Year 7 Measurement: revision mind map

1Metric units of length

1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.

2.5 m = 250 cm

3400 m = 3.4 km

45 mm = 4.5 cm

Big unit to small: multiply. Small unit to big: divide.

2Perimeter

Add all the sides.

Rectangle 7 by 4: $2(7 + 4) = 22$

Square side 5: $4 \times 5 = 20$

Regular hexagon, side 3: $6 \times 3 = 18$

3Circles and circumference

$C = \pi d = 2\pi r$. The radius is half the diameter.

$d = 6$: $C = 6\pi \approx 18.8$

$r = 4$: $C = 8\pi \approx 25.1$

$\pi \approx 3.14$

4Arcs and sectors

Arc length $= \tfrac{\theta}{360} \times 2\pi r$. Add the straight edges for the perimeter.

Quarter circle $r = 4$: arc $2\pi \approx 6.3$, perimeter $8 + 2\pi \approx 14.3$

5Area of rectangles

$A = lw$, in square units.

$8 \times 3 = 24$ cm²

1 cm² = 100 mm², 1 m² = 10 000 cm²

Square, side 5: $25$ cm²

2 m by 3 m: $6$ m²

Watch out: to convert area units, square the length conversion.

6Area of parallelograms

$A = bh$, with the height at right angles to the base.

Base 6, height 4: $A = 24$

Base 8 cm, height 5 cm: $A = 40$ cm²

Watch out: use the perpendicular height, not the slanted side.

7Area of triangles

$A = \tfrac12 bh$: half a parallelogram.

Base 10, height 3: $A = 15$

Watch out: don't forget the $\tfrac12$.

8Composite shapes

Split into shapes you know and add, or take a shape away.

L shape: $8 \times 3 + 4 \times 2 = 24 + 8 = 32$

10 by 6 with a 2 by 2 hole: $60 - 4 = 56$

9Volume of rectangular prisms

$V = lwh$, in cubic units.

$5 \times 3 \times 2 = 30$ cm³

Cube, side 3: $3 \times 3 \times 3 = 27$ cm³

10Volume of triangular prisms

$V = Ah$: area of the triangle times the length.

Triangle $\tfrac12 \times 4 \times 3 = 6$, length 10: $V = 60$

Triangle base 6, height 5: area 15. Length 4: $V = 60$

11Capacity

1 L = 1000 mL, 1 cm³ = 1 mL, 1 m³ = 1000 L.

250 mL = 0.25 L

A 10 cm cube holds 1000 cm³, or 1 L

1.5 L = 1500 mL

12Mass and temperature

1 t = 1000 kg, 1 kg = 1000 g.

2.5 kg = 2500 g

Water freezes at 0°C and boils at 100°C

750 g = 0.75 kg

From $-2^\circ$C to $5^\circ$C is a rise of $7^\circ$