### Here are all 3rd grade resources. Click on the navigation to see resources designed for specific strands.

What are the missing digits of this equation? Think strategically about the possibilities, then click the buttons to find out. Play this game slowly with lots of conversations about what you know/don't know. See this Marilyn Burns blog post for more information and instructional ideas.

This is a hundreds chart, but with a twist. Every number in the hundreds chart has been multiplied by a random number [1,10]. Can you figure out the pattern? (See also Number Path, which explores the same idea on a normal hundreds chart.)

## Area and Perimeter of a Rectangle

See the area and perimeter of any rectangle.

## Area Comparison (easier)

How many of one shape fits into the other. Intended to serve as a bridge to division.

## Broken Clock (3rd grade version)

Estimate the random time shown by only the hour hand. Click a button to slowly put the clock back together and refine your estimate. This version can be any time; the second grade version has minutes that are multiples of 5.

## Cash Register

Set the max price, then click start. A random price is generated for an item. Drag the coins onto the cash register to pay for it. Toggle the "Show total" to see how much you've paid (if needed), then click "Check" to see if you've paid the right amount.

## Centered Number Line

Start by entering a number that will be the center of the number line. Then enter additional numbers to see how their positions on the number line relative to the center number. Meant to develop understanding of proximity and rounding. (e.g. Start with 500. Enter a few numbers that would round to 500.) Two boxes at the bottom allow you to check the rounding.

## Clock

A simple tool for exploring how a clock works. How does the minute hand move compared to the hour hand? What do we know about what time it is by looking at the hour hand?

## Close to 1000

Arrange the digits 1-9 into three 3-digit numbers. Try to get the sum as close to 1000 as possible.

## Common Multiples

A simple tool for students who need support when finding a common denominator (or any other context in which they are looking for a common multiple).

## Comparing and Estimating Whole Numbers

Use the given quantity to estimate the others. Use the sliders to adjust the size of the numbers (10 to 1000) and number of questions. Kindergartners might use this to talk about more/less, while 6th graders might have highly sophisticated approaches involving unit rate.

## Comparing Fractions on Number Lines

Use this simple applet to compare two fractions. Adjust the denominators, then drag the point to whatever fraction you're interested in. The points (and number text) will turn purple when the fractions are equivalent.

## Connecting Perimeters

Use this for a conversation for the perimeter and/or area of a complex polygon composed of non-overlapping rectangles. Drag the blue points to create a shape, then click one of the two buttons. Drag the sliders to move the sides.

## Deciding Division

Enter two whole numbers, then move the slider to see what happens when each is the dividend and divisor. (Works better with smaller numbers). Meant to help students understand the significance of dividend and divisor, including situations where the quotient would be a fraction.

## Deciding Multiplication or Division

This applet, while designed primarily to accompany contextual multiplication and division tasks, will work to illustrate any situation in which students are multiplying or dividing whole numbers. The main thinking behind it is that students can struggle with conceptualizing the three components of the majority of these problems: total number of objects, number of groups, and objects in each group. By providing a visual to accompany their thinking, we can help them to see the math they are doing, whether correct or incorrect based on the context. A specific way of using this would be to pair it with the Mathematical Language Routine Co-Craft Questions. Provide the beginning of the stem (like "Four friends have a recipe that makes 15 cookies"), and use this to help students consider different questions they could pose based on it.

## Division on the Number Line

This resource is intended to get students to use proportional reasoning to estimate quotients. Use the sliders to generate random dividends and divisors, or input your own numbers. Start by dragging the numbers to the correct locations, then predict the number of "jumps" to land on the dividend.

## Division Visuals

This is designed to help students connect division algorithms to the "action" that is actually taking place. As students develop repeated subtraction or partial quotient approaches, use this to support them thinking "What is happening here?" as they represent the problem mathematically and attend to the meaning of the quantities.

## Elapsed Time

Set a start and end time. The elapsed time is shown by unwrapping the number line from the clock. Several options for what is displayed.

## Elapsed Time on Number Line

This is based on the idea that we could approach elapsed time by comparing the relative size of the interval to the length of a day. The discussion at the end begins with "So how long would that be?" Use these visuals to make predictions, then compare it to the precise answer you get from whatever strategy you use.

## Equivalent Fraction Maker

Start by entering a fraction (or use the random one provided). Click the More/Less buttons to change the size of the fractional parts (denominator), then drag the point to change the shading (numerator). Click "Check Answer" to see if your fraction is equivalent to the original fraction.

## Estimating Sums

Use the sliders to adjust the addends, then consider the size of the sum relative to the two bounds you are given. "Would the sum be closer to ___ or ___? How do you know?" As the level of precision increases, the level of mathematical reasoning increases with it. And the GRAND purpose behind this is to get students using an estimation strategy called front-end addition. Consider building this around a central question of "How do we make our estimates more precise?"

## Filling the Number Line

How do fractions map to the number line? How big do the numerator and denominator need to be to make it "full"? Is it even possible? Explore some of these questions and many others (like finding patterns in equivalent fractions) with this simple, but powerful applet.

## Five by Five

A 2-player, GeoGebra version of Sara VanDerWerf's game. You will place (up to) 25 numbers in the grid. You score by placing (by clicking) matching numbers in adjacent squares. Decide whether you want to play a timed or untimed game, and whether you'd like the scores to be calculated by sums or products. See Sara's blog post for more information.

## Fraction Bars and Fraction Wedges

Two similar tools for recognizing and comparing fractions.

## Fraction Guesser

A rectangle (representing one whole) is shaded with a random fraction (under 1). Guess the fraction. Additional information is provided after each incorrect guess.

## Fraction Path

What if we took a hundreds chart and replaced the whole numbers with fractions? Explore this idea by clicking "Add to path," then click on a square to show its values...but try to predict the value first!

## Fraction Slider

Set upper and lower bounds. (For 3rd grade, set the upper bound to 1.) A random fraction in generated between the two bounds, with denominators limited to 2,3,4,5,6,8, and 10. Drag a dot to the correct location on the number line for the given fraction. Feedback provided.

## Fractions of a Whole

Enter any denominator, then drag the slider to see all sorts of different ways of partitioning the whole. Then shade it in various ways to gain understanding of the numerator, explore many ways of making the same size fraction, and see equivalent fractions. Or use it (along with a screen capture tool) to create fraction templates for your students.

## Fractions on the Number Line

Use this resource to explore various fraction relationships, particularly how fractions can be composed and decomposed and the relationship between improper and mixed number forms. Make predictions about the result of a "little jump" (a unit fraction) and a "big jump" (a whole).

## Geometry Sandbox

This is a simplified version of GeoGebra. Students have access to 3rd grade-appropriate tools to make points, lines, and segments.

## Guess the Sort - Whole Number Rules

Enter a whole number, and the program will sort it in the Venn Diagram according to the two randomly determined rules. Play along with your students as you try various numbers to figure out the rules. Once you know the rules, add additional numbers to each part of the diagram. Possible rules include: bove or below a certain number; Rounds within 100 to a 10; Rounds within 1000 to a 100; Multiple of 3,4,5,6,7,8,9,10,11,or 12; Prime; Composite; Even; Odd

## How Many?

A random number of objects (between 0 and the upper limit you specify) flashes on the screen. Estimate how many you saw. Then display the picture again, reconsider your guess, and finally see the answer. Designed to develop solid connection between a number and how "big" it actually is.

## How Many? (with grouping)

An updated version of "How Many?" with a new feature: once you see the squares, you can arrange them into groups. Use this to connect estimation and quantity to skip counting. Or use it to have a conversation about multiplication or division.

## Make a Dollar

Drag coins onto a dollar bill until you've got \$1.00 in pennies, nickels, dimes, and/or quarters.

## Many Names for a Fraction

Enter a fraction or let the applet generate a random one for you. Estimate, name it, find some equivalent fractions, write it as an improper or mixed number, or (maybe) even as a decimal!

## Missing Side Lengths (Complex Polygon)

A randomly generated (L-shaped) complex polygon starts as just two sides. Drag the sliders to make the rest. Meant to allow students to see the part/part/whole relationship between opposing sides.

## Move the Number

This activity is meant to develop flexible, creative thinking about numbers and operations. Your goal is to move a from a starting number to a target number, but there are many ways to do this! Adjust the sliders to control the bounds of the numbers involved.

## Ordering Products

A simple activity in which you put multiplication expressions in increasing order. Adjust the sliders to change the number of expressions and the number of digits in the factors, focusing more on estimation for large products.

## Ordering Quotients

A simple activity in which you put division expressions in increasing order. Adjust the slider to change the number of questions.

## Part-Part-Whole Estimation

Adjust the slider to control the size of the numbers. One of the pieces (a part or the whole) is randomly provided. Use estimation to fill in the rest. Feedback provided.

## Part-Whole Rectangles

Designed to develop ability to estimate reasonable answers in subtraction situations. Specify your own subtraction problem (or generate a random one), then represent the relative size of the subtrahend by shading a rectangle representing the minuend. Feedback on accuracy of shading is provided. (Not included but recommended: finish by estimate the size of the difference before actually doing the subtraction.)

## Partial Number Line

Meant to help develop the idea of possible rounding outcomes by exploring the numbers on an interval of 10, 100, or 1000. Name numbers on an interval (and predict their location!) or drag a randomly generated number to the correct spot (with feedback on the placement provided).

## Perimeter and Area of a Rectangle (Animated)

Drag the point to change the dimensions of the rectangle. Then click the "Go" button to see the perimeter upwrap and the area fly out. Perimeter and area lie along the number line to allow conversations about their value. Works better for small rectangles.

## Piggy Bank

Drag coins or \$1 bills into the piggy bank. Click to show the total amount.

## Place Value Bars

Enter a whole number (under 1 million) and it will be shown as a bar partitioned along base-10 values. Use this for a visual demonstration of, for example, why 543 > 345, beyond "because 5 is bigger than 3".

## Placing Whole Numbers on the Number Line

Drag whole numbers to the correct locations on a (mostly) blank number line. Feedback provided. Adjust the upper limit for the size of the number and how many are placed on the line.

## Random Places

The purpose of this tool is to help students see the connection between (a modeled representation of ) expanded form and the digits that make up a number. Use the slider to select which places to use (ones and tens are required, but hundreds - for 2nd grade - and thousands - for 3rd grade - are optional). This program will then make a number by randomly choosing one base-ten block for each place (up to 9) that you choose. Once you click start, the number gets covered up by a purple rectangle that you reveal once you've had a chance to discuss what might be under it. Consider the following questions:

• What's a number that might be under here?

• What's a number that couldn't possibly be under here?

• What's the smallest number that might be under here?

• What's the biggest number that might be under here?

• What's something that ALL possible numbers have in common?

## Relative Number Sizes Via Area

Designed to make a more concrete connection between dividend, divisor, and quotient. Use number sense to estimate the relative size of dividend and divisor, then use that to estimate the quotient.

## Rounding within 100 and Rounding within 1000

A different approach to rounding. Based upon the location of the number, predict its value, then predict what it would be rounded to. Start by rounding to the nearest hundred (in Rounding within 1000) or nearest 10 (Rounding within 100). Refine your guess as you learn more. Finish by revealing what the number is. The intent is for students to learn that rounding is based off of proximity to multiples of 10 or 100, not a pattern with the digits. The digits merely reveal location.

## Seeing Division

Enter a division expression, then select an approach to the division (partitive or quotative).

## Seeing Multiplication

Enter a multiplication expression, then select a visualization (jumps on a number line, array, or equal sized groups).

## Separable Clock

A simple tool that allows you to separate the hour and minute hands of an analog clock in order to analyze them independently.

## Several Fraction Bars

Type any denominator into the box, drag the slider to change the number of wholes (up to 10). Drag the dots to shade various amounts. This tool has a wide variety of uses. Possibilities include:

• Comparing fractions

• Equivalent fractions

• Mixed improper forms

• Fraction sums and differences

Really, this can handle just about anything you'd want to do with fractions!

## Showing Numbers with Place Value

Enter a number (up to 1000), then regroup it into ones, tens, and hundreds. See also "Making Tens." Designed to allow students to see lots of equivalent representations of numbers.

## Subtraction on Number Line

Designed to develop a specific strategy when faced with a regrouping problem in subtraction. Specify a subtraction problem, then see that represented on the number line as the distance between the two numbers. Since that is a fixed distance, explore how it can be found by adjusting the minuend and subtrahend to generate equivalent subtraction problems, some which would not require regrouping.

## Two Piggy Banks

Drag coins onto both banks (or Fill Randomly on both)

• Which bank has more? (I like that there'd be lots of ways to answer this)

• What coins would we add to make the banks equal?

Drag some coins onto one piggy bank (or Fill Randomly)

• Students tell you the value. Click to show total.

• Students tell you another way to reach the same total. Drag that onto the other piggy bank. Click show totals for both. Do they match?

## Vertical Partitions - Square vs. Circle

Can we partition a circle the same way we partition a square? This applet allows you to compare the resulting areas of vertical partitions in each shape. Adjust the slider to change the denominator then click the button to see the transformation.

## Volume Guesser

Select the units you want to use, then guess the volume of the liquid in the container. Feedback provided.

## Weird Rounding

It's easy for students to develop bad habits when rounding. By rounding to "weird" numbers (i.e. those that are NOT powers of ten), we can focus on proximity to multiples, not just digits. Choose your own numbers - which can be "weird" (like 27 or 3.13) or "normal" (like 10, 100, 0.1, etc.) - or let the applet pick them randomly. Then slowly reveal the information on the number line, with lots of predictions and discussion along the way. When you DO switch to focusing on powers of 10, focus your students' attentions on the patterns that emerge.

## What Shapes?

Use this activity to develop definitions of simple polygons by noticing patterns. Build math language from informal to formal.

## What's the Fraction?

A random fraction is placed on the number line between 0 and the upper limit of your choosing (up to 10). Guess what it is, then click the buttons to provide additional information and refine your guess. When you're ready, see the answer in mixed number form.

## What's the Number?

A random number (upper limit is adjustable) is generated and placed on a blank number line. Your job is to guess where it landed. Click "more info" to zoom in and refine your guess.

## What's Happening? Area and Perimeter

This is a set of three dynamic illustrations meant to develop understanding of perimeter and area. "What's happening to the perimeter? What's happening to the area?" See also this student handout.