Shape and Space: Area, Perimeter and Angle Facts
GCSE MATHS RESIT · EDEXCEL FOUNDATION · 5 OF 7
Shape and space
Area, perimeter and angle facts. Draw it, label it, and the marks follow.
Paper 1 · Paper 2 · Paper 3
Lesson duration is: 60 minIntroduction
Items in this lesson
GCSE MATHS RESIT · EDEXCEL FOUNDATION · 5 OF 7
Shape and space
Area, perimeter and angle facts. Draw it, label it, and the marks follow.
Paper 1 · Paper 2 · Paper 3
Lesson 5 of 7, about 60 minutes. Timings: do now 5 min, area and perimeter 15 min, angle facts 15 min, units 8 min, exam question and exit 17 min.
Every diagram in this lesson is drawn to scale, so students can check answers by eye. In the exam, diagrams are usually marked "not drawn accurately": tell students to trust the numbers, not the picture.
Students need a ruler and a pencil today. Device-free fallback for the whole lesson: every activity works on mini whiteboards or paper; the notes on each slide say how. Image credit: Lorin Both / Unsplash
DO NOW · 4 MINUTES
Four from last lesson
Simplify 3x + 5 − x + 2
2x + 7
Solve x + 9 = 15
x = 6
C = 3 + 2m. Find C when m = 4
11
Find the nth term of 2, 4, 6, 8, …
2n
Students answer on paper as they arrive. Click four times to reveal the answers.
Device-free: questions on the board before the lesson.
PERIMETER AND AREA
Around the edge, or the space inside?
8 cm
5 cm
Perimeter is the distance around the edge.
8 + 5 + 8 + 5 = 26 cm
Area is the number of squares inside.
8 × 5 = 40 cm²
Perimeter is a length, so it is in cm. Area counts squares, so it is in cm². The units are worth a mark on their own.
The rectangle is drawn to scale (30 units per cm) with every 1 cm square marked: count them, there are 40.
Two clicks: perimeter, then area.
The most common mix-up in the whole topic is adding when the question wants area, or multiplying for perimeter. "Peri" means around (like a periscope looking round).
Device-free: draw an 8 by 5 grid on squared paper and count.
AREA OF A TRIANGLE
A triangle is half a rectangle
base 10 cm
6 cm
Area = 30 cm²
The height must meet the base at a right angle. Never use the sloping side as the height.
Drawn to scale: base 10 cm, height 6 cm (30 units per cm). The grey outline is the 10 by 6 rectangle: the triangle fills exactly half of it, which is why there is a half in the formula.
One click: the working and the answer.
Common slips: forgetting the half (answer 60), and using the slanted side as the height.
Device-free: draw the rectangle and triangle on the board; cut a paper rectangle in half diagonally to show it.
COMPOUND SHAPES
Split it into rectangles you know
4 m
4 m
6 m
4 m
10 m
8 m
A
B
A: 4 × 8 = 32 m²
B: 6 × 4 = 24 m²
Total area: 32 + 24 = 56 m²
Perimeter: add all six sides.
4 + 4 + 6 + 4 + 10 + 8 = 36 m
Drawn to scale at 30 units per metre: a 10 m by 8 m rectangle with a 6 m by 4 m piece missing from the top right.
Five clicks: the split line and labels, area A, area B, total area, perimeter.
Exam questions often leave out one or two side lengths. Here the 4 m along the top is 10 − 6, and the 4 m inner side is 8 − 4: show students how to find a missing side before they start.
Common slip: multiplying the two longest sides (10 × 8 = 80) and forgetting the missing corner. Check: 80 − 24 = 56, same answer.
Device-free: draw the L-shape on squared paper.
A triangle has base 9 cm and height 4 cm. Find its area.
18 cm²
36 cm²
13 cm²
26 cm²
Answer: 18 cm² (½ × 9 × 4).
Slips: 36 cm² forgot the half. 13 cm² added base and height. 26 cm² treated it like a perimeter (9 + 4 + 9 + 4).
ANGLE FACTS
Four facts, and the reason is worth a mark
50°
130°
125°
115°
120°
60°
70°
50°
40°
40°
140°
140°
Angles on a straight line add up to 180°
Angles around a point add up to 360°
Angles in a triangle add up to 180°
Vertically opposite angles are equal
Exam questions say "Give a reason for your answer". Write the fact in words, exactly like the boxes above.
All four diagrams are drawn accurately: the angles shown are the real angles, so students can check them with a protractor.
Check the sums: 50 + 130 = 180. 125 + 115 + 120 = 360. 60 + 70 + 50 = 180. 40 and 40, 140 and 140 (and 40 + 140 = 180 along each line).
The reason mark: "angles on a straight line add to 180°" earns it; "because it's a straight line" usually does not.
Device-free: students copy the four facts into their books with a quick sketch of each.
Drag the value of x under each diagram
50°
x
125°
x
120°
60°
70°
x
40°
x
50°
140°
130°
40°
65°
115°
Same four diagrams as the last slide, drawn accurately, with one angle hidden in each.
Answers, with the reason students should say out loud: Straight line: x = 180 − 50 = 130° (angles on a straight line add to 180°). Point: x = 360 − 125 − 120 = 115° (angles around a point add to 360°). Triangle: x = 180 − 60 − 70 = 50° (angles in a triangle add to 180°). Crossing lines: x = 40° (vertically opposite angles are equal).
Distractors: 140° (the angle next to the 40°, not opposite it) and 65° (180 − 115, using the wrong fact).
Device-free: sketch the four diagrams on the board; students write the four values and reasons.
UNITS
Convert before you calculate
km
m
cm
mm
× 1000
× 100
× 10
÷ 1000
÷ 100
÷ 10
1 kg = 1000 g
1 litre = 1000 ml
1 hour = 60 min
Big unit to small unit, the number gets bigger, so multiply. Time is the odd one out. 1.5 hours is 1 hour 30 minutes, not 1 hour 50.
The arrows show the direction: going right (to smaller units) multiply, going left (to bigger units) divide.
Time is in coral because it does not work in tens. A calculator answer of 2.25 hours is 2 hours 15 minutes.
Questions often mix units, like a room in metres and tiles in centimetres. Convert everything to one unit before calculating.
Device-free: students copy the ladder into their books.
Convert each one
1. 3.5 m = 350 cm
2. 2400 g = 2.4 kg
3. 1.25 litres = 1250 ml
4. 2 hours 15 minutes = 135 minutes
Answers: 350, 2.4, 1250, 135.
Distractors match slips: 35 (× 10 instead of × 100), 24 (÷ 100 instead of ÷ 1000), 125 (a place value slip), 215 (treating time as decimal), 3500 (× 1000).
Device-free: board and whiteboards.
EXAM-STYLE · PAPER 2 · CALCULATOR
Kim is painting one wall. The wall is a rectangle 4.5 m long and 2.4 m high.
One tin of paint covers 5 m² and costs £12.99.
How much will Kim spend on paint?
(4 marks)
5
minute
00
second
4.5 m
2.4 m
5 minutes on the timer. The small wall diagram is drawn to scale (30 units per metre).
Mark scheme style: M1 for 4.5 × 2.4 (= 10.8 m²). M1 for 10.8 ÷ 5 (= 2.16). M1 for rounding up to 3 tins and 3 × 12.99. A1 £38.97.
The rounding step is where most marks go: 2.16 tins means Kim needs 3, because 2 tins only covers 10 m². This is "rounding in context", and it is a favourite Paper 2 trap.
Device-free: same question on paper; the teacher keeps time. Image credit: Theme Photos / Unsplash
10.8 ÷ 5 = 2.16. How many tins must Kim buy?
3
2
2.16
2.2
Answer: 3. Two tins cover only 10 m², and the wall is 10.8 m².
2 is ordinary rounding, which leaves part of the wall unpainted. 2.16 and 2.2 are not possible: shops do not sell part of a tin.
Ask: "When would you round down instead?" (For example, how many £3 tickets can I buy with £10? Three, not four.)
How much will Kim spend on paint?
Answer: £38.97 (3 × £12.99).
If someone has £25.98, they rounded 2.16 down to 2 tins: go back to the last slide.
Which shape skill feels strongest now?
Area and perimeter
Triangles and compound shapes
Angle facts and reasons
Converting units
Exit poll. The weakest skill goes into next lesson's do now.
Device-free: thumbs up, sideways or down for each one.
BEFORE NEXT LESSON · 10 MINUTES
Three to try at home
1
A rectangle is 9 cm by 6 cm. Find its perimeter and its area.
2
A triangle has base 12 cm and height 5 cm. Find its area.
3
Two angles sit on a straight line. One is 74°. Find the other and give a reason.
Remember the units on every answer. Free practice by topic at corbettmaths.com and mathsgenie.co.uk
Answers: 1) Perimeter 30 cm, area 54 cm². 2) 30 cm². 3) 106°, because angles on a straight line add up to 180°.
Next lesson: data and chance. Averages, charts and probability are some of the most reliable marks on Paper 3.
