## 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 Mean, Median, and Mode

Enter data in a list (or click RANDOMIZE), then see it displayed as a lineplot and/or boxplot. Select which of {Mean, Median, Mode} you want shown for each data set. Possible teaching moves include:

• Make predictions about where each measure of center will fall

• Justify why the mean would be above or below the median

• Look for the connections between the lineplot and boxplot ## 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. ## Double Number Line

This tool is designed for students as they are getting introduced to the double number line. Use it to notice patterns and explore the proportional relationships that a double number line organizes and displays. Move the red "dot" around to generate new data points. Before you click "Capture," ask questions like "Based upon what we know so far, if there are 5 apples, how many oranges do you think there will be?" and "What did you notice that helped you predict that?" ## Draw the Box Plot to Match the Dot Plot

This tool lets students practice drawing box plots from dot plots. Consider what a box plot DOES before getting into that 5 number summary stuff. "What are you noticing about how these overlap?" ## Drawing with Points - Four Quadrants

In the style of "connect the dots." Enter ordered pairs and this will draw the lines connecting them. Note that this version allows coordinates in all four quadrants (but the GIF shows the first quadrant-only version). ## Egyptian Fractions

An Egyptian fraction is the expansion of a non-unit fraction into a sum on unique unit fractions. For instance, 2/3 = 1/2 + 1/6 is an Egyptian fraction expansion, while 2/3 = 1/3 + 1/3 (not unique) and 2/3 = 1/3 + 2/9 + 1/10 + 1/90 (not all unit fractions) are not. Use this resource to explore these ideas, while getting some visual supports and an answer if needed. The provided answer is generated with what is called the Greedy Algorithm, which is not always the "best" expansion. See https://en.wikipedia.org/wiki/Egyptian_fraction for further explanation. ## 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 the non-negative rational numbers 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. ## Fold a Box

This demonstrates how, by removing squares from the corners of a rectangle, we create the net for an open-topped rectangular prism. For a given set of dimensions, experiment to see what size squares will maximize the volume of the prism. ## Four Numbers

Place 4 randomly generated rational numbers on the number line. Feedback provided. Note that this version uses positive and negative numbers (but the GIF shows the fifth grade version using only positive numbers). ## 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. ## Given Part, Find Whole

Use proportional reasoning to estimate the size of a rectangle. Meant to develop intuitive understanding of unit rate. ## 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 ## 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. ## Mystery Point (6th grade version)

There's a randomly generated point somewhere on the coordinate plane (-10 ≤ x ≤ 10 and -10 ≤ y ≤ 10). You have 10 guesses to find it, with hints provided along the way. Note that the GIF is showing the fifth grade version, which is restricted to the first quadrant. ## One Variable Linear Inequalities

A simple tool for graphing the solutions to linear inequalities (in one variable) and checking individual numbers as solutions. Try to check solutions before looking at the graph. ## Ordering Quotients - Adjust and Estimate

Estimate the quotients and put them in order. Adjust the slider to change the number of questions and the size of the dividend and divisor. This will have non-integer quotients more often than no, so the emphasis will be on using number sense to get an idea of their relative size, not on exact answers. ## Rectangular Prism in 3D

Drag the sliders to change the dimensions of the prism. Allow students to "see" how the volume formula is the product of the 3 dimensions, and how a 3D array evolves from a 2D array. ## Relative Unit Sizes (length)

Put various lengths (randomly generated) in the correct order. Select the units you want to use. Feedback provided. ## Resistance of Mean and Median

A tool designed to investigating the notion of resistance in measures of center. A randomly generated dot plot is drawn (size determined by user). Drag the blue point to see how the mean and median are affected. ## Seeing Factors

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. ## Solving a Linear Equation on the Number Line

This activity is meant to give students a more concrete understanding of the steps involved in solving a linear equation of the form ax + b = c (where a, b, c can be any numbers - positive or negative). After you enter your equation, use the properties of equality to solve it, and you'll see the resulting action on the number line. Click "Show solution" at any point in the process. ## Tape Diagram

A simple tool that allows you to draw and compute with ratios using a tape diagram. ## Volume Guesser

Select the units you want to use, then guess the volume of the liquid in the container. Feedback provided. ## 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. ## What's the Point?

A random point is placed in any of the four quadrants. Guess its coordinates, then refine that guess as more information is provided. 