Area, perimeter and angles

يعتمد على

عدد المتطلبات السابقة الإلزامية (حتى الأساس): 6

ستتعلّم

• 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.

تعريف

• 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°.

مبرهنة

• 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.

مفاهيم خاطئة شائعة

• 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.

يقود إلى

اكتشافات اختيارية

• 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.

مسارات التعلّم

• Conventional K–12 progression

قراءات إضافية

• Paul Lockhart, Measurement (2012) — For teachers and curious adults.