Interactive Fraction Wall

Fraction walls are a great way to teach about fractions and in particular equivalent fractions. In a fraction wall each row or layer of the wall represents one whole number. The layers are divided into a number of bricks and hence each brick represents a fraction whose denominator is equal to the number of bricks in that layer. Each brick can be turned on or off by clicking it. This wall also allows the display of decimal and percentage values. To the right of the wall are boxes which can be hidden, the value of each box is fraction of the wall that has been turned on.

Selecting different walls

When you launch this interactive teaching program the initial wall is a mixed one showing 3 distinct fraction families. Change the wall by using the mode control. ‘Large’ displays a wall in which the layers are split 1,2,3 up to 12. The others split the wall along 2s, 3s or 5s. The 5s also includes a lower wall of 100 bricks, this naturally works quite well in explaining percentages since each brick represent ¹⁄₁₀₀ or 1%.

Fractions, decimals or percentages

Use the display type control to display decimals (rounded to 2dp), percentages (rounded to 1dp), fractions or none.

The equivalent fraction control

Normally when you click a brick to turn it on or off, only that brick is affected. However if you turn on the equivalent fraction function by clicking the ‘Eq’ toggle button. Now when a brick is clicked the other layers will turn on bricks if they can match an equivalent fraction. Note, this is not always possible, in fact if you select the primes wall it is never possible to show an equivalent fraction. In this case all the other layers have bricks turned off.

Least Common Multiple

Also known as ‘the lowest common multiple’ or ‘smallest common multiple’ is crucial when adding, subtracting or comparing fractions. This button will calculate the LCM based on the rows that have active bricks. Pressing the LCM button will create a new wall that contains the originally selected fraction but also a new layer with the number of divisions equalling the least common multiple of the denominators of the other rows. Sounds complicated, but it really just means that it is always possible to create an equivalent fraction in the LCM row from the other rows.

Other controls

The other controls are:

• ‘On’ button when clicked will turn on all the bricks
• ‘Off’ button when clicked will turn off all the bricks
• ‘Random’ button creates a randomized wall in which roughly half the bricks are on. Usually you would hide the totals before pressing this and then the class can work out each fraction in the random wall.
• ’ < ’ button will align all the bricks to the left hand side of the wall. This is often pressed after using the randomize function. Fractions can then be compared by considering the length of each row of on bricks.
• hide totals click to hide all the totals. The individuals total can then be clicked to show the value.
• show totals reveal all the totals.

Advanced Section

To show or hide the advanced section click the advanced toggle button.

When the advance controls are on, each layer of the wall has a dedicated slider, move this to change the number the number of bricks in that layer.

• Automatic 1 button when clicked create a new wall by dividing the top layer by all its ascending prime factors. So for example if you move the top slider so the top layer has 42 bricks and then click the button. The primefactors of 42 are 2,3 and 7. So the second layer will have 42÷2=21 bricks, the third layer will have 21÷3=7 bricks and the final layer will have 7÷7= 1 brick.
• Automatic 2 is similar but creates a layer for every factor of the top layer value.
• Add Layer adds a new layer to the bottom of the wall.
• total type select control will change the type of total to display. The default is to match what the wall shows, so in this case if the wall is showing fraction the total will be a fraction. But using this control it is now possible for fractions to be shown in the wall but the total to be given as a percentage.

Further fractions

Closely related to this activity is the percentage fraction and decimals grid, which can be used to display a square or circle fraction representation.

Other activities that can be used to teach fractions are the clock activity which uses the clock face to show the fraction of minutes passed in an hour. Launch the activity and select the fractions mode, this mode also show equivalent fractions for example ³⁰⁄₆₀ = ¹⁄₂. The number explorer activity can show the fraction resulting from division of a number.