Middle-school students learn how certain shapes, such as squares, triangles, six-sided hexagons and rectangles can fit together to “tessellate,” or cover a flat surface with no gaps or overlaps. This concept becomes clearer to students when they create their own tessellating patterns, similar to what they’d see on a tiled floor or wall. They can choose one or two shapes and draw or trace them, filling a sheet of art paper. For a more interesting design, the student can use heavy paper to cut a square with two-inch sides. He cuts a random design from the left side of the square, slides it to the right side and tapes it along the edge. If he traces this pattern repeatedly on a sheet of art paper, adding colors and design elements, he’ll create a unique tessellation.
It’s important for middle school students to be able to identify various geometric shapes. They can create drawings that include a pre-determined set of shapes, such as two triangles, three rectangles, a five-sided pentagon and a six-sided hexagon. The creation could be a scene from nature, such as a boat on an ocean that incorporates a long, flat rectangle for the bottom of the boat and triangles for the sails. Parents can buy a set of tangrams -- seven plastic geometric shapes -- at a teacher’s supply store. The student could create pictures with the tangrams. She traces all seven pieces onto a sheet of art paper in a way that results in a design, such as an animal shape.
Fractions, decimals and percents are connected, and middle-school students need to understand the relationship of one to the other. Using colored pencils or markers, the learner can color a random design on a sheet of paper that is divided into 100 squares on a 10 by 10 grid. Once the design is completed, she can figure out how many squares she used for each color and then write it underneath the picture as a fraction, decimal and percent. For example, if she colored 20 of the 100 squares blue, she’d represent 20 out of 100 by writing the fraction, 20/100. She could reduce that fraction to 1/5. She'd also include the decimal .20, or .2, and 20 percent.
Middle-school children learn that scale drawings are larger or smaller representations of actual objects. They can practice this skill by choosing some object at home or in the classroom and sketching it. It might be a desk or a door. They measure the item and then come up with a scale to use when they replicate it on paper. It might be that an inch on the paper represents a foot on the actual item. Once students have some experience with the concept, they can attempt to duplicate an entire area, such as a bedroom.