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
- Calculate the area of a circle from a given radius or diameter
- Calculate the circumference of a circle from a given radius or diameter
- Calculate the enclosed area of a semicircle
- Calculate the complete perimeter of a semicircle
- Calculate the enclosed area of a quarter circle
- Calculate the complete perimeter of a quarter circle
- Calculate retained area in composite polygon and circular figures
- Calculate the complete perimeter of composite polygon and circular figures
- Find a cuboid dimension from volume and two known dimensions
- Find the edge of a cube from its volume
- Find a cuboid height from volume and base area
- Find a cuboid face area from volume and its perpendicular dimension
- Evaluate a nonnegative square root
- Evaluate a nonnegative cube root
- Use right corners and angle partitions between connected rectangles or squares
- Connect triangle, rectangle and square facts to deduce angles in a drawn composite figure
- 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
Syllabus statements covered
- area and circumference of circle
- finding the area and perimeter of • semicircle • quarter circle
- finding the area and perimeter of composite figures made up of square, rectangle, triangle, semicircle and quarter circle
- finding one dimension of a cuboid given its volume and the other dimensions
- finding the length of one edge of a cube given its volume
- finding the height of a cuboid given its volume and base area
- finding the area of a face of a cuboid given its volume and one dimension
- use of √ and ∛
- finding unknown angles, without additional construction of lines, in composite geometric figures involving • square • rectangle • triangle • parallelogram • rhombus • trapezium
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.
- Circles and composite boundariesUse the radius for circle area and trace every part of a composite boundary.
- Areas and boundaries of circular compositesChoose retained parts for area and trace complete boundaries without counting shared internal edges.
- Missing dimensions and rootsReverse area and volume calculations and interpret square and cube roots as lengths.
- Angles between rectangles and squaresUse right corners and distinguish separate gaps from overlapping corner parts.
- Angles in composite figuresUse marked shape properties and shared angles without inventing new lines.