Teacher Information: Fraction Pieces

This virtual manipulative is an electronic version of a common physical manipulative and incorporates all of the options or versions commonly available.

Basically, the user can choose among pieces that represent fractional portions of either a circular or square region. The manipulative opens with the circle version and one circular region showing. The user can add another circular region or choose to have no region at all showing in the workspace. The same options are available for square regions (one, two, or no squares in the workspace). Click on the radio buttons at the upper left to switch between squares and circles.

For the circle version, the fraction pieces are all wedges, representing 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 19, 1/10, and 1/12 of the whole.

For square wholes, there are two shapes of size 1/2, two of size 1/4, and two of 1/8, and a trapezoid of size 3/8. In addition, there are pieces representing 1/3, 1/5, 1/6, 1/10, and 1/12.

Clicking on the appropriate bin puts a piece into the workspace, and the piece can be dragged or rotated as desired. After clicking to select a piece in the workspace, the user can change colors as desired by clicking on the color palette at the bottom. The size label option can be turned off or on. With the Show Label on, the size of a fraction piece appears when the cursor is over the piece.

Young children can play with patterns and colors and symmetry relations without having to learn fraction names (preferably with the Show Label off). Since the pieces can be dragged over one another, it is easy to show that "Two yellows just cover one red," (or dark green and pink in the circle version) without worrying about names. Later, we want to use three 1/3-piece to cover the whole (square) region and six 1/6-pieces to cover either the same or a separate square. By the time fractions are named and it makes sense to talk about a 1/3-piece and 1/6-pieces, exactly the same relation is expressed by the sentence "Two 1/6-pieces cover one 1/3-piece," showing that 1/6 + 1/6 = 1/3. Without a Flip button, it may be awkward to combine the 3/8-trapezoids, but it should be easy to see what is needed to add to 3/8 to get 1/2, or by putting two 3/8-pieces into the square region and completing the square with two 1/8-pieces.

The only limit to the way Fraction Pieces can be used is the imagination of the teacher. For more experienced students, for example, one can ask questions that require some computational skills. After filling half of the unit square with a 3/8-piece and a 1/8-piece, cover half of the same region with the 1/4- triangle. What is the size of the portion of the 1/8-piece left uncovered by the 1/4- triangle? How much is covered? What about the covered and uncovered portions of the 3/8-trapezoid? Or similarly with the circular pieces. We can illustrate addition by adding a 1/12-piece to a 1/8 piece, rotating to place them together in the circular whole. What color piece exactly covers the sum? How would we add 1/12 and 1/8 symbolically? The same kind of exercise illustrates subtraction: after placing a 1/5 yellow piece in the circular region, cover part of the yellow with a brown 1/8-wedge, so they have one edge in common. What fractional part is represented by the part of the yellow showing? After subtracting 1/8 from 1/5, it should be possible to check the answer by showing that a 1/12-piece exactly covers the yellow. Similarly some simple products can be shown. To see 1/3 of 1/2, we see what size pieces are needed to make three exactly cover a 1/2-piece.