## Course Standards

## General Course Information and Notes

### General Notes

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

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

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

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

### General Information

**Course Number:**5012015

**Course Path:**

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

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

**Course Attributes:**

- Class Size Core Required

**Course Status:**Course Approved

**Grade Level(s):**3,4,5

## Educator Certifications

## Student Resources

## Original Student Tutorials

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

Learn to divide whole numbers by unit fractions as you help Allie and Cameron create equal shares of candy and prizes for guests at a carnival in this interactive tutorial.

Type: Original Student Tutorial

Learn how to find a missing value when there are subtraction expressions on both sides of an equal sign by using comparative relational thinking and a number line in this interactive tutorial.

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

**Part 1: Think Fast! Comparative Strategies (Addition expressions on both sides of the equal sign)****Part 2: Think Fast! Comparative Strategies (Subtraction expressions on both sides of the equal sign)**

Type: Original Student Tutorial

Learn how to think fast to find a missing value when there are subtraction expressions on both sides of an equal sign by using using comparative relational thinking and a part-whole board in this interactive tutorial.

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

**Part 1: Think Fast! Comparative Strategies (Addition expressions on both sides of the equal sign)**- Part 3: Think Fast! Comparative Strategies [COMING SOON]

Type: Original Student Tutorial

Solve real-world word problems involving dividing a unit fraction by a whole number and dividing a whole number by a unit fraction using number lines in this chocolate-themed, interactive tutorial.

This is part 2 of a 2-part series. Click **HERE** to open "Chocolate Shop Challenge Part 1: Dividing Unit Fractions and Whole Numbers Using Fraction Bar Models"

Click **HERE** to open the related tutorial, "David Divides Desserts: Divide a Unit Fraction by a Whole Number"

Type: Original Student Tutorial

Divide unit fractions by whole numbers and divide whole numbers by unit fractions in this chocolate-themed, interactive tutorial.

This is part 1 of a 2-part series. Click **HERE **to open "Chocolate Shop Challenge Part 2: Dividing Unit Fractions and Whole Numbers Using Number Lines"

Type: Original Student Tutorial

Learn how to think fast and compare the parts in addition expressions on different sides of the equal sign to find an unknown number with this interactive tutorial.

Type: Original Student Tutorial

Learn to solve word problems involving division of a unit fraction by a whole number by using models, expressions, equations, and strategic thinking in this interactive, dessert-themed tutorial.

Type: Original Student Tutorial

Learn how to divide a unit fraction by a whole number to share yummy picnic goodies equally in this interactive tutorial.

Type: Original Student Tutorial

Learn to solve addition and subtraction word problems involving fractions with unlike denominators. As you complete this art-themed, interactive tutorial, you'll use visual models, write and solve equations, and check the reasonableness of results based on estimates.

This is part 2 of a two-part series. Click below to open part 1.

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

Apply your understanding of the defining attributes of all 2-dimensional figures covered in this series to classify their relationships using Euler and Venn Diagrams.

This part 8 in a 8-part series. Click below to explore the other tutorials in the series.

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

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

Type: Original Student Tutorial

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

By the end of this tutorial you should be able to identify examples of quadrilaterals and their defining attributes to classify them using diagrams. We will focus on kites and other quadrilaterals in this tutorial.

This part 7 in a 8-part series. Click below to explore the other tutorials in the series.

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

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

Part 5: Quadrilaterals

Part 6: Trapezoids

Part 8: (Coming Soon)

Type: Original Student Tutorial

Read word problems and use number lines with benchmarks to solve multi-step problems involving addition and subtraction of fractions with unlike denominators. In this tutorial, you will help Daisy and Angie paint pictures using fractions.

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

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

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

Part 1: "Figuring Out" 2D Figures

Part 2: Exploring Relationships with Venn & Euler Diagrams

Part 3: Classifying Triangles by Angles Using Euler Diagrams

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

Type: Original Student Tutorial

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 how to classify quadrilaterals--including parallelograms, rectangles, rhombi, and squares--based on their defining attributes using diagrams in this interactive tutorial.

This is part 5 in a 6-part series. Click below to explore the other tutorials in the series.

**Part 1: "Figuring Out" 2D Figures****Part 2: Exploring Relationships with Venn & Euler Diagrams****Part 3: Classifying Triangles by Angles Using Euler Diagrams****Part 4: Classifying Triangles by Sides & Angles Using Venn and Euler Diagrams**- Part 6: (Coming Soon)

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

Help out at the fishing tournament while comparing decimals through the thousandths place in this interactive tutorial.

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

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

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

This is part 1 of a 4-part series. Click below to open other tutorials in the series.

**Part 2: Multiplying Fractions****Part 3 Using Models to Multiply a Fraction by a Whole Number****Part 4: Multiplying a Fraction by a Whole Number - Standard Algorithm**

Type: Original Student Tutorial

Find the total amounts of repeated fraction quantities by multiplying a fraction by a whole number using visual models that represent real-world problems and cookies 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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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 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 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

Explore base 10 and exponents in this baseball-themed, interactive tutorial.

Type: Original Student Tutorial

Help your town build a dog park by multiplying whole numbers by decimals to the tenths place in this interactive tutorial.

Note: this is an introductory tutorial on multiplying whole numbers by decimals before students move on to multiplying decimals by decimals.

Type: Original Student Tutorial

Learn to subtract decimals to the hundredths place using place-value models and written expressions as you fix the topsy-turvy playground in this interactive tutorial.

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

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

Type: Original Student Tutorial

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 these aliens clean up the Sweet Treats Factory by learning to add decimals in this interactive mathematics tutorial.

Type: Original Student Tutorial

Learn how to show relationships represented in Venn & Euler Diagrams as you complete this interactive geometry tutorial.

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

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

Type: Original Student Tutorial

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

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

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

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

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

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

Type: Original Student Tutorial

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

Note: this tutorial is an introductory lesson on multiplying a given number without calculating before working with fractions.

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

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

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

Type: Original Student Tutorial

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

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

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

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

Type: Original Student Tutorial

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

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

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

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

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

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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 use repeat loops in this interactive tutorial. Repeat loops iterate though a list of instructions based on a desired number of times. Combined with variables, condition statements, if statements, and repeat loops we practice using order of operations to code.

This is part 1 of a 4-part series. Click below to check out the other tutorials in the series.

**Bee A Coder Part 1: Declare Variables****Bee A Coder Part 2: Condition Statements****Bee A Coder Part 3: If Statements**

Type: Original Student Tutorial

Learn how to perform instructions using an if statement and explore relational operators (less than, greater than, equal and not equal to) and how they are used to compare to values in this interactive tutorial.

Type: Original Student Tutorial

Construct efficient lines of code using condition- and if-statements to solve equations as you complete this interactive tutorial. You'll also review the order of operations in expressions.

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

**Bee A Coder Part 1: Declare Variables****Bee A Coder Part 3: If Statements****Bee A Coder Part 4: Repeat Loops**

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

This is part 1 of a 4-part series on coding. Click below to open the other tutorials in the series.

**Bee A Coder Part 2: Condition Statements****Bee A Coder Part 3: If Statements****Bee A Coder Part 4: Repeat Loops**

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

Learn how to write mathematical expressions while making faces 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 interpret data presented on a line plot and use operations on fractions to solve problems involving information presented in line plots as you complete this beach-themed, interactive tutorial.

Type: Original Student Tutorial

Learn how to convert among different-sized customary units of weight, length, capacity, and units of time at the skate park in the 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 evaluate expressions that have all four operations (multiplication, division, addition, and subtraction) and parentheses as you settle debates in this interactive tutorial.

Type: Original Student Tutorial

By the end of this tutorial, you will be able to read and write decimals to the thousandths using base-ten numerals, number names, and expanded form.

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

Type: Original Student Tutorial

Learn how to accurately plot coordinates on a plane in 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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

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

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

Type: Original Student Tutorial

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

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

Type: Original Student Tutorial

Join Andy as he travels through his dream, learning about the attributes of rhombi along the way. Together we’ll learn what makes a rhombus unique and how to create a rhombus using its attributes. We’ll help Andy journey through his dream and wake up for school 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 applet gives students practice in making change in U.S. dollars and in four other currencies. Students are presented with a purchase amount and the amount paid, and they must enter the quantity of each denomination that make up the correct change. Students are rewarded for correct answers and are shown the correct change if they err. There are four levels of difficulty, ranging from amounts less than a dollar to amounts over $100.

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

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

Type: Educational Game

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

In this activity, students enter coordinates to make a path to get to a target destination while avoiding mines. This activity allows students to explore Cartesian coordinates and the Cartesian coordinate plane. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

## Educational Software / 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

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

Students are asked to apply knowledge of volume of rectangular prisms to find the volume of an irregularly shaped object using the principle of displacement.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

This task provides a familiar context allowing students to visualize multiplication of a fraction by a whole number. This task could form part of a very rich activity which includes studying soda can labels.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

This 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

This task asks students to exercise both of these complementary skills, writing an expression in part (a) and interpreting a given expression in (b). The numbers given in the problem are deliberately large and "ugly" to discourage students from calculating Eric's and Leila's scores. The focus of this problem is not on numerical answers, but instead on building and interpreting expressions that could be entered in a calculator or communicated to another student unfamiliar with the context.

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

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

The purpose of this task is to help students see the connection between a÷b and a/b in a particular concrete example. This task is probably best suited for instruction or formative assessment.

Type: Problem-Solving Task

This task provides a context for performing division of a whole number by a unit fraction. This problem is a "How many groups?'' example of division: the "groups'' in this case are the servings of oatmeal and the question is asking how many servings (or groups) there are in the package.

Type: Problem-Solving Task

The purpose of this task is to provide students with a situation in which it is natural for them to divide a unit fraction by a non-zero whole number. Determining the amount of paint that Kulani needs for each wall illustrates an understanding of the meaning of dividing a unit fraction by a non-zero whole number.

Type: Problem-Solving Task

The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication.

Type: Problem-Solving Task

The purpose of this task is to present students with a situation in which they need to divide a whole number by a unit fraction in order to find a solution. Calculating the number of origami stars that Avery and Megan can make illustrates student understanding of the process of dividing a whole number by a unit fraction.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

The purpose of this task is to help students see that 4×(9+2) is four times as big as (9+2). Though this task may seem very simple, it provides students and teachers with a very useful visual for interpreting an expression without evaluating it because they can see for themselves that 4×(9+2) is four times as big as (9+2).

Type: Problem-Solving Task

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

Type: Problem-Solving Task

The task could be one of the first activities for introducing the multiplication of fractions. The task has fractions which are easy to draw and provides a linear situation. Students benefit from reasoning through the solution to such word problems before they are told that they can be solved by multiplying the fractions; this helps them develop meaning for fraction multiplication.

Type: Problem-Solving Task

The solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The students need to explain why that is so.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

This problem allows student to see words that can describe an expression although the solution requires nested parentheses. Additionally , the words (add, sum) and (product, multiply) are all strategically used so that the student can see that these words have related meanings.

Type: Problem-Solving Task

This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have differing results due to placement of parentheses. This type of problem helps students to see structure in numerical expressions. In later grades they will be working with similar ideas in the context of seeing and using structure in algebraic expressions.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

The purpose of this task is to provide students with a concrete experience they can relate to fraction multiplication. Perhaps more importantly, the task also purposefully relates length and locations of points on a number line, a common trouble spot for students. This task is meant for instruction and would be a useful as part of an introductory unit on fraction multiplication.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

This task is intended to complement "How many servings of oatmeal?" and "Molly's run.'' All three tasks address the division problem 4÷1/3 but from different points of view. This task provides a how many in each group version of 4÷1/3. This task should be done together with the "How many servings of oatmeal" task with specific attention paid to the very different pictures representing the two situations.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

This task requires students to recognize both "number of groups unknown" (part (a)) and "group size unknown" (part (d)) division problems in the context of a whole number divided by a unit fraction. It also addresses a common misconception that students have where they confuse dividing by 2 or multiplying by 1/2 with dividing by 1/2.

Type: Problem-Solving Task

The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

The purpose of this task is to provide students with a concrete situation they can model by dividing a whole number by a unit fraction. For students who are just beginning to think about the meaning of division by a unit fraction (or students who have never cooked), the teacher can bring in a 1/4 cup measuring cup so that students can act it out. If students can reason through parts (a) and (b) successfully, they will be well-situated to think about part (c) which could yield different solution methods.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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 explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10. Exponents are NOT discussed.

Type: Tutorial

This Khan Academy tutorial video presents the methodology of understanding and using patterns in the number of zeros of products that have a factor that is a power of 10. While the standard does not mention exponents, the place value understanding of multiplying or dividing by powers of ten will help students understand multiplying and dividing by decimals.

Type: Tutorial

This Khan Academy tutorial video presents the pattern, when multiplying tens, that develops when we compare the number of factors of tens with the number of zeros in the product. The vocabulary, *exponent *and* base*, are introduced.

Type: Tutorial

This Khan Academy tutorial video interprets written statements and writes them as mathematical expressions.

Type: Tutorial

This Khan Academy tutorial video presents the impact of parentheses notation in an expression. As the tutorial does the same problem with and without parenthesis, negative numbers are part of the solution.

Type: Tutorial

This Khan Academy tutorial video demonstrates how to write a simple expression from a word problem.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

This Khan Academy tutorial video illustrates how to find the volume of an irregular solid figure by dividing the figure into two rectangular prisms and finding the volume of each. Although the tutorial works from a drawing, individual volume cubes are not drawn so students must work from the formula.

Type: Tutorial

This Khan Academy tutorial video illustrates finding the volume of an irregular figure made up of unit cubes by separating the figure into two rectangular prisms and finding the volume of each part.

Type: Tutorial

This Khan Academy tutorial video illustrates measuring volume by counting unit cubes. Models in this video include composite figure of rectangular prisms although only counting is used to find volume, not an equation.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

This Khan Academy tutorial video 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 a strategy for computing the amount of change to be received after making a purchase.

Type: Tutorial

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

Type: Tutorial

This Khan Academy tutorial video presents 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 converting between gallons, quarts, pints, cups, and fluid ounces.

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 conversion of units of time between hours, minutes and seconds.

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

In this Khan Academy tutorial video two decimals are compared using grid diagrams.

Type: Tutorial

This Khan Academy tutorial video presents using place-value to compare two decimals expressed to thousandths.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

In this Khan Academy video visual fraction models are used to represent the multiplication of a whole number times a fraction.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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, you will work through an example to correctly use the order of operations.

Type: Tutorial

In this video, you will see why it is important to have one agreed upon order of operations.

Type: Tutorial

In this video tutorial from Khan Academy, learn about the importance of place value when dividing. The tutorial uses place value up to thousands to help students think about division.

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

In this tutorial, the four operations are applied to fractions with the visualization of the number line. This tutorial starts by adding fractions with the same denominators and explains the logic behind multiplication of fractions. This tutorial also highlights the application and extension of previous understandings of mulitplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (* a*/

*) x*

**b***as*

**q***parts of a partition of*

**a***into*

**q***equal parts; equivalently, as the result of a sequence of operations*

**b***x*

**a***. In general, (*

**qb***/*

**a***) x (*

**b***/*

**c***) =*

**d***/*

**ac***.*

**bd**Type: Tutorial

This tutorial explores the addition and subtraction of fractions with unlike denominators. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd). The video number line does show negative numbers which goes beyond elementary standards so an elementary teacher would need to reflect on whether this video will enrich student knowledge or cause confusion.

Type: Tutorial

In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases. Elementary teachers should note this is not a requirement for elementary standards and consider whether this video will further student knowledge or create confusion. This chapter explains how to find the smallest possible common denominator. *For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. *

Type: Tutorial

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

Type: Tutorial

The Cartesian Coordinate system, formed from the Cartesian product of the real number line with itself, allows algebraic equations to be visualized as geometric shapes in two or three dimensions. While this tutorial includes the basis of Coordinate system, it also includes ideas beyond fifth grade standards. Most likely only advanced fifth graders would find the video engaging.

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 provide a basic introduction to decimals. The tutorial presents a decimal as another way to represent a fraction. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer gaining an orange circle and a wrong answer graying out. Some "Try This" sections will read the decimal to the students as well.

Type: Tutorial

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

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting with decimals. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

This 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

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

Type: Tutorial

The video describes how to multiply fractions and state the answer in lowest terms.

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

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

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

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

Type: Virtual Manipulative

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

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

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

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 >