Kids of all ages can have fun learning geometry by making models of objects such as triangles, squares, cubes, pyramids and rectangles using miniature marshmallows and toothpicks. Primary school students can identify shapes and their properties, while high school students can investigate the relationships between corresponding sides, perimeters and areas of similar figures.

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## Primary School Activity: Geometric Model Comparison

Armed with marshmallows and toothpicks, primary grade students can make models of a triangle and a square. As a class, compare the number of sides and vertices of each model and discuss the similarities and differences. Have students compare their triangles and squares with their classmates' models to find matching, or congruent, figures. Congruent figures have the same size and shape.

## Elementary School Activity: Geometric Concepts

Third- and fourth-grade curriculums cover geometric concepts such as point, line segment, parallel, intersecting, perpendicular and angles. Have students use toothpicks and marshmallows to demonstrate representations of these concepts. Instruct students to build models of a square and a triangle, describing each polygon with appropriate geometric vocabulary. Using each of the models, students should construct models of a tetrahedron, or triangular pyramid, and a cube. The class can describe and discuss the geometric concepts of face, edge and vertices. Tell students that the toothpicks represent the edges and the marshmallows are the vertices.

## Middle School Activity: Area

Middle school students can construct polygon marshmallow and toothpick models whose areas can be found by subdividing them into triangles or rectangles. Instruct students to brainstorm ways to calculate the area of the polygon they built by dividing the object into smaller, familiar polygons. Have students use a nonstandard measurement, such as the length of a toothpick, to express the area of the original polygon. Finally, have students find the area of an irrational polygon whose dimensions cannot be measured in toothpicks. Use the Pythagorean Theorem and the subdividing procedure to calculate the area.

## High School Activity: Ratios

By building similar squares, rectangles and triangles using marshmallows and toothpicks, students can investigate the relationships between the corresponding sides, perimeters and areas of the figures. Instruct students to use up to 45 marshmallows and toothpicks to make two triangles, 36 to make two rectangles, and 20 for two squares. Have students find the lengths of sides, perimeters and areas of the similar figures, and determine the ratios of the corresponding sides, perimeters and areas. Students can analyse their results and explain the relationships that are evident in the activity.