# Algebra Virtual Manipulatives

A useful VM from the excellent Freudenthal Institute. Students can experiment with a variety of sequence's formulae using the variable ‘n’ (as opposed to ‘x’) - see Physical World Sequences and this help video (scroll down the page) for an idea of how to use this manipulative. Students can see the ‘n’ terms, the nth terms and a graph of these terms. The interface is simple to use and it stresses sequences notation, using ‘n’, rather than function notation in ‘x’. Numbers can be expressed as fractions or as decimals. Multiple, related sequences can be created.

## Algebra Virtual Manipulatives

'Great tools, freely available on the web for teaching Algebra!'

The following page lists some examples of some of the best freely available virtual manipulatives on the web for teaching Algebra. Where possible they will link to an example of how they can be used in the classroom. Entries are listed by topic subheading, although its not always easy to separate so its worth looking through the lists!

### Simplifying

#### Pacman Algebra

Why is it that I'm still surprised how much children enjoy even the simplest of games?  No 21st Century graphics in this game of pacman, but still lots of fun.  The gamer is encouraged to practise their algebraic skills at the same time as avoiding thse pesky ghosts, and eating the one with the correct answer.  Skills tested: collecting like terms, substitution and expanding brackets.

### Functions

#### Guess the Function

A game to get students to guess the operation of a single stage functions.  Choose the input, receive the output and guess the function.  A simple introduction to functions that can be played with a whole class or individually.  Students love the function machine noises!

#### Double Function

Another guess the function game, but this time the function is made up of two steps. Lots of functionality on this virtual manipulative, which takes a little getting used to: select input, press calculate then try to work out the two functions and fill in operation 1 and 2.  You can records results in a table in notepad.

### Sequences

#### Painted Cubes

This lovely animation saves loads of time (and the need to have enough multilink cubes for the whole class) to recreate the classic painted cubes activity.  You can separate the cube and look at different layers individually for up to 5 by 5 by 5 cube.  The father activity gives away a little too much for this investigation, but this VM is superb!

#### Number Grid Sequences

Oodles of potential for this lovely show me/hide me grid from John Mason.  Each cell has two parts: a calculation (yellow), and a result (blue). How few cells can you uncover in order to predict all the others?
You can preset the relationships for use with a class. To find out how best to exploit this number grid read what John has to say about them.

#### The Frog Problem

This is a classic problem that has been around for a while. In the  Frogs activity, the aim is to get students acting this one out for themselves, but once they have done so it can be helpful to have this virtual manipulative to help students check their results. Students are looking at breaking down a quadratic sequence in this problem and this manipulative helps by not giving too much away. It is fun and it simply counts the moves!

#### The Tower of Hanoi

This is a fabulous game and a great challenge! It is probably best done by hand, but there are many advantages to using an online version. For starters it counts correctly and it is quickly available to a whole class of students. The screencast below shows the   The Tower of Hanoi game generates a lovely exponential sequence and makes for a great investigation for all ages. Look at the activity  Tower of Hanoi on this website.

#### Sequences Formulae

A useful VM from the excellent Freudenthal Institute. Students can experiment with a variety of sequence's formulae using the variable ‘n’ (as opposed to ‘x’) - see Physical World Sequences. Students can see the ‘n’ terms, the nth terms and a graph of these terms. The interface is simple to use and it stresses sequences notation, using ‘n’, rather than function notation in ‘x’. Numbers can be expressed as fractions or as decimals.

### Solving Linear Equations

#### Algebra Balance Scales

This virtual manipulative from NLVM allows you to solve equations using a balance scale.  You can create a visual image of the equation then remove or add items from both sides to solve it.  Negative values are represented by balloons lifting up each side.  A great way to introduce solving equations.  To see how best to exploit this activity see Balancing Equations

#### Solving Equations Game

This VM from The Freudenthal Institute is best used after Algebra Balance Scales.  The balance scales have been removed, but the applet provides scaffolding by checking the steps of working as the students go along.  In this way they can concentrate on what operations to carry out to solve the equation and rely on the computer to do the rest (a tick comes in the form of a green squiggle).  A game provides a competitive element which students love.

Graphs

#### Car Race - Slopes & Intercepts

This is a lovely Geogebra applet to introduce distance-time graphs and give an application for the intersection of straight lines.  Adjust the initial positions of two cars and their speeds and see/calculate where they overtake.  Lots of potential.

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