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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.
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.
Establish the decimal/fraction/percent connection by seeing three connected representations of a number [0,1).
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.
Place 4 randomly generated rational numbers on the number line. Feedback provided.
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.
Set upper and lower bounds. 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 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
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!
How does multiplying or dividing by a power of 10 affect a number? Is the decimal point moving? (No!) Or are the digits? (Yes!) If I wanted to change 723.1 into 72,310, how would I do that?
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".
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!
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.
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.
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