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