## Add and Subtract Integers with Counters

This shows how we can find sums or differences two integers y using zero pairs, which are represented here by yellow (for positive) and red (for negative) counters.

## 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

## Draw the Slope

Drag the points to make the line match the given slope. Then click "Check" to see how closely you matched it.

## Equations of Lines

Adjust the line(s) with sliders, either in slope-intercept (y=mx+b) or standard (Ax+By=C) form (or both). Use this to develop understanding of how the parameters affect the graph of the line, or to examine the relationship between the two forms of the line.

## 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?"

## 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.

## 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.

## Go Fish!

Use this resource to predict the population from repeated samples. Catch (and release) a fish a few times. Keep track of the fish you catch to predict the population of 25 fish in the lake.

## Graphing in Point-Slope and Slope-Intercept Forms

Click on two points to draw the line matching the given information. You have two chances to draw the line, after which the answer will be given.

## Linear Equation Guesser

Here's what I was picturing: Everyone in the class writes down an equation. Collect several to put on the board, then click "More info." As information is slowly revealed about the line, which equations are still viable? How could we revise those that aren't?

## Make a Linear Function

Drag the numbers to the table to create points. Can you make a line? What patterns can we notice about the relationship between x and y?

## 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.

## 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.

## Prime Factorization

This is a visual approach to prime factorization. Enter a whole number (<1000 works best), then select one of its prime factors to see it made into an array. The process is repeated using only one row of the previous array (which is the non-prime factor of the original number).

## 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.

## Similar Triangles

Starting with a pre-image, draws the image for scale factor of your choosing. Click on the sides to show/hide their lengths.

## Slope Guesser

A random line is generated and displayed. Guess the slope, then refine that guess as more information is provided. The final step is to see how the slope is calculated by selecting points on the line.

## 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.

## Supplementary and Complementary Angles

Simple program that shows the supplement and complement of the angle. You can choose to show/hide angle measures.

## Triangle Side Lengths

What patterns can we notice about possible combinations of side lengths? In other words, can we discover the Triangle Inequality Theorem?