Constructions and loci – Year 8 maths lesson
Lesson 16 of 35 in the Year 8 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 8 (ages 12–13) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 8 (ages 12–13)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Where could you stand to be the same distance from two friends?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Drawing a line instead of a region for "less than 3 cm from A". The locus of points within a distance is a filled circle.
- Rubbing out construction arcs. Leave the arcs: they show the method.
Tip for home: Mark out a locus in the garden: everywhere 2 m from a tree.
What your child will learn
We are learning to know the facts behind constructions and use loci to describe regions.
Success looks like
- I can describe common loci.
- I can choose the right construction.
- I can find a region that fits several rules.
Key words
- locus
- all the points that follow a rule (loci)
- perpendicular bisector
- cuts a line in half at right angles
- angle bisector
- cuts an angle in half
- compasses
- a tool for drawing arcs and circles
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use a ruler and compasses to bisect a line and an angle on paper. An adult checks the drawing. No rulers? A pencil tied to string makes a simple pair of compasses.
The big ideas (for the adult)
A locus is the set of points that follow a rule: points a fixed distance from a point make a circle.
Points equally distant from two points lie on the perpendicular bisector. Points equally distant from two lines lie on the angle bisector.
Constructions with a ruler and compasses use these facts. In this lesson the computer checks the facts; drawing the construction yourself is checked by an adult.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 8 maths lessons
- Ordering numbers, decimals and negatives
- Calculating with negative numbers
- Prime factors, HCF and LCM
- Rounding and estimation
- Powers and roots
- Written methods with decimals
- BIDMAS: order of operations
- Calculating with fractions
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Angle facts and parallel lines
- Angles in polygons
- Transformations
- Quadrilaterals and symmetry
- Averages and range
- Scatter graphs and correlation
- Probability
- Relative frequency and expected outcomes
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- One quantity as a fraction or percentage of another
- Percentages
- Direct and inverse proportion
- Speed, density and pressure
- Best buys and exchange rates
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 8: “derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line”
National Curriculum for England, Year 8: “draw and measure line segments and angles in geometric figures, including interpreting scale drawings”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.