Good Learning Co.
SavannahYear 8
← Maths
MathsShape and space22 min★ difficulty

Geometric language, sketching and construction

Maths has its own shorthand for shapes — arrows for parallel lines, little squares for right angles — so a sketch can say as much as a paragraph.

Part of your national curriculum
  • Geometry and measures: Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, polygons, reflections and rotations

Lesson overview

What you'll learn in this lesson

Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, polygons, reflections and rotations

Key learning points

  • • Notation basics
  • • Transformations
  • • Worked example

This lesson at a glance

  • 22 minutes
  • 14 parts to scroll through
  • 3 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

sketchconventionalnotationspointsparallel

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%
1

Watch & discover

Part 1 of 14

Watch first

Geometric language, sketching and construction

An English teaching video on this topic from Homeschool Pop. Watch it, then scroll down for the lesson.

In a nutshell

Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, polygons, reflections and rotations

2

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · Notation basics

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 14

Learn

Notation basics

Parallel lines are marked with matching arrows (>>). Perpendicular lines meet at a right angle, shown with a small square. A polygon is a closed shape made of straight sides, such as a pentagon (5 sides) or hexagon (6 sides).

4

Explore the idea

Part 4 of 14

Learn

Transformations

A reflection flips a shape over a mirror line, producing a mirror image the same distance from the line. A rotation turns a shape around a fixed centre point by a given angle, such as 90° clockwise.

5

Quick check

Part 5 of 14

Quick check

How are parallel lines marked in a diagram?

6

Reset break

Part 6 of 14

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
7

Quick check

Part 7 of 14

Quick check

Point A(2,3) is reflected in the y-axis (x = 0). What is the image?

8

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Worked example

A short piece of teaching, then a check to make sure it has landed.

9

Explore the idea

Part 9 of 14

Learn

Worked example

Point A(2,3) is reflected in the line x = 0 (the y-axis). The y-coordinate stays the same and the x-coordinate changes sign: the image is A'(-2, 3).

10

Quick check

Part 10 of 14

Quick check

What symbol usually shows a right angle in a diagram?

11

Challenge round

Part 11 of 14

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

12

Challenge round

Part 12 of 14

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

____ lines are marked with matching arrows (>>).

13

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Geometric language, sketching and construction

3 questions, marked with the reasoning shown. No timer.

  1. 1. How are parallel lines marked in a diagram?

  2. 2. Point A(2,3) is reflected in the y-axis (x = 0). What is the image?

  3. 3. What symbol usually shows a right angle in a diagram?

14

Lesson round-up

Part 14 of 14

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 14 · Watch & discover

How this is going

  • Not looked at yet

    Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, polygons, reflections and rotations

Good Learning Co. — personalised UK curriculum learning, built around what each learner loves.