# The Center for Algebraic Thinking has resources related to technology use in the classroom:

#### iPad Apps and BOOKS and INSTRUCTIONAL TECHNOLOGIES DATABASE

## APPS FOR THE IPAD/IPHONE/IPOD TOUCH

The Center for Algebraic Thinking is developing mobile applications to facilitate middle and high school students’ algebraic understanding. These apps change learning algebraic concepts from static to dynamic. Students interact in game and learning modes to construct meaning with important algebraic topics. These are not apps that are intended for students to "play" with for hours but apps that focus on development of specific concepts for a short period of time. Most of these apps are meant to be easily integrated into instruction rather than used for drill or fill time. If you have feedback about our apps and/or ideas for new apps, please let us know: algebrathinking[at]gmail.com. Most apps can be found for FREE on iTunes. All work on iPads. Some work on iPhones. We have also developed a Classroom Response app. ** **

*NEW!*

*NEW!*

*The Center for Algebraic Thinking*

has just published "Teaching Algebra with iPad Apps"

It is a Teaching Resource ebook

that helps teachers implement the Center's apps

in their classroom.

You can find the iBook at the iTunes store. ($5.99)

(you can search by title or by one of the authors: Doug Neill or Steve Rhine)

has just published "Teaching Algebra with iPad Apps"

It is a Teaching Resource ebook

that helps teachers implement the Center's apps

in their classroom.

You can find the iBook at the iTunes store. ($5.99)

(you can search by title or by one of the authors: Doug Neill or Steve Rhine)

*You can also find the iBook, Kindle, or just the pdfs for the Student pages at *https://gumroad.com/algebrathinking* *

### Also new to the iOS App Store is Help Me Choose! This app is designed to help teachers pick students randomly in class or create random groups of any size. It can also be used to teach probability by weighting different choices. As a multipurpose app it can also help you choose which restaurant to go for dinner or any other choice you need to make!

__The following apps are available on iTunes for FREE!____ __

(except as noted)

(except as noted)

**ACTION GRAPHER (link)**

**ACTION GRAPHER (link)**

#### DEVELOPED IN COORDINATION WITH SHODOR

Three apps in one! Students often have difficulty understanding the relationship between axes in a graph and how the two variables interact. They tend to believe the graph will look like reality. To develop a more comprehensive understanding of the dynamic taking place in graphs, each of these apps challenge the student to explore how the information from each axis influences the graph. In Bicycle, the user takes a bike on a journey up and down a hill and sees different graphical representations of what is going on based on considering different variables. In Flask, the user draws a flask of any shape, watches it fill up with water, and sees how the graph is influenced by the shape of the flask.In Doodle Pad the user can draw an action and instantly watch two distinct graphs appear, demonstrating different representations of what is happening mathematically.*Programmer: Shodor*

** ALGEBRA CARD SORT (link)**

Algebra Card Sort is a way for students to develop their understanding of the relationships between different representations of math ideas. Students match cards of different types of representation with the same concepts such as a table that coincides with a graph. The initial version of the app includes two different card sorts. First, combining equations and word problems with integers. Second, combining tables, graphs, equations, and word problems involving distance and time. The second card sort is based on the work of the Mathematics Assessment Project at the University of Nottingham (http://map.mathshell.org/). If you have a set of cards that might be appropriate for the app and focus on an area of algebraic thinking, please contact us! We will try to include it in the next version.*Programmer: Chris Barnes*

**MATH FLYER ($0.99)**

**MATH FLYER ($0.99)**

**DEVELOPED IN COORDINATION WITH SHODOR (SHODOR.ORG/MATH FLYER)**

Traditional education uses static, motionless graphs to indicate the relationships between variables. While this works for some concepts, a student with a function and a picture of a graph gains no intuitive sense of the elements of the function and the relationship of each to the shape of the graph. With Math Flyer, a student can plot a graph and manipulate all of the variables and constants in that graph, allowing him or her to see the relationships firsthand. Math Flyer plots polynomials, all of the trig functions, exponentials, absolute value, square and saw waves, and so much more.

**SLOPE SLIDER**

**SLOPE SLIDER**

**DEVELOPED IN COORDINATION WITH SHODOR.**

Easily compare lines and manipulate the slope and y-intercept dynamically to develop understanding of key elements of a linear equation. Free/Basic version of Math Flyer.

ALGEBRA EQUATION BUILDER (link)

Research tells us that students struggle to understand the nature of the equal sign, an essential idea in algebra. Rather than seeing the equal sign as a message to compute from left to right, seeing it as a sense of balance. *Algebra Equation Builder* encourages students to develop that sense of balance as they build and decompose equations. Four levels of equation building are provided.*Programmer:** Tyler Higley*

**LINEAR MODEL (link)**

**LINEAR MODEL (link)**

Students that learn how multiple representations of mathematical ideas fit together have more comprehensive understanding of a concept. Linear Model has an adjustable line, a function input and y-intercept input, and an x-y table. Any adjustment of the line, equation, or table automatically changes the other two representations so students can see how they are connected.

This linear grapher has several options and features: an adjustable line, a function input and y-intercept input, and an x-y table. The adjustable line has three points along it. The point in between allows the user to move the line when touched and dragged, changing the y-intercept and the base value of the function. The other two points allow the user to rotate the line, also changing the y-intercept and changing the multiplier of the function.

Aside from changing the graph via the line itself, the user also has the option of changing the line by entering values in the y-intercept field and in the function field. If the user enters a function that is not in y=mx+b form or in ax+by=c form, the app will not utilize and will give the user a warning that the app cannot use the function.**Programmer:** Kameron Schadt

**DISTANCE RATE TIME PROBLEM SOLVER (link)**

**DISTANCE RATE TIME PROBLEM SOLVER (link)**

D=R*T

Distance Rate Time problems are the classic math problems that are often challenging for people. Use this app to create a visual representation of the problem you are trying to solve. The app has two different activities. First, the app will give you a problem for you to represent and then solve. Second, you can use it in "Explorer" mode and use it to visually represent any DRT problem. Sometimes, seeing how the trains, planes, boats, or cars are moving can help you think about the math in the problem. This app helps you do that!**Programmer: **Chris Barnes

**ALGEBRA TILES for Factoring and Solving (link)**

**ALGEBRA TILES for Factoring and Solving (link)**

We know from research that having visual representations helps students develop conceptual understanding of algebraic topics. Algebra Tiles help students represent and solve algebra problems using tiles to represent variables and constants. The game consists of solving equations for x, substituting in variable expressions, and expanding and factoring equations. Some of the functions that the app has are the ability to remove zero pairs, rearrange tiles to help visualize the expressions, and add and take away tiles. Other functions:

Selecting tiles of opposite but equal value will be removed.

Copying tiles - Selected tile will be duplicated

Negating the value of tiles - Selected tiles will have their values changed from positive to negative or negative to positive.*Programmer: **Jose Alvarado*

**POINT PLOTTER (link)**

**POINT PLOTTER (link)**

One misconception that students develop in algebra is that there are no points or a limited number of points between two points on a graph. This game uses students’ knowledge of the 2D coordinate system and ability to recognize patterns to develop the concept there are an infinite number of points between two points. The premise is simple: you are shown a line segment, and you must identify as many points as possible that lie within that line segment. But you have just two minutes per round to do that. Submit enough correct points and you will make your way to the top of the High Scores let. With three difficulty levels you will be challenged no matter what your current skill level.

The ultimate goal of this app is to give students the opportunity to discover for themselves the relationship that exists between all of the points that lie along a line. For that purpose, all correct points that a player submits are collected into a table. After the game finishes, we encourage players to take a look at that table and try to describe how those points are related. Can you come up with a way to accurately predict other points that lie on the line? If you were given a random coordinate point, could you develop a test that would check to see whether or not that new point lies on the line?**Programmer**: Doug Neil

** INEQUALITY KICKOFF (link)**

**INEQUALITY KICKOFF (link)**

In *Inequality Kickoff *it is your job to set up the football on the field for the perfect kick! Set up the ball according to the given inequality and let the pigskin fly! Guess right and you'll have that ball sailing all day! Get it wrong and your kicker will be the one taking the heat. 12 levels of football themed inequality solving that help students understand the meaning by using inequalities on a number line. We know from research that students have significant difficulty understanding which direction to shade lines and the meaning of that shaded line. They struggle to understand how values work in an inequality. This program helps students practice thinking about those concepts.**Programmer**: Kameron Schadt

*HOP THE NUMBER LINE (link)*

*HOP THE NUMBER LINE (link)*

Drag the Bunny across the number line of carrots to answer addition and subtraction problems in this fun race against the clock math game. Students struggle with integers and understanding negative numbers, in particular. This app helps students practice combinations of integers.

Levels 1-4: Two term integer equations

Levels 4-8: Three term integer equations

Levels 9-11: Three term decimal and fraction equations**Programmer**: Tyler Higley

**COMPOUNDING INTEREST SIMULATOR (link)**

**COMPOUNDING INTEREST SIMULATOR (link)**

The Compound Interest Simulator helps students learn about the impact that changes in interest rates, time, and principal have upon the ending balance. Using sliders to adjust the different variables, students can watch how a table or graph are impacted by their manipulation. Students also have the option of considering interest compounded yearly, quarterly, monthly, or daily.

**Programmer**: Jose Alvarado

**LI****ON GRAPHER (link)**

**LI**

**ON GRAPHER (link)**

Develop students’ understanding of slope and y-intercept with this game environment which requires students to write equations to get a line into a lion’s mouth. Multiple features in this great app that helps students use and construct meaning for all aspects of a linear equation. The app pushes students to understand how manipulation of the slope and y-intercept influence the graph of a line.**Programmer**: Sean Sharma

**COVER UP (link)**

**COVER UP (link)**

In math classes we tend to ignore students' intuition when helping them learn how to solve equations. Sometimes, their intuition is more likely to help them find meaning than rote procedures. Young students can solve complex equations when they don't have to rely on a mechanical use of the order of operations. Cover Up helps students develop a strategy for solving algebraic equations that is more intuitive than the traditional use of order of operations. Given an equation that is “messy” with fractions, exponents, square roots, etc., students cover up the challenging part of the equation to make it more intuitive to solve. Five different levels of problems are included. A great way to develop confidence in solving challenging algebraic equations in a way that makes sense!**Programmer**: Code Monkeys

**TORTOISE AND THE HARE ALGEBRA (link)**

**TORTOISE AND THE HARE ALGEBRA (link)**

One of the most challenging topics to understand in algebra is rate of change. This app helps students explore the effects of different rates of change on the classic race between the tortoise and the hare. Students can manipulate how many feet per second each racer travels, including a little nap time for the hare and then watch the race be animated. Students can also change perspectives between seeing the overall map of the race and watching the individual racers up close and see how the rates of change for each racer look in each context.**Programmer**: Code Monkeys

**ALGEBRA EQUATION BALANCER (link)**

**ALGEBRA EQUATION BALANCER (link)**

** **Learn to solve algebraic equations! Research shows that students have difficulty in algebra understanding the equal sign as a balance between two equal expressions. Using tiles you can take away something from both sides of the equation. The app features a balance beam scale with colored objects (that correspond to numbers in the equation) that allows the user to remove equal objects simultaneously to help visualize simplifying equations. The user is given an equation in two different forms: one with numbers, the other in colored objects. The user can remove equal objects from both sides until it cannot be simplified further to get the answer to the numbered equation. There is also a place to enter answers and have them checked. There are multiple levels of increasing difficulty including things such as parentheses, fractions, and multiple variables.**Programmer**: Chris Barnes

**CARD CLUTTER (link)**

**CARD CLUTTER (link)**

Help students develop understanding of the relative values of numeric expressions. We know from research that students have difficulty understanding the relative values of integers. In this game, you have a bunch of cards with numbers and other numeric expressions, and your pesky friend has put them in the wrong order on a table. Your job is to pick up the cards in the order, so you can put them away. Each level is one table full of cards, and later levels introduce more complicated expressions. Levels either have 5 or 10 cards, so the difficulty can be increased without transition to more complicated expressions. Each session keeps track of total time. Mistakes do not remove the card, but do add to your total time, thus decreasing your "score" (i.e. your time). When the game is over your score is recorded and you can enter your name in the leader boards.**Programmers**: Brian Mock and Ashley Fisher

**F****UNCTION MYSTERY MACHINE (link)**

**F**

**UNCTION MYSTERY MACHINE (link)**

A simple, fun way to practice algebraic functions. Choose a level or go head-to-head with a friend as you try to guess the mystery function. The game supports algebra functions ranging from simple “x + 5” equations to ones such as quadratics and “x + a” for two-players. Developing hypotheses and testing those hypotheses helps students understand the role of variables within a function and the influence of order of operations upon those variables.**Programmer**: Kameron Schadt

**D****IAMOND FACTOR (link)**

**D**

**IAMOND FACTOR (link)**

Diamond Factor helps you to learn how to factor trinomials of various difficulties through the use of a diamond. Players can practice levels which range from trinomials with small positive coefficients to larger, negative or decimal coefficients. Players can also factor trinomials in game mode which keeps track of accuracy and time. This is a standard approach to factoring used in schools that pushes students to consider the relationship between the factored and unfactored forms of a trinomial, particularly in regard to how multiplication and addition create the terms.**Programmer**: Stephanie Jones

**SUBMARINER ALGEBRA (link)**

**SUBMARINER ALGEBRA (link)**Develop students’ understanding of points on a line, slope, and y-intercept with this game environment. Similar to the game “Battleship”, students graph submarine paths (3 lines) for a competing student to find. Dropping depth charges (x,y points), students seek the submarine paths. After a couple of hits, students use the points to identify the equation of a line to determine if they have found one of the submarine paths. The app pushes students to understand how manipulation of the slope and y-intercept influence the graph of a line.**Programmer**: Eoin Sinclair

**LIST SELECTOR ($0.99) (link)**

**LIST SELECTOR ($0.99) (link)**

This app allows teacher to randomly select a student or group. Also, it randomly creates small groups of 2-10. Teachers load class lists into the app and the app does the rest!**Programmer**: Eoin Sinclair

**ALGEBRA C****LASS RESPONSE**

**ALGEBRA C**

**LASS RESPONSE**

**(AVAILABLE NOW! HERE!)**

There are two apps associated with Algebra Class Response. The Student iPad app and the Teacher laptop/desktop app. The laptop/desktop based app functions on both Mac and Windows to deliver formative assessments to students’ iPads. Schools often are not able to use the Internet in classooms. This app does not need (but can use) the Internet. Instead, it uses a local network (wireless router) and browser software to create and then deliver assessments to students. The app allows teachers to either create their own assessments or use problems from the Center for Algebraic Thinking's Formative Assessment Database. Results are tabulated and graphed instantly for use in instructional decision making. Email the project for a copy of the app.** **The "Algebra Class Response Student" iPad app is now available on iTunes to quickly access the assessments.

**ALGEBLOKS **

**ALGEBLOKS**

This is more of a game than for developing any concepts in algebra. Algebloks is a game that plays similarly to Tetris. The user has sets of Bloks in specific shapes. Each of these Bloks have a number, a mathematical sign, or a variable. The object of the game is to line up Bloks so that they make a coherent mathematical equation, such as 3x + 3 = 9, among others. The user forms these equations either horizontally or vertically.

When an equation is made, the set of Bloks will have a bright outline. If the user taps this set of Bloks, the line will disappear, and the resulting equation will be stored in a Queue. After the first equation is made, the user then must make a Blok set that solves the equation for the given variable(s). For example, if the user has made an equation like 2x = 4, the user then must make a set of Bloks that read x = 2, either horizontally or vertically. After the user is able to do this, they will either win points or come closer to progressing to the next level, depending on the mode they are in.**Programmer**: Kameron Schadt

**INSTRUCTIONAL TECHNOLOGIES DATABASE**

**The Instructional Technologies Database is a description of technological tools that facilitate the development of students’ understanding of challenging topics in algebra. (Click here to view the database)**

**The database includes:**

**a description of a technology****connections to Common Core State Standards,****the domain and mathematical topic it addresses,****platform (Mac, PC, web based, iOS, Android, etc.),****cost,****a rating in regard to how well it facilitates students’ development of concepts****a rating in regard to how well it helps them practice skills****how it might be useful in helping students develop an algebraic concept, and****any research that explored its effectiveness.**

**If you have a technology that you find useful in developing students’ understanding of an algebraic concept, please fill out our survey so we can add it to the database. You can find the survey at www.tinyurl.com/algebratechnology.**