Measurement and shapes
Build and connect the representations and methods in measurement and shapes.
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Before you begin
Build and connect the representations and methods in measurement and shapes.
Learning goals
- Identify a triangle's base and perpendicular height
- Calculate the area of a triangle
- Calculate the area of a composite plane figure
- Distinguish area, perimeter and volume and their units
- Construct geometric figures from stated conditions
- Calculate the volume of a cube or cuboid
- Calculate the volume of liquid in a rectangular tank
- Relate cubic centimetres to millilitres and litres
- Apply the sum of parts of a right angle
- Apply the sum of angles on a straight line
- Apply the sum of angles around a point
- Deduce all unknown angles at two intersecting lines
- Connect triangle, rectangle and square facts to deduce angles in a drawn composite figure
- Apply the sum of the three interior triangle angles
- Deduce every missing angle from the equal sides of an isosceles triangle
- Deduce all three angles from an equilateral triangle
- Deduce missing angles in a right-angled triangle
- Use the guaranteed side and angle properties of an isosceles triangle
- Use the guaranteed side and angle properties of an equilateral triangle
- Use perpendicular sides and complementary angles of a right-angled triangle
- Connect parallelogram and connected shape facts to deduce angles using existing lines
- Connect rhombus and connected shape facts to deduce angles using existing lines
- Connect trapezium and connected shape facts to deduce angles using existing lines
- Deduce every missing angle in a parallelogram
- Deduce every missing angle in a rhombus
- Deduce missing angles on both nonparallel sides of a trapezium
- Use all guaranteed side and angle relations of a parallelogram
- Use all guaranteed side and angle relations of a rhombus
- Identify a trapezium's parallel pair and corresponding angle sums
Syllabus statements covered
- concepts of base and height of a triangle
- area of triangle
- finding the area of composite figures made up of rectangles, squares and triangles
- building solids with unit cubes
- measuring volume in cubic units, cm³/m³, excluding conversion between cm³ and m³
- drawing cubes and cuboids on isometric grid
- volume of a cube/cuboid
- finding the volume of liquid in a rectangular tank
- relationship between ℓ (or ml) with cm³
- angles on a straight line
- angles at a point
- vertically opposite angles
- finding unknown angles
- properties of • isosceles triangle • equilateral triangle • right-angled triangle
- angle sum of a triangle
- finding unknown angles without additional construction of lines
- properties of • parallelogram • rhombus • trapezium
- finding unknown angles without additional construction of lines
Lessons
Work through them in order.
About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Triangle base, height and areaFind a perpendicular height and connect triangle area with half a parallelogram.
- Unit cubes and volumeCount three-dimensional space in equal cubes and read a layered cube drawing.
- Cuboids and liquid volumeUse complete layers to derive cuboid volume and measure liquid in a rectangular tank.
- Angles on lines and at a pointChoose the correct angle relationship and state why it applies.
- Triangle angle propertiesUse the angle sum and equal-side markings to justify unknown triangle angles.
- Parallel quadrilaterals and their anglesUse marked parallel sides and named quadrilateral properties to justify unknown angles.