Grades 3–5Geometry & TopologyPlanned
Area, perimeter and angles
Area as the number of unit squares that cover a shape, perimeter as the distance around it, area of rectangles, first volumes, and angles as amounts of turn measured in degrees.
math.geom.area-angles
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 6
You will learn to
- Find areas by counting unit squares and by multiplying length by width, and compute perimeters.
- Show that shapes with the same perimeter can have different areas, and vice versa.
- Measure and draw angles in degrees, and classify triangles and quadrilaterals by their sides and angles.
- Find the volume of a rectangular box by counting unit cubes.
Definition
- Area is the amount of surface a shape covers, measured in square units.
- Perimeter is the total length of the boundary of a shape.
- An angle is the amount of turn between two rays from a common point; a full turn is 360°.
Theorem
- The area of a rectangle is length × width.
- The angles of a triangle in the plane add up to 180°.
- The volume of a rectangular box is length × width × height.
Common misconceptions
- Confusing area with perimeter.
- Thinking an angle gets bigger when its arms are drawn longer.
- Believing that shapes with equal perimeters must have equal areas.
Leads to
Optional discoveries
- Measure theory and integration Which sets of points have an area at all? Measure theory answers this; with the axiom of choice, some sets cannot be given a countably additive area that is unchanged by sliding them.
Learning pathways
Further reading
- Paul Lockhart, Measurement (2012) — For teachers and curious adults.