# Pre-Algebra/Beginning Algebra Concepts - Computer Resources

The intention of this curriculum guide is to provide teachers with supplemental materials to use to support students in strengthening their skills in various concept areas that are crucial for understanding beginning algebra. The activities are broken down by skill with links provided below. This is intended as a way to provide students with engaging, primarily computer-based activities to get extra practice with material that is covered elsewhere in the curriculum. This collection focuses on simulations and games using the computer—some resources may be ripe for teachers to develop unique activities to accompany the simulation and some possible suggestions are included with the descriptions. This series is intended to be pick-and-choose.

In this Curriculum Guide:

Activities and practice with: Integers, Exponents, Order of Operations, Distributive Property, Expressions, Equations and Basic Graphing

## INTEGERS:

### -Tug of War

This game of tug of war, which can be played with online dice, is a fun way for students to practice adding positive and negative numbers. Students work in pairs; one is positive and the other is negative. They have to add their number to whatever remains. When one of the partners reaches an absolute value of 13, they are the winner. [Slide the red dot to track where you are].

https://nrich.maths.org/content/id/5898/TugWar2.swf

### -Exploring Integers with the Number Line

This is a Geogebra simulation that allows you to add and see integer addition by moving the slider. The first digit goes from -21 through 21 and the second digit goes from -10 through 10. This might work best accompanied by a worksheet for integer addition. Have students check their work from the worksheet using this visualization. Students who are still having a hard time adding integers accurately can have this up alongside another activity on the computer so that they can continue to check their work and be certain about their integers as they are working with new concepts.

https://www.oercommons.org/courses/exploring-integers-with-the-number-line-geogebra

### -Introduction to Negative Numbers - Remix

This resource is a collection of videos introducing integers, including integer addition and subtraction. More description of the different videos is available through the link.

https://www.oercommons.org/authoring/2548-introduction-to-negative-integers-remix/view

## EXPONENTS:

### -Folding Paper to the Height of the Empire State Building

This activity and short videos help explain the concept of exponential growth. They help build number sense around exponents:

https://www.oercommons.org/authoring/10161-folding-paper-to-the-height-of-the-empire-state-bu/view

### -Rules for Exponents

This is a full lesson on learning exponent rules. The lesson includes explanations, worked examples, videos, and interactive practice. It is a ready-to-use computer-based student activity.

https://www.oercommons.org/courses/rules-for-exponents/view

## ORDER OF OPERATIONS:

### -Which Comes First?

This simulation (game) has students practice the order of operations by selecting the next operation. It is good at running down what steps a student would take without requiring them to do the calculations. For students who are still working to solidify their understanding of integers, working on order of operations can be difficult because their miscalculations cause their answer to come out wrong. This activity helps narrow the practice to “Which Comes Next” while doing the calculations on behalf of the students. (You may have to refresh the page after opening it to get the simulation to work. Also, make sure to click maximize—at the bottom in the middle—to see the whole thing).

http://hippocampus.org/HippoCampus/Arithmetic?loadLeftClass=Course&loadLeftId=91&loadTopicId=7979

## DISTRIBUTIVE PROPERTY:

### -Geometric Proof of the Distributive Property

This resource made with Geogebra has a slider to adjust values for the distributive property. You can see how the area of the two sections and overall change in relation to each other as you slide each dimension. This could accompany a worksheet with distributive property problems or be used to generate new problems.

https://www.oercommons.org/courses/geometric-proof-of-the-distributive-property-geogebra

### -Area Model Algebra

Area Model Algebra is good for seeing visually how the distributive property works (much like the resource above). It can be used with numbers or variables. Level 1 of the game is good for working with the distributive property. Levels 2-6 are good for practicing multiplying and factoring binomials.

https://www.oercommons.org/courses/area-model-algebra/view

## EXPRESSIONS:

### -Match Expressions with Words

This activity has students practice matching expressions with words. There isn’t anything by way of explanation, so it will already have to have been taught. However, it is useful practice.

### -Expressions Exchange

This simulation by PhET gives practice building and matching simplified expressions. The game starts out with coins that you connect to build specific values and then transitions into constants and variables.

https://www.oercommons.org/courses/simplifying-expressions-phet-interactive-simulations/view

## PRINCIPLES OF EQUATION AND INEQUALITY:

### -Basic Equations

These Khan Academy videos are a review of basic equations to support students who are having trouble with how to solve equations.

One Step Equations: https://khancontent.nroc.org/html5/Khan%20Academy/video-7100/Media/402956.mp4

Two Step Equations: https://khancontent.nroc.org/html5/Khan%20Academy/video-7101/Media/448468.mp4

Multi-Step Equations: https://khancontent.nroc.org/html5/Khan%20Academy/video-7102/Media/398877.mp4

### -What's More?

This simulation (game) has students compare different items on a scale to figure out which one is heaviest. It supports the kind of thinking necessary for Algebra in that it helps students look at different sides of an equation and understand relative values. This activity would be a good, fun, low-pressure activity for students to practice independently, especially when the practice of solving equations becomes overwhelming. (You may have to refresh the page after opening it to get the simulation to work. Also, make sure to click maximize—at the bottom in the middle—to see the whole thing).

http://hippocampus.org/HippoCampus/Algebra & Geometry?loadLeftClass=Course&loadLeftId=94&loadTopicId=8173

### -Pan Balance: Expressions

This interactive allows students to put different expressions on opposite sides of a scale and then turns that into a graph. Teacher-designed activities could help students build practice on a wide variety of things from basic principles around equality, graphing lines, systems of equations, and quadratic equations. One challenge is that because this is so versatile, it may be difficult for some students to decide what to pay attention to without teacher guidance.

You could start by providing students with specific expressions to put on each side of the balance and asking them if they are equal or not and to write why not (one way to see that the expressions are equal is that the blue line and red line will be on top of each other). Starting with this will give them practice with how to use the simulation. After that, you can challenge them to create new expressions that are equal and to see how complex they can make their expressions while keeping them equal. You could also have students manipulate the expressions on both sides of the balance to keep them equal. You could do this as they are solving linear equations, manipulating one side and then the other to keep the scale balanced.

http://www.oercommons.org/courses/pan-balance-expressions/view

## GRAPHING:

### -Graph the Line

This game provides lots of practice manipulating the graph of a line until it matches the equation provided. Students move the points on the graph which changes the orientation of the line. When their line matches the equations, the simulation says, “You did it!” Students can use this when working on plugging in points to graph a line as well as using y=mx+b to graph.

Activity option one:

For each equation provided, use substitution to find two different points. Record on a piece of paper all of the lines that you graph and points that you find.

Activity option two:

For each equation, use the y-intercept and slope to graph the line. Consider how the line looks different based on the slope. For each line, write the two points that you plotted.

https://www.geogebra.org/m/WVGxwKKn

### -Bermuda Triangles

This game is good for supporting student understanding of slope. Students look at objects and try to identify the slope of the objects. It is a visual search game where they look for an object with a provided slope. For example, the right triangle formed by a block of cheese in the picture might have a slope of ½.