## Course Standards

## General Course Information and Notes

### General Notes

MAFS.3

In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing 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 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.

(3) 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.

(4) 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.

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

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

https://cpalmsmediaprod.blob.core.windows.net/uploads/docs/standards/eld/ma.pdf

**Florida Standards Implementation Guide Focus Section:**

The Mathematics Florida Standards Implementation Guide was created to support the teaching and learning of the Mathematics Florida Standards. The guide is compartmentalized into three components: focus, coherence, and rigor.Focus means narrowing the scope of content in each grade or course, so students achieve higher levels of understanding and experience math concepts more deeply. The Mathematics standards allow for the teaching and learning of mathematical concepts focused around major clusters at each grade level, enhanced by supporting and additional clusters. The major, supporting and additional clusters are identified, in relation to each grade or course. The cluster designations for this course are below.

**Major Clusters**

MAFS.3.OA.1 Represent and solve problems involving multiplication and division.

MAFS.3.OA.2 Understand properties of multiplication and the relationship between multiplication and division.

MAFS.3.OA.3 Multiply and divide within 100.

MAFS.3.OA.4 Solve problems involving the four operations, and identify and explain patterns in arithmetic.

MAFS.3.NF.1 Develop understanding of fractions as numbers.

MAFS.3.MD.1 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

MAFS.3.MD.3 Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

**Supporting Clusters**

MAFS.3.MD.2 Represent and interpret data.

MAFS.3.G.1 Reason with shapes and their attributes.

**Additional Clusters**

MAFS.3.NBT.1 Use place value understanding and properties of operations to perform multi-digit arithmetic.

MAFS.3.MD.4 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

**Note:** Clusters should not be sorted from major to supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting and additional clusters.

### General Information

**Course Number:**5012050

**Course Path:**

**Abbreviated Title:**MATH GRADE THREE

**Course Length:**Year (Y)

**Course Attributes:**

- Class Size Core Required

**Course Type:**Core Academic Course

**Course Status:**Course Approved

**Grade Level(s):**3

## Educator Certifications

## Student Resources

## Original Student Tutorials

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

Learn how to 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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

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

Explore how multiplication can help you solve division problems during this moon-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

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

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

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

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

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

Type: Original Student Tutorial

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

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

## 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 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

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/Slideshow

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

## Problem-Solving Tasks

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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 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

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

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

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 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

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 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

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

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 >