## Course Standards

## General Course Information and Notes

### Version Description

This course supports students who need additional instruction in foundational mathematics skills as it relates to core instruction. Instruction will use explicit, systematic, and sequential approaches to mathematics instruction addressing all domains including number sense & operations, fractions, algebraic reasoning, geometric reasoning, measurement and data analysis & probability. Teachers will use the listed standards that correspond to each students’ needs.

Effective instruction matches instruction to the need of the students in the group and provides multiple opportunities to practice the skill and receive feedback. The additional time allotted for this course is in addition to core instruction. The intervention includes materials and strategies designed to supplement core instruction.

### General Notes

** Florida’s Benchmarks for Excellent Student Thinking (B.E.S.T.) Standards**This course includes Florida’s B.E.S.T. ELA Expectations (EE) and Mathematical Thinking and Reasoning Standards (MTRs) for students. Florida educators should intentionally embed these standards within the content and their instruction as applicable. For guidance on the implementation of the EEs and MTRs, please visit https://www.cpalms.org/Standards/BEST_Standards.aspx and select the appropriate B.E.S.T. Standards package.

**English Language Development ELD Standards Special Notes Section:**

Teachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade-level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL’s need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link: http://www.cpalms.org/uploads/docs/standards/eld/MA.pdf

### General Information

**Course Number:**5012015

**Course Path:**

**Abbreviated Title:**FDN SKILLS MATH 3-5

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

**Course Attributes:**

- Class Size Core Required

**Course Type:**Elective Course

**Course Level:**1

**Course Status:**State Board Approved

## Educator Certifications

## Student Resources

## Original Student Tutorials

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

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!

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" [coming soon].

Type: Original Student Tutorial

Learn to determine the key 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!

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" [coming soon].

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

Explore the defining attributes of trapezoids--a special type of quadrilateral--and classify them using diagrams in this interactive tutorial. You'll also learn how two different definitions for a trapezoid can change affect classifications of quadrilaterals.

This part 6 in a 6-part series. Click below to explore the other tutorials in the series.

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

Part 4: Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams

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 rounding decimals through the thousandths place as you help Tyrese the Turtle train to race the hare in this interactive tutorial.

Type: Original Student Tutorial

Explore the mysterious poem “The House on the Hill” by Edwin Arlington Robinson in this interactive tutorial. As you explore the poem's message about the past, you’ll identify the features of a villanelle in the poem. By the end of this tutorial, you should be able to explain how the form of a villanelle contributes to the poem's meaning.

Type: Original Student Tutorial

Learn 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 explore excerpts from the beginning of the historical fiction novel *The Red Umbrella *by Christina Diaz Gonzalez in Part Two of this two-part series. In Part Two, you'll examine how setting influences characters.

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

Learn more about division with larger numbers in this aquarium-themed, interactive tutorial.

This is part 3 of in a three-part series. Click below to learn different strategies to help you become more efficient with division.

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 how to write a great "CER" paragraph that includes a claim, evidence, and reasoning with this interactive tutorial.

Type: Original Student Tutorial

Learn how to convert time from seconds to minutes, minutes to hours, and hours to days. In this interactive tutorial, you will also practice converting time to fractional amounts.

Type: Original Student Tutorial

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

Type: Original Student Tutorial

Help Buffy multiply fractions by whole numbers using the standard algorithm in addition to visual fraction models in this bakery-themed, interactive tutorial.

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

**Part 1: Visual Models and Multiplying Fractions****Part 2: Multiplying Fractions****Part 3 Using Models to Multiply a Fraction by a Whole Number**

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

Help Buffy the Baker multiply a fraction by a whole using models in this sweet interactive tutorial.

This is part 3 of a 4-part series. Click below to open other tutorials in the series.

**Part 1: Visual Models and Multiplying Fractions****Part 2: Multiplying Fractions****Part 4: Multiplying a Fraction by a Whole Number - Standard Algorithm**

Type: Original Student Tutorial

Help Buffy the Baker multiply fractions less than one by relating the standard algorithm to visual models as he runs his bakery in this interactive tutorial.

This is part 2 of a 4-part series. Click below to open other tutorials in the series.

Type: Original Student Tutorial

Explore how to add fractions less than one with unlike denominators in this magical, interactive tutorial.

Type: Original Student Tutorial

Learn why it's sometimes important to use social distancing to reduce the spread of germs and how to estimate and convert this customary distance with 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 **HERE** to open Part 1, “Mama’s Pizza, Butterflies, & Comparing Fractions.”

Type: Original Student Tutorial

Help build a Grasshopper Hut for Gus by creating line plots and answering questions about the line plots in this interactive tutorial.

Type: Original Student Tutorial

Learn about decimals on a number line and comparing decimals to save the Decis from a wizard's spell in this interactive tutorial.

Type: Original Student Tutorial

Help solve the problem of shipping video games and accessories to customers by calculating the volume of the containers needed in this interactive tutorial.

Type: Original Student Tutorial

Build on your previous knowledge of area and learn how to calculate volume in cubic units with this interactive tutorial.

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 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

Learn to solve division challenges using the partial quotients strategy with this interactive tutorial.

This is the second tutorial is a series on division strategies.

Type: Original Student Tutorial

Explore the poem “The Railway Train” by Emily Dickinson in this interactive tutorial. Learn about personification and vivid descriptions and determine how they contribute to the meaning of a poem.

Type: Original Student Tutorial

Learn how multiplication connects to division to help understand what division is in this aquarium-themed, interactive tutorial.

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

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

Learn how triangles can be sorted and classified using side lengths and angle measures in this interactive tutorial.

This is the final tutorial in a four-part series. Click below to open the other tutorials in the series.

**Part 1: "Figuring Out" 2D Figures - Part 1****Part 2 Exploring Relationships with Venn & Euler Diagrams****Part 3: Classifying Triangles by Angles using Euler Diagrams**- Part 4: Classifying Triangles by Sides and Angles using Venn and Euler Diagrams

Type: Original Student Tutorial

Try to escape from this room using multiplication as scaling in this interactive tutorial.

Type: Original Student Tutorial

Learn to classify triangles and use Euler diagrams to show relationships, in this interactive tutorial.

This is part-three of four. Click below to open the other tutorials in the series.

**Part 1: "Figuring Out" 2D Figures - Part 1****Part 2 Exploring Relationships with Venn & Euler Diagrams**- Part 3: Classifying Triangles by Angles using Euler Diagrams
**Part 4: Classifying Triangles by Sides and Angles using Venn and Euler Diagrams**

Type: Original Student Tutorial

Explore 2D (two-dimensional) figures and see how every 2D figure possesses unique attributes in this interactive tutorial.

This is part one of four. Click below to open the other tutorials in the series.

- Part 1: "Figuring Out" 2D Figures - Part 1
**Part 2 Exploring Relationships with Venn & Euler Diagrams****Part 3: Classifying Triangles by Angles using Euler Diagrams****Part 4: Classifying Triangles by Sides and Angles using Venn and Euler Diagrams**

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. **Click HERE to open Part 1**.

Type: Original Student Tutorial

Learn how to create a line plot and analyze data in the line plot in this interactive tutorial. You will also see how to add and subtract using the line plot to solve problems based on the line plots.

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

Help Rich escape Deci Land by learning how to write decimals that are related to fractions with denominators of 10 and 100 in this interactive tutorial.

Type: Original Student Tutorial

Help solve mysteries built on patterns of ten to discover the treasure of our number system in this interactive student tutorial.

Type: Original Student Tutorial

Practice plotting coordinates, in Quadrant I, using ordered pairs in this interactive tutorial for students.

Type: Original Student Tutorial

Learn about the basics of the coordinate plane, focus on Quadrant I and see why the coordinate plane is useful in everyday life in this interactive tutorial.

Type: Original Student Tutorial

Learn how the standard algorithm for multiplying numbers works and practice your skills in this interactive tutorial.

Type: Original Student Tutorial

Learn more about that dreaded word--*plagiarism*--in this interactive tutorial that's all about citing your sources, creating a Works Cited page, and avoiding academic dishonesty!

Type: Original Student Tutorial

Learn how to 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

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.

Type: Original Student Tutorial

Learn how to define, declare and initialize variables as you start the journey to "bee" a coder in this interactive tutorial. Variables are structures used by computer programs to store information. You'll use your math skills to represent a fraction as a decimal to be stored in a variable. This is part 1 of a series of 4 in learning how to code.

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

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 to interpret data presented on a line plot and use operations on fractions to solve problems involving information presented in line plots as you complete this beach-themed, interactive tutorial.

Type: Original Student Tutorial

By the end of this tutorial you’ll know how to convert among different-sized customary units of weight, length, capacity, and units of time.

Type: Original Student Tutorial

Take flight as you learn to recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right with this interactive tutorial.

Type: Original Student Tutorial

Learn to identify a fraction as division of the numerator by the denominator using fraction models in this interactive tutorial.

Type: Original Student Tutorial

Learn how to accurately plot coordinates on a plane.

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

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 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.

Type: Original Student Tutorial

Demonstrate how a rectangular prism can be carefully filled without gaps or overlaps using the same size unit cubes and then use this model to determine its volume.

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 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

## Educational Games

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

This website is a game that incorporates algebraic thinking with patterning. It can be used for third or fourth grade students.

Type: Educational Game

In this activity, students play a game of connect four, but to place a piece on the board they have to correctly estimate an addition, multiplication, or percentage problem. Students can adjust the difficulty of the problems as well as how close the estimate has to be to the actual result. This activity allows students to practice estimating addition, multiplication, and percentages of large numbers (100s). This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

In this activity, students 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

This interactive Flash applet has students match fractions with their equivalent one- or two-place decimals. Students have a chance to correct errors until all matches are made.

Type: Educational Game

## Educational Software / Tools

A printable hundreds chart featuring a 10x10 table numbered 1 to 100. (found on Illuminations website under "Trading for Quarters")

Type: 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

## Problem-Solving Tasks

Students are asked to determine the number of unit cubes needed to construct cubes with given dimensions.

Type: Problem-Solving Task

Students are asked to find the volume of water in a tank that is 3/4 of the way full.

Type: Problem-Solving Task

Students are asked to find the height of a rectangular prism when given the length, width and volume.

Type: Problem-Solving Task

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

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

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

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 purpose of this task is to help students gain a better understanding of fractions through the use of dimes and pennies.

Type: Problem-Solving Task

Each part of this task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.

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 is designed to help students focus on the whole that a fraction refers to. It provides a context where there are two natural ways to view the coins: As equal parts of the set of coins in the piggy bank, and As money so each coin is assigned its monetary value. The important thing to realize here is that two different fractions can describe the same situation depending on what you choose to be the whole.

Type: Problem-Solving Task

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

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

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Type: Problem-Solving Task

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

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

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

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 purpose of this task is for students to "Solve problems involving the four operations" (3.OA.A) and "Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories" (3.MD.3).

Type: Problem-Solving Task

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

Type: Problem-Solving Task

When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them.

Type: Problem-Solving Task

The purpose of this task is to help students see the connection between a÷b and ab in a particular concrete example. The relationship between the division problem 3÷8 and the fraction 3/8 is actually very subtle. This task is probably best suited for instruction or formative assessment.

Type: Problem-Solving Task

The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting. The two primary ways one can expect students to add are converting the mixed numbers to fractions greater than 1 or adding the whole numbers and fractional parts separately. It is good for students to develop a sense of which approach would be better in a particular context.

Type: Problem-Solving Task

The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have students moving back and forth between the abstract representation of the fractions and the meaning of the fractions in the context.

Type: Problem-Solving Task

This tasks lends itself very well to multiple solution methods. Students may learn a lot by comparing different methods. Students who are already comfortable with fraction multiplication can go straight to the numeric solutions given below. Students who are still unsure of the meanings of these operations can draw pictures or diagrams.

Type: Problem-Solving Task

The purpose of this task is to present students with a situation where it is natural to add fractions with unlike denominators; it can be used for either assessment or instructional purposes. Teachers should anticipate two types of solutions: one where students calculate the distance Alex ran to determine an answer, and one where students compare the two parts of his run to benchmark fractions.

Type: Problem-Solving Task

The purpose of this task is to familiarize students with multiplying fractions with real-world questions.

Type: Problem-Solving Task

The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of addition as joining two separate quantities.

Type: Problem-Solving Task

Since tasks such as this will be among the first that students see, solutions which involve (sub)dividing a quantity into equal parts in order to find a fraction of the quantity should be emphasized. In particular, such solutions should be introduced if students do not generate them on their own. Students benefit from reasoning through the solution to such word problems before they are told that they can be solved by multiplying the fractions; this helps them develop meaning for fraction multiplication.

Type: Problem-Solving Task

The two solutions reflect different competencies described in 5.NF.5. The first solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The second actually uses the meaning of multiplying by 89 to explain why multiplying by that fraction will result in a smaller value.

Type: Problem-Solving Task

This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and the magnitude of the product.

Type: Problem-Solving Task

This task requires division of multi-digit numbers in the context of changing units and so illustrates 5.NBT.6 and 5.MD.1. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.

Type: Problem-Solving Task

This is the third problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. The first, 5.NF Running to school, does not require that the unit fractions that comprise 3/4 be subdivided in order to find 1/3 of 3/4. The second task, 5.NF Drinking Juice, does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2. This task also requires subdivision and involves multiplying a fraction and a mixed number.

Type: Problem-Solving Task

The purpose of this task is to gain a better understanding of multiplying and dividing with fractions. Students should use the diagram provided to support their findings.

Type: Problem-Solving Task

This problem helps students gain a better understanding of dividing with fractions.

Type: Problem-Solving Task

Part (a) of this task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator. Part (b) does not ask students to do it in more than one way; the purpose is to give them an opportunity to choose a denominator and possibly compare with another student who chose a different denominator. The purpose of part (c) is to help students move away from a reliance on drawing pictures. Students can draw a picture if they want, but this subtraction problem is easier to do symbolically, which helps students appreciate the power of symbolic notation.

Type: Problem-Solving Task

Part (a) of this task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator. Part (b) does not ask students to solve the given addition problem in more than one way. Instead, the purpose of this question is to give students an opportunity to choose a denominator and possibly to compare their solution method with another student who chose a different denominator. The purpose of part (c) is to give students who are ready to work symbolically a chance to work more efficiently.

Type: Problem-Solving Task

The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.

Type: Problem-Solving Task

One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions.

Type: Problem-Solving Task

This is the second problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. This task does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2.

Type: Problem-Solving Task

This task addresses common errors that students make when adding fractions. It is very important for students to recognize that they only add fractions when the fractions refer to the same whole, and also when the fractions of the whole being added do not overlap. This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions.

Type: Problem-Solving Task

The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.

Type: Problem-Solving Task

This particular problem deals with multiplication. Even though students can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number.

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 site uses visual models to better understand what is actually happening when students multiply and divide fractions. Using area models -- one that superimposes squares that are partitioned into the appropriate number of regions, and shaded as needed -- students multiply, divide, and translate the processes to decimals. The lesson uses an interactive simulation that allows students to create their own area models and is embedded with problems throughout for students to solve.

Type: Problem-Solving Task

In this activity, students highlight portions of circles or squares that are equivalent to a given fraction. As the student highlights sections, a pointer on a number line between zero and one updates so they can see when they are close or equal to the given fraction. This activity allows students to explore equivalent fractions by making it necessary that each of the three fractions have a different denominator but have the fractions be equal. 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: Problem-Solving Task

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

This Khan Academy tutorial video illustrates the conversion equivalence of liters, milliliters, and kiloliters.

Type: Tutorial

This Khan Academy tutorial video presentation represents a word problem's solution on a coordinate plane to determine the number of blocks walked from a home to a school.

Type: Tutorial

This Khan Academy tutorial video presents how to graph an ordered pair of positive numbers on the x- and y-axis of a coordinate plane.

Type: Tutorial

This Khan Academy tutorial video presents a strategy for solving the following problem: given a dot plot with different measurements of trail mix in bags, find the amount of trail mix each bag would contain, if the total amount in all the bags was equally redistributed.

Type: Tutorial

This Khan Academy tutorial video develops a visual diagram to use to solve a distance problem that requires converting feet to yards and other computations.

Type: Tutorial

This Khan Academy tutorial video demonstrates a strategy for ordering four different-sized metric units.

Type: Tutorial

This Khan Academy tutorial video describes measurement in one, two, and three dimensions.

Type: Tutorial

In this Khan Academy tutorial video a table is used to track a growing sequence of design.

Type: Tutorial

in this tutorial, students will learn about central angles and arcs of a circle.

Type: Tutorial

This Khan Academy tutorial video introduces quadrilaterals. their categories, and subcategories.

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 two decimals are compared using grid diagrams.

Type: Tutorial

In this Khan Academy video decimals are written and spoken in words.

Type: Tutorial

The Khan Academy video uses grid diagrams and number-line representations to say and write equivalent decimals and fractions.

Type: Tutorial

The Khan Academy video illustrates how to determine and write the decimal represented by shaded grids.

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 Khan Academy video four fractions are compared by plotting them on a number line and drawing models.

Type: Tutorial

In this video tutorial from Khan Academy, learn about the importance of place value when dividing. Being able to perform the standard algorithm is the end goal, but it helps to understand how and why this process works.

Type: Tutorial

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial

Use fraction models and a number line to represent 1 as a fraction.

Type: Tutorial

Solve a two-step word problem by drawing a picture and creating an equation.

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

In this video tutorial from Khan Academy, explore the distributive property of multiplication: Why does it work? How does it work? Why would I put it to use?

Type: Tutorial

In this video tutorial from Khan Academy, use arrays to explore the commutative and associative properties of multiplication.

Type: Tutorial

Find the number to replace the symbol for the unknown in multiplication and division equations.

Type: Tutorial

In this tutorial video from Khan Academy, discover attributes and features of four-sided shapes, including parallelograms, rhombuses, rectangles, and squares.

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

In this Khan Academy video tutorial, learn how to subtract three-digit numbers by subtracting ones, tens, and hundreds represented with base ten blocks and the standard algorithm.

Type: Tutorial

In this video tutorial from Khan Academy, learn how to subtract 1, 10, or 100 from a three-digit number while making a connection between the standard algorithm and a concrete representation using base ten blocks.

Type: Tutorial

In this video tutorial from Khan Academy, learn how to add three-digit numbers by adding ones, tens, and hundreds by thinking about the connection between base ten block representation and the standard algorithm.

Type: Tutorial

In this video tutorial from Khan Academy, learn how to add 10 or 100 to a number using base ten blocks.

Type: Tutorial

This video discusses the definition of an angle and how to name an angle.

Type: Tutorial

This tutorial explores the addition and subtraction of fractions with unlike denominators. Performing these operations on fractions with unlike denominators requires the creation of a 'common' denominator. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd).

Type: Tutorial

In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases. Sometimes when finding a common denominator, an unnecessarily large common denominator is created (** a/b x c/d** =

*+*

**ad***). This chapter explains how to find the smallest possible common denominator.*

**bc****/bd***For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.*

Type: Tutorial

The Cartesian Coordinate system, formed from the Cartesian product of the real number line with itself, allows algebraic equations to be visualized as geometric shapes in two or three dimensions.

Type: Tutorial

This lesson reviews the commutative and associative properties as it applies to addition and multiplication. These properties are useful with mental math and with solving equations. This resource includes a video lesson, video examples and a short quiz.

Type: Tutorial

This tutorial for student audiences will provide a basic introduction to decimals. The tutorial presents a decimal as another way to represent a fraction. 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 gaining an orange circle and a wrong answer graying out. Some "Try This" sections will read the decimal to the students as well.

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting 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

This combination of illustrations and narration defines convex as well as concave polygons and describes the features of various polygons. Examples of polygons shown include triangles and quadrilaterals of various types, including some that are convex and some that are concave, and even one that has a hole in it. Narration or read-along text describes the shapes for the user. Copyright 2005 Eisenhower National Clearinghouse

Type: Tutorial

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

Type: Tutorial

## Virtual Manipulatives

This drag and drop Venn diagram simulation gives students the opportunity to solve a mathematical problem based on number properties using a range of different Venn diagrams. There are five different levels involving a range of multiples and simply odds and evens. The three core layouts cover simple separate sets, two intersecting sets, and a three way intersecting Venn Diagram. The odds and evens layout is limited to two intersecting sets, of course.

Type: Virtual Manipulative

This virtual manipulative requires the learners to create equivalent fractions, by dividing and shading squares or circles, and match each fraction to its location on the number line. Learners have to understand that equivalent fractions have the same value, even though they may look different.

Type: Virtual Manipulative

This virtual manipulative offers activities that allow the learner to explore fractions by building fractions, making equivalent fractions, and matching fractions.

Type: Virtual Manipulative

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

Match shapes and numbers to earn stars in this fractions game.

- Match fractions using numbers and pictures
- make the same fractions using different numbers
- Match fractions in different picture patterns
- Compare fractions using numbers and patterns

Type: Virtual Manipulative

In this activity, you will graphically determine the value of two given fractions represented as points on a number line. You will then graphically find a fraction whose value is between the two given fractions and determine its value.

Type: Virtual Manipulative

This interactive Flash activity asks the user to sort shapes into a 2 by 2 chart, known as a Carroll Diagram, based on their properties. Properties used to sort include "quadrilateral" or "not quadrilateral" and "regular polygon" or "not regular polygon."

Type: Virtual Manipulative

The students will be given mutiplication and division problems which they must answer. They also have the option of being given a number then stating the factors of how that number was attained using either multiplication or division.

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

This virtual manipulative allows you to create, color, enlarge, shrink, rotate, reflect, slice, and glue geometric shapes, such as: squares, triangles, rhombi, trapezoids and hexagons.

Type: Virtual Manipulative

Students select the shape that goes next in the pattern and place it in the row, then identify the overall pattern.

Type: Virtual Manipulative

In this activity, students practice solving algebraic expressions using order of operations. The applet records their score so the student can track their progress. This activity allows students to practice applying the order of operations when solving problems. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

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