Level 4: Area and volume

Measurement · level 4 of 8 · rough age 11-12 (a guide for parents; anyone can start anywhere)

In level 3 you found the area of rectangles by counting rows of squares. In this level you find the area of parallelograms, triangles and trapezoids by cutting and moving pieces until they become rectangles, so each formula comes with a reason you can see. Then you build shapes out of shapes, step up from squares to cubes to measure volume, join volume to litres, and finish by measuring the size of Mars itself.

Lesson	You will be able to
Area of a parallelogram	Show why a parallelogram's area is base × height, and pick the true height instead of the slanted side
Area of a triangle	Show why a triangle is half a parallelogram, find the area of any triangle (obtuse ones too), and choose the right height
Area of a trapezoid	Use two copies to explain the trapezoid formula, and find a trapezoid's area or a missing side
Composite shapes	Find the area of L-shapes, rooms and gardens by adding pieces or subtracting holes
Volume by counting cubes	Measure volume in cubic centimetres, fill a box layer by layer, and explain length × width × height
Capacity and volume together	Use 1 mL = 1 cm³ and 1 L = 1000 cm³ to find how many litres a tank holds, and measure odd shapes by water
How big is Mars?	Compare the sizes of Mars, Earth and the Moon with numbers, a ruler and a ball model

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