## Course Standards

## General Course Information and Notes

### Version Description

In grade 3 accelerated, instructional time will emphasize five areas: (1) extending understanding of place value in multi-digit whole numbers; (2) adding and subtracting multi-digit whole numbers, including using a standard algorithm; (3) building an understanding of multiplication and division, the relationship between them and the connection to area of rectangles; (4) developing an understanding of fractions and (5) extending geometric reasoning to lines, angles and attributes of quadrilaterals.

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

** Honors and Accelerated Level Course Note: **Accelerated courses require a greater demand on students through increased academic rigor. Academic rigor is obtained through the application, analysis, evaluation, and creation of complex ideas that are often abstract and multi-faceted. Students are challenged to think and collaborate critically on the content they are learning. Honors level rigor will be achieved by increasing text complexity through text selection, focus on high-level qualitative measures, and complexity of task. Instruction will be structured to give students a deeper understanding of conceptual themes and organization within and across disciplines. Academic rigor is more than simply assigning to students a greater quantity of work.

**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:**5012055

**Course Path:**

**Abbreviated Title:**GR 3 ACCEL MATH

**Course Length:**Year (Y)

**Course Attributes:**

- Class Size Core Required

**Course Type:**Core Academic Course

**Course Level:**3

**Course Status:**State Board Approved

**Grade Level(s):**K,1,2,3,4,5

## Educator Certifications

## State Adopted Instructional Materials

**Author:**R. Charles, et al -

**Company:**Savvas Learning Company LLC -

**Edition:**1 -

**Copyright:**2023

**Author:**Linda Gojak, M.Ed.; Annie Fetter, B.A.; Susie Katt, Ed.D.; Georgina Rivera, M.Ed.; John SanGiovanni, M.Ed.; Raj Shah, Ph.D.; Nicki Newton, Ed.D.; Cheryl Tobey M.Ed.; Ralph Connelly, Ph.D.; Ruth Harbin Miles, Ed.S.; Jeff Shih, Ph.D.; Dinah Zike, M.Ed.; Sharon Griffin, Ph.D. -

**Company:**McGraw Hill LLC -

**Edition:**1 -

**Copyright:**2023

**Author:**Dr. Jarrett Reid Whitaker -

**Company:**Accelerate Learning -

**Edition:**First Edition -

**Copyright:**2022

## Student Resources

## Original Student Tutorials

Learn more about how to empower and enourage others with your leadership skills in this interactive resiliency tutorial.

Type: Original Student Tutorial

Learn how to measure the mass of liquids (and some solids) using containers while Devin helps Chef Kyle in the bakery with this interactive 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 three-part series.

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

Learn about the defining attributes of a rectangle to identify and create rectangles as we visit various national parks in this interactive tutorial.

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

Ariana explores Area as she plants vegetables in her rectangular garden boxes. Help Ariana cover rectangles with unit squares without gaps or overlaps and count the squares to find the area with this interactive tutorial.

Type: Original Student Tutorial

Learn how to use a bar graph to summarize voting results at school in this interactive tutorial.

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

Type: Original Student Tutorial

United States citizens have a responsibility to vote. In this integrated civics and math tutorial, a class collects voting data to display in a table showing the students' and teachers' choices for a new school project.

Type: Original Student Tutorial

Learn about unit fractions and how to partition number lines to plot unit fractions' locations. Join Nik, Natalia, and their neighborhood friends on a number line fraction finding adventure in this interactive tutorial.

Type: Original Student Tutorial

Use visuals and formulas to find the perimeter and help Penelope as she creates a rectangular herb garden. Find the perimeter of rectangles using visuals and formulas in this student tutorial.

Type: Original Student Tutorial

Learn how to determine whether a whole number is a multiple of another whole number by using multiplication facts and skip-counting. You will be able to help Detective Barker in solving this mystery of which multiples belong to which whole numbers.

Type: Original Student Tutorial

Discover how multiplicative comparison problems, from outer space, can be solved using division in this online 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

Help pack for a square picnic while learning about the defining attributes of a square in comparison to rectangles in this interactive tutorial.

Type: Original Student Tutorial

Learn about the defining attributes of a square and what makes a square different from a rhombus in this interactive tutorial.

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

Determine if the sum of three odd or three even numbers will be odd or even as Lilly prepares for a math celebration in this interactive tutorial.

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

- Part 1 - Party Patterns: Odds and Evens in Addition
- Part 2 - Party Patterns: Odds and Evens in Addition

Type: Original Student Tutorial

Explore addition patterns to find if the sum of an odd and an even number will be odd or even in this interactive tutorial.

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

- Part 1 - Party Patterns: Evens and Odds in Addition
- Part 3 - Party Patterns: Evens and Odds in Addition (COMING SOON)

Type: Original Student Tutorial

Determine whether the sum of two odd numbers is odd or even and whether the sum of two even numbers is odd or even by helping Lilly prepare for a math celebration in this interactive tutorial.

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

- Part 2: Party Patterns: Evens and Odds in Addition (COMING SOON)
- Part 3: Party Patterns: Evens and Odds in Addition (COMING SOON)

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

Help Barkley learn to round numbers to the nearest hundred and bury delicious bones in this dog-themed, interactive tutorial.

Click **HERE **to open "Rounding Whole Numbers Part 1: To the Nearest Ten"

Type: Original Student Tutorial

Decompose and compose various angles while exploring clocks and windows in this interactive tutorial.

Note: this tutorial exceeds clarification limits and is meant as enrichment for students to improve their problem-solving skills.

Type: Original Student Tutorial

Joey uses his knowledge of fractions to win games at camp by knowing where fractions greater than one are located on number lines, in this interactive tutorial.

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

Help Jaliah continue to plan her birthday party and be fluent in her math facts using helpful facts she already knows, and the relationship between multiplication and division in Part 2 of this interactive tutorial.

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

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

Jaliah is ready to celebrate her birthday and use strategies of doubling and halving and relating multiplication and division for building fluency with multiplication and division facts in this interactive tutorial.

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

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 to use number lines to represent fractions as Emmy explores nature 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

Joey learns about the location of unit fractions on a number line while at camp in this interactive tutorial.

Type: Original Student Tutorial

Solve some two-step word problems and write equations about sea turtles and how pollution created by people is impacting their survival in this interactive tutorial.

Type: Original Student Tutorial

Learn about equivalent 10ths and 100ths and how to calculate these equivalent fractions at the fair in this interactive tutorial.

Type: Original Student Tutorial

Learn how to round larger whole numbers to any place value while exploring endangered species in this interactive tutorial.

Note: this tutorial exceeds clarification limits and is meant as enrichment for students who met the standards to increase problem-solving skills.

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

Are you up for a challenge? You will use tile designs to explore how angles can be decomposed into smaller angles and how those parts can be shown as addends in equations in this interactive tutorial.

Note: this tutorial exceeds clarification limits and is meant as enrichment for students who met the standards to increase problem-solving skills.

Type: Original Student Tutorial

Launch into solving word problems that use multiplicative comparisons, drawings, and symbols in this space-themed interactive tutorial.

Type: Original Student Tutorial

Explore how multiplication can help you solve division problems during this moon-themed, interactive tutorial.

Type: Original Student Tutorial

Join Pete as he explores patterns within patterns with feisty Wubbles and Dipples in this interactive tutorial.

Type: Original Student Tutorial

Learn how tilling can be used to find the area of different rectangular rooms in this interactive tutorial.

Type: Original Student Tutorial

Come play with Marty the monkey as he teaches you how to understand the concept of multiplication in this interactive tutorial.

Type: Original Student Tutorial

Use equivalent fractions to compare fractions in this garden-themed, interactive tutorials

This is Part 2 in a two-part series. Click to open Part 1, “Mama’s Pizza, Butterflies, & Comparing Fractions.”

Type: Original Student Tutorial

Help a family settle an argument about who got the most pizza and which butterfly was longer by comparing fractions using benchmarks and area models, in this interactive tutorial.

Type: Original Student Tutorial

In this video Sam-1 introduces a Model Eliciting Activity (MEA) challenge. Students will take their prior experiences from the properties unit and apply their knowledge of investigating sea turtle nesting temperatures.

Students will develop a hypothesis, design an experiment, and support their reasoning to determine how to best study different methods for cooling sea turtle nesting areas.

Type: Original Student Tutorial

In this video, SaM-1 introduces a part 2 twist to the Model Eliciting Activity (MEA). In the optional twist, students will need to modify their original diet for a senior chimpanzee. The first video provided meal planning information to add to the knowledge students gained throughout the unit to start the challenge.

Type: Original Student Tutorial

In this video, SaM-1 introduces a Model Eliciting Activity (MEA) challenge for the students. This video provides meal planning information to add to the knowledge students gained throughout the unit. Students will be asked to develop a varied diet for a chimpanzee at the CPALMS Rehabilitation and Conservation Center based on the color, shape, texture, and hardness of the food.

In the optional twist, students will need to modify their original diet for a senior chimpanzee. The optional twist also has a SaM-1 video to introduce the twist challenge.

Type: Original Student Tutorial

In this video, SaM-1 introduces a part 2 twist to the Model Eliciting Activity (MEA) challenge. In the optional twist, students will need to design a prototype toy suitable for a Florida panther with an injured leg. This first video provides background information on why and how animals need to be entertained.

Type: Original Student Tutorial

In this video, SaM-1 introduces a Model Eliciting Activity (MEA) challenge for the students. This video provides background information on why and how animals need to be entertained. Students will have the opportunity to apply what they learned about physical properties and measuring linear lengths as they are asked to design a prototype toy for Florida panthers housed at the CPALMS Rehabilitation and Conservation Center.

In the optional twist, students will need to design a prototype toy suitable for a Florida panther with an injured leg. The optional twist also has a SaM-1 video to introduce the twist challenge.

Type: Original Student Tutorial

In this video, SaM-1 introduces a part 2 twist to the Model Eliciting Activity (MEA) challenge. In the first video, students were asked to design a habitat for an elephant or gorilla that will be housed at the CPALMS Rehabilitation and Conservation Center. In this twist, students will need to modify their design to accommodate a senior elephant or gorilla.

Type: Original Student Tutorial

In this video, SaM-1 introduces a Model Eliciting Activity (MEA) challenge for the students. This video provides habitat information to help the students use the knowledge they gained throughout the unit. Students are asked to design a habitat for an elephant or gorilla that will be housed at the CPALMS Rehabilitation and Conservation Center. Students will need to describe the physical properties (color, shape, texture, hardness) of the features they selected for the habitat while explaining the rationale behind their design choices.

In the optional twist, students will need to modify their design to accommodate a senior elephant or gorilla. The optional twist also has a SaM-1 video to introduce the twist challenge.

Type: Original Student Tutorial

In this SaM-1 video, students will learn how to use a graduated cylinder to make observations based on the volume of liquids.

Type: Original Student Tutorial

Help SaM-1 make observations and sort items based on the mass of materials using a triple-beam balance and equal-arm balance. In this video, you will also become familiar with metric units for measuring mass: gram and kilogram.

Type: Original Student Tutorial

In this video, students will make observations based on the property of size, specifically length. Students will learn about the metric and customary measurement systems and use line plots to organize and sort data.

Type: Original Student Tutorial

Learn to calculate the perimeter of rectangular and composite shapes to help April finish designing her dream home in this interactive tutorial.

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

Type: Original Student Tutorial

Learn how to calculate perimeter and find a missing side measurement for a shape given the perimeter in this interactive tutorial.

This is the third in a three-part series about designing a dream house. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Help Barkley learn how to round numbers to the nearest ten with this interactive tutorial.

Type: Original Student Tutorial

Plan some gardens by applying what you learn about perimeter in this interactive tutorial.

Type: Original Student Tutorial

Help April calculate area and missing measurements for items in her perfect dream home in this interactive tutorial.

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

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 what makes prime and composite numbers unique thanks to an interesting backyard problem in 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

Learn how to compare numbers using the greater than and less than symbols in this interactive tutorial that compares some pretty cool things!

Type: Original Student Tutorial

Read and write multi-digit whole numbers using base-ten numerals and number names using the Base 10 place value system in this interactive tutorial.

Note: this tutorial exceeds the number limits of the benchmark.

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 how to write numbers using place value in different forms like standard, word, and expanded notation in this interactive tutorial.

Type: Original Student Tutorial

Calculate the product of multi-digit factors by decomposing factors and recording partial products in this interactive tutorial.

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

**Multi-Digit Multiplication Magic Part 1: Arrays****Multi-Digit Multiplication Magic Part 2: Area Models**- Multi-Digit Multiplication Magic Part 3: Recording Partial Products (current tutorial)

Type: Original Student Tutorial

See the magical power of area models when multiplying multi-digit numbers in this interactive tutorial.

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

**Multi-Digit Multiplication Magic Part 1: Arrays**- Multi-Digit Multiplication Magic Part 2: Area Models (Current Tutorial)
**Multi-Digit Multiplication Magic Part 3: Recording Partial Products**

Type: Original Student Tutorial

Learn to multiply by multiples of ten, in this interactive tutorial!

This is the second tutorial in a two-part series. .

Type: Original Student Tutorial

Learn to use arrays to solve multi-digit multiplication problems in this interactive tutorial.

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

**Multi-Digit Multiplication Magic Part 1: Arrays****Multi-Digit Multiplication Magic Part 2: Area Models****Multi-Digit Multiplication Magic Part 3: Recording Partial Products**

Type: Original Student Tutorial

Learn how to multiply a 1-digit number by ten using a pattern to help you. This interactive tutorial is Part 1 in a two-part series about multiplying by multiples of ten.

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

Help a surfing crab learn how to find parallel and perpendicular sides in a variety of polygons as you complete this interactive tutorial!

Type: Original Student Tutorial

Learn how to measure angles with a protractor to help get a robot through an obstacle course 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

Classify and name angles in two-dimensional shapes to help a robot create a path using angles in this interactive tutorial.

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 create equivalent fractions and visually see how they are equivalent in this interactive tutorial.

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

Type: Original Student Tutorial

Discover what an angle is by helping to program a robot through an obstacle course in this interactive tutorial.

Type: Original Student Tutorial

Learn strategies, like the commutative property, to help you become better at multiplying 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

Explore the relationships between tiling an area, multiplication arrays and calculating area using a formula in this interactive tutorial.

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 add multi-digit numbers using a standard algorithm in this interactive tutorial.

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 name or identify fractions, especially unit fractions, and justify the fractional value using an area model in this pizza-themed, 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 to read analog and digital clocks to the nearest minute in this interactive tutorial.

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

Learn to identify one square unit that can be used to measure area in this brief interactive tutorial.

Type: Original Student Tutorial

Help the Symmetry Sisters save the City of Symmetry Line and the State of Arithmetic from the Radical Rat in this interactive tutorial!

Type: Original Student Tutorial

Learn how to decompose a fraction into a sum of fractions with common denominators with this interactive tutorial.

Type: Original Student Tutorial

Learn to use the information presented in scaled bar graphs to solve one-step “how many more” and “how many fewer” problems.

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

Discover how square units can be used to cover the interior of a rectangle and measure its area of a rectangle in this interactive tutorial.

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

Learn how different-sized fractional parts can represent the same amount of a whole, different-sized fractional parts in different orientations can represent the same amount of a whole, and a number line can be used to represent fractional parts of a whole in this interactive tutorial.

Type: Original Student Tutorial

Identify right triangles and explain the properties shared by all right triangles in this interactive tutorial.

Type: Original Student Tutorial

Identify parallel lines and line segments, as well as perpendicular lines and line segments in two-dimensional figures by joining Parallel Man and Perpendicular Man as they help Mayor Mathematics save Mathopolis in this interactive tutorial.

Type: Original Student Tutorial

Help Speedy Sam add and subtract as quickly as possible by using the properties of addition and subtraction in this interactive tutorial.

Type: Original Student Tutorial

Learn how to round two-, three-, and four-digit numbers to the nearest 10 or 100 in this party-themed, interactive tutorial.

Type: Original Student Tutorial

Learn how to think differently to see if an equation is true or false, without even having to do the given math problem in this interactive tutorial on addition and subtraction relationships.

Type: Original Student Tutorial

Allie learns to be fair when she shares and she learns more about division in this interactive tutorial.

Type: Original Student Tutorial

Learn how to find equivalent fractions in a multiplication table in this interactive tutorial.

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

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

Learning about the attributes of a rhombus and how to create a rhombus using its attributes in this interactive tutorial.

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

## Educational Games

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

Type: Educational Game

This fun and engaging game will test your knowledge of whole numbers as prime or composite. As you shoot the asteroids with a particular factor, the asteroids will break down by that chosen factor. Keep shooting the correct factors to totally eliminate the asteroids. But be careful, shooting the wrong factor has consequences!

Type: Educational Game

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

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

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

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

*Percentages: *Identify the percentage of a whole number.

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

Type: Educational Game

This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

Type: Educational Game

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

Type: Educational Game

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

## Educational Software / Tool

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

Type: Educational Software / Tool

## Lesson Plan

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

Type: Lesson Plan

## Problem-Solving Tasks

This is a rectangle subdivision task; ideally instead of counting each square. students should break the letters into rectangles, multiply to find the areas, and add up the areas. However, students should not be discouraged from using individual counting to start if they are stuck. Often students will get tired of counting and devise the shortcut method themselves.

Type: Problem-Solving Task

The purpose of this task is to answer multiple questions regarding rounding. There still may be students who laboriously list every number; the teacher should encourage a more thoughtful approach.

Type: Problem-Solving Task

This task continues "Which pictures represent half of a circle?" moving into more complex shapes where geometric arguments about cutting or work using simple equivalences of fractions is required to analyze the picture. In order for students to be successful with this task, they need to understand that area is additive.

Type: Problem-Solving Task

This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal. In order for students to be successful with this task, they need to understand that area is additive.

Type: Problem-Solving Task

After students have drawn and measured their ten line segments, it might be more useful for the class to discuss part (b) as a whole group. It is a good idea to have the students use color to help them keep track of the connection between a line that they have drawn and the corresponding data point on the graph.

Type: Problem-Solving Task

For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

Type: Problem-Solving Task

Both of the questions are solved by the division problem 12÷3 but what happens to the ribbon is different in each case. The problem can be solved with a drawing of a tape diagram or number line. For problem 1, the line must be divided into 3 equal parts. The second problem can be solved by successive subtraction of 3 feet to see how many times it fits in 12.

Type: Problem-Solving Task

This task presents an incomplete problem and asks students to choose numbers to subtract (subtrahends) so that the resulting problem requires different types of regrouping. This way students have to recognize the pattern and not just follow a memorized algorithm--in other words, they have to think about what happens in the subtraction process when we regroup. This task is appropriate to use after students have learned the standard US algorithm.

Type: Problem-Solving Task

It is common for students to compare multi-digit numbers just by comparing the first digit, then the second digit, and so on. This task includes three-digit numbers with large hundreds digits and four-digit numbers with small thousands digits so that students must infer the presence of a 0 in the thousands place in order to compare. It also includes numbers with strategically placed zeros and an unusual request to order them from greatest to least in addition to the more traditional least to greatest.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

This is an instructional task that gives students a chance to reason about lines of symmetry and discover that a circle has an an infinite number of lines of symmetry. Even though the concept of an infinite number of lines is fairly abstract, students can understand infinity in an informal way.

Type: Problem-Solving Task

The purpose of this task is to give students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90° and that angle measure is additive.

Type: Problem-Solving Task

The purpose of this task is adding fractions with a focus on tenths and hundredths.

Type: Problem-Solving Task

This task is a straightforward task related to adding fractions with the same denominator. The main purpose is to emphasize that there are many ways to decompose a fraction as a sum of fractions.

Type: Problem-Solving Task

The fractions for this task have been carefully chosen to encourage and reward different methods of comparison. The first solution judiciously uses each of the following strategies when appropriate: comparing to benchmark fractions, finding a common denominator, finding a common numerator. The second and third solution shown use only either common denominators or numerators. Teachers should encourage multiple approaches to solving the problem. This task is mostly intended for instructional purposes, although it has value as a formative assessment item as well.

Type: Problem-Solving Task

The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.

Type: Problem-Solving Task

Students may not articulate every detail, but the basic idea for a case like the one shown here is that when you have equivalent fractions, you have just cut the pieces that represent the fraction into more but smaller pieces. Explaining fraction equivalences at higher grades can be a bit more involved (e.g. 6/8=9/12), but it can always be framed as subdividing the same quantity in different ways.

Type: Problem-Solving Task

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example. Students will need more opportunities to think about fraction equivalence with different examples and models, but this task represents a good first step.

Type: Problem-Solving Task

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Type: Problem-Solving Task

The focus of this task is on understanding that fractions, in an explicit context, are fractions of a specific whole. In this this problem there are three different wholes: the medium pizza, the large pizza, and the two pizzas taken together. This task is best suited for instruction. Students can practice explaining their reasoning to each other in pairs or as part of a whole group discussion.

Type: Problem-Solving Task

The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task. Notice that students are not asked to find the sum so this may be given to students who are limited to computing sums of fractions with the same denominator. Rather, they need to apply a firm understanding of unit fractions (fractions with one in the numerator) and reason about their relative size.

Type: Problem-Solving Task

The purpose of this task is to help students understand and articulate the reasons for the steps in the usual algorithm for converting a mixed number into an equivalent fraction. Step two shows that the algorithm is merely a shortcut for finding a common denominator between two fractions. This concept is an important precursor to adding mixed numbers and fractions with like denominators and as such, step two should be a point of emphasis. This task is appropriate for either instruction or formative assessment.

Type: Problem-Solving Task

This task is intended primarily for instruction. The goal is to provide examples for comparing two fractions, 1/5 and 2/7 in this case, by finding a benchmark fraction which lies in between the two. In Melissa's example, she chooses 1/4 as being larger than 1/5 and smaller than 2/7.

Type: Problem-Solving Task

This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes. For this particular task, teachers should anticipate two types of solution approaches: one where students subtract the whole numbers and the fractions separately and one where students convert the mixed numbers to improper fractions and then proceed to subtract.

Type: Problem-Solving Task

This task is designed to help students focus on the whole that a fraction refers. It provides a context where there are two natural ways to view the coins. While the intent is to deepen a student's understanding of fractions, it does go outside the requirements of the standard.

Type: Problem-Solving Task

The purpose of this task is to help students gain a better understanding of patterns. This task is meant to be used in an instructional setting.

Type: Problem-Solving Task

The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money.

Type: Problem-Solving Task

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions.

Type: Problem-Solving Task

The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

Type: Problem-Solving Task

How students tackle the problem and the amount of work they show on the number line can provide insight into the sophistication of their thinking. As students partition the interval between 0 and 1 into eighths, they will need to recognize that 1/2=4/8. Students who systematically plot every point, even 9/8, which is larger even than 1 may still be coming to grips with the relative size of fractions.

Type: Problem-Solving Task

The goal of this task is to help students gain a better understanding of fractions and their place on the number line.

Type: Problem-Solving Task

The purpose of this task is to present students with a context where they need to explain why two simple fractions are equivalent and is most appropriate for instruction.

Type: Problem-Solving Task

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

Type: Problem-Solving Task

This task includes the seeds of several important ideas. Part a presents the student with the opportunity to use a unit fraction to find 1 on the number line. Part b helps reinforce the notion that when a fraction has a numerator that is larger than the denominator, it has a value greater than 1 on the number line.

Type: Problem-Solving Task

The purpose of this task is for students to identify which fraction is closest to the whole number 1.

Type: Problem-Solving Task

The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.

Type: Problem-Solving Task

The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.

Type: Problem-Solving Task

In every part of this task, students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s).

Type: Problem-Solving Task

The first of these is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group?"

Type: Problem-Solving Task

In this task, the students are not asked to find an answer, but are asked to analyze the problems and explain their thinking. In the process, they are faced with varying ways of thinking about multiplication.

Type: Problem-Solving Task

The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication. Since addition is both commutative and associative, we can reorder or regroup addends any way we like. Students often believe the same is true for multiplication.

Type: Problem-Solving Task

The goal of this task is to work on finding multiples of some whole numbers on a multiplication grid. After shading in the multiples of 2, 3, and 4 on the table, students will see a key difference. The focus can be on identifying patterns or this can be an introduction or review of prime and composite numbers.

Type: Problem-Solving Task

The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.

Type: Problem-Solving Task

The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades. It builds on applying properties of operations as strategies to multiply and divide and interpreting a multiplication equation as a comparison.

Type: Problem-Solving Task

The purpose of this task is to have students add mixed numbers with like denominators. This task illustrates the different kinds of solution approaches students might take to such a task. Two general approaches should be anticipated: one where students calculate exactly how many buckets of blocks the boys have to determine an answer, and one where students compare the given numbers to benchmark numbers.

Type: Problem-Solving Task

The purpose of this task is for students to compare two fractions that arise in a context. Because the fractions are equal, students need to be able to explain how they know that. Some students might stop at the second-to-last picture and note that it looks like they ran the same distance, but the explanation is not yet complete at that point.

Type: Problem-Solving Task

This task is intended to assess adding of four numbers as given in the standard while still being placed in a problem-solving context. As written this task is instructional; due to the random aspect regarding when the correct route is found, it is not appropriate for assessment. This puzzle works well as a physical re-enactment, with paper plates marking the islands and strings with papers attached for the tolls.

Type: Problem-Solving Task

## Text Resources

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

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 Khan Academy tutorial video reviews how to determine if a number is prime or composite.

Type: Tutorial

In this tutorial, you will look at regrouping a number by different place values.

Type: Tutorial

The Khan Academy tutorial video presents a visual fraction model for adding 3/10 + 7/100 .

Type: Tutorial

This Khan Academy tutorial video presents the strategy for finding the measure of one of two adjacent angles, when the sum of both and measure of one are known.

Type: Tutorial

This Khan Academy tutorial video defines and illustrates parallel and perpendicular lines.

Type: Tutorial

This Khan Academy tutorial video identifies acute, right, and obtuse angles and justifies each identification.

Type: Tutorial

This Khan Academy tutorial video demonstrates the relationship between the measurement of an angle and the arc of a circle.

Type: Tutorial

This Khan Academy tutorial video presents how an angle is formed and labeled.

Type: Tutorial

In this Khan Academy tutorial video Chris is told to be home by 6:15. You know the number of minutes it takes him to get home. What time should he leave?

Type: Tutorial

This Khan Academy tutorial video presents a step-by-step solution for finding the length and width of a table when given its area and perimeter.

Type: Tutorial

In this Khan Academy video a fraction is converted from tenths to hundredths using grid diagrams.

Type: Tutorial

This Khan Academy video uses authentic pictures to present addition of two fractions with common denominators.

Type: Tutorial

This Khan Academy video solves two word problems using visual fraction models.

Type: Tutorial

This Khan Academy video illustrates that fraction a/b is equivalent to fraction (a *x* n)/(b x n).

Type: Tutorial

In this video tutorial from Khan Academy, view a demonstration of how to set-up an area model for multiplying a two-digit number by a two-digit number on graph or grid paper and then link this to the standard algorithm.

Type: Tutorial

In this tutorial video from Khan Academy, view an example of how to multiply a two-digit number by a two-digit number using the area model. The video makes a connection between partial products and the area model.

Type: Tutorial

In this video tutorial from Khan Academy, view an example and a description of how the distributive property can be used to multiply a two-digit number by a two-digit number. The second example uses the area model with the distributive property.

Type: Tutorial

In this Khan Academy video tutorial, view an example of multiplying a 4-digit number by a 1-digit number by expanding the 4-digit number and multiplying by each digit individually in an area model. This video will help to build an understanding before teaching the standard algorithm. Multiplying with a 4-digit factor is larger than some standards which limit factors to 3-digits.

Type: Tutorial

In this tutorial video from Khan Academy, view an example of how to multiply a 2-digit number by another 2-digit number. Be sure to stick around for the second example! The key is understanding the value of each digit!

Type: Tutorial

In this video tutorial from Khan Academy, view an example of how to solve a problem in which a **3-digit** number is being multiplied by a 1-digit number using the standard algorithm.

Type: Tutorial

In this video tutorial from Khan Academy, learn how to subtract in situations that require regrouping twice using the expanded forms of numbers, as well as the standard algorithm.

Type: Tutorial

Find area of two rectangles to solve a word problem.

Type: Tutorial

In this tutorial video from Khan Academy, explore the relationship between area and perimeter. For example, if you know the area and the length, can you find the perimeter?

Type: Tutorial

In this Khan Academy video tutorial, consider an alternate algorithm for subtracting multi-digit numbers mentally. This video is best for students that are already comfortable with using regrouping to subtract using the standard algorithm.

Type: Tutorial

In this tutorial video from Khan Academy, learn to use an abacus to represent multi-digit numbers. This video will explain how the beads on an abacus can each represent ten times the value of the bead to its right.

Type: Tutorial

This video discusses the differences between lines, line segments and rays.

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding that fractions are a way of showing part of a whole. Yet some fractions are larger than others. So this tutorial will help to refresh the understanding for the comparison of fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

## Virtual Manipulatives

This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.

Some of the sample learning goals can be:

- Build equivalent fractions using numbers and pictures.
- Compare fractions using numbers and patterns
- Recognize equivalent simplified and unsimplified fractions

Type: Virtual Manipulative

This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)

Type: Virtual Manipulative

Section:Grades PreK to 12 Education Courses >Grade Group:Grades PreK to 5 Education Courses >Subject:Mathematics >SubSubject:General Mathematics >