Using Polypad: Algebra

Introduction

This tutorial provides an overview of the Algebra Tiles. Below are the topics covered.

• Algebra Tiles
• The Balance Scale
• Evaluating Expressions
• Coordinate Axes
• Variable Sliders

Algebra Tiles

Dragging Algebra Tiles on top of each other creates a zero pair.

The Balance Scale

All objects above the Balance Scale in the tile panel have an initial starting value of 1. The initial x value is 5 and the initial y value is 4. Select the scale and click on "Balance" at the bottom of the canvas to assign a new value to the object or variable so the scale will be balanced.

Click and drag the black circle on the balance scale to change the size of the scale.

Objects can be assigned negative values.

Objects can be assigned fractional values using the equation editor tool or using fraction bars.

Imported images can be assigned values as well.

Assigned values remain saved to the object or variable within the canvas and on saved canvasses. This feature works with the Algebra tiles as well.

Define variables first to create systems of equations to then share with others. The example below shows how to set up the system 5x-7=3y and 2y+10=4x.

Here is one example of how to use the Polypad tiles to solve this system of equations.

Evaluating Expressions

Polypad will evaluate expressions creating using the Equation Editor. Turn this option on and off in the Customize UI settings menu. The expressions work appropriately on the balance scale.

Coordinate System

To plot functions on the coordinate system, create a function in the equation editor text box. Next, drag the blue triangle on the right side of the equation editor onto the coordinate system.

Plot any expression with one variable, an equation of the form y = f(x), an implicit function containing x and y, as well as polar functions of the form r = f(θ).

Enter values of $\pi$ (or multiples of $\pi$) as needed for the x and y labels.

Plotting Points from a Table of Values

To plot points, use the blue triangle in a table to connect the table to a coordinate system. Double click on the plotted points or functions to change colors.

Sliders and Variables

Insert equations with variables and use the sliders to control the variable. Click on each slider to reveal the settings menu for that variable.

Explore our Tasks and Learn More

Visit the Activities page to see lesson plans, student explorations, puzzles, and teaching ideas. Visit the Tutorial page to learn more about using Polypad.