A shape has more than one size. This unit separates them: the distance round the edge, the ground it covers, the space inside a solid, and the card it takes to wrap it. It starts with rectangles, where the squares can be counted, and shows that the same fence can enclose very different areas.
Cutting and sliding turns a parallelogram into a rectangle, and copying and turning turns a triangle into a parallelogram, which gives the two formulas and why they work. The same splitting handles shapes that are not rectangles. The unit ends in three dimensions: volume as layers of cubes, then nets that unfold a box so every face can be added. Nothing needs a calculator, and every drawing is worked out exactly, not sketched.
The lessons, in order
- Lesson 1 · Perimeter and area of rectangles Perimeter as the distance round, area as squares inside, area of a rectangle as rows times squares per row, their units, and what happens when every side is multiplied by the same number. Stretch a rectangle on a grid and read its perimeter and area, then multiply every side and watch the area grow faster. No calculator
- Lesson 2 · Same fence, different area Whole-number rectangles with a fixed perimeter or a fixed area, the square as the largest area for a perimeter and the smallest perimeter for an area, and why. Slide the width of a rectangle with a fixed fence and watch the area rise and fall, then compare every rectangle with the same area. No calculator
- Lesson 3 · Area of triangles and parallelograms Area of a parallelogram by cutting and sliding, area of a triangle by copying and turning, the perpendicular height (inside or outside the base), and finding a missing base or height. Cut a parallelogram and slide the piece to make a rectangle, then copy a triangle to make a parallelogram. No calculator
- Lesson 4 · Area of compound shapes Area of shapes made from rectangles and triangles, by splitting or by subtracting, including the trapezium; perimeter as the outside edges only; missing lengths in compound shapes. Split one L-shape three ways and watch the area stay the same, then see which edges count for the perimeter. No calculator
- Lesson 5 · Volume of cuboids and prisms Volume as the number of unit cubes, cuboids as layers, any prism as cross-section area times length, units of volume, and finding a missing dimension. Fill a box layer by layer with unit cubes, then give three different shapes the same length and compare their volumes. No calculator
- Lesson 6 · Nets and surface area Nets of cuboids and triangular prisms, which patterns fold into a cube, surface area as the total of the faces, open boxes, and how the same volume can need different amounts of card. Unfold a cuboid and a triangular prism, and add up every face. No calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.