## 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:**1204000

**Course Path:**

**Abbreviated Title:**M/J FDNSKLS MATH 6-8

**Course Length:**Multiple (M) - Course length can vary

**Course Attributes:**

- Class Size Core Required

**Course Type:**Elective Course

**Course Level:**2

**Course Status:**State Board Approved

**Grade Level(s):**6,7,8

## Educator Certifications

## Student Resources

## Original Student Tutorials

Get ready for an epic Capture the Flag Tournament as you explore the coordinate plane in this interactive tutorial.

Type: Original Student Tutorial

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

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

Use scientific notation to compare the distances of planets and other objects from the Sun in this interactive tutorial.

Type: Original Student Tutorial

Use astronomical units to compare distances betweeen objects in our solar system in this interactive tutorial.

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

Use the Pythagorean Theorem to find the legs of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

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

Type: Original Student Tutorial

Use the Pythagorean Theorem to find the hypotenuse of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 2 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

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

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

Learn what the Pythagorean Theorem and its converse mean, and what Pythagorean Triples are in this interactive tutorial.

This is part 1 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

Learn how to simplify radicals in this interactive tutorial.

Type: Original Student Tutorial

Follow George as he explores the formula for the area of a triangle and uses it to find the area of various triangles in this interactive student tutorial.

Type: Original Student Tutorial

Roll up your sleeves and learn how proportions can be used in everyday life in this interactive tutorial.

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

Learn what perfect squares are and find their square roots in this interactive tutorial.

Type: Original Student Tutorial

Continue to 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 Part Two, you’ll cite textual evidence that supports an analysis of what the text states explicitly, or directly. You'll also make inferences, support them with textual evidence, and use them to explain how the bet transformed the lawyer and the banker by the end of the story.

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

Make sure to complete Part Three *after *you finish Part Two. Click **HERE **to view "Risky Betting: Analyzing a Universal Theme (Part Three)."

Type: Original Student Tutorial

Follow Jamal as he represents algebraic inequalities on a number line while visiting a theme park with his family in this interactive tutorial.

This is part 2 in a two-part series on inequalities. Click **HERE **to open part 1.

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

Help Oscar translate written real-world descriptions of multiplication and division into algebraic expressions in this interactive tutorial.

This is part 2 of 3. Click below to open the other tutorials in this series.

**Algebraic Expressions Part 1: Addition and Subtraction**- Part 3 (Coming Soon)

Type: Original Student Tutorial

Follow Oscar as he writes algebraic expressions of addition and subtraction about his new puppy Scooter in this interactive tutorial.

Type: Original Student Tutorial

Explore how to express large quantities using scientific notation in this interactive tutorial.

Type: Original Student Tutorial

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

This is part 1 in a two-part series.

Type: Original Student Tutorial

Help Cindy find the missing dimension of a rectangular prism in her delivery services job with this interactive tutorial.

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

Type: Original Student Tutorial

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

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

Follow Cindy as she explores fractional unit cubes and finds the volume of rectangular prisms that have rational number dimensions in this interactive tutorial.

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

Type: Original Student Tutorial

Learn to identify imagery in William Shakespeare's "Sonnet 18" and explain how that imagery contributes to the poem's meaning with this interactive tutorial.

Type: Original Student Tutorial

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

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

Follow Cindy as she learns about the volume formulas to create boxes in this interactive tutorial.

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

Type: Original Student Tutorial

Help Lily identify and create equivalent ratios in this interactive tutorial.

Type: Original Student Tutorial

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

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

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

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

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

Follow Hailey and Kenna as they estimate tips and sales tax at the mall, restaurants, and the hair salon in this interactive tutorial.

Type: Original Student Tutorial

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

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

Follow Matteo as he explores opposite numbers, positive and negative rational numbers, and zero in real-world contexts while planning and going on a cruise in Alaska in this interactive tutorial.

Type: Original Student Tutorial

Let's calculate markups and markdowns at the mall and follow Paige and Miriam working in this interactive tutorial.

Type: Original Student Tutorial

Calculate simple interest and estimate monthly payments alongside a loan officer named Jordan in this interactive tutorial.

Type: Original Student Tutorial

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

Explore sales tax, fees, and commission by following a customer service representative named Julian in this interactive tutorial.

Type: Original Student Tutorial

Learn to solve percent change problems involving percent increases and decreases in in this interactive tutorial.

Type: Original Student Tutorial

Explore complementary and supplementary angles around the playground with Jacob in this interactive tutorial.

This is Part 1 in a two-part series. Click HERE to open Playground Angles: Part 2.

Type: Original Student Tutorial

Help Jacob write and solve equations to find missing angle measures based on the relationship between angles that sum to 90 degrees and 180 degrees in this playground-themed, interactive tutorial.

This is Part 2 in a two-part series. Click** HERE** to open Playground Angles: Part 1.

Type: Original Student Tutorial

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

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

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

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

What is a function? Where do we see functions in real life? Explore these questions and more using different contexts in this interactive tutorial.

This is part 1 in a two-part series on functions. Click HERE to open Part 2.

Type: Original Student Tutorial

Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial.

Type: Original Student Tutorial

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

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

Learn how similar right triangles can show how the slope is the same between any two distinct points on a non-vertical line as you help Hailey build stairs to her tree house in this interactive tutorial.

Type: Original Student Tutorial

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

Type: Original Student Tutorial

Learn to construct a function to model a linear relationship between two quantities and determine the slope and y-intercept given two points that represent the function with this interactive tutorial.

Type: Original Student Tutorial

Explore base 10 and exponents in this baseball-themed, interactive tutorial.

Type: Original Student Tutorial

Learn how equations can have 1 solution, no solution or infinitely many solutions in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

- Click
**HERE**to open Part 1: Combining Like Terms - Click
**HERE**to open Part 2: The Distributive Property - Click
**HERE**to open Part 3: Variables on Both Sides - Click
**HERE**to open Part 4: Putting It All Together - [CURRENT TUTORIAL] Part 5: How Many Solutions?

Type: Original Student Tutorial

Learn alternative methods of solving multi-step equations in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

- Click
**HERE**to open Part 1: Combining Like Terms - Click
**HERE**to open Part 2: The Distributive Property - Click
**HERE**to open Part 3: Variables on Both Sides - [CURRENT TUTORIAL] Part 4: Putting It All Together
- Click
**HERE**to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Learn how to solve multi-step equations that contain variables on both sides of the equation in this interactive tutorial.

This is part five of five in a series on solving multi-step equations.

- Click
**HERE**to open Part 1: Combining Like Terms - Click
**HERE**to open Part 2: The Distributive Property - [CURRENT TUTORIAL] Part 3: Variables on Both Sides
- Click
**HERE**to open Part 4: Putting It All Together - Click
**HERE**to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Explore how to solve multi-step equations using the distributive property in this interactive tutorial.

This is part two of five in a series on solving multi-step equations.

- Click
**HERE**to open Part 1: Combining Like Terms - [CURRENT TUTORIAL] Part 2: The Distributive Property
- Click
**HERE**to open Part 3: Variables on Both Sides - Click
**HERE**to open Part 4: Putting It All Together - Click
**HERE**to open Part 5: How Many Solutions?

Type: Original Student Tutorial

Cruise along as you discover how to qualitatively describe functions in this interactive tutorial.

Type: Original Student Tutorial

Learn how to solve multi-step equations that contain like terms in this interactive tutorial.

This is part one of five in a series on solving multi-step equations.

- [CURRENT TUTORIAL] Part 1: Combining Like Terms
- Click
**HERE**to open Part 2: The Distributive Property - Click
**HERE**to open Part 3: Variables on Both Sides - Click
**HERE**to open Part 4: Putting It All Together - Click
**HERE**to open Part 5: How Many Solutions?

Type: Original Student Tutorial

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

Practice solving and checking two-step equations with rational numbers in this interactive tutorial.

This is part 2 of the two-part series on two-step equations. **Click HERE to open Part 1.**

Type: Original Student Tutorial

Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.

This is part 1 of a two-part series about solving 2-step equations. **Click HERE to open Part 2.**

Type: Original Student Tutorial

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

Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials. You'll also learn how to check your answers to make sure your answer is the solution to the equation.

Type: Original Student Tutorial

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

See how sweet it can be to determine the slope of linear functions and compare them in this interactive tutorial. Determine and compare the slopes or the rates of change by using verbal descriptions, tables of values, equations and graphical forms.

Type: Original Student Tutorial

Learn how to solve and check one-step addition and subtraction equations with Dr. E. Quation as you complete this interactive tutorial.

**Click here to open Dr. E. Quation Part 2: One-Step Multiplication and Division Equations**

Type: Original Student Tutorial

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

Type: Original Student Tutorial

Have some fun with FUNctions! Learn how to identify linear and non-linear functions in this interactive tutorial.

Type: Original Student Tutorial

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

Learn how to determine if a relationship is a function in this interactive tutorial that shows you inputs, outputs, equations, graphs and verbal descriptions.

Type: Original Student Tutorial

Learn how to interpret histograms to analyze data, and help an inventor predict the range of a catapult in part 2 of this interactive tutorial series. More specifically, you'll learn to describe the shape and spread of data distributions.

Click **HERE** to open part 1.

Type: Original Student Tutorial

Learn how to create a histogram to display continuous data from projectiles launched by a catapult in this interactive tutorial.

This is part 1 in a 2-part series. Click **HERE** to open part 2.

Type: Original Student Tutorial

Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

**MacCoder’s Farm Part 1: Declare Variables****MacCoder’s Farm Part 2: Condition Statements****MacCoder's Farm Part 3: IF Statements**

Type: Original Student Tutorial

Explore computer coding on the farm by using relational operators and IF statements to evaluate expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

**MacCoder’s Farm Part 1: Declare Variables****MacCoder's Farm Part 2: Condition Statements****MacCoder's Farm Part 4: Repeat Loops**

Type: Original Student Tutorial

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

Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.

Click below to check out the other tutorials in the series.

**MacCoder's Farm Part 1: Declare Variables****MacCoder’s Farm Part 3: If Statements****MacCoder's Farm Part 4: Repeat Loops**

Type: Original Student Tutorial

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

Learn what slope is in mathematics and how to calculate it on a graph and with the slope formula in this interactive tutorial.

Type: Original Student Tutorial

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

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

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

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

Learn how to combine like terms to create equivalent expressions in this cooking-themed, interactive tutorial.

Type: Original Student Tutorial

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

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

Explore the origins of Pi as the ratio of Circumference to diameter of a circle. In this interactive tutorial you'll work with the circumference formula to determine the circumference of a circle and work backwards to determine the diameter and radius of a circle.

Type: Original Student Tutorial

Learn how to calculate the probability of simple events, that probability is the likeliness of an event occurring, and that some events may be more likely than others to occur in this interactive tutorial.

Type: Original Student Tutorial

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

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

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

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.

- Drones and Glaciers: Eyes in the Sky (Part 1)
- Drones and Glaciers: Eyes in the Sky (Part 2)
- Expository Writing: Eyes in the Sky (Part 3)
- Expository Writing: Eyes in the Sky (Part 4)

Type: Original Student Tutorial

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

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.

- Drones and Glaciers: Eyes in the Sky (Part 1)
- Drones and Glaciers: Eyes in the Sky (Part 2)
- Expository Writing: Eyes in the Sky (Part 3)
- Expository Writing: Eyes in the Sky (Part 4)

Type: Original Student Tutorial

Continue an exploration of kinematics to describe linear motion by focusing on position-time measurements from the motion trial in part 1. In this interactive tutorial, you'll identify position measurements from the spark tape, analyze a scatterplot of the position-time data, calculate and interpret slope on the position-time graph, and make inferences about the dune buggy’s average speed

Type: Original Student Tutorial

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.

- Drones and Glaciers: Eyes in the Sky (Part 1)
- Drones and Glaciers: Eyes in the Sky (Part 2)
- Expository Writing: Eyes in the Sky (Part 3)
- Expository Writing: Eyes in the Sky (Part 4)

Type: Original Student Tutorial

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.

- Drones and Glaciers: Eyes in the Sky (Part 1)
- Drones and Glaciers: Eyes in the Sky (Part 2)
- Expository Writing: Eyes in the Sky (Part 3)
- Expository Writing: Eyes in the Sky (Part 4)

Type: Original Student Tutorial

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

Help Alice discover that compound probabilities can be determined through calculations or by drawing tree diagrams in this interactive tutorial.

Type: Original Student Tutorial

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

Explore how to calculate the area of circles in terms of pi and with pi approximations in this interactive tutorial. You will also experience irregular area situations that require the use of the area of a circle formula.

Type: Original Student Tutorial

Learn how to use the equation of a linear trend line to interpolate and extrapolate bivariate data plotted in a scatterplot. You will see the usefulness of trend lines and how they are used in this interactive tutorial.

This is part 6 in 6-part series. Click below to open the other tutorials in the series.

- Scatterplots Part 1: Graphing
- Scatterplots Part 2: Patterns, Associations and Correlations
- Scatterplots Part 3: Trend Lines
- Scatterplots Part 4: Equation of the Trend Line
- Scatterplots Part 5: Interpreting the Equation of the Trend Line

Type: Original Student Tutorial

Explore how to interpret the slope and y-intercept of a linear trend line when bivariate data is graphed on a scatterplot in this interactive tutorial.

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

- Scatterplots Part 1: Graphing
- Scatterplots Part 2: Patterns, Associations and Correlations
- Scatterplots Part 3: Trend Lines
- Scatterplots Part 4: Equation of the Trend Line
- Scatterplots Part 6: Using Linear Models

Type: Original Student Tutorial

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

- Scatterplots Part 1: Graphing
- Scatterplots Part 2: Patterns, Associations and Correlations
- Scatterplots Part 3: Trend Lines
- Scatterplots Part 5: Interpreting the Equation of the Trend Line
- Scatterplots Part 6: Using Linear Models

Type: Original Student Tutorial

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

Explore informally fitting a trend line to data graphed in a scatter plot in this interactive online tutorial.

This is part 3 in 6-part series. Click below to open the other tutorials in the series.

- Scatterplots Part 1: Graphing
- Scatterplots Part 2: Patterns, Associations and Correlations
- Scatterolots Part 4: Equation of the Trend Line
- Scatterplots Part 5: Interpreting the Equation of the Trend Line
- Scatterplots Part 6: Using Linear Models

Type: Original Student Tutorial

Explore the different types of associations that can exist between bivariate data in this interactive tutorial.

This is part 2 in 6-part series. Click below to open the other tutorials in the series.

- Scatterplots Part 1: Graphing
- Scatterplots Part 3: Trend Lines
- Scatterolots Part 4: Equation of the Trend Line
- Scatterplots Part 5: Interpreting the Equation of the Trend Line
- Scatterplots Part 6: Using Linear Models

Type: Original Student Tutorial

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

Type: Original Student Tutorial

Learn how to graph bivariate data in a scatterplot in this interactive tutorial.

This is part 1 in 6-part series. Click below to open the other tutorials in the series.

- Scatterplots Part 2: Patterns, Associations and Correlations
- Scatterplots Part 3: Trend Lines
- Scatterolots Part 4: Equation of the Trend Line
- Scatterplots Part 5: Interpreting the Equation of the Trend Line
- Scatterplots Part 6: Using Linear Models

Type: Original Student Tutorial

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

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

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

Learn how to make and interpret boxplots in this pet-themed, interactive tutorial.

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

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

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

You will organize information in a table and write ratios equivalent to a given ratio in order to solve real-world and mathematical problems in this interactive tutorial.

Type: Original Student Tutorial

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

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

Learn how to explain the steps used to solve multi-step linear equations and provide reasons to support those steps with this interactive tutorial.

Type: Original Student Tutorial

Learn to solve problems involving the circumference and area of circle-shaped pools in this interactive tutorial.

Type: Original Student Tutorial

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

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

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

Learn to construct linear functions from tables that contain sets of data that relate to each other in special ways as you complete this interactive tutorial.

Type: Original Student Tutorial

Learn to use architectural scale drawings to build a new horse arena and solve problems involving scale drawings in this interactive tutorial. By the end, you should be able to calculate actual lengths using a scale and proportions.

Type: Original Student Tutorial

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

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

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

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

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

Type: Original Student Tutorial

Follow Jamal as he translates theme park written descriptions into algebraic inequalities in this interactive tutorial.

Type: Original Student Tutorial

Type: Original Student Tutorial

Apply the Pythagorean Theorem to solve mathematical and real-rorld problems in this interactive tutorial.

Type: Original Student Tutorial

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

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

Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.

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

Type: Original Student Tutorial

## Educational Games

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

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. 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 Game

In this activity, students enter coordinates to make a path to get to a target destination while avoiding mines. This activity allows students to explore Cartesian coordinates and the Cartesian coordinate plane. 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 Game

## Educational Software / Tool

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 Plan

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

## Perspectives Video: Experts

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

A math teacher describes the relationship between area and circumference and gives examples in nature.

Type: Perspectives Video: Expert

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

Type: Perspectives Video: Expert

How do scientists collect information from the world? They sample it! Learn how scientists take samples of phytoplankton not only to monitor their populations, but also to make inferences about the rest of the ecosystem!

Type: Perspectives Video: Expert

Don't be a square! Learn about how even grids help archaeologists track provenience!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Invasive lionfish are taking a bite out of the ecosystem of Biscayne Bay. Biologists are looking for new ways to remove them, including encouraging recreational divers to bite back!

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Get fired up as you learn more about ceramic glaze recipes and mathematical units.

Type: Perspectives Video: Professional/Enthusiast

Understand 3D modeling from a new angle when you learn about surface geometry and 3D printing.

Type: Perspectives Video: Professional/Enthusiast

Find out how math and technology can help you (try to) get away from civilization.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

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

Type: Perspectives Video: Professional/Enthusiast

Ceramic glaze recipes are fluid and not set in stone, but can only be formulated consistently with a good understanding of math!

Type: Perspectives Video: Professional/Enthusiast

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

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

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

Students are asked to use a diagram or table to write an algebraic expression and use the expression to solve problems.

Type: Problem-Solving Task

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

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

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

Type: Problem-Solving Task

This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle which is crucial for many further developments in the subject.

Type: Problem-Solving Task

The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race.

Type: Problem-Solving Task

In this problem, geometry is applied to a 400 meter track to find the perimeter of the track.

Type: Problem-Solving Task

In this task, a typographic grid system serves as the background for a standard paper clip. A metric measurement scale is drawn across the bottom of the grid and the paper clip extends in both directions slightly beyond the grid. Students are given the approximate length of the paper clip and determine the number of like paper clips made from a given length of wire.

Type: Problem-Solving Task

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

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

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

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

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

This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. They then have to use the expression to evaluate the perimeter for specific values of the two variables.

Type: Problem-Solving Task

Students are asked to determine if given expressions are equivalent.

Type: Problem-Solving Task

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

Type: Problem-Solving Task

This problem asks the student to find a 3% sales tax on a vase valued at $450.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

Students are asked to use the given information to determine the cost of painting a barn.

Type: Problem-Solving Task

In this task, students are asked to determine the unit price of a product under two different circumstances. They are also asked to generalize the cost of producing *x* items in each case.

Type: Problem-Solving Task

The purpose of this task is to gain a better understanding of factors and common factors. Students should use the distributive property to show that the sum of two numbers that have a common factor is also a multiple of the common factor.

Type: Problem-Solving Task

Students are asked to reason about and explain the position of two locations relative to sea level.

Type: Problem-Solving Task

The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students are asked to compare the buying power of $20 in 1987 and 2012, at least with respect to movie tickets.

Type: Problem-Solving Task

Given the fact 13 x 17 = 221, students are asked to reason about and explain the decimal placement in multiplication and division problems where some of the numbers involved have been changed by powers of ten.

Type: Problem-Solving Task

Students are asked to solve a distance problem involving fractions.

Type: Problem-Solving Task

Students are asked to solve a fraction division problem using both a visual model and the standard algorithm within a real-world context.

Type: Problem-Solving Task

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

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

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

Students are asked to determine the percent of the area of a store covered by a security camera. Then, students are asked to determine the "best" place to position the camera and support their answer.

Type: Problem-Solving Task

Use the information provided to find out the original price of Selina's shirt. There are several different ways to reason through this problem; two approaches are shown.

Type: Problem-Solving Task

This problem is the fifth in a series of seven about ratios. Even though there are three quantities (the number of each candidates' votes), they are only considered two at a time.

Type: Problem-Solving Task

This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex. In this problem, the students are asked to determine the difference in votes received by two of the three candidates.

Type: Problem-Solving Task

This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions.

Type: Problem-Solving Task

This problem is the third in a series of tasks set in the context of a class election. Students are given a ratio and total number of voters and are asked to determine the difference between the winning number of votes received and the number of votes needed for victory.

Type: Problem-Solving Task

This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Students are given a ratio and total number of voters and are asked to determine the number of votes received by each candidate.

Type: Problem-Solving Task

This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes.

Type: Problem-Solving Task

This is the fourth in a series of tasks about ratios set in the context of a classroom election. Given only a ratio, students are asked to determine the fractional difference between votes received and votes required.

Type: Problem-Solving Task

Students are given a context and a dotplot and are asked a number of questions regarding shape, center, and spread of the data.

Type: Problem-Solving Task

Students are given a context and a series of questions and are asked to identify whether each question is statistical and to provide their reasoning. Students are asked to compose an original statistical question for the given context.

Type: Problem-Solving Task

Using the information provided, create an appropriate graphical display and answer the questions regarding shape, center and variability.

Type: Problem-Solving Task

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols. This requires converting simple percentages to decimals as well as identifying equivalent expressions without variables.

Type: Problem-Solving Task

Students are asked to determine if two expressions are equivalent and explain their reasoning.

Type: Problem-Solving Task

Students are asked to write and solve an inequality to determine the number of people that can safely rent a boat.

Type: Problem-Solving Task

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

Type: Problem-Solving Task

In this task students are asked to write two expressions from verbal descriptions and determine if they are equivalent. The expressions involve both percent and fractions. This task is most appropriate for a classroom discussion since the statement of the problem has some ambiguity.

Type: Problem-Solving Task

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

The student is asked to write and solve a two-step inequality to match the context.

Type: Problem-Solving Task

Students are asked to find the area of a shaded region using a diagram and the information provided. The purpose of this task is to strengthen student understanding of area.

Type: Problem-Solving Task

The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing. If used in an instructional setting, it would be good for students to have an opportunity to see other solution methods, perhaps by having students with different approaches explain their strategies to the class. Students who can only solve this by first converting the linear measurements will have a hard time solving problems where only area measures are given.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

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

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

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

Type: Problem-Solving Task

The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?

Type: Problem-Solving Task

Students are asked to use ratios and proportional reasoning to compare paint mixtures numerically and graphically.

Type: Problem-Solving Task

This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations.

Type: Problem-Solving Task

Students are asked to make comparisons among the Egyptian, Gregorian, and Julian methods of measuring a year.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

5,000 people visited a book fair in the first week. The number of visitors increased by 10% in the second week. How many people visited the book fair in the second week?

Type: Problem-Solving Task

Using the information provided find out how fast Anya rode her bike.

Type: Problem-Solving Task

This problem has multiple steps. In order to solve the problem it is necessary to compute: the value of the TunesTown shares; the total value of the BeatStreet offer of 20 million shares at $25 per share; the difference between these two amounts; and the cost per share of each of the extra 2 million shares MusicMind offers to equal to the difference.

Type: Problem-Solving Task

In this activity, the student is asked to solve a variety of equations (one solution, infinite solutions, no solution) in the traditional algebraic manner and to use pictures of a pan balance to show the solution process.

Type: Problem-Solving Task

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

This task asks the student to graph and compare two proportional relationships and interpret the unit rate as the slope of the graph. Students are also asked to write an equation and graph each scenario.

Type: Problem-Solving Task

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

The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

Type: Problem-Solving Task

This task emphasizes the importance of the "every input has exactly one output" clause in the definition of a function, which is violated in the table of values of the two populations. Noteworthy is that since the data is a collection of input-output pairs, no verbal description of the function is given, so part of the task is processing what the "rule form" of the proposed functions would look like.

Type: Problem-Solving Task

This task can be played as a game where students have to guess the rule and the instructor gives more and more input output pairs. Giving only three input output pairs might not be enough to clarify the rule. Instructors might consider varying the inputs in, for example, the second table, to provide non-integer entries. A nice variation on the game is to have students who think they found the rule supply input output pairs, and the teachers confirms or denies that they are right. Verbalizing the rule requires precision of language. This task can be used to introduce the idea of a function as a rule that assigns a unique output to every input.

Type: Problem-Solving Task

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.

Type: Problem-Solving Task

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

Type: Problem-Solving Task

This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents.

Type: Problem-Solving Task

In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable. This task could be used in different ways: To generate a class discussion about graphing. As a quick assessment about graphing, for example during a class warm-up. To engage students in small group discussion.

Type: Problem-Solving Task

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

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

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

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

This task provides an opportunity to apply the Pythagorean theorem to multiple triangles in order to determine the length of the hypotenuse; the converse of the Pythagorean theorem is also required in order to conclude that certain angles are right angles.

Type: Problem-Solving Task

Students are asked to determine which sale option results in the largest percent decrease in cost.

Type: Problem-Solving Task

The sales team at an electronics store sold 48 computers last month. The manager at the store wants to encourage the sales team to sell more computers and is going to give all the sales team members a bonus if the number of computers sold increases by 30% in the next month. How many computers must the sales team sell to receive the bonus? Explain your reasoning.

Type: Problem-Solving Task

Students are asked to solve a problem using proportional reasoning in a real world context to determine the number of shares needed to complete a stock purchase.

Type: Problem-Solving Task

Students are asked to solve a multistep ratio problem in a real-world context.

Type: Problem-Solving Task

After eating at your favorite restaurant, you know that the bill before tax is $52.60 and that the sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much should you leave for the waiter? How much will the total bill be, including tax and tip?

Type: Problem-Solving Task

The purpose of this task is for students to calculate the percent increase and relative cost in a real-world context. Inflation, one of the big ideas in economics, is the rise in price of goods and services over time. This is considered in relation to the amount of money you have.

Type: Problem-Solving Task

The purpose of this task is to see how well students students understand and reason with ratios.

Type: Problem-Solving Task

In a poll of Mr. Briggs's math class, 67% of the students say that math is their favorite academic subject. The editor of the school paper is in the class, and he wants to write an article for the paper saying that math is the most popular subject at the school. Explain why this is not a valid conclusion and suggest a way to gather better data to determine what subject is most popular.

Type: Problem-Solving Task

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

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

In this resource, students experiment with the reflection of a triangle in a coordinate plane.

Type: Problem-Solving Task

This resource involves a simple data-gathering activity which furnishes data that students organize into a table. They are then asked to refer to the data and determine the probability of various outcomes.

Type: Problem-Solving Task

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

This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). There are two important goals in this task: seeing the need for random sampling and using randomization to investigate the behavior of a sample statistic. These introduce the basic ideas of statistical inference and can be accomplished with minimal knowledge of probability.

Type: Problem-Solving Task

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

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

The purpose of this task is for students to compute the theoretical probability of a compound event. Teachers may wish to emphasize the distinction between theoretical and experimental probabilities for this problem. For students learning to distinguish between theoretical and experimental probability, it would be good to find an experimental probability either before or after students have calculated the theoretical probability.

Type: Problem-Solving Task

The purpose of this task is for students to compute the theoretical probability of a seating configuration. There are 24 possible configurations of the four friends at the table in this problem. Students could draw all 24 configurations to solve the problem but this is time consuming and so they should be encouraged to look for a more systematic method.

Type: Problem-Solving Task

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

The purpose of this task is for students to apply a reflection to a single point. The standard asks students to apply the effect of a single transformation on two-dimensional figures. Although this problem only applies a reflection to a single point, it has high cognitive demand if the students are prompted to supply a picture. This is because the coordinates of the point (1000,2012) are very large. If students try to plot this point and the line of reflection on the usual x-y coordinate grid, then either the graph will be too big or else the point will lie so close to the line of reflection that it is not clear whether or not it lies on this line. A good picture requires a careful choice of the appropriate region in the plane and the corresponding labels. Moreover, reflections of two-dimensional figures are found by reflecting individual points.

Type: Problem-Solving Task

The task is intended for instructional purposes and assumes that students know the properties of rigid transformations. Note that the vertices of the rectangles in question do not fall exactly at intersections of the horizontal and vertical lines on the grid. This means that students need to approximate and this provides an extra challenge. Also providing a challenge is the fact that the grids have been drawn so that they are aligned with the diagonal of the rectangles rather than being aligned with the vertical and horizontal directions of the page. However, this choice of grid also makes it easier to reason about the reflections.

Type: Problem-Solving Task

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

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

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

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

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

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

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

This task is ideally suited for instruction purposes where students can take their time and develop several of the standards, as the mathematical content is directly related to, but somewhat exceeds, the content of the standard on sums of angles in triangles. Careful analysis of the angles requires students to construct valid arguments using abstract and quantitative reasoning. Producing the picture in part (c) helps students identify a common mathematical argument repeated multiple times. Students may use pattern blocks to develop the intuition for decomposing the hexagon into triangles.

Type: Problem-Solving Task

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

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

Students are asked to examine a scatter plot and then interpret its meaning. Students should identify the form of the relationship (linear, curved, etc.), the direction or correlation (positive or negative), any specific outliers, the strength of the relationship between the two variables, and any other relevant observations.

Type: Problem-Solving Task

In this resource, real-world bivariate data is displayed in a scatter plot. The equation of the linear function which models the relationship between the two variables is provided, and it is graphed on the scatter plot. Students are asked to use the model to interpret the data and to make predictions.

Type: Problem-Solving Task

This purpose of this task is to help students understand what happens when you scale the dimensions of a right rectangular solid. This task provides an opportunity to compare the relative volumes of boxes in order to calculate the mass of clay required to fill them. These relative volumes can be calculated geometrically, filling the larger box with smaller boxes, or arithmetically using the given dimensions.

Type: Problem-Solving Task

This task provides the opportunity for students to reason about graphs, slopes, and rates without having a scale on the axes or an equation to represent the graphs. Students who prefer to work with specific numbers can write in scales on the axes to help them get started.

Type: Problem-Solving Task

In this task students interpret two graphs that look the same but show very different quantities. The first graph gives information about how fast a car is moving while the second graph gives information about the position of the car. This problem works well to generate a class or small group discussion. Students learn that graphs tell stories and have to be interpreted by carefully thinking about the quantities shown.

Type: Problem-Solving Task

In this task, the rule of the function is more conceptual. We assign to a year (an input) the total amount of garbage produced in that year (the corresponding output). Even if we didn't know the exact amount for a year, it is clear that there will not be two different amounts of garbage produced in the same year. Thus, this makes sense as a "rule" even though there is no algorithmic way to determine the output for a given input except looking it up in the table.

Type: Problem-Solving Task

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

Students are asked a series of questions involving a fraction and a whole number within the context of a recipe. Students are asked to solve a problem using both a visual model and the standard algorithm.

Type: Problem-Solving Task

Students are asked to solve a distance problem involving fractions. The purpose of this task is to help students extend their understanding of division of whole numbers to division of fractions, and given the simple numbers used, it is most appropriate for students just learning about fraction division because it lends itself easily to a pictorial solution.

Type: Problem-Solving Task

The purpose of this task is for students to solve problems involving multiplication and division of decimals in the real-world context of setting financial goals. The focus of the task is on modeling and understanding the concept of setting financial goals, so fluency with the computations will allow students to focus on other aspects of the task.

Type: Problem-Solving Task

In this problem-solving task students are challenged to apply their understanding of linear relationships to determine the amount of chicken and steak needed for a barbecue, which will include creating an equation, sketching a graph, and interpreting both. This resource also includes annotated solutions.

Type: Problem-Solving Task

Students are asked to create and graph linear equations to compare the savings of two individuals. The purpose of the table in (a) is to help students complete (b) by noticing regularity in the repeated reasoning required to complete the table.

Type: Problem-Solving Task

This task asks students to reason about the relative costs per pound of two fruits without actually knowing what the costs are. Students who find this difficult may add a scale to the graph and reason about the meanings of the ordered pairs. Comparing the two approaches in a class discussion can be a profitable way to help students make sense of slope.

Type: Problem-Solving Task

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Type: Problem-Solving Task

Students need to reason as to how they can use the Pythagorean Theorem to find the distances ran by Ben Watson and Champ Bailey. The focus here should not be on who ran a greater distance but on seeing how to set up right triangles to apply the Pythagorean Theorem to this problem. Students must use their measurement skills and make reasonable estimates to set up triangles and correctly apply the Theorem.

Type: Problem-Solving Task

Students are asked to solve a real-world problem involving common multiples.

Type: Problem-Solving Task

Students are asked to use fractions to determine how many hours it will take a car to travel a given distance.

Type: Problem-Solving Task

Students are asked to use fractions to determine how long a video game can be played.

Type: Problem-Solving Task

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

Use the information provided to find out what percentage of Dana's lot won't be covered by the house.

Type: Problem-Solving Task

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

In this problem-solving task students are challenged to apply their understanding of linear relationships to determine the amount of chicken and steak needed for a barbecue, which will include creating an equation, sketching a graph, and interpreting both. This resource also includes annotated solutions.

Type: Problem-Solving Task

This problem-solving task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation. Commentary and illustrated solutions are included.

Type: Problem-Solving Task

This task asks the student to understand the relationship between slope and changes in *x*- and *y*-values of a linear function.

Type: Problem-Solving Task

This activity challenges students to recognize the relationship between slope and the difference in *x-* and *y-*values of a linear function. Help students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation.

Type: Problem-Solving Task

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

The student is asked to perform operations with numbers expressed in scientific notation to decide whether 7% of Americans really do eat at Giantburger every day.

Type: Problem-Solving Task

This is an instructional task meant to generate a conversation around the meaning of negative integer exponents. It is good for students to learn the convention that negative time is simply any time before t=0.

Type: Problem-Solving Task

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

Students are asked to write complete sentences to describe ratios for the context.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

The purpose of this task is to help students explore the meaning of fraction division and to connect it to what they know about whole-number division. Students are asked to explain why the quotient of two fractions with common denominators is equal to the quotient of the numerators of those fractions.

Type: Problem-Solving Task

This task builds on a fifth grade fraction multiplication task, "Drinking Juice." This task uses the identical context, but asks the corresponding "Number of Groups Unknown" division problem. See "Drinking Juice, Variation 3" for the "Group Size Unknown" version.

Type: Problem-Solving Task

Students are asked to solve a fraction division problem using a visual model and the standard algorithm.

Type: Problem-Solving Task

Students are asked to solve problems from context by using multiplication or division of decimals.

Type: Problem-Solving Task

This instructional task requires that the students model each problem with some type of fractions manipulatives or drawings. This could be pattern blocks, student or teacher-made fraction strips, or commercially produced fraction pieces. At a minimum, students should draw pictures of each. The above problems are meant to be a progression which require more sophisticated understandings of the meaning of fractions as students progress through them.

Type: Problem-Solving Task

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

The purpose of this task is for students to apply their knowledge of integers in a real-world context.

Type: Problem-Solving Task

Students are asked to add or subtract decimals to solve problems in context.

Type: Problem-Solving Task

Students are asked to write and solve an equation in one variable to answer a real world question.

Type: Problem-Solving Task

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

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

Type: Problem-Solving Task

Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.

Type: Problem-Solving Task

In this task students are asked to write an equation to solve a real-world problem.

Type: Problem-Solving Task

Students are asked to write an equation with one variable in order to find the distance walked.

Type: Problem-Solving Task

This purpose of this task is to help students understand the absolute value of a number as its distance from 0 on the number line. The context is not realistic, nor is meant to be; it is a thought experiment to help students focus on the relative position of numbers on the number line.

Type: Problem-Solving Task

Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete.

Type: Problem-Solving Task

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

Students are asked to use a given ratio to determine if two different interpretations of the ratio are correct and to determine the maximum quantity that could be purchased within a given context.

Type: Problem-Solving Task

Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time.

Type: Problem-Solving Task

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

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

Type: Text Resource

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

Type: Text Resource

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

Type: Text Resource

## Tutorials

This Khan Academy tutorial video explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10. Exponents are NOT discussed.

Type: Tutorial

This Khan Academy tutorial video presents the methodology of understanding and using patterns in the number of zeros of products that have a factor that is a power of 10. While the standard does not mention exponents, the place value understanding of multiplying or dividing by powers of ten will help students understand multiplying and dividing by decimals.

Type: Tutorial

This Khan Academy tutorial video presents the pattern, when multiplying tens, that develops when we compare the number of factors of tens with the number of zeros in the product. The vocabulary, *exponent *and* base*, are introduced.

Type: Tutorial

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

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

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

In this video, we find missing angle measures from a variety of examples.

Type: Tutorial

The video will use algebra to find the measure of two angles whose sum equals 90 degrees, better known as complementary angles.

Type: Tutorial

Watch as we use algebra to find the measure of two complementary angles.

Type: Tutorial

Watch as we use algebra to find the measure of supplementary angles, whose sum is 180 degrees.

Type: Tutorial

This video will show how to solve a consecutive integer problem.

Type: Tutorial

In this video, you will practice describing the shape of distributions as skewed left, skewed right, or symmetrical.

Type: Tutorial

Students will learn that non-zero numbers to the zero power equal one. They will also learn that zero to any positive exponent equals zero.

Type: Tutorial

This video demonstrates several examples of finding probability of random events.

Type: Tutorial

This video discusses the limits of probability as between 0 and 1.

Type: Tutorial

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

Type: Tutorial

This video shows how the area and circumference relate to each other and how changing the radius of a circle affects the area and circumference.

Type: Tutorial

In this video, students are shown the parts of a circle and how the radius, diameter, circumference and Pi relate to each other.

Type: Tutorial

This video shows how to find the circumference, the distance around a circle, given the area.

Type: Tutorial

This video demonstrates how to find the probability of a simple event.

Type: Tutorial

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

Type: Tutorial

This video demonstrates development and use of a probability model.

Type: Tutorial

This video explores how to create sample spaces as tree diagrams, lists and tables.

Type: Tutorial

This video shows how to use a sample space diagram to find probability.

Type: Tutorial

The video will show how to use a table to find the probability of a compound event.

Type: Tutorial

This video shows an example of using a tree diagram to find the probability of a compound event.

Type: Tutorial

This video uses knowledge of vertical angles to solve for the variable and the angle measures.

Type: Tutorial

This video uses facts about supplementary and adjacent angles to introduce vertical angles.

Type: Tutorial

This video demonstrates solving a word problem involving angle measures.

Type: Tutorial

This video discusses constructing a right isosceles triangle with given constraints and deciding if the triangle is unique.

Type: Tutorial

This video demonstrates drawing a triangle when the side lengths are given.

Type: Tutorial

In this video, watch as we find the area of a circle when given the diameter.

Type: Tutorial

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

Type: Tutorial

This video shows how to construct and solve a basic linear equation to solve a word problem.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

In this video, you will practice using arithmetic properties with integers to determine if expressions are equivalent.

Type: Tutorial

In this video, you will work through an example to correctly use the order of operations.

Type: Tutorial

You will discover rules to help you determine the sign of an exponential expression with a base of -1.

Type: Tutorial

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

Type: Tutorial

This video shows how to find the value of a missing piece of data if you know the mean of the data set.

Type: Tutorial

This video shows how to recognize and understand graphs of proportional relationships to find the constant of proportionality.

Type: Tutorial

This introductory video teaches about combining like terms in linear equations.

Type: Tutorial

This video demonstrates how to construct a box plot, formerly known as a box and whisker plot.

Type: Tutorial

In this tutorial, you will apply what you know about multiplying negative numbers to determine how negative bases with exponents are affected and what patterns develop.

Type: Tutorial

Find the volume of an object, given dimensions of a rectangular prism filled with water, and the incremental volume after the object is dropped into the water.

Type: Tutorial

This video involves packing a larger rectangular prism with smaller ones which is solved in two different ways.

Type: Tutorial

The video will demonstrate the difference between supplementary angles and complementary angles, by using the given measurements of angles.

Type: Tutorial

In this tutorial, you will see how mixed numbers can be divided.

Type: Tutorial

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

Type: Tutorial

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

In this video, discover another way of finding the volume of a rectangular prism involves dividing it into fractional cubes, finding the volume of one, and then multiplying that area by the number of cubes that fit into the rectangular prism.

Type: Tutorial

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

This video shows how to solve a word problem involving rectangular prisms.

Type: Tutorial

This video demonstrates finding a unit rate from a rate containing fractions.

Type: Tutorial

This video demonstrates how to construct nets for 3-D shapes.

Type: Tutorial

Watch as we solve a rate problem finding speed in meters per second using distance (in meters) and time (in seconds).

Type: Tutorial

This video demonstrates using a net to find surface area.

Type: Tutorial

Learn how to create histograms, which summarize data by sorting it into groups.

Type: Tutorial

Here's an introduction to basic algebraic equations of the form ax = b in this tutorial.

Type: Tutorial

In this tutorial, we will solve equations in one step by multiplying or dividing a number on both sides.

Type: Tutorial

The video will solve the inequality and graph the solution.

Type: Tutorial

Learn how to test if a certain value of a variable makes an inequality true in this tutorial.

Type: Tutorial

Learn how to test if a certain value of a variable makes an equation true in this tutorial.

Type: Tutorial

This video demonstrates how to write and solve a one-step addition equation.

Type: Tutorial

To find the value of a variable, you have to get it on one side of the equation alone. To do that, you'll need to do something to BOTH sides of the equation.

Type: Tutorial

This video provides a conceptual explanation of why one needs to divide both sides of an equation to solve for a variable.

Type: Tutorial

In an equation with 2 variables, we will be able to determine which is the dependent variable, and which is the independent variable.

Type: Tutorial

Learn how to write basic algebraic expressions.

Type: Tutorial

Learn how to write inequalities to model real-world situations.

Type: Tutorial

Learn how to write simple algebraic expressions.

Type: Tutorial

Learn how to write basic expressions with variables to portray situations described in word problems.

Type: Tutorial

Learn how to apply the distributive law of multiplication over addition and why it works. This is sometimes just called the distributive law or the distributive property.

Type: Tutorial

Learn how to apply the distributive property of multiplication over subtraction. This is sometimes just called the distributive property or distributive law.

Type: Tutorial

Learn how to apply the distributive property to algebraic expressions.

Type: Tutorial

This video demonstrates solving word problems involving the coordinate plane.

Type: Tutorial

The focus here is understanding that a variable is just a symbol that can represent different values in an expression.

Type: Tutorial

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

Type: Tutorial

This video demonstrates evaluating expressions with two variables.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

Students will simplify an expression by combining like terms.

Type: Tutorial

Students will plot an ordered pair on the x (horizontal) axis and y (vertical) axis of the coordinate plane.

Type: Tutorial

This tutorial is an explanation on how to combine like terms in algebra.

Type: Tutorial

This video demonstrates the prime factorization method to find the lcm (least common multiple).

Type: Tutorial

This video contains examples of plotting coordinate pairs and identifying their quadrant.

Type: Tutorial

This video discusses the negative sign as meaning "opposite."

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

In this tutorial you will compare the absolute value of numbers using the concepts of greater than (>), less than (<), and equal to (=).

Type: Tutorial

This video guides you through comparisons of values, including opposites.

Type: Tutorial

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

Type: Tutorial

This video demonstrates evaluating inequality statements, some involving absolute value, using a number line.

Type: Tutorial

This is an introduction to combining like terms in this tutorial.

Type: Tutorial

This video demonstrates solving absolute value inequality statements.

Type: Tutorial

Students will evaluate expressions using the order of operations.

Type: Tutorial

This video is about interpreting absolute value in a real-life situation.

Type: Tutorial

Students will learn how to identify the four quadrants in the coordinate plane.

Type: Tutorial

This video uses a number line to describe the opposite of a number.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

This video demonstrates dividing two numbers that are decimals.

Type: Tutorial

This video portrays a proof of the formula for area of a parallelogram.

Type: Tutorial

This video demonstrates how to evaluate expressions with whole number exponents.

Type: Tutorial

A trapezoid is a type of quadrilateral with one set of parallel sides. Here we explain how to find its area.

Type: Tutorial

We will be able to find the area of a triangle in a coordinate grid. The formula for the area of a triangle is given in this tutorial.

Type: Tutorial

Students will learn the basics of finding the perimeter and area of squares and rectangles.

Type: Tutorial

Let's show subtracting with digits up to the thousandths place in this tutorial.

Type: Tutorial

Watch as we align decimals before subtracting in this tutorial.

Type: Tutorial

Learn how to add decimals and use place value in this tutorial.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

In the video, we find the percent when given the part and the whole.

Type: Tutorial

This video demonstrates how to find percent of a whole number.

Type: Tutorial

You're asked to find the whole when given the part and the percent.

Type: Tutorial

Learn how to find the full price when you know the discount price in this percent word problem.

Type: Tutorial

This video demonstrates how to write a decimal as a percent.

Type: Tutorial

This video demonstrates solving a unit price problem using equivalent ratios.

Type: Tutorial

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

This video deals with what percent really means by looking at a 10 by 10 grid.

Type: Tutorial

This video demonstrates a visual model of a percent greater than 100.

Type: Tutorial

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

Type: Tutorial

This tutorial explores the addition and subtraction of fractions with unlike denominators. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd). The video number line does show negative numbers which goes beyond elementary standards so an elementary teacher would need to reflect on whether this video will enrich student knowledge or cause confusion.

Type: Tutorial

In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases. Elementary teachers should note this is not a requirement for elementary standards and consider whether this video will further student knowledge or create confusion. This chapter explains how to find the smallest possible common denominator. *For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. *

Type: Tutorial

The Cartesian Coordinate system, formed from the Cartesian product of the real number line with itself, allows algebraic equations to be visualized as geometric shapes in two or three dimensions. While this tutorial includes the basis of Coordinate system, it also includes ideas beyond fifth grade standards. Most likely only advanced fifth graders would find the video engaging.

Type: Tutorial

A graph in Cartesian coordinates may represent a function or may only represent a binary relation. The "vertical line test" is a visual way to determine whether or not a graph represents a function.

Type: Tutorial

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

Type: Tutorial

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

## Video/Audio/Animations

Based upon the definition of speed, linear equations can be created which allow us to solve problems involving constant speeds, time, and distance.

Note: This video exceeds basic expectations for the mathematical concept(s) at this grade level. The video is intended for students who have demonstrated mastery within the scope of instruction who may be ready for a more rigorous extension of the mathematical concept(s). As with all materials, ensure to gauge the readiness of students or adapt according to student's needs prior to administration.

Type: Video/Audio/Animation

The video explains the process of creating linear equations to solve real-world problems.

Type: Video/Audio/Animation

When working with fractions, divisions can be converted to multiplication by the divisor's reciprocal. This chapter explains why.

Type: Video/Audio/Animation

Although the domain and codomain of functions can consist of any type of objects, the most common functions encountered in Algebra are real-valued functions of a real variable, whose domain and codomain are the set of real numbers, R.

Type: Video/Audio/Animation

Exponentiation can be understood in terms of repeated multiplication much like multiplication can be understood in terms of repeated addition. Properties of multiplication and division of exponential expressions with the same base are derived.

Type: Video/Audio/Animation

Percentages are one method of describing a fraction of a quantity. the percent is the numerator of a fraction whose denominator is understood to be one-hundred.

Type: Video/Audio/Animation

Two sets which are often of primary interest when studying binary relations are the domain and range of the relation.

Type: Video/Audio/Animation

"Slope" is a fundamental concept in mathematics. Slope of a linear function is often defined as " the rise over the run"....but why?

Type: Video/Audio/Animation

## Virtual Manipulative

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

Section:Grades PreK to 12 Education Courses >Grade Group:Grades 6 to 8 Education Courses >Subject:Mathematics >SubSubject:Remedial Mathematics >