic dishonesty!

Type: Original Student Tutorial

Cyberwar! Citing Evidence and Making Inferences:

Learn how to cite evidence and draw inferences in this interactive tutorial. Using an informational text about cyber attacks, you'll practice identifying text evidence and making inferences based on the text.

Type: Original Student Tutorial

Go For the Gold: Writing Claims & Using Evidence:

Learn how to define and identify claims being made within a text. This tutorial will also show you how evidence can be used effectively to support the claim being made. Lastly, this tutorial will help you write strong, convincing claims of your own.

Type: Original Student Tutorial

Westward Bound: Exploring Evidence and Inferences:

Learn to identify explicit textual evidence and make inferences based on the text. In this interactive tutorial, you'll sharpen your analysis skills while reading about the famed American explorers, Lewis and Clark, and their trusted companion, Sacagawea. You'll practice analyzing the explicit textual evidence wihtin the text, and you'll also make your own inferences based on the available evidence. 

Type: Original Student Tutorial

Predicting Outcomes at the Carnival:

Learn how to use probability to predict expected outcomes at the Carnival in this interactive tutorial.

Type: Original Student Tutorial

It Can Be a Zoo of Data!:

Discover how to calculate and interpret the mean, median, mode and range of data sets from the zoo in this interactive tutorial.

Type: Original Student Tutorial

Home Transformations:

Learn to describe a sequence of transformations that will produce similar figures. This interactive tutorial will allow you to practice with rotations, translations, reflections, and dilations.

Type: Original Student Tutorial

The Mystery of Muscle Cell Metabolism:

Explore the mystery of muscle cell metabolism and how cells are able to meet the need for a constant supply of energy. In this interactive tutorial, you'll identify the basic structure of adenosine triphosphate (ATP), explain how ATP’s structure is related it its job in the cell, and connect this role to energy transfers in living things.

Type: Original Student Tutorial

Data and Frequencies:

Learn to define, calculate, and interpret marginal frequencies, joint frequencies, and conditional frequencies in the context of the data with this interactive tutorial.

Type: Original Student Tutorial

Finding the Maximum or Minimum of a Quadratic Function:

Learn to complete the square of a quadratic expression and identify the maximum or minimum value of the quadratic function it defines. In this interactive tutorial, you'll also interpret the meaning of the maximum and minimum of a quadratic function in a real world context.

Type: Original Student Tutorial

Wild Words: Analyzing the Extended Metaphor in "The Stolen Child":

Learn to identify and analyze extended metaphors using W.B. Yeats' poem, "The Stolen Child." In this interactive tutorial, we'll examine how Yeats uses figurative language to express the extended metaphor throughout this poem. We'll focus on his use of these seven types of imagery: visual, auditory, gustatory, olfactory, tactile, kinesthetic, and organic. Finally, we'll analyze how the poem's extended metaphor conveys a deeper meaning within the text.

Type: Original Student Tutorial

Graphing Linear Inequalities:

Learn to graph linear inequalities in two variables to display their solutions as you complete this interactive tutorial.

Type: Original Student Tutorial

The Blueprints of Construction:

Learn to construct the perpendicular bisector of a line segment using a straightedge and compass with this interactive tutorial.

Type: Original Student Tutorial

Creating Exponential Functions:

Follow as we construct an exponential function from a graph, from a table of values, and from a description of a relationship in the real world in this interactive tutorial.

Type: Original Student Tutorial

Amazing Adventures:

Learn how to explain the meaning of additive inverse, identify the additive inverse of a given rational number, and justify your answer on a number line in this original tutorial.

Type: Original Student Tutorial

Ninja Nancy Slices:

Learn how to determine the shape of a cross-section created by the intersection of a slicing plane with a pyramid or prism in this ninja-themed, interactive tutorial.

Type: Original Student Tutorial

Around the World with Right Triangles:

Learn how to use trigonometric ratios to find the heights of famous monuments and solve a real-world application in this interactive tutorial.

Type: Original Student Tutorial

Set Sail: Analyzing the Central Idea:

Learn to identify and analyze the central idea of an informational text. In this interactive tutorial, you'll read several informational passages about the history of pirates. First, you'll learn the four-step process for pinpointing the central idea. Then you'll analyze each passage to see how the central idea is developed throughout the text.

Type: Original Student Tutorial

Changing Rates:

Learn how to calculate and interpret an average rate of change over a specific interval on a graph in this interactive tutorial.

Type: Original Student Tutorial

Proving Theorems About Triangles:

Use properties, postulates, and theorems to prove a theorem about a triangle. In this interactive tutorial, you'll also learn how to prove that a line parallel to one side of a triangle divides the other two proportionally.

Type: Original Student Tutorial

Finding Solutions on a Graph:

Learn to determine the number of possible solutions for a linear equation with this interactive tutorial.

Type: Original Student Tutorial

Solving an Equation Using a Graph:

Follow as we learn why the x-coordinate of the point of intersection of two functions is the solution of the equation f(x) = g(x) in this interactive tutorial.

Type: Original Student Tutorial

"The Last Leaf" – Making Inferences:

Learn how to make inferences based on the information included in the text in this interactive tutorial. Using the short story "The Last Leaf" by O. Henry, you'll practice identifying both the explicit and implicit information in the story. You'll apply your own reasoning to make inferences based on what is stated both explicitly and implicitly in the text. 

Type: Original Student Tutorial

"Beary" Good Details:

Join Baby Bear to answer questions about key details in his favorite stories with this interactive tutorial. Learn about characters, setting, and events as you answer who, where, and what questions.

Type: Original Student Tutorial

Golf: Where Negative Numbers are a Positive Thing:

Learn how to create and use number lines with positive and negative numbers, graph positive and negative numbers, find their distance from zero, find a number’s opposite using a number line and signs, and recognize that zero is its own opposite with this interactive, golf-themed tutorial.

Type: Original Student Tutorial

Graphing Quadratic Functions:

Follow as we discover key features of a quadratic equation written in vertex form in this interactive tutorial.

Type: Original Student Tutorial

I Scream! You Scream! We All Scream for... Volume!:

Learn to calculate the volume of a cone as you solve real-world problems in this ice cream-themed, interactive tutorial.

Type: Original Student Tutorial

Surviving Extreme Conditions:

In this tutorial, you will practice identifying relevant evidence within a text as you read excerpts from Jack London's short story "To Build a Fire." Then, you'll practice your writing skills as you draft a short response using examples of relevant evidence from the story.

Type: Original Student Tutorial

Exploring Texts:

Learn how to make inferences using the novel Hoot in this interactive tutorial. You'll learn how to identify both explicit and implicit information in the story to make inferences about characters and events.

Type: Original Student Tutorial

The Joy That Kills:

Learn how to make inferences when reading a fictional text using the textual evidence provided. In this tutorial, you'll read the short story "The Story of an Hour" by Kate Chopin. You'll practice identifying what is directly stated in the text and what requires the use of inference. You'll practice making your own inferences and supporting them with evidence from the text.

Type: Original Student Tutorial

Why Does a Negative Times a Negative Equal a Positive?:

Use mathematical properties to explain why a negative factor times a negative factor equals a positive product instead of just quoting a rule with this interactive tutorial.

Type: Original Student Tutorial

Writing Inequalities with Money, Money, Money:

Write linear inequalities for different money situations in this interactive tutorial.

Type: Original Student Tutorial

Factoring Polynomials Using Special Cases:

Learn how to factor quadratic polynomials that follow special cases, difference of squares and perfect square trinomials, in this interactive tutorial.

This is part 2 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Order of Operations with Whole Numbers:

Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Area of Triangles: Missing Dimensions:

Follow George as he calculates the missing values for the base and height of triangles in this interactive tutorial. 

Type: Original Student Tutorial

Analyzing an Author’s Use of Juxtaposition in Jane Eyre (Part Two):

In Part Two of this two-part series, you'll continue to explore excerpts from the Romantic novel Jane Eyre by Charlotte Brontë. In this tutorial, you'll examine the author's use of juxtaposition, which is a technique of putting two or more elements side by side to invite comparison or contrast. By the end of this tutorial, you should be able to explain how the author’s use of juxtaposition in excerpts from the first two chapters of Jane Eyre defines Jane’s perspective regarding her treatment in the Reed household.

Make sure to complete Part One before beginning Part Two. Click HERE to view Part One. 

Type: Original Student Tutorial

Risky Betting: Analyzing a Universal Theme (Part Three):

Dive deeper into the famous short story “The Bet” by Anton Chekhov and explore the impact of a fifteen-year bet made between a lawyer and a banker.

In Part Three, you’ll learn about universal themes and explain how a specific universal theme is developed throughout “The Bet.”

Make sure to complete the first two parts in the series before beginning Part three. Click HERE to view Part One. Click HERE to view Part Two.

Type: Original Student Tutorial

Educational Games

Arithmetic Workout:

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game. 

Type: Educational Game

Ice Ice Maybe: An Operations Estimation Game:


This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

Type: Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Educational Software / Tool

Arithmetic Quiz:

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Software / Tool

Lesson Plans

Holidays that Celebrate America:

In this lesson plan, students will explore the history and meaning behind various patriotic holidays and make personal connections with those holidays including, Constitution Day, Memorial Day, Veteran’s Day, Patriot Day, President’s Day, Independence Day, and Medal of Honor Day.

 

Type: Lesson Plan

Do Credit Cards Make You Gain Weight? What is Correlation, and How to Distinguish It from Causation:

This lesson introduces the students to the concepts of correlation and causation, and the difference between the two. The main learning objective is to encourage students to think critically about various possible explanations for a correlation, and to evaluate their plausibility, rather than passively taking presented information on faith. To give students the right tools for such analysis, the lesson covers most common reasons behind a correlation, and different possible types of causation.

Type: Lesson Plan

Interpret Population Data with Graphs and Tables:

Students will use the calculated population totals to create graphs that help to visualize the totals for analyzing and representation. Census data is used as the data to provide information to analyze. Students will then use basic functions and formulas in spreadsheets to help analyze and represent the data.

Type: Lesson Plan

Perspectives Video: Experts

Jumping Robots and Quadratics:

<p>Jump to it and learn more about how quadratic equations are&nbsp;used in robot navigation problem solving!</p>

Type: Perspectives Video: Expert

Mathematically Exploring the Wakulla Caves:

The tide is high! How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

MicroGravity Sensors & Statistics:

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Problem Solving with Project Constraints:

<p>It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!</p>

Type: Perspectives Video: Expert

Using Statistics to Estimate Lionfish Population Size:

<p>It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.</p>

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Base 16 Notation in Computing:

Listen in as a computing enthusiast describes how hexadecimal notation is used to express big numbers in just a little space.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Unit Conversions:

<p>Get fired up as you learn more about ceramic glaze recipes and mathematical units.</p>

Type: Perspectives Video: Professional/Enthusiast

Making Candy: Illuminating Exponential Growth:

<p>No need to sugar coat it: making candy involves math and muscles. Learn how light refraction and exponential growth help make candy colors just right!</p>

Type: Perspectives Video: Professional/Enthusiast

Making Candy: Uniform Scaling:

<p>Don't be a shrinking violet. Learn how uniform scaling is important for candy production.</p>

Type: Perspectives Video: Professional/Enthusiast

Building Scale Models to Solve an Archaeological Mystery:

<p>An archaeologist describes how mathematics can help prove a theory about mysterious prehistoric structures called shell rings.</p>

Type: Perspectives Video: Professional/Enthusiast

Using Geometry and Computers to make Art with CNC Machining:

<p>See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.</p>

Type: Perspectives Video: Professional/Enthusiast

Correlation and Causation in a Scientific Study:

Watching this video will cause your critical thinking skills to improve. You might also have a great day, but that's just correlation.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Estimating Oil Seep Production by Bubble Volume:

<p>You'll need to bring your computer skills and math knowledge to estimate oil volume and rate as it seeps from the ocean floor. Dive in!</p>

Type: Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

<p>Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.</p>

Type: Perspectives Video: Professional/Enthusiast

Quadratic Equations and Robots:

<p>Get in gear with robotics as this engineer explains how quadratic equations are used in programming robotic navigation.</p>

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Tasks

Quadrupling Leads to Halving:

Students explore the structure of the operation s/(vn). This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of n, then dividing the result of that operation into s.

Type: Problem-Solving Task

Tile Patterns I: octagons and squares:

Students use interior and exterior angles to to verify attributes of an octagon and square. Students are given a tile pattern involving congruent regular octagons and squares.

Type: Problem-Solving Task

Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

Type: Problem-Solving Task

Musical Preferences:

This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table.

Type: Problem-Solving Task

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

Type: Problem-Solving Task

Golf and Divorce:

This is a simple task addressing the distinction between correlation and causation. Students are given information indicating a correlation between two variables, and are asked to reason out whether or not a causation can be inferred.

Type: Problem-Solving Task

Texting and Grades II:

The purpose of this task is to assess ability to interpret the slope and intercept of the line of fit in context.

Type: Problem-Solving Task

Coffee and Crime:

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

Type: Problem-Solving Task

The Titanic 1:

This task asks students to calculate probabilities using information presented in a two-way frequency table.

Type: Problem-Solving Task

Random Walk III:

The task provides a context to calculate discrete probabilities and represent them on a bar graph.

Type: Problem-Solving Task

Bank Shot:

This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.

Type: Problem-Solving Task

Are They Similar?:

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other, using the definition of similarity in terms of similarity transformations.

Type: Problem-Solving Task

Extensions, Bisections and Dissections in a Rectangle:

This task involves a reasonably direct application of similar triangles, coupled with a moderately challenging procedure of constructing a diagram from a verbal description.

Type: Problem-Solving Task

Toilet Roll:

The purpose of this task is to engage students in geometric modeling, and in particular to deduce algebraic relationships between variables stemming from geometric constraints.

Type: Problem-Solving Task

The Titanic 3:

This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic using a table of data.

Type: Problem-Solving Task

Partitioning a Hexagon:

The purpose of this task is for students to find a way to decompose a regular hexagon into congruent figures. This is meant as an instructional task that gives students some practice working with transformations.

Type: Problem-Solving Task

Algae Blooms:

In this example, students are asked to write a function describing the population growth of algae. It is implied that this is exponential growth.

Type: Problem-Solving Task

Coins in a circular pattern:

Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin. (For this task, United States coins are used, but the task can be adapted for coins from other countries.)

Type: Problem-Solving Task

Finding the area of an equilateral triangle:

This problem solving task asks students to find the area of an equilateral triangle. Various solutions are presented that include the Pythagoren theorem and trigonometric functions.

Type: Problem-Solving Task

The Lighthouse Problem:

This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat.

Type: Problem-Solving Task

Solar Eclipse:

This problem solving task encourages students to explore why solar eclipses are rare by examining the radius of the sun and the furthest distance between the moon and the earth.

Type: Problem-Solving Task

A Midpoint Miracle:

This problem solving task gives students the opportunity to prove a fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.

Type: Problem-Solving Task

Mt. Whitney to Death Valley:

This task engages students in an open-ended modeling task that uses similarity of right triangles.

Type: Problem-Solving Task

Joining two midpoints of sides of a triangle:

Using a triangle with line through it, students are tasked to show the congruent angles, and conclude if one triangle is similar to the other.

Type: Problem-Solving Task

Ice Cream Cone:

In this task, students will provide a sketch of a paper ice cream cone wrapper, use the sketch to develop a formula for the surface area of the wrapper, and estimate the maximum number of wrappers that could be cut from a rectangular piece of paper.

Type: Problem-Solving Task

How thick is a soda can? (Variation II):

This problem solving task asks students to explain which measurements are needed to estimate the thickness of a soda can. Multiple solution processes are presented.

Type: Problem-Solving Task

How thick is a soda can? (Variation I):

This problem solving task challenges students to find the surface area of a soda can, calculate how many cubic centimeters of aluminum it contains, and estimate how thick it is.

Type: Problem-Solving Task

How many leaves on a tree? (Version 2):

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

Type: Problem-Solving Task

How many leaves on a tree?:

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

Type: Problem-Solving Task

How many cells are in the human body?:

This problem solving task challenges students to apply the concepts of mass, volume, and density in the real-world context to find how many cells are in the human body.

Type: Problem-Solving Task

Hexagonal pattern of beehives:

The goal of this task is to use geometry to study the structure of beehives.

Type: Problem-Solving Task

Global Positioning System II:

Reflective of the modernness of the technology involved, this is a challenging geometric modeling task in which students discover from scratch the geometric principles underlying the software used by GPS systems.

Type: Problem-Solving Task

Eratosthenes and the circumference of the earth:

This problem solving task gives an interesting context for implementing ideas from geometry and trigonometry.

Type: Problem-Solving Task

Archimedes and the King's Crown:

This problem solving task uses the tale of Archimedes and the King of Syracuse's crown to determine the volume and mass of gold and silver.

Type: Problem-Solving Task

Slopes and Circles:

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever angle AXB is a right angle.

Type: Problem-Solving Task

Unit Squares and Triangles:

This problem solving task asks students to find the area of a triangle by using unit squares and line segments.

Type: Problem-Solving Task

Triangles inscribed in a circle:

This problem solving task challenges students to use ideas about linear functions in order to determine when certain angles are right angles.

Type: Problem-Solving Task

Doctor's Appointment:

The purpose of the task is to analyze a plausible real-life scenario using a geometric model. The task requires knowledge of volume formulas for cylinders and cones, some geometric reasoning involving similar triangles, and pays attention to reasonable approximations and maintaining reasonable levels of accuracy throughout.

Type: Problem-Solving Task

Why Does ASA Work?:

This problem solving task ask students to show the reflection of one triangle maps to another triangle.

Type: Problem-Solving Task

When Does SSA Work to Determine Triangle Congruence?:

In this problem, we considered SSA. The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence.

Type: Problem-Solving Task

Seven Circles II:

This task provides a concrete geometric setting in which to study rigid transformations of the plane.

Type: Problem-Solving Task

Points equidistant from two points in the plane:

This task asks students to show how certain points on a plane are equidistant to points on a segment when placed on a perpendicular bisector.

Type: Problem-Solving Task

Midpoints of the Side of a Parallelogram:

This is a reasonably direct task aimed at having students use previously-derived results to learn new facts about parallelograms, as opposed to deriving them from first principles.

Type: Problem-Solving Task

Inscribing a square in a circle:

This task provides an opportunity for students to apply triangle congruence theorems in an explicit, interesting context.

Type: Problem-Solving Task

Inscribing a hexagon in a circle:

This problem solving task challenges students to inscribe equilateral triangles and regular hexagons on a circle with a compass and straightedge.

Type: Problem-Solving Task

Construction of perpendicular bisector:

This problem solving task challenges students to construct a perpendicular bisector of a given segment.

Type: Problem-Solving Task

Why Does SAS Work?:

This problem solving task challenges students to explain the reason why the given triangles are congruent, and to construct reflections of the points.

Type: Problem-Solving Task

Reflections and Isosceles Triangles:

This activity uses rigid transformations of the plane to explore symmetries of classes of triangles.

Type: Problem-Solving Task

Reflections and Equilateral Triangles:

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focusing on the class of equilaterial triangles

Type: Problem-Solving Task

Reflected Triangles:

This task asks students to use a straightedge and compass to construct the line across which a triangle is reflected.

Type: Problem-Solving Task

Centerpiece:

The purpose of this task is to use geometric and algebraic reasoning to model a real-life scenario. In particular, students are in several places (implicitly or explicitly) to reason as to when making approximations is reasonable and when to round, when to use equalities vs. inequalities, and the choice of units to work with (e.g., mm vs. cm).

Type: Problem-Solving Task

Use Cavalieri’s Principle to Compare Aquarium Volumes:

This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere.

Type: Problem-Solving Task

Tennis Balls in a Can:

This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a "double-naped cone" with vertex at the center of the sphere and bases equal to the bases of the cylinder

Type: Problem-Solving Task

Two Wheels and a Belt:

This task combines two skills: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment, and computing lengths of circular arcs given the radii and central angles.

Type: Problem-Solving Task

Tangent to a circle from a point:

This problem solving task challenges students to describe and compare different angles.

Type: Problem-Solving Task

Right triangles inscribed in circles II:

This problem solving task asks students to explain certain characteristics about a triangle.

Type: Problem-Solving Task

Placing a Fire Hydrant:

This problem solving task asks students to place a fire hydrant so that it is equal distance from three given points.

Type: Problem-Solving Task

Why does SSS work?:

This particular problem solving task exhibits congruency between two triangles, demonstrating translation, reflection and rotation.

Type: Problem-Solving Task

Building a tile pattern by reflecting octagons:

This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral: the focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square.

Type: Problem-Solving Task

Building a tile pattern by reflecting hexagons:

This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh: the focus of the task is on using the properties of reflections to deduce this seven hexagon pattern.

Type: Problem-Solving Task

Bisecting an angle:

This problem solving task challenges students to bisect a given angle.

Type: Problem-Solving Task

Are the Triangles Congruent?:

The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.

Type: Problem-Solving Task

Locating Warehouse:

This problem solving task challenges students to place a warehouse (point) an equal distance from three roads (lines).

Type: Problem-Solving Task

Inscribing a triangle in a circle:

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle.

Type: Problem-Solving Task

Circumcenter of a triangle:

This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment.

Type: Problem-Solving Task

Tangent Lines and the Radius of a Circle:

This problem solving task challenges students to find the perpendicular meeting point of a segment from the center of a circle and a tangent.

Type: Problem-Solving Task

Seven Circles I:

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

Type: Problem-Solving Task

Setting Up Sprinklers:

This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles, using trigonometric ratios to solve right triangles, and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found.

Type: Problem-Solving Task

Neglecting the Curvature of the Earth:

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

Type: Problem-Solving Task

Angle bisection and midpoints of line segments:

This task provides a construction of the angle bisector of an angle by reducing it to the bisection of an angle to finding the midpoint of a line segment. It is worth observing the symmetry -- for both finding midpoints and bisecting angles, the goal is to cut an object into two equal parts.

Type: Problem-Solving Task

Inscribing a circle in a triangle II:

This problem solving task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.

Type: Problem-Solving Task

As the Wheel Turns:

In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context.

Type: Problem-Solving Task

What functions do two graph points determine?:

This problem solving task challenges students to find the linear, exponential and quadratic functions based on two points.

Type: Problem-Solving Task

US Population 1982-1988:

This problem solving task asks students to predict and model US population based on a chart of US population data from 1982 to 1988.

Type: Problem-Solving Task

US Population 1790-1860:

This problem solving task asks students to solve five exponential and linear function problems based on a US population chart for the years 1790-1860.

Type: Problem-Solving Task

Two Points Determine an Exponential Function II:

This problem solving tasks asks students to find the values of points on a graph.

Type: Problem-Solving Task

Two Points Determine an Exponential Function I:

This problem solving task asks students to graph a function and find the values of points on a graph.

Type: Problem-Solving Task

Taxi!:

This simple conceptual problem does not require algebraic manipulation, but requires students to articulate the reasoning behind each statement. Students are asked to verify a given linear equation from data in a table and interpret its key components in context.

Type: Problem-Solving Task

Sandia Aerial Tram:

The task provides an opportunity for students to engage in detailed analysis of the rate of change of the elevation.

Type: Problem-Solving Task

Rumors:

This problem is an exponential function example that uses the real-world problem of how fast rumors spread.

Type: Problem-Solving Task

Rising Gas Prices - Compounding and Inflation:

The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills. In particular, students are introduced to the idea of inflation of prices of a single commodity, and are given a very brief introduction to the notion of the Consumer Price Index for measuring inflation of a body of goods.

Type: Problem-Solving Task

Newton's Law of Cooling:

The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

Type: Problem-Solving Task

Linear or exponential?:

This task gives a variation of real-life contexts which could be modeled by a linear or exponential function. The key distinguishing feature between the two is whether the change by equal factors over equal intervals (exponential functions), or by a constant increase per unit interval (linear functions). The task could either be used as an assessment problem on this distinction, or used as an introduction to the differences between these very important classes of functions.

Type: Problem-Solving Task

Linear Functions:

This task requires students to use the fact that on the graph of the linear function h(x) = ax + b, the y-coordinate increases by a when x increases by one. Specific values for a and b were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.

Type: Problem-Solving Task

Solution Sets:

The typical system of equations or inequalities problem gives the system and asks for the graph of the solution. This task turns the problem around. It gives a solution set and asks for the system that corresponds to it. The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations. Students have to focus on what the graph is showing. When you are describing a region, why does the inequality have to go one way or another? When you pick a point that clearly lies in a region, what has to be true about its coordinates so that it satisfies the associated system of inequalities?

Type: Problem-Solving Task

Radical Equations:

To engage this task meaningfully, students must be aware of the convention that the square root of "a" for a positive number "a" refers to the positive square root of "a". The purpose of this task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one.

Type: Problem-Solving Task

Quinoa Pasta 3:

This mathematical modeling task also illustrates making sense of a problem. Students are only told that there are two ingredients in the pasta and they have a picture of the box. It might even be better to just show the picture of the box, or to bring in the box and ask the students to pose the question themselves. The brand of pasta is quite commonly available at supermarkets or health food stores such as Whole Foods and even at Amazon.com. The box has the nutritional label and a reference to the website where the students can find other information about the ingredients

Type: Problem-Solving Task

Quinoa Pasta 2:

This mathematical modeling task also illustrates making sense of a problem. Students are given all the relevant information on the nutritional labels, but they have to figure out how to use this information. They have to come up with the idea that they can set up two equations in two unknowns to solve the problem.

Type: Problem-Solving Task

Pairs of Whole Numbers:

This task addresses solving systems of linear equations, and provides a simple example of a system with three equations and three unknown. Two (of many) methods for solving the system are presented. The first takes the given information to make three equations in three unknowns which can then be solved via algebraic manipulation to find the three numbers. The second solution is more clever, creating a single equation in three unknowns from the given information. This equation is then combined with the given information about the sums of pairs of numbers to deduce what the third number is. In reality, this solution is not simpler than the first: rather it sets up a slightly different set of equations which can be readily solved (the key being to take the sum of the three equations in the first solution). It provides a good opportunity for the instructor to show different methods for solving the same system of linear equations.

Type: Problem-Solving Task

How does the solution change?:

The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level. By asking students to reason about solutions without explicitly solving them, we get to the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally simple; the point of the task is not to test techniques in solving equations, but to encourage students to reason about them.

Type: Problem-Solving Task

Do two points always determine an exponential function?:

This problem complements the problem "Do two points always determine a linear function?'' There are two constraints on a pair of points R1 and R2 if there is an exponential function f(x) = ae^bx whose graph contains R1 and R2.

Type: Problem-Solving Task

Do two points always determine a linear function?:

In a geometric context, two distinct points ??1 and ??2 always determine a unique line in the Cartesian plane (this is one of the basic postulates of Euclidean geometry). Only the non-vertical lines, however, can be described by the graph of a function ??(??)=????+??. This task focuses on producing an explicit function ??(??) as long as the line is not vertical.

This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations to find the explicit equation of the line through two points (when that line is not vertical).

Type: Problem-Solving Task

Carbon 14 Dating, Variation 2:

This exploratory task requires the student to use properties of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.

Type: Problem-Solving Task

Carbon 14 Dating in Practice II:

This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies.

Type: Problem-Solving Task

Basketball Rebounds:

This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.

Type: Problem-Solving Task

A Saturating Exponential:

This task provides an interesting context to ask students to estimate values in an exponential function using a graph.

Type: Problem-Solving Task

Cash Box:

The given solutions for this task involve the creation and solving of a system of two equations and two unknowns, with the caveat that the context of the problem implies that we are interested only in non-negative integer solutions. Indeed, in the first solution, we must also restrict our attention to the case that one of the variables is further even. This aspect of the task is illustrative of the mathematical practice of modeling with mathematics, and crucial as the system has an integer solution for both situations, that is, whether we include the dollar on the floor in the cash box or not.

Type: Problem-Solving Task

Accurately weighing pennies II:

This task is a somewhat more complicated version of "Accurately weighing pennies I'' as a third equation is needed in order to solve part (a) explicitly. Instead, students have to combine the algebraic techniques with some additional problem-solving (numerical reasoning, informed guess-and-check, etc.) Part (b) is new to this task, as with only two types of pennies the weight of the collection determines how many pennies of each type are in the collection. This is no longer the case with three different weights but in this particular case, a collection of 50 is too small to show any ambiguity. This is part of the reason for part (c) of the question where the weight alone no longer determines which type of pennies are in the roll. This shows how important levels of accuracy in measurement are as the answer to part (b) could be different if we were to measure on a scale which is only accurate to the nearest tenth of a gram instead of to the nearest hundredth of a gram.

Type: Problem-Solving Task

Accurately weighing pennies I:

This problem involves solving a system of algebraic equations from a context: depending how the problem is interpreted, there may be one equation or two. The main work in parts (a) and (b) is in setting up the equation(s) appropriately. Question (c) is more subtle and it requires thinking carefully about the accuracy available in a particular measurement (weight). The first two parts of this task could be used for instructional or assessment purposes while the third part should strictly be implemented for instructional purposes.

Type: Problem-Solving Task

Base and Height:

Students are asked to determine and illustrate all possible descriptions for the base and height of a given triangle.

Type: Problem-Solving Task

Finding Areas of Polygons, Variation 1:

Students are asked to demonstrate two different strategies for finding the area of polygons shown on grids.

Type: Problem-Solving Task

Converting Square Units:

The purpose of this task is converting square units. Use the information provided to answer the questions posed. This task asks students to critique Jada's reasoning.

Type: Problem-Solving Task

Jim and Jesse's Money:

Students are asked to use a ratio to determine how much money Jim and Jesse had at the start of their trip.

Type: Problem-Solving Task

Glasses:

In this resource, students will determine the volumes of three different shaped drinking glasses. They will need prior knowledge with volume formulas for cylinders, cones, and spheres, as well as experience with equation solving, simplifying square roots, and applying the Pythagorean theorem.

Type: Problem-Solving Task

How Is the Weather?:

This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match. The first and third graphs look very similar at first glance, but the function values are very different since the scales on the vertical axes are very different. The task could also be used to generate a group discussion on interpreting functions given by graphs.

Type: Problem-Solving Task

Equations and Formulas:

In this task, students will use inverse operations to solve the equations for the unknown variable or for the designated variable if there is more than one.

Type: Problem-Solving Task

Interpreting the Graph:

The purpose of this task is to help students learn to read information about a function from its graph, by asking them to show the part of the graph that exhibits a certain property of the function. The task could be used to further instruction on understanding functions or as an assessment tool, with the caveat that it requires some amount of creativity to decide how to best illustrate some of the statements.

Type: Problem-Solving Task

Shrinking:

Students are asked to determine the change in height in inches when given a constant rate of change in centimeters. The answer is rounded to the nearest half inch.

Type: Problem-Solving Task

Comparing Freezing Points:

In this task, students answer a question about the difference between two temperatures that are negative numbers.

Type: Problem-Solving Task

Coupon Versus Discount:

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Type: Problem-Solving Task

Operations on the Number Line:

The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole.

Type: Problem-Solving Task

Repeating Decimal as Approximation:

The student is asked to complete a long division which results in a repeating decimal, and then use multiplication to "check" their answer. The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation.

Type: Problem-Solving Task

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Type: Problem-Solving Task

Cooking with the Whole Cup:

Students are asked to use proportional reasoning to answer a series of questions in the context of a recipe.

Type: Problem-Solving Task

Quinoa Pasta 1:

This task asks students to find the amount of two ingredients in a pasta blend. The task provides all the information necessary to solve the problem by setting up two linear equations in two unknowns. This progression of tasks helps distinguish between 8th grade and high school expectations related to systems of linear equations.

Type: Problem-Solving Task

Cell Phone Plans:

This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations. The students are required to find the solution algebraically to complete the task.

Type: Problem-Solving Task

The Sign of Solutions:

It is possible to say a lot about the solution to an equation without actually solving it, just by looking at the structure and operations that make up the equation. This exercise turns the focus away from the familiar "finding the solution" problem to thinking about what it really means for a number to be a solution of an equation.

Type: Problem-Solving Task

Two Lines:

In this task, we are given the graph of two lines including the coordinates of the intersection point and the coordinates of the two vertical intercepts and are asked for the corresponding equations of the lines. It is a very straightforward task that connects graphs and equations and solutions and intersection points.

Type: Problem-Solving Task

Coffee by the Pound:

Students will answer questions about unit price of coffee, make a graph of the information, and explain the meaning of constant of proportionality/slope in the given context.

Type: Problem-Solving Task

Calculating the Square Root of 2:

This task is intended for instructional purposes so that students can become familiar and confident with using a calculator and understanding what it can and cannot do. This task gives an opportunity to work on the notion of place value (in parts [b] and [c]) and also to understand part of an argument for why the square root of 2 is not a rational number.

Type: Problem-Solving Task

Comparing Snow Cones:

Students will just be learning about similarity in this grade, so they may not recognize that it is needed in this context. Teachers should be prepared to give support to students who are struggling with this part of the task. To simplify the task, the teacher can just tell the students that based on the slant of the truncated conical cup, the complete cone would be 14 in tall and the part that was sliced off was 10 inches tall. (See solution for an explanation.) There is a worthwhile discussion to be had about parts (c) and (e). The percentage increase is smaller for the snow cones than it was for the juice treats. The snow cones have volume which is equal to those of the juice treats plus the volume of the dome, which is the same in both cases. Adding the same number to two numbers in a ratio will always make their ratio closer to one, which in this case means that the ratio - and thus percentage increase - would be smaller.

Type: Problem-Solving Task

Congruent Segments:

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

Type: Problem-Solving Task

Congruent Triangles:

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b). Each time the plane is reflected about a line, this reverses the notions of ''clockwise'' and ''counterclockwise.''

Type: Problem-Solving Task

Offensive Linemen:

In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale.

Type: Problem-Solving Task

Tossing Cylinders:

The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data. The cylindrical objects used in this task typically have three different resting positions but not all of these may be equally likely and some may be extremely unlikely or impossible when the object is tossed. Furthermore, obtaining the probabilities of the outcomes is perhaps only possible through the use of long-run relative frequencies. This is because these cylinders do not have the same types of symmetries as objects that are often used as dice, such as cubes or tetrahedrons, where each outcome is equally likely.

Type: Problem-Solving Task

Election Poll, Variation 2:

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members. Variation 2 leads students through a physical simulation for generating sample proportions by sampling, and re-sampling, marbles from a box.

Type: Problem-Solving Task

Waiting Times:

As studies in statistics and probability unfold, students will not yet know the rules of probability for compound events. Thus, simulation is used to find an approximate answer to these questions. In fact, part b would be a challenge to students who do know the rules of probability, further illustrating the power of simulation to provide relatively easy approximate answers to wide-ranging problems.

Type: Problem-Solving Task

Rolling Dice:

This task is intended as a classroom activity. Students pool the results of many repetitions of the random phenomenon (rolling dice) and compare their results to the theoretical expectation they develop by considering all possible outcomes of rolling two dice. This gives them a concrete example of what we mean by long term relative frequency.

Type: Problem-Solving Task

Estimating Square Roots:

By definition, the square root of a number n is the number you square to get n. The purpose of this task is to have students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. Students may need guidance in thinking about how to approach the task.

Type: Problem-Solving Task

Converting Decimal Representations of Rational Numbers to Fraction Representations:

Requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of the choice of representation. For example, 0.333¯ and 1/3 are two different ways of representing the same number.

Type: Problem-Solving Task

Downhill:

This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.

Type: Problem-Solving Task

Find the Angle:

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Type: Problem-Solving Task

Find the Missing Angle:

This task provides students the opportunity to see how the mathematical ideas embedded in the standards and clusters mature over time. The task uses facts about supplementary, complementary, vertical, adjacent, and alternate interior angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. It is a good introduction to writing paragraphs, 2-column, and/or flow chart proofs.

Type: Problem-Solving Task

Flower Vases:

The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.

Type: Problem-Solving Task

Is This a Rectangle?:

The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle. Creativity will be essential here as the only given information is the Cartesian coordinates of the quadrilateral's vertices. Using this information to show that the four angles are right angles will require some auxiliary constructions. Students will need ample time and, for some of the methods provided below, guidance. The reward of going through this task thoroughly should justify the effort because it provides students an opportunity to see multiple geometric and algebraic constructions unified to achieve a common purpose. The teacher may wish to have students first brainstorm for methods of showing that a quadrilateral is rectangle (before presenting them with the explicit coordinates of the rectangle for this problem): ideally, they can then divide into groups and get to work straightaway once presented with the coordinates of the quadrilateral for this problem.

Type: Problem-Solving Task

Identifying Rational Numbers:

The task assumes that students can express a given repeating decimal as a fraction. Teachers looking for a task to fill in this background knowledge could consider the related task "Converting Decimal Representations of Rational Numbers to Fraction Representations".

Type: Problem-Solving Task

Irrational Numbers on the Number Line:

When students plot irrational numbers on the number line, it helps reinforce the idea that they fit into a number system that includes the more familiar integer and rational numbers. This is a good time for teachers to start using the term "real number line" to emphasize the fact that the number system represented by the number line is the real numbers. When students begin to study complex numbers in high school, they will encounter numbers that are not on the real number line (and are, in fact, on a "number plane"). This task could be used for assessment, or if elaborated a bit, could be used in an instructional setting.

Type: Problem-Solving Task

Shipping Rolled Oats:

Students should think of different ways the cylindrical containers can be set up in a rectangular box. Through the process, students should realize that although some setups may seem different, they result in a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations.

Type: Problem-Solving Task

Radius of a Cylinder:

Students are asked to interpret the effect on the value of an expression given a change in value of one of the variables.

Type: Problem-Solving Task

Triangle congruence with coordinates:

In this resource, students will decide how to use transformations in the coordinate plane to translate a triangle onto a congruent triangle. Exploratory examples are included to prompt analytical thinking.

Type: Problem-Solving Task

Comparing Rational and Irrational Numbers:

Students are given a pair of numbers. They are asked to determine which is larger, and then justify their answer. The numbers involved are rational numbers and common irrational numbers, such p and square roots. This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers.

Type: Problem-Solving Task

Lines of symmetry for triangles:

This activity provides students an opportunity to recognize these distinguishing features of the different types of triangles before the technical language has been introduced. For finding the lines of symmetry, cut-out models of the four triangles would be helpful so that the students can fold them to find the lines.

Type: Problem-Solving Task

Lines of symmetry for quadrilaterals:

This task provides students a chance to experiment with reflections of the plane and their impact on specific types of quadrilaterals. It is both interesting and important that these types of quadrilaterals can be distinguished by their lines of symmetry.

Type: Problem-Solving Task

Are these right?:

The purpose of this task is for students to measure angles and decide whether the triangles are right or not. Students should already understand concepts of angle measurement  and know how to measure angles using a protractor before working on this task.

Type: Problem-Solving Task

Mixing Fertilizer:

Students examine and answer questions related to a scenario similar to a "mixture" problem involving two different mixtures of fertilizer. In this example, students determine and then compare expressions that correspond to concentrations of various mixtures. Ultimately, students generalize the problem and verify conclusions using algebraic rather than numerical expressions.

Type: Problem-Solving Task

Mixing Candies:

Students are asked to interpret expressions and equations within the context of the amounts of caramels and truffles in a box of candy.

Type: Problem-Solving Task

Kitchen Floor Tiles:

This problem asks students to consider algebraic expressions calculating the number of floor tiles in given patterns. The purpose of this task is to give students practice in reading, analyzing, and constructing algebraic expressions, attending to the relationship between the form of an expression and the context from which it arises. The context here is intentionally thin; the point is not to provide a practical application to kitchen floors, but to give a framework that imbues the expressions with an external meaning.

Type: Problem-Solving Task

Delivery Trucks:

This resource describes a simple scenario which can be represented by the use of variables. Students are asked to examine several variable expressions, interpret their meaning, and describe what quantities they each represent in the given context.

Type: Problem-Solving Task

Music and Sports:

This task asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.

Type: Problem-Solving Task

Animal Populations:

In this task students interpret the relative size of variable expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Type: Problem-Solving Task

What's Your Favorite Subject?:

Students are asked to examine data given in table format and then calculate either row percentages or column percentages and state a conclusion about the meaning of the data. Either calculation is appropriate for the solution since there is no clear relationship between the variables. Whether the student sees a strong association or not is less important than whether his or her answer uses the data appropriately and demonstrates understanding that an association means the distribution of favorite subject is different for 7th graders and 8th graders.

Type: Problem-Solving Task

Seeing Dots:

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.

Type: Problem-Solving Task

Selling Fuel Oil at a Loss:

The task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the business.

Type: Problem-Solving Task

Currency Exchange:

The purpose of this task is to have students convert multiple currencies to answer the problem. Students may find the CDN abbreviation for Canada confusing. Teachers may need to explain the fact that money in Canada is also called dollars, so to distinguish them, we call them Canadian dollars.

Type: Problem-Solving Task

Data Transfer:

This task asks the students to solve a real-world problem involving unit rates (data per unit time) using units that many teens and pre-teens have heard of but may not know the definition for. While the computations involved are not particularly complex, the units will be abstract for many students. The first solution relies more on reasoning about the meaning of multiplication and division, while the second solution uses units to help keep track of the steps in the solution process.

Type: Problem-Solving Task

Fixing the Furnace:

Students are asked to write equations to model the repair costs of three different companies and determine the conditions for which each company would be least expensive. This task can be used to both assess student understanding of systems of linear equations or to promote discussion and student thinking that would allow for a stronger solidification of these concepts. The solution can be determined in multiple ways, including either a graphical or algebraic approach.

Type: Problem-Solving Task

Friends Meeting on Bicycles:

Students are asked to use knowledge of rates and ratios to answer a series of questions involving time, distance, and speed.

Type: Problem-Solving Task

Comparing Temperatures:

The purpose of the task is for students to compare signed numbers in a real-world context.

Type: Problem-Solving Task

Integers on the Number Line 2:

The purpose of this task is for students to get a better understanding of the relative positions and values of positive and negative numbers.

Type: Problem-Solving Task

Chocolate Bar Sales:

In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations. In the later part of the problem, the numbers are big enough so that using the formula is the most efficient way to solve the problem; however, creative use of the table or graph will also work.

Type: Problem-Solving Task

Overlapping Squares:

This problem provides an interesting geometric context to work on the notion of percent. Two different methods for analyzing the geometry are provided: the first places the two squares next to one another and then moves one so that they overlap. The second solution sets up an equation to find the overlap in terms of given information which reflects the mathematical ideas reason about and solve one-variable equations and inequalities.

Type: Problem-Solving Task

How Many Solutions?:

The student is given the equation 5x-2y=3 and asked, if possible, to write a second linear equation creating systems resulting in one, two, infinite, and no solutions.

Type: Problem-Solving Task

Text Resources

Case Study: Understanding How Copyright Law Impacts A Production:

Using this case study, students can answer the question, "What are the limits of fair use regarding copyright protection?"

Type: Text Resource

Case Study: Understanding the Psychological Effects of Composition:

Using this case study, students can answer the question, "How does the composition of a scene influence how the viewer feels?"

Type: Text Resource

Case Study: Getting Noticed in the Workplace:

Using this case study students can discuss "How can an employee"s behaviors and actions drive their career stability and path?"

Type: Text Resource

Tutorials

Coordinate Plane: Graphing Points Word Problem:

This Khan Academy tutorial video presentation represents a word problem's solution on a coordinate plane to determine the number of blocks walked from a home to a school.

Type: Tutorial

Volume through Decomposition:

This Khan Academy tutorial video illustrates how to find the volume of an irregular solid figure by dividing the figure into two rectangular prisms and finding the volume of each.  Although the tutorial works from a drawing, individual volume cubes are not drawn so students must work from the formula. 

Type: Tutorial

Volume: Decomposing a Solid Figure Example:

This Khan Academy tutorial video illustrates finding the volume of an irregular figure made up of unit cubes by separating the figure into two rectangular prisms and finding the volume of each part.

Type: Tutorial

Categorizing Geometric Shapes: Practice Examples:

This Khan Academy tutorial video presents examples and explanations for categorizations of perpendicular sides and right, obtuse, and acute triangles.

Type: Tutorial

Examples of Triangle Categories:

In this Khan Academy tutorial video triangles are categorized by angles or side lengths of a specified size.

Type: Tutorial

Example 3: Solving Systems by Elimination:

This video is an example of solving a system of linear equations by elimination where the system has infinite solutions.

Type: Tutorial

Solving Systems of Linear Equations with Elimination Example 1:

This video shows how to solve a system of equations through simple elimination.

Type: Tutorial

Inconsistent Systems of Equations:

This video explains how to identify systems of equations without a solution.

Type: Tutorial

Quadrilateral Overview:

This Khan Academy tutorial video introduces quadrilaterals. their categories, and subcategories.

Type: Tutorial

Example 2: Solving Systems by Elimination:

This video shows how to solve systems of equations by elimination.

Type: Tutorial

Addition Elimination Example 1:

This video is an introduction to the elimination method of solving a system of equations.

Type: Tutorial

Systems of Equations Word Problems Example 1:

This video demonstrates solving a word problem by creating a system of linear equations that represents the situation and solving them using elimination.

Type: Tutorial

Graphing systems of equations:

In this tutorial, students will learn how to solve and graph a system of equations.

 

Type: Tutorial

Solving system of equations by graphing:

This tutorial shows students how to solve a system of linear equations by graphing the two equations on the same coordinate plane and identifying the intersection point. 

 

Type: Tutorial

Solving a system of equations by graphing:

This tutorial shows how to solve a system of equations by graphing. Students will see what a no solution system of equations looks like in a graph.

Type: Tutorial

Solving a system of equations using substitution:

This tutorial shows how to solve a system of equations using substitution.  

 

Type: Tutorial

Solving a literal equation:

Students will learn to solve a literal equation. 

Type: Tutorial

Division of Polynomials:

This resource discusses dividing a polynomial by a monomial and also dividing a polynomial by a polynomial using long division.

Type: Tutorial

Introduction to the Coordinate Plane:

In this video, you will learn about Rene Descartes, and how he bridged the gap between algebra and geometry.

Type: Tutorial

Comparing Theoretical to Experimental Probabilites:

This video compares theoretical and experimantal probabilities and sources of possible discrepancy.

Type: Tutorial

Making Predictions with Probability:

Watch the video as it predicts the number of times a spinner will land on a given outcome.

Type: Tutorial

Factor a Linear Expression by Taking a Common Factor:

This video demonstrates how to factor a linear expression by taking a common factor.

Type: Tutorial

Proportion Word Problem:

This introductory video demonstrates the basic skill of how to write and solve a basic equation for a proportional relationship. 

Type: Tutorial

Adding and Subtracting Numbers in Different Formats:

In this example, we will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

Comparing Rational Numbers:

In this tutorial, you will compare rational numbers using a number line.

Type: Tutorial

Statistics Introduction: Mean, Median, and Mode:

The focus of this video is to help you understand the core concepts of arithmetic mean, median, and mode.

Type: Tutorial

Find the Volume of a Triangular Prism and Cube:

This video will show to find the volume of a triangular prism, and a cube by applying the formula for volume.

Type: Tutorial

Finding Area by Decomposing a Shape:

This tutorial demonstrates how the area of an irregular geometric shape may be determined by decomposition to smaller familiar shapes.

Type: Tutorial

Solving a Proportion with an Unknown Variable :

Here's an introductory video explaining the basic reasoning behind solving proportions and shows three different methods for solving proportions which you will use later on to solve more difficult problems. 

Type: Tutorial

Setting up Proportions to Solve Word Problems:

This introductory video shows some basic examples of writing two ratios and setting them equal to each other. This is just step 1 when solving word problems with proportions. 

Type: Tutorial

Coordinate Plane: Word Problem Exercises:

This video demonstrates solving word problems involving the coordinate plane.

Type: Tutorial

How to Evaluate an Expression with Variables:

Learn how to evaluate an expression with variables using a technique called substitution.

Type: Tutorial

How to Evaluate Expressions with Two Variables:

This video demonstrates evaluating expressions with two variables.

Type: Tutorial

Thinking About the Changing Values of Variables and Expressions:

Explore how the value of an algebraic expression changes as the value of its variable changes. 

Type: Tutorial

How to Evaluate an Expression Using Substitution:

In this example, we have a formula for converting a Celsius temperature to Fahrenheit. 

Type: Tutorial

Decimals and Fractions on a Number Line:

Locate fractions and decimals on the same number line in this tutorial.

Type: Tutorial

Ordering Negative Numbers:

Let's order negative numbers from least to greatest in this video.

Type: Tutorial

Ordering Rational Numbers:

In this tutorial, you will learn how to order rational numbers using a number line.

Type: Tutorial

Sorting Values on Number Line:

This video demonstrates sorting values including absolute value from least to greatest using a number line.

Type: Tutorial

Introduction to Order of Operations:

Students will evaluate expressions using the order of operations.

Type: Tutorial

Order of Operations: PEMDAS:

Work through a challenging order of operations example with only positive numbers.

Type: Tutorial

Order of Operations :

Work through a challenging order of operations example with only positive numbers.

Type: Tutorial

Order of Operations :

This video will show how to evaluate expressions with exponents using the order of operations.

 

Type: Tutorial

Geometric sequence or progression:

We will learn how to write a geometric sequence.

Type: Tutorial

Ratio Word Problem: Centimeters to Kilometers:

In this video, watch as we solve this word problem using what we know about equivalent ratios.

Type: Tutorial

Ratio Word Problem:

In this video, a ratio is given and then applied to solve a problem. 

Type: Tutorial

Graphing Quadractic Functions in Vertex Form:

This tutorial will help the students to identify the vertex of a parabola from the equation, and then graph the parabola.

Type: Tutorial

Graphing Quadratic Equations:

This tutorial helps the learners to graph the equation of a quadratic function using the coordinates of the vertex of a parabola and its x- intercepts.

Type: Tutorial

Graphing Exponential Equations:

This tutorial will help you to learn about exponential functions by graphing various equations representing exponential growth and decay.

Type: Tutorial

How to evaluate an expression using substitution:

In this example we have a formula for converting Celsius temperature to Fahrenheit. Let's substitute the variable with a value (Celsius temp) to get the degrees in Fahrenheit. Great problem to practice with us!

Type: Tutorial

Why aren't we using the multiplication sign?:

Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.

Type: Tutorial

Calculating Mixtures of Solutions:

This lecture shows how algebra is used to solve problems involving mixtures of solutions of different concentrations.

Type: Tutorial

Inconsistent, Dependent, and Independent Systems:

Systems of two linear equations in two variables can have a single solution, no solutions, or an infinite number of solutions. This video gives a great description of inconsistent, dependent, and independent systems. A consistent independent system of equations will have one solution. A consistent dependent system of equations will have infinite number of solutions, and an inconsistent system of equations will have no solution. This tutorial also provides information on how to distinguish a given system of linear equations as inconsistent, independent, or dependent system by looking at the slope and intercept.

Type: Tutorial

Solving Systems of Equations by Elimination:

Systems of two equations in x and y can be solved by adding the equations to create a new equation with one variable eliminated. This new equation can then be solved to find the value of the remaining variable. That value is then substituted into either equation to find the value of other variable.

Type: Tutorial

Solving Systems of Equations by Substitution:

A system of two equations in x and y can be solved by rearranging one equation to represent x in terms of y, and "substituting" this expression for x in the other equation. This creates an equation with only y which can then be solved to find y's value. This value can then be substituted into either equation to find the value of x.

Type: Tutorial

Converting Speed Units:

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

Video/Audio/Animations

Using Systems of Equations Versus One Equation:

When should a system of equations with multiple variables be used to solve an Algebra problem, instead of using a single equation with a single variable?

Type: Video/Audio/Animation

Why the Elimination Method Works:

This chapter presents a new look at the logic behind adding equations- the essential technique used when solving systems of equations by elimination.

Type: Video/Audio/Animation

Point-Slope Form:

The point-slope form of the equation for a line can describe any non-vertical line in the Cartesian plane, given the slope and the coordinates of a single point which lies on the line.

Type: Video/Audio/Animation

Two Point Form:

The two point form of the equation for a line can describe any non-vertical line in the Cartesian plane, given the coordinates of two points which lie on the line.

Type: Video/Audio/Animation

Solving Literal Equations:

Literal equations are formulas for calculating the value of one unknown quantity from one or more known quantities. Variables in the formula are replaced by the actual or 'literal' values corresponding to a specific instance of the relationship.

Type: Video/Audio/Animation

Virtual Manipulative

Order of Operations Quiz:

In this activity, students practice solving algebraic expressions using order of operations. The applet records their score so the student can track their progress. This activity allows students to practice applying the order of operations when solving problems. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this course.