In this section, students describe, compare, and sort a variety of shapes. They have previously used terms such as square, rectangle, triangle, quadrilateral, pentagon, and hexagon to name shapes. In this section, students think about ways to further categorize triangles and quadrilaterals. They see that triangles and quadrilaterals can be classified based on their sides (whether some are of equal length) and their angles (whether one or more right angles are present).

Although students will not learn the formal definition of an angle until grade 4, they are introduced to the terms “angle in a shape” and “right angle in a shape” to describe the corners of shapes. This allows students to distinguish right triangles and to describe defining attributes of squares and rectangles.

These are right triangles.

These are not right triangles.

What makes a shape a right triangle?

Students come to understand that a shape can have more than one name if it has attributes that define it as a different type of shape. They also see that some quadrilaterals aren’t squares, rhombuses, or rectangles because they don’t have the defining attributes of these shapes.

For example, here are three quadrilaterals. The first one is a rectangle, a rhombus, and a square. The other two are not squares, rhombuses, or rectangles.

In this section, students are introduced to the idea of perimeter. Students begin to conceptualize perimeter as a measurable geometric attribute with a concrete experience: using paper clips to build the boundary of shapes and using the length of a paper clip as the unit for measuring the distance around each shape.

Students transition to analyzing shapes with equal-size intervals marked on their sides or shapes drawn on dot paper or grid paper. They quantify the distance around the shape by counting the intervals or adding the number of units on each side.

Later, students find the perimeter of shapes labeled with their side lengths. They learn to leverage the geometric attributes of shapes to find perimeter more efficiently (for instance, they recognize sides that are the same length and use multiplication).

Students see that different shapes can have the same perimeter and draw shapes with a specified perimeter. Finally, students find missing side lengths of shapes given the perimeter and solve perimeter problems in context.

This pentagon has a perimeter of 32 cm. What is the length of the missing side?

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In this section, students apply what they’ve learned about shapes, geometric attributes, perimeter, and area to solve problems and create designs in different contexts.

Students begin by designing a small park with certain features and then finding the area and perimeter of the park. Next, they examine geometric features in West African wax print patterns and then design their own pattern. Finally, in the modeling lesson, students use their knowledge of area and perimeter to design a space to keep chickens.

Throughout these activities, students draw on dot paper and use the intervals between dots as a unit of measurement.

In this section, students analyze the area and perimeter of shapes. They begin by solving contextual problems that require considerations of both measurements. They then draw rectangles with the same perimeter and different areas, and rectangles with the same area and different perimeters.

Students recognize that given the perimeter of a rectangle, they can find rectangles with different whole-number areas. Likewise, given the area, they can find rectangles with different perimeters.

rectangles with a perimeter of 16 units

rectangles with an area of 24 square units