Transformations – Grade 10 math lesson
Lesson 11 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: “Which transformations keep a shape exactly the same size?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Describing a rotation without the center or the direction. Give all three: angle, direction, center.
- Translating the wrong way with a negative vector. Negative top number: left. Negative bottom number: down.
Tip for home: Spot reflections, rotations and translations in wallpaper and tile patterns.
What your child will learn
Learning goal: describe and carry out reflections, rotations, translations and enlargements.
Success looks like
- I can carry out each transformation.
- I can describe a transformation fully.
- I can say what each transformation keeps the same.
Key words
- reflection
- a flip over a line
- rotation
- a turn about a point
- translation
- a slide
- dilation
- a change of size from a center
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use tracing paper to rotate and reflect shapes on squared paper.
The big ideas (for the adult)
A reflection needs a line of reflection; a rotation needs a center, an angle and a direction; a translation needs a vector.
A dilation needs a center and a scale factor. A fractional scale factor makes the shape smaller.
Reflections, rotations and translations keep lengths and angles the same (congruent). Enlargements keep angles but change lengths (similar).
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
- Similarity and congruence
- Properties of quadrilaterals
- Coordinate geometry
- Cross sections of 3-D figures
- Geometric constructions
Curriculum
Common Core State Standards 8.G.A.2: “Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.”
Common Core State Standards HSG.CO.A.2: “Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.