4th Grade Number Sense Resources

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

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).

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.

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?

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

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.

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

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.

Two similar tools for recognizing and comparing fractions.

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

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. (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

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.

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.

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.

Designed to give an understanding of factors and prime/composite numbers. Enter an integer, then see it arranged in arrays. Move the slider to see the resulting array for various divisors.

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.

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.