Geometry for kids

What kids learn about geometry, grade by grade

• Kindergarten to grade 2: name 2D and 3D shapes in any position, describe them by sides, corners and faces, and split shapes into halves, thirds and fourths. See shapes for kids.
• Grade 3: area by counting squares and multiplying, and perimeter; types of quadrilaterals.
• Grade 4: points, lines, rays and angles; measuring angles with a protractor; lines of symmetry.
• Grade 5: volume of rectangular prisms and plotting points on the coordinate plane.
• Grade 6: area of triangles and other polygons, surface area using nets, and volume with fractional edges.
• Grade 7: circles (area and circumference), angle relationships, and scale drawings.
• Grade 8: transformations, the angle sum of a triangle, the Pythagorean theorem, and volume of cylinders, cones and spheres.

Where to start with geometry

With real objects and drawing. Children who have built shapes, unfolded boxes and walked around a room learn the vocabulary and formulas far more easily. Start with 2D and 3D shapes, then area and perimeter.

The big ideas behind geometry

Shapes are defined by their properties, not by how they look: a square turned on its corner is still a square. Measurement grows with dimensions: length is measured in units, area in square units and volume in cubic units. Most mistakes in geometry come from mixing these up.

Types of angles

An angle measures a turn, in degrees. A full turn is 360°, a quarter turn is a right angle of 90°.

Geometry formulas, by grade

What	Formula	Learned in
Perimeter of a rectangle	2 × (length + width)	Grade 3
Area of a rectangle	length × width	Grade 3
Volume of a rectangular prism	length × width × height	Grade 5
Area of a triangle	½ × base × height	Grade 6
Circumference of a circle	2 × π × radius	Grade 7
Area of a circle	π × radius²	Grade 7
Angles in a triangle	add up to 180°	Grade 8
Volume of a cylinder	π × radius² × height	Grade 8
Pythagorean theorem	a² + b² = c²	Grade 8

Every formula comes from counting. Area of a rectangle counts rows of squares; a triangle is half a rectangle; volume counts layers of cubes. Showing where a formula comes from makes it much easier to remember.

Where kids get stuck in geometry

Area or perimeter?

The most common mix-up. Perimeter is the fence around the garden; area is the grass inside. Try the tool above with the same perimeter but different areas.

Forgetting square and cubic units

Writing 24 cm for an area. Fix: ask “what did you count?” Squares give cm², cubes give cm³.

Reading the wrong protractor scale

An angle of 50° read as 130°. Fix: decide first whether the angle is acute or obtuse, then pick the scale that agrees.

Judging shapes by position

Calling a turned square a “diamond”, or thinking a triangle must point up. Fix: count sides and corners whatever way the shape faces.

Geometry worksheets

Kindergarten to grade 5

• Naming 2D shapesKindergarten–grade 1
• PerimeterGrades 2–3
• Area of rectanglesGrades 3–4
• Types of anglesGrade 4
• Volume of rectangular prismsGrade 5
• Coordinate planeGrades 5–6

Grades 6 to 8

• Area of trianglesGrade 6
• Surface areaGrade 6
• Circles: area and circumferenceGrade 7
• Angle relationshipsGrade 7
• Triangle anglesGrades 7–8
• Volume of cylindersGrade 8
• Volume of cones and spheresGrade 8
• Pythagorean theoremGrade 8

Make a fresh area and perimeter test · Make an angles test

How to teach geometry at home

Measure a room

Measure a bedroom floor in feet. The perimeter tells you how much skirting board it needs; the area tells you how much carpet.

Unfold boxes

Cut a cereal box along its edges and lay it flat. That is a net: count the faces, and add up their areas for the surface area.

Find angles

Open a door or a laptop to make acute, right and obtuse angles. A book corner is a handy right-angle checker.

Fill and pour

Fill a box with sugar cubes or blocks to measure its volume, then check with length × width × height.