Geometric constructions – Grade 10 math lesson
Lesson 16 of 16 in the Grade 10 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 10 (ages 15–16) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 10 (ages 15–16)
- You need
- Paper, a pencil and this page
- Graded
- 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 graded straight away with a worked explanation, so you never have to grade 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
Learning goal: 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
- compass
- 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 | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded 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 graded instantly.
More practice
More Grade 10 math lessons
- Factoring
- Quadratic equations
- Identities and proof
- Functions
- Graphing functions
- Exponential functions
- Circles: circumference and area
- Volume and surface area
- The Pythagorean theorem
- Right triangle trigonometry
- Transformations
- Similarity and congruence
- Properties of quadrilaterals
- Coordinate geometry
- Cross sections of 3-D figures
Curriculum
Common Core State Standards HSG.CO.D.12: “Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.”
Common Core State Standards HSG.CO.D.13: “Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.