For many students algebra seems too abstract and hard to learn. They often resort to ineffective memorization and in the long run find only frustration and failure.
Now there’s a new free iPad app that can turn frustration into success. The Fun Way to Learn Algebra: Hands-On Equations 1 Lite gives even the youngest students visual and kinesthetic ways to understand abstract algebraic equations.
The app is intended for children from age 8 onward. No user needs a background in algebra to learn the concepts presented. This app is a digital version of the traditional Hands-On Equations program, which uses physical game pieces, that is widely used in schools and by homeschooling parents across the United States.
The app, like the physical version, is also well suited for helping older students who are struggling in traditional algebra classes.
Each of the three lessons of this free app is introduced by a short three- to four-minute video. The video is followed by two practice examples and then by ten exercises. If the app is used in a classroom, the teacher should first verify that all students can solve the two practice examples for the lesson before asking students to do the ten exercises for that lesson on their own.
In the first lesson the student learns that a pawn, or marker, has an unknown weight, or value, and that a number cube has the value shown on the cube. When these game pieces appear on the image of a balance scale, the setup symbolizes an equation.
The “scale” does not actually move. Rather, it is used to symbolize the equality between the two sides of the equation. The goal is to determine the value of the pawn that will make the sides balance, or equal.
The sample image below is from Lesson 1B, which requires the student to find the value of the pawn that will make both sides have the same value. This is a thinking question. The student uses inspection or trial and error, as the game pieces do not move in this first lesson.
After a short while the student will see that the value of 5 for the pawn will give both sides the same value, namely 13. The student then uses the number wheel to enter 5 for x. To conduct the check, the student evaluates each side and enters the value of each side using the number wheel. Once the student has entered both the correct value for x and the correct value for the check, a reward box pops up to the sound of a trumpet and says, “Great!”
In the second lesson the student learns how to set up an abstract equation using the game pieces, keeping in mind that x is represented by the blue pawn and the positive constants by the number cubes. For example, in Lesson 2B the student is asked to set up the equation 3x + 1 = x + 7, shown below.
The student tries different values for the pawn to find the value that will make both sides the same. Say the student tries a value of 2 for the pawn. The left side will then have a value of 7 while the right side will have a value of 9, showing that x = 2 is not the correct answer. The correct value of x, namely x = 3, will make both sides equal; each will have a value of 10.
The experience of the first two lessons helps to ensure that the student understands the meaning of the pawns and cubes and the concept of equality. The third lesson then gives the student a powerful strategy for solving basic algebraic equations.
Consider example 3B. The equation is 5x + 2 = 2x + 14. Unless the student has been using the physical version of Hands-On Equations at home or in school, it is not likely that he or she will have encountered such a problem at the age 8, the intended age for a child to begin using this app.
The setup for the above equation is show below.
In Lesson 3 the student learns the concept of a “legal move.” The essential idea is that removing a pawn from each side of a balanced system maintains the balance. Therefore, the student uses the iPad’s touchscreen feature to physically remove one pawn from each side of the scale in order to simplify the equation.
The student repeats this legal move a second time, so that the scale now has three blue pawns and a 2-cube on the left side and two cubes worth 14 on the right side, as shown below.
From this point the student can reason that the three pawns have a total value of 12 and so the value of a single pawn is 4. The student enters 4 for x using the number wheel.
If the student attempts to conduct the check in the simplified setup, the student will get a value of 14 on each side. However, that is not the check value for the original equation, and so the student will see an error message asking that the original equation be reset and then to do the check.
After resetting the original equation the student evaluates each side to get the correct check value of 22, as shown below.
If the student makes a computation error while doing the check, the app shows an error message asking the student to try the check again. Should the student continue to have trouble with the arithmetic, the student can use the Auto Check feature. Clicking the Auto Check button to the right of the check spaces enables the app to conduct the check for the student using the game pieces that are on the scale. With this feature, each game piece is enlarged as the app provides the sum to that point.
Some students like the Auto Check feature because they can challenge themselves to do the calculations before the app does them. However, the student should not routinely rely on Auto Check to confirm his or her answer because it is important for the student to determine independently whether the value for x is correct.
From this free app, links are available to purchase the full-scale Hands-On Equations apps for Levels 1, 2, and 3, which successively lead students to solve more advanced algebraic equations using similar methods.
The Fun Way to Learn Algebra: Hands-On Equations (Level 1 Lite) app for the iPad has an average user rating of 4.5 and has been designated as an Editor’s Choice app by Bestappsforkids.com.
One reviewer enthused, “I struggled with algebra my whole life…problems that would have taken me five minutes to figure out I can now do in a few seconds! Everyone needs this app…kids and adults!”
For a free app, you can’t beat that!