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This version of the course is updated to include additional certification information. No standards, benchmarks or clarifications have been changed.
Course Standards
General Course Information and Notes
Version Description
The benchmarks in this course are mastery goals that students are expected to attain by the end of the year. To build mastery, students will continue to review and apply earlier grade-level benchmarks and expectations.
General Notes
In grade 8, instructional time will emphasize six areas: (1) representing numbers in scientific notation and extending the set of numbers to the system of real numbers, which includes irrational numbers; (2) generate equivalent numeric and algebraic expressions including using the Laws of Exponents; (3) creating and reasoning about linear relationships including modeling an association in bivariate data with a linear equation; (4) solving linear equations, inequalities and systems of linear equations; (5) developing an understanding of the concept of a function and (6) analyzing two-dimensional figures, particularly triangles, using distance, angle and applying the Pythagorean Theorem.
Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
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
Educator Certifications
Section 1012.55(5), F.S., authorizes the issuance of a classical education teaching certificate, upon the request of a classical school, to any applicant who fulfills the requirements of s. 1012.56(2)(a)-(f) and (11), F.S., and Rule 6A-4.004, F.A.C. Classical schools must meet the requirements outlined in s. 1012.55(5), F.S., and be listed in the FLDOE Master School ID database, to request a restricted classical education teaching certificate on behalf of an applicant.
Student Resources
Original Student Tutorials
Explore the topic of Electricity including: how it is transformed into other types of energy, how a circuit works, and electrical conductors and insulators with this interactive research page.
Type: Original Student Tutorial
Glimpse into the variety of animal adaptations on Earth and the reasons these adaptations allow different animals to survive in various environments with this interactive research page.
Type: Original Student Tutorial
Learn how plants are adapted to their environment, including their life cycles, responses, physical characteristics, and ability to survive harsh environments with this interactive research page.
Type: Original Student Tutorial
Learn about organs and structures of the human body, including the senses, skin, muscles, and skeleton, with this interactive research page.
This is part 2 in a three-part series.
- Open Human Body: Part 1 (Heart, Lungs, Stomach, Brain, Reproductive)
- Open Human Body: Part 2 (Senses, Skin, Muscles, Skeleton)
- Open Human Body: Part 3 (Liver, Pancreas, Kidneys, Intestines, and Bladder)
Type: Original Student Tutorial
Explore forms of energy, including mechanical, electrical, heat, light, sound, and chemical, discover ways to investigate these forms of energy, and learn about related technology with this interactive tutorial.
Type: Original Student Tutorial
Explore the major climate zones on Earth and learn about the related weather patterns with this interactive research page.
Type: Original Student Tutorial
Learn about the impact of the growth and development of space exploration on the culture and economy of Florida and how the inclusion of private partners helped reach new goals with this interactive tutorial.
This is part 3 in a three-part series. Click below to view the other tutorials in the series.
- Part 1: To the Moon - Space and the Florida Frontier
- Part 2: The Space Shuttle Era - Space and the Florida Frontier
- Part 3: Partners in Exploration - Space and the Florida Frontier
Type: Original Student Tutorial
Learn about organs and structures of the human body, including the Liver, pancreas, kidneys, intestines, and bladder in this interactive research page.
This is part 3 in a three-part series.
- Open Human Body: Part 1 (Heart, Lungs, Stomach, Brain, Reproductive)
- Open Human Body: Part 2 (Senses, Skin, Muscles, Skeleton)
- Open Human Body: Part 3 (Liver, Pancreas, Kidneys, Intestines, and Bladder)
Type: Original Student Tutorial
Learn how the Space Shuttle program revived the area near Cape Canaveral, Florida, and how the possibility of living in space on the Space Station brought new jobs and excitement with this interactive tutorial.
This is part 2 in a three-part series. Click below to view the other tutorials in the series.
- Part 1: To the Moon - Space and the Florida Frontier
- Part 2: The Space Shuttle Era - Space and the Florida Frontier
- Part 3: Partners in Exploration - Space and the Florida Frontier
Type: Original Student Tutorial
Learn about the early days of NASA, the work at Cape Canaveral during the Moon missions, and how this work affected the people and economy of Florida with this interactive tutorial.
This is part 1 in a three-part series. Click below to view the other tutorials in the series.
- Part 1: To the Moon - Space and the Florida Frontier
- Part 2: The Space Shuttle Era - Space and the Florida Frontier
- Part 3: Partners in Exploration - Space and the Florida Frontier
Type: Original Student Tutorial
Learn more about how to empower and enourage others with your leadership skills in this interactive resiliency tutorial.
Type: Original Student Tutorial
Learn to measure and compare the mass of solids as Devin helps Chef Kyle in the bakery with this interactive tutorial.
Type: Original Student Tutorial
Learn about the heart, lungs, stomach, brain, and reproductive organs in this interactive research page on the organs and structures of the human body.
This is part 1 in a three-part series.
- Open Human Body: Part 1 (Heart, Lungs, Stomach, Brain, Reproductive)
- Open Human Body: Part 2 (Senses, Skin, Muscles, Skeleton)
- Open Human Body: Part 3 (Liver, Pancreas, Kidneys, Intestines, and Bladder)
Type: Original Student Tutorial
Learn about the water cycle's major stages and the importance of the ocean in the water cycle with this Interactive Science Research Page.
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
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
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
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
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
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
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
Explore how to express large quantities using scientific notation in this interactive tutorial.
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
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
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
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
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 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
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
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
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
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
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 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 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 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
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
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
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 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
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
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 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 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
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
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
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: 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
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
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
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
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
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
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
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 write and solve an inequality to determine the number of people that can safely rent a boat.
Type: Problem-Solving Task
The student is asked to write and solve a two-step inequality to match the context.
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
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' 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
In this resource, students experiment with the reflection of a triangle in a coordinate plane.
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
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 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
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
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 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
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
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
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 answer the question, "How does the composition of a scene influence how the viewer feels?"
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 discuss "How can an employee"s behaviors and actions drive their career stability and path?"
Type: Text Resource
Tutorials
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
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
This video demonstrates how to factor a linear expression by taking a common factor.
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
The video will demonstrate the difference between supplementary angles and complementary angles, by using the given measurements of angles.
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
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
Video/Audio/Animations
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
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
Congratulations
