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Course Standards
General Course Information and Notes
Version Description
In Mathematics for College Liberal Arts, instructional time will emphasize five areas: (1) analyzing and applying linear and exponential functions within a real-world context; (2) utilizing geometric concepts to solve real-world problems; (3) extending understanding of probability theory; (4) representing and interpreting univariate and bivariate data and (5) developing understanding of logic and set theory.
All clarifications stated, whether general or specific to Mathematics for College Liberal Arts, are expectations for instruction of that benchmark.
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.
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
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
Students will explore the impact of inflation in this financial literacy tutorial.
Type: Original Student Tutorial
Students will explore and compare simple and compound interest calculations.
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
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
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
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
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
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
Follow Jake along as he relates box plots with other plots and identifies possible outliers in real-world data from surveys of moviegoers' ages in part 2 in this interactive tutorial.
This is part 2 of 2-part series, click HERE to view part 1.
Type: Original Student Tutorial
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 Jake as he displays real-world data by creating box plots showing the 5 number summary and compares the spread of the data from surveys of the ages of moviegoers in part 1 of this interactive tutorial.
This is part 1 of 2-part series, click HERE to view part 2.
Type: Original Student Tutorial
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
Learn about exponential decay as you calculate the value of used cars by examining equations, graphs, and tables in this interactive tutorial.
Type: Original Student Tutorial
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
Learn how to interpret key features of linear functions and translate between representations of linear functions through exploring jobs for teenagers in this interactive tutorial.
Type: Original Student Tutorial
Learn about exponential growth in the context of interest earned as money is put in a savings account by examining equations, graphs, and tables in this interactive tutorial.
Type: Original Student Tutorial
Learn about exponential functions and how they are different from linear functions by examining real world situations, their graphs and their tables in this interactive tutorial.
Type: Original Student Tutorial
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
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 to calculate the volume of spheres while learning how they make Bubble Tea in this interactive tutorial.
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
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 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
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
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
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 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
Cite text evidence and make inferences about the "real" history of Halloween in this spooky interactive tutorial.
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
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
Follow as we construct an exponential function from a graph, from a table of values, and from a description of a relationship in the real world in this interactive tutorial.
Type: Original Student Tutorial
Learn how to use trigonometric ratios to find the heights of famous monuments and solve a real-world application in this interactive tutorial.
Type: Original Student Tutorial
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 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 calculate the volume of a cone as you solve real-world problems in this ice cream-themed, 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
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 Plans
Students will use the calculated population totals to create graphs that help to visualize the totals for analyzing and representation. Census data is used as the data to provide information to analyze. Students will then use basic functions and formulas in spreadsheets to help analyze and represent the data.
Type: Lesson Plan
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
Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.
Download the CPALMS Perspectives video student note taking guide.
Type: Perspectives Video: Expert
<p>It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!</p>
Type: Perspectives Video: Expert
Perspectives Video: Professional/Enthusiasts
<p>No need to sugar coat it: making candy involves math and muscles. Learn how light refraction and exponential growth help make candy colors just right!</p>
Type: Perspectives Video: Professional/Enthusiast
<p>Don't be a shrinking violet. Learn how uniform scaling is important for candy production.</p>
Type: Perspectives Video: Professional/Enthusiast
<p>See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.</p>
Type: Perspectives Video: Professional/Enthusiast
<p>You'll need to bring your computer skills and math knowledge to estimate oil volume and rate as it seeps from the ocean floor. Dive in!</p>
Type: Perspectives Video: Professional/Enthusiast
Problem-Solving Tasks
This problem solving task challenges students to determine if two weather events are independent, and use that conclusion to find the probability of having similar weather events under certain conditions.
Type: Problem-Solving Task
The task is intended to address sample space, independence, probability distributions and permutations/combinations.
Type: Problem-Solving Task
Students answer questions about the probabilities of independent and dependent events.
Type: Problem-Solving Task
This problem solving task lets students explore the concept of independence of events.
Type: Problem-Solving Task
This task combines the concept of independent events with computational tools for counting combinations, requiring fluent understanding of probability in a series of independent events.
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 task assesses a student's ability to use the addition rule to compute a probability and to interpret a probability in context.
Type: Problem-Solving Task
The purpose of this task is to assess a student's ability to explain the meaning of independence in a simple context.
Type: Problem-Solving Task
This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table.
Type: Problem-Solving Task
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
The purpose of this task is to assess ability to interpret the slope and intercept of the line of fit in context.
Type: Problem-Solving Task
This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.
Type: Problem-Solving Task
This task lets students explore the concepts of probability as a fraction of outcomes using two-way tables.
Type: Problem-Solving Task
This task asks students to calculate probabilities using information presented in a two-way frequency table.
Type: Problem-Solving Task
The task provides a context to calculate discrete probabilities and represent them on a bar graph.
Type: Problem-Solving Task
This problem solving task on probability combinations gives a situation where the numbers are too large to calculate, so abstract reasoning is required in order to compare the different probabilities.
Type: Problem-Solving Task
This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.
Type: Problem-Solving Task
This task involves a reasonably direct application of similar triangles, coupled with a moderately challenging procedure of constructing a diagram from a verbal description.
Type: Problem-Solving Task
The purpose of this task is to engage students in geometric modeling, and in particular to deduce algebraic relationships between variables stemming from geometric constraints.
Type: Problem-Solving Task
This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic using a table of data.
Type: Problem-Solving Task
In this example, students are asked to write a function describing the population growth of algae. It is implied that this is exponential growth.
Type: Problem-Solving Task
Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin. (For this task, United States coins are used, but the task can be adapted for coins from other countries.)
Type: Problem-Solving Task
This problem solving task asks students to find the area of an equilateral triangle. Various solutions are presented that include the Pythagoren theorem and trigonometric functions.
Type: Problem-Solving Task
This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat.
Type: Problem-Solving Task
This problem solving task encourages students to explore why solar eclipses are rare by examining the radius of the sun and the furthest distance between the moon and the earth.
Type: Problem-Solving Task
This task engages students in an open-ended modeling task that uses similarity of right triangles.
Type: Problem-Solving Task
Using a triangle with line through it, students are tasked to show the congruent angles, and conclude if one triangle is similar to the other.
Type: Problem-Solving Task
In this task, students will provide a sketch of a paper ice cream cone wrapper, use the sketch to develop a formula for the surface area of the wrapper, and estimate the maximum number of wrappers that could be cut from a rectangular piece of paper.
Type: Problem-Solving Task
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 find the surface area of a soda can, calculate how many cubic centimeters of aluminum it contains, and estimate how thick it is.
Type: Problem-Solving Task
This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.
Type: Problem-Solving Task
This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.
Type: Problem-Solving Task
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 goal of this task is to use geometry to study the structure of beehives.
Type: Problem-Solving Task
This problem solving task gives an interesting context for implementing ideas from geometry and trigonometry.
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
This problem solving task asks students to find the area of a triangle by using unit squares and line segments.
Type: Problem-Solving Task
The purpose of the task is to analyze a plausible real-life scenario using a geometric model. The task requires knowledge of volume formulas for cylinders and cones, some geometric reasoning involving similar triangles, and pays attention to reasonable approximations and maintaining reasonable levels of accuracy throughout.
Type: Problem-Solving Task
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 task provides an opportunity for students to apply triangle congruence theorems in an explicit, interesting context.
Type: Problem-Solving Task
This problem solving task challenges students to inscribe equilateral triangles and regular hexagons on a circle with a compass and straightedge.
Type: Problem-Solving Task
This problem solving task challenges students to construct a perpendicular bisector of a given segment.
Type: Problem-Solving Task
This task asks students to use a straightedge and compass to construct the line across which a triangle is reflected.
Type: Problem-Solving Task
The purpose of this task is to use geometric and algebraic reasoning to model a real-life scenario. In particular, students are in several places (implicitly or explicitly) to reason as to when making approximations is reasonable and when to round, when to use equalities vs. inequalities, and the choice of units to work with (e.g., mm vs. cm).
Type: Problem-Solving Task
This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere.
Type: Problem-Solving Task
This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a "double-naped cone" with vertex at the center of the sphere and bases equal to the bases of the cylinder
Type: Problem-Solving Task
This problem solving task asks students to explain certain characteristics about a triangle.
Type: Problem-Solving Task
This problem solving task challenges students to place a warehouse (point) an equal distance from three roads (lines).
Type: Problem-Solving Task
This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.
Type: Problem-Solving Task
This task provides a construction of the angle bisector of an angle by reducing it to the bisection of an angle to finding the midpoint of a line segment. It is worth observing the symmetry -- for both finding midpoints and bisecting angles, the goal is to cut an object into two equal parts.
Type: Problem-Solving Task
In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context.
Type: Problem-Solving Task
This problem solving task challenges students to find the linear, exponential and quadratic functions based on two points.
Type: Problem-Solving Task
This problem solving task asks students to predict and model US population based on a chart of US population data from 1982 to 1988.
Type: Problem-Solving Task
This problem solving task asks students to solve five exponential and linear function problems based on a US population chart for the years 1790-1860.
Type: Problem-Solving Task
This problem solving tasks asks students to find the values of points on a graph.
Type: Problem-Solving Task
This problem solving task asks students to graph a function and find the values of points on a graph.
Type: Problem-Solving Task
This problem is an exponential function example that uses the real-world problem of how fast rumors spread.
Type: Problem-Solving Task
The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills. In particular, students are introduced to the idea of inflation of prices of a single commodity, and are given a very brief introduction to the notion of the Consumer Price Index for measuring inflation of a body of goods.
Type: Problem-Solving Task
This task gives a variation of real-life contexts which could be modeled by a linear or exponential function. The key distinguishing feature between the two is whether the change by equal factors over equal intervals (exponential functions), or by a constant increase per unit interval (linear functions). The task could either be used as an assessment problem on this distinction, or used as an introduction to the differences between these very important classes of functions.
Type: Problem-Solving Task
This problem complements the problem "Do two points always determine a linear function?'' There are two constraints on a pair of points R1 and R2 if there is an exponential function f(x) = ae^bx whose graph contains R1 and R2.
Type: Problem-Solving Task
This exploratory task requires the student to use properties of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.
Type: Problem-Solving Task
This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies.
Type: Problem-Solving Task
This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.
Type: Problem-Solving Task
This task provides an interesting context to ask students to estimate values in an exponential function using a graph.
Type: Problem-Solving Task
The given solutions for this task involve the creation and solving of a system of two equations and two unknowns, with the caveat that the context of the problem implies that we are interested only in non-negative integer solutions. Indeed, in the first solution, we must also restrict our attention to the case that one of the variables is further even. This aspect of the task is illustrative of the mathematical practice of modeling with mathematics, and crucial as the system has an integer solution for both situations, that is, whether we include the dollar on the floor in the cash box or not.
Type: Problem-Solving Task
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
This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match. The first and third graphs look very similar at first glance, but the function values are very different since the scales on the vertical axes are very different. The task could also be used to generate a group discussion on interpreting functions given by graphs.
Type: Problem-Solving Task
The purpose of this task is to help students learn to read information about a function from its graph, by asking them to show the part of the graph that exhibits a certain property of the function. The task could be used to further instruction on understanding functions or as an assessment tool, with the caveat that it requires some amount of creativity to decide how to best illustrate some of the statements.
Type: Problem-Solving Task
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
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
The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.
Type: Problem-Solving Task
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
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 asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.
Type: Problem-Solving Task
Students are asked to examine data given in table format and then calculate either row percentages or column percentages and state a conclusion about the meaning of the data. Either calculation is appropriate for the solution since there is no clear relationship between the variables. Whether the student sees a strong association or not is less important than whether his or her answer uses the data appropriately and demonstrates understanding that an association means the distribution of favorite subject is different for 7th graders and 8th graders.
Type: Problem-Solving Task
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
This video will show to find the volume of a triangular prism, and a cube by applying the formula for volume.
Type: Tutorial
This tutorial will help you to learn about exponential functions by graphing various equations representing exponential growth and decay.
Type: Tutorial
Congratulations
