# 4th Grade Resources

## Adding Fractions -- Visual

Enter two fractions, then watch as they are added together. "Why is the sum partitioned like that?"

## Adjustable Area Model

This uses an area model approach for multiplication. Use as a tool to support students as they learn multi-digit multiplication, or take an inquiry approach by clicking "Randomize" and working slowly, carefully to figure out the two factors. What's the fewest pieces of information you need?

## Advanced Number Path

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 Model of Multiplication

Use the sliders to adjust the factors, then "Slide me" to see the area model being constructed. This particular approach is meant to give additional visual support to students as they gain understanding of how tens x tens = hundreds, tens x tens = tens, and ones x ones = ones.

## Broken Protractor

A random angle is shown on a "broken" protractor with a red arrow. Take a guess, then click "More info" to slowly put the protractor back together and finally see the measure.

## Circle of Factors

For any natural number <= 500, see its factors arranged artfully in a circle.

## 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.

## Converting Mixed Number Fractions to Improper Fractions

This resource uses an array approach to help students understand the relationship between the mixed number and improper forms of a fraction. Can students figure out the pattern?

## 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.

## Decimal in Three Forms

Establish the decimal/fraction/percent connection by seeing three connected representations of a number [0,1).

## Distance Maker

An "Open Middle" format problem: What combination of digits and units would give you the greatest distance? What would give you the least? You must combine your number sense with an understanding of relative unit sizes as you develop a strategy.

## 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.

## Estimating Fraction Sums and Differences

Place fractions sums and/or differences on the number line. You'll have (mostly) different denominators, so you'll have to use number sense to estimate. (These should be relatively QUICK placements!) Feedback provided.

## 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.

## Equivalent Fractions -- Visual Approach

A discovery-based activity for equivalent fractions. "Shade" a fraction, then use the tool to find equivalent fractions. What patterns are you noticing?

## 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?"

## Factors of a Fraction

Use this applet to engage in some pre-algorithmic thinking. Enter any fraction, then use the sliders to see it arranged in various ways. Make connections to multiplication, division, addition, and (perhaps) even subtraction. Notice and describe patterns!

## 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 (4th Grade Denominators)

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 Size

This tool is designed for students to explore the relationships within (and between) a mixed number fraction. The two main goals I'm envisioning are (1) make the number as big (or as small) as possible and (2) make some equivalent fractions. The best part is when students realize that the numerator can be bigger than the denominator.

## 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).

## Function Machine

A random function (or "rule") is generated based on the sliders. Send the numbers through the machine to figure out what the rule is. Click on the boxes to see the rule in equation or word form. Alternatively, show the rule then predict the outputs before sending the number through.

## 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

## 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.

## 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.

## 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.

## Relative Unit Sizes (length)

Put various lengths (randomly generated) in the correct order. Select the units you want to use. Feedback provided.

## Repeated Angles

Designed specifically with standard 4.M.5 in mind. See how much of a circle angles of various size are.

## 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 Divisibility

Enter a dividend, then adjust the slider to see it "divided" into groups and, if necessary, a remainder. If you wish, display the division equation and the related multiplication equation.

## 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).

## 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.

## Subtracting Fractions

This is designed to accompany students as they begin to develop algorithmic approaches to subtracting mixed number fractions. This uses a comparison approach. (Do you see the difference, 2 5/6, in the GIF?) Go slowly and really dig into the conversation when you "regroup" (like when 5 2/6 4 8/6) so that students develop fluency with a strong conceptual base.

## 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.

## 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 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.

## What's the Angle?

Estimate the measure (0-180 degrees) of a randomly generated angle. Use hints to refine your answer.

## 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? -- Decimal Version

Set the bounds (-1000 to 1000) and the level of precision (wholes, tenths, hundredths, thousandths). Then a random number is generated and placed on a blank number line. Your job is to guess where it landed. Click "next" to zoom in and refine your guess.