Essential Strategy 4. Provide opportunities for students to work with changing units.
When given the size of an object, the student will be able to first determine the size of the unit, then use that information to determine the values of fractional parts. Therefore the student is not using a color to automatically represent a value but understands that the value of the fractional part is directly related to the size of the whole.
Tool Example: Unitizing Fractions on a Grid
The teacher can set up this tool so that the part shaded red on the grid represent a variety of fractional amounts. Students then determine the fractional amounts represented by the remaining colors.
Unitize Fractions on a Grid
Below are some examples of how the tool can be used to create some of the sample activities from the book that are designed to help students develop an understanding that fractions are fractions are always fractions of something, and that a fraction name such as one-fourth is not merely a label for a block or a shape but a description of a relationship between a part and a whole.
Tool: Unitizing on a Grid
This example is a variation of the Fraction Brick activity but instead of exploring the value of parts of a brick in relation to a whole brick students explore areas and patterns on a grid. They can be required to represent fractional amounts by shading and/or to determine the value of a given amount by completing the key. Students can create using linear shapes or they can create designs such as the one displayed below.
A variation of the Fraction Brick activity using the Unitizing Grid
Tool: Unitizing with Pattern Blocks
In this activity, students explore the relationship between the blocks when different grey areas are designated as the whole. The teacher can stamp on blocks only as shown in the first example or create a shaded pattern as shown in the second example. The third example shows how the gray areas can also represent other values instead of one whole.
Students explore fraction relationship of shapes in relation to whole, which is a hexagon.
Area representing the whole created by stamping multiple times or with multiple shapes.
Area can represent amounts less than or greater than one whole.