## Course Standards

## General Course Information and Notes

### Version Description

In Geometry, instructional time will emphasize five areas: (1) proving and applying relationships and theorems involving two-dimensional figures using Euclidean geometry and coordinate geometry; (2) establishing congruence and similarity using criteria from Euclidean geometry and using rigid transformations; (3) extending knowledge of geometric measurement to two-dimensional figures and three-dimensional figures; (4) creating and applying equations of circles in the coordinate plane and (5)developing an understanding of right triangle trigonometry.

*All clarifications stated, whether general or specific to Geometry, 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

**Course Number:**1206310

**Course Path:**

**Abbreviated Title:**GEO

**Number of Credits:**One (1) credit

**Course Length:**Year (Y)

**Course Attributes:**

- Class Size Core Required

**Course Type:**Core Academic Course

**Course Level:**2

**Course Status:**State Board Approved

**Grade Level(s):**9,10,11,12

**Graduation Requirement:**Geometry

## Educator Certifications

## State Adopted Instructional Materials

**Author:**Sandy Bartle Finocchi and Amy Jones Lewis -

**Company:**Carnegie Learning, Inc. dba EMC Publishing & Mondo Ed -

**Edition:**1st -

**Copyright:**2023

**Author:**Kennedy, Milou, Thomas, Zbiek & Cuoco -

**Company:**Savvas Learning Company LLC -

**Edition:**1 -

**Copyright:**2023

**Author:**Agile Mind, the Charles A. Dana Center at the University of Texas at Austin -

**Company:**Agile Mind Educational Holdings, Inc. -

**Edition:**2021 -

**Copyright:**2021

**Author:**Cathy L. Seeley , Ed.D; Raj Shah, Ph.D.; Cheryl R. Tobey, M.Ed.; Dinah Zike, M.Ed.; Walter Secada, Ph.D. -

**Company:**McGraw Hill LLC -

**Edition:**1 -

**Copyright:**2023

**Author:**Ron Larson and Laurie Boswell -

**Company:**Big Ideas Learning, LLC -

**Edition:**1 -

**Copyright:**2023

**Author:**Math Nation -

**Company:**Math Nation (a division of Study Edge) -

**Edition:**1 -

**Copyright:**2023

**Author:**Hoyt, A., et al. -

**Company:**Mathspace Inc. -

**Edition:**1 -

**Copyright:**2022

## Student Resources

## Original Student Tutorials

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

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

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

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

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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 find the point on a directed line segment that partitions it into a given ratio 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 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

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

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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 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

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

## Perspectives Video: Professional/Enthusiasts

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

Type: Perspectives Video: Professional/Enthusiast

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

Type: Perspectives Video: Professional/Enthusiast

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!

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 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

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

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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

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

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

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

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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

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

## Text Resources

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

Type: Text Resource

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

Type: Text Resource

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

Type: Text Resource

## Tutorial

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

Type: Tutorial

Section:Grades PreK to 12 Education Courses >Grade Group:Grades 9 to 12 and Adult Education Courses >Subject:Mathematics >SubSubject:Geometry >