## Course Standards

## General Course Information and Notes

### Version Description

In this course, instructional time should focus on five critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) using place value to develop an understanding and fluency with multi-digit multiplication; (3) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (4) developing understanding of the structure of rectangular arrays and of area; and (5) describing, analyzing, and classifying two-dimensional shapes.

(1) Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.

(2) Students generalize their understanding of place values to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalization methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems.

(3) Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators. Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions

(4) Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle.

(5) Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole. Students describe, analyze, compare, and classify two-dimensional shapes based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

** Honors and Advanced Level Course Note: **Advanced 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: {{AzureStorageLink}}/uploads/docs/standards/eld/ma.pdf

For additional information on the development and implementation of the ELD standards, please contact the Bureau of Student Achievement through Language Acquisition at sala@fldoe.org.

### General Information

**Course Number:**5012055

**Course Path:**

**Abbreviated Title:**ACCEL MATH GRADE 3

**Course Length:**Year (Y)

**Course Attributes:**

- Honors
- Class Size Core Required

**Course Type:**Core Academic Course

**Course Level:**3

**Course Status:**Course Approved

**Grade Level(s):**3

## Educator Certifications

## Student Resources

## Original Student Tutorials

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

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

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

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

Learn to use number lines to represent fractions as Emmy explores nature in this interactive tutorial.

Type: Original Student Tutorial

In this SaM-1 video, students will learn how to measure the mass of solids and liquids using a balance. Students will learn that they need to subtract the mass of the container the solid or liquid is in to determine the mass of only the solid or liquid. Students will then make observations and sort items based on mass.

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 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

Learn to convert a larger customary measurement unit into equivalent smaller units, including converting miles to yards and feet in this sports-themed interactive tutorial.

This is Part 2 of a two-part series. Click **HERE** to open Part 1: Measuring Length with Customary Units.

Type: Original Student Tutorial

Learn to convert a larger customary measurement unit into equivalent smaller units, including converting yards to feet and inches, in this sports-themed 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

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

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

Join us as Breanna learns to use a line plot to examine measurement data she needs to create bracelets for her friends, in 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 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 use their listening and writing skills to watch a video to learn about the affects temperature has on sea turtles' nests, preparing them for an investigation in subsequent lessons within the unit.

Type: Original Student Tutorial

In this SaM-1 video, students will learn how to make observations based on the property of temperature using thermometers, while representing the data in line graphs.

Type: Original Student Tutorial

In this SaM-1 video, students will use their listening and writing skills to learn about sea turtles, preparing them for subsequent lessons in the unit.

Type: Original Student Tutorial

In this SaM-1 Video, students will learn how to find the volume of irregular objects using a graduated cylinder and the displacement method.

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

Discover what makes prime and composite numbers unique thanks to an interesting backyard problem in this interactive tutorial.

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

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

Overcome the nightmare of quadrilateral classification based on the presence of parallel, perpendicular, and congruent sides as you complete this interactive tutorial.

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 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

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

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

Learn when to write the remainder of a multi-step division process as a fraction or decimal in this interactive tutorial.

This is the final tutorial in the Field Trip Frenzy Series about remainders. Click below to open the other tutorials in this series.

Note: This tutorial extends beyond whole number quotients with whole number remainders to whole number quotients with fractional or decimal remainders.

Type: Original Student Tutorial

Learn how to interpret remainders in multi-step division problems in this interactive tutorial

This is the third tutorial in the Field Trip Frenzy Series about remainders. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Learn how to interpret remainders in multi-step division problems related to a field trip in this interactive tutorial.

This tutorial is Part 2 in a four-part series about remainders. Click below to open the other tutorials in this series.

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

Take a field trip while learning how to interpret remainders in multi-step division word problems.

This is part 1 of a four-part series of interactive tutorials. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Learn how to write multiplication equations based on multiplication comparisons and story problems in this magical math online tutorial!

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

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 estimate and measure the masses of objects in grams and kilograms in this interactive tutorial with an animal hospital theme.

Type: Original Student Tutorial

Learn to read analog and digital clocks to the nearest minute in this interactive tutorial.

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

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

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 in this interactive tutorial.

Type: Original Student Tutorial

Learn how to write a topic sentence to introduce a topic, group related information together, develop a topic by adding details, and add an image to support the text with this ocean-themed, 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 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

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

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

Test your factors skills with this fun factor game. Take turns choosing numbers from the board and identifying its factors. Outscore your opponent by identifying factors and using strategy to limit their score. Play against the computer or a friend.

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

You are trying to build the tallest ice cream cone by multiplying 2 whole numbers! Be careful! You are competing against to other kids! Go as fast as you can, but use the special powers to help you get ahead!

Type: Educational Game

This interactive Flash version of the familiar Concentration game ("pelmanism" in the UK) helps a single user practice fluency and memory of multiplication facts. The player can choose an array of 16, 20, or 24 cards, which appear face down. The goal is to flip two cards at a time to match all the pairs of factors with their products as efficiently as possible. A scoring feature discourages random guessing. Users can select to work with factors in three ranges. By selecting 2x-10x, the game addresses part of the standard: By the end of Grade 3, students will know from memory all products of two one-digit numbers. Printable versions of the game cards are available to download.

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 is a basic 10 by 10 multiplication box presented in an easy to use, online setting. All the answers are given like a jumble of puzzle pieces. It has a timer and keeps score of correct answers. Incorrect answers simply do not "stick" to the grid.

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 game for two players develops students' fluency with multiplication facts, their understanding of the relationship between factors and products, and their strategic thinking. On a board displaying all the factors of the numbers 1-9, players take turns moving markers on the factor list and claiming their products. The first player to get four in a row wins the game.

Type: Educational Game

This interactive Java applet allows the user to practice finding elapsed time using analog or digital clocks. Using the "See" mode the user advances a clock from the beginning time to the ending time and the applet calculates the elapsed time. Using the "Guess" mode, the user must calculate the elapsed time between the given beginning and ending times. Three difficulty levels allow the user to practice with hour, five minute, or single minute increments. An optional scoring feature allows the user to keep track of number correct, though this feature is optional.

Type: Educational Game

In this interactive Flash game, students are challenged to identify a fraction from a picture of a group of objects or from a geometric diagram, or they are asked to create a diagram or picture given a common fraction. Motivation is provided by earning buckets of sand to built a sand castle.

Type: Educational Game

The students will be presented with two shapes and must estimate how many times the smaller will fit in the larger. They will be surprised at some of the results but will quickly learn and make adjustments.

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

Students can practice elapsed time on this easy-to-use online math game. It also comes with a printable recording sheet for tracking progress.

Type: Educational Software / Tool

This interactive, online game is a fun way for students to practice identifying fractions. In this lesson students identify fractions to help a man hop his way across a river.

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

## Presentation/Slideshows

This is an accessible, easy-to-read book introducing fractions. It can be downloaded in PowerPoint, Impress, and Flash formats. For struggling or non-readers the book can be read aloud in a variety of voices. All of the books on the Tar Heel Reader site can be used with the Intellikeys keyboard with a custom overlay, a touch screen, and/or 1-3 switches. The text and background colors can be modified for students with visual impairments.

Type: Presentation/Slideshow

This online resource is a story of a girl and her father planting flowers that your children and you interact with. Help them fill in the fractions as they practice dividing the garden up for their flowers!

Type: Presentation/Slideshow

## 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 "3.G 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 in the sense described in 3.G.7.d.

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 in the sense described in 3.G.7.d.

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

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 for students to measure angles and decide whether the triangles are right or not. Students should already understand concepts of angle measurement and know how to measure angles using a protractor before working on this task.

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 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 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

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. 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 assess students’ understanding of multiplicative and additive reasoning. We would hope that students would be able to identify that Student A is just looking at how many feet are being added on, while Student B is comparing how much the snakes grew in comparison to how long they were to begin with.

Type: Problem-Solving Task

The purpose of this task is to foster a classroom discussion that will highlight the difference between multiplicative and additive reasoning. Some students will argue that they grew the same amount (an example of "additive thinking"). Students who are studying multiplicative comparison problems might argue that Jewel grew more since it grew more with respect to its original length (an example of "multiplicative thinking").

Type: Problem-Solving Task

The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases.

Type: Problem-Solving Task

The goal of this task is to help students understand the commutative property of addition by examining the addition facts for single digit numbers. This is important as it gives students a chance, at a young age, to do more than memorize these arithmetic facts which they will use throughout their education.

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 give students a better understanding of multiplicative comparison word problems with money.

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

Part (a) of the standard is about representing unit fractions and part (b) is about representing fractions in terms of unit fractions. The tasks require attention to the whole when thinking about fractions; on a number line, the whole is the interval from 0 to 1.

Type: Problem-Solving Task

Part (a) of the standard is about representing unit fractions and part (b) is about representing fractions in terms of unit fractions. Each requires that students "understand a fraction as a number on the number line" and "represent fractions on a number line diagram."

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 lin

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, a critical aspect for meeting standard 3.NF.2b. 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

This task asks students to study more carefully the make-a-ten strategy that they should already know and use intuitively. In this strategy, knowledge of which sums make a ten, together with some of the properties of addition and subtraction, are used to evaluate sums which are larger than 10. This task is intended for instruction purposes as it takes time to identify the patterns involved and understand the steps in the procedures.

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 this task is to study some patterns in a small addition table. Each pattern identified persists for a larger table and if more time is available for this activity students should be encouraged to explore these patterns in larger tables.

Type: Problem-Solving Task

The goal is to look for structure and identify patterns and then try to find the mathematical explanation for this. This problem examines the ''checkerboard'' pattern of even and odd numbers in a single digit multiplication table. The even numbers in the table are examined in depth using a grade appropriate notion of even, namely the possibility of reaching the number counting by 2's or expressing the number as a whole number of pairs.

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" (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

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 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 help students gain a better understanding of fractions and the conversion of fractions into smaller units.

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

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 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

This Khan Academy tutorial video presents examples and explanations for categorizations of perpendicular sides and right, obtuse, and acute triangles.

Type: Tutorial

In this Khan Academy tutorial video triangles are categorized by angles or side lengths of a specified size.

Type: Tutorial

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

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

This Khan Academy tutorial video presents conventional examples that use specific customary units

Type: Tutorial

In this tutorial video from Khan Academy, explore the differences and similarities involved when converting between measurements in the metric and customary systems.

Type: Tutorial

In this video tutorial from Khan Academy, explore conversion within metric units of length, such as: kilometers, meters and centimeters.

Type: Tutorial

In this video tutorial from Khan Academy, explore U.S. customary units of fluid volume (teaspoon, tablespoon, fluid ounce, cup, pint, quart, and gallon).

Type: Tutorial

In this video tutorial from Khan Academy, explore pounds, ounces and tons.

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

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

Type: Tutorial

This Khan Academy video presents finding perimeter by adding side-lengths of various polygons.

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, 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, 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, view an example of how to solve a multiplication problem with a two-digit number multiplied by a one-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

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

In this Khan Academy video tutorial, see examples of how to round up to four-digit numbers to the nearest ten and hundred.

Type: Tutorial

In this Khan Academy video tutorial, use a number line to round three-digit numbers to the nearest hundred.

Type: Tutorial

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

Type: Tutorial

In this Khan Academy video, use a number line to round two-digit numbers to the nearest ten.

Type: Tutorial

Use a picture and understanding of multiplication to solve a division word problem. Watch out for unnecessary information.

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 tutorial video from Khan Academy, explore questions such as: What is the volume of a jar of milk? How about a spoon? A swimming pool?

Type: Tutorial

In this Khan Academy video tutorial, explore how to solve an elapsed time word problem using a number line. Mom asks you to be home by 5:45. You know the number of minutes it takes to get home. What time do you leave?

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 tutorial video from Khan Academy, students who understand how to count unit squares to find the area of a rectangle can explore the connection between this method and the area formula for rectangles (length times width or base times height).

Type: Tutorial

In this Khan Academy video tutorial, learn to use arrays and repeated addition to multiply. This is not an introductory video to either concept, to either concept. An array of 8 items is used to show how one array can be represented in multiple ways, using different factors of the whole.

Type: Tutorial

In this Khan Acadmey tutorial video, learn to use arrays to show different groups of objects while relating this to multiplication.

Type: Tutorial

In this Khan Academy tutorial vidoe, learn to use arrays and repeated addition to visualize multiplication.

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 differences between lines, line segments and rays.

Type: Tutorial

Students will view a video that explains that a fraction is the quantity formed by 1 part when a whole is partitioned into equal parts. Students will then have opportunities to practice this concept with assorted problems and are given immediate feedback as to the accuracy of their responses.

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 assist learners in furthering their understanding of multiplying with the use of a times table. 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. On the 5th section of the tutorial students are provided with additional practice problems that self-check as well.

Type: Tutorial

This tutorial for student audiences reviews basic introductory information on fractions. Students will review that a fraction is part of a whole, a fraction is less than 1 whole thing, but more than 0, how to determine pieces of a whole and how to write fractions.

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

## 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 activity allows the user to test his or her skill at calculating the perimeter of a random shape. The user is given a random shape and asked to enter a value for the perimeter. The applet then informs the user whether or not the value is correct. The user may continue trying until he or she gets the correct answer.

This activity would work well in mixed ability groups of two or three for about 25 minutes if you use the exploration questions, and 10-15 minutes otherwise.

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

Students use this interactive tool to explore the connections between data sets and their representations in charts and graphs. Enter data in a table (1 to 6 columns, unlimited rows), and preview or print bar graphs, line graphs, pie charts, and pictographs. Students can select which set(s) of data to display in each graph, and compare the effects of different representations of the same data. Instructions and exploration questions are provided using the expandable "+" signs above the tool.

Type: Virtual Manipulative

This activity operates in one of two modes: auto draw and create shape mode, allowing you to explore relationships between area and perimeter. Shape Builder is one of the Interactivate assessment explorers.

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 tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing.

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 use repeated addition as a strategy to solve multiplication story problems.

Type: Virtual Manipulative

Students use arrays to understand the meaning of multiplication.

Type: Virtual Manipulative

This online slideshow is another way to introduce parts of a whole to your class.

This lesson could be presented to the whole class or completed by students independently.

Type: Virtual Manipulative

In this activity, students can create and view a histogram using existing data sets or original data entered. Students can adjust the interval size using a slider bar, and they can also adjust the other scales on the graph. This activity allows students to explore histograms as a way to represent data as well as the concepts of mean, standard deviation, and scale. 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

## Worksheet

In this worksheet, students are directed to find the perimeter and area for a clubhouse in the form of rectangles, composite figures, and other polygons. The second sheet urged them to make their own designs for a clubhouse and find the perimeter and area. This resource is recommended as an introduction or review of perimeter and area.

(Found under "Finding Perimeter and Area" on NCTM's Illuminations)

Type: Worksheet

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