Grade 6 Math: Geometry and Transformations unit
Students describe quadrilaterals by their sides, angles, diagonals and symmetries, build cube objects from top, front and side views, and plot points in all four quadrants. They then translate, reflect and rotate shapes on the coordinate plane and predict the results of combining these moves. In the performance task they design a courtyard mural: a tile shape with a property list, a cube sculpture built from its views, and a border pattern made by a chain of transformations.
What's included
- Unit overviewBig ideas, expectations by code, learning goals and success criteria
- Day-by-day calendar17 days planned, including catch-up and review days
- 12 three-part lessonsMinds On, Action and Consolidation, with timings, questions to ask and common mistakes
- Lesson slidesA ready-to-project deck for every lesson: goals, worked examples, discussion questions and exit tickets, with your lesson steps in the speaker notes
- Student worksheets with answer keys107 questions in all, every numeric answer checked by software
- Diagnostic and quick checksA Day 1 diagnostic and 3 quick checks to adjust your teaching
- Performance task and rubric“Courtyard mural design”, with a rubric across all four achievement chart categories
- Unit test and answer key40 marks, sorted by achievement chart category
- AccommodationsSupports for students with IEPs, English language learners, and extensions
Look inside
These are real pages from the unit.
Day-by-day calendar
| Day | Lesson or assessment | Expectations |
|---|---|---|
| 1 | Diagnostic and unit launch | |
| 2 | Lesson 1: Sides and angles of quadrilaterals | E1.1 |
| 3 | Lesson 2: Diagonals of quadrilaterals | E1.1 |
| 4 | Lesson 3: Line symmetry in quadrilaterals | E1.1 |
| 5 | Lesson 4: Rotational symmetry in quadrilaterals | E1.1 |
| 6 | Lesson 5: Property lists and minimum property lists (Quick check 1) | E1.1 |
| 7 | Lesson 6: Building from top, front and side views | E1.2 |
| 8 | Lesson 7: Are the views enough? Fewest and most cubes (Quick check 2) | E1.2 |
| 9 | Lesson 8: Plotting points in all four quadrants | E1.3 |
| 10 | Lesson 9: Translations on the plane | E1.3, E1.4 |
| 11 | Lesson 10: Reflections on the plane | E1.4 |
| 12 | Lesson 11: Rotations about the origin (Quick check 3) | E1.4 |
| 13 | Lesson 12: Combining and predicting transformations | E1.4 |
| 14 | Catch-up and conferencing day (reteach from quick checks) | All |
| 15 | Performance task, day 1 | E1.1, E1.2 |
| 16 | Performance task, day 2 | E1.3, E1.4 |
| 17 | Unit test | All |
Lesson 1: Sides and angles of quadrilaterals
Learning goal: We are learning to describe quadrilaterals by looking at their sides and angles.
Success criteria:
- I can count pairs of parallel sides and right angles in a quadrilateral.
- I can use marks on a diagram to tell which sides are equal.
- I can find a missing angle because the four angles add to 360°.
- I can spot a reflex angle.
Minds On (10 min)
- Hold up the seven cut-outs. Students sort them any way they like into two groups and name their rule.
- Collect rules such as has a slanted side and push toward mathematical words. Ask: "Name two things that are true for every rectangle."
Action (35 min)
- Model reading marks: arrows mean parallel, tick marks mean equal length, a small square means a right angle.
- In pairs, students describe each cut-out using sides (equal? parallel?) and angles (right? reflex?). They record one fact per shape.
- Show that the four angles of any quadrilateral add to 360° by tearing off the corners of one and fitting them around a point.
- Students complete the worksheet.
Consolidation (15 min)
- Discuss question 3: how did the tick marks help name the shape?
- Remind students that Ontario classes use an inclusive trapezoid: at least one pair of parallel sides.
- Exit: "Name one quadrilateral that has two pairs of parallel sides."
Sides and angles
Marks on a diagram: arrows mean parallel, ticks mean equal length, a small square means a right angle. Show your thinking.
- Count the pairs of parallel sides in parallelogram ABCD.
- How many right angles does rectangle ABCD have?
- The tick marks show equal sides. What can you say about the sides of quadrilateral ABCD, and what is its name?
- Three angles of a quadrilateral are 85°, 110° and 70°. Find the fourth angle.
- Quadrilateral ABCD has one angle larger than 180°. Which vertex has the reflex angle, and what is this shape called?
- A classmate says a parallelogram cannot be a trapezoid. Do you agree? Explain.
Answer keys with worked steps are in the Teacher Guide.
Performance task: Courtyard mural design
The school is painting a courtyard mural. You design three parts: a tile shape, a small cube sculpture, and a border pattern. You must explain every choice using geometry.
| Category | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| Knowledge and Understanding | Lists few correct properties; transformations are mostly wrong. | Lists some properties; performs single transformations with several errors. | Lists most properties correctly; performs transformations with few errors. | Lists complete, accurate properties; performs every transformation correctly, including rotation direction. |
| Thinking | Does not pick out a minimum property list; cannot say if views are enough. | Gives a partial minimum list; recognises that views may leave choices. | Gives a sound minimum list; finds the fewest and most cubes; compares two orders of transformations. | Gives an efficient minimum list; explains clearly why views allow more than one building and why order matters. |
| Communication | Poster is hard to follow; coordinates unlabelled. | Poster shows some steps; labels and words are sometimes missing. | Poster is clear; steps, coordinates and vocabulary are labelled. | Poster is very clear and organized; uses precise terms such as bisect, reflex, clockwise and image throughout. |
| Application | Design does not use the geometry needed. | Design uses some geometry with major gaps. | Design uses properties, views and transformations correctly in a realistic mural. | Design connects all three parts in a thoughtful, accurate mural and justifies each choice. |
Lessons in this unit
- Sides and angles of quadrilateralsLearning to describe quadrilaterals by looking at their sides and angles.E1.1
- Diagonals of quadrilateralsLearning to compare the diagonals of different quadrilaterals.E1.1
- Line symmetry in quadrilateralsLearning to find the lines of symmetry in quadrilaterals.E1.1
- Rotational symmetry in quadrilateralsLearning to find the order of rotational symmetry of a quadrilateral.E1.1
- Property lists and minimum property listsLearning to build property lists for quadrilaterals and to use them in short arguments.E1.1
- Building from top, front and side viewsLearning to build a cube object when we are given its top, front and side views.E1.2
- Are the views enough? Fewest and most cubesLearning to decide when the views give enough information to build a cube object.E1.2
- Plotting points in all four quadrantsLearning to plot and read points in all four quadrants of the Cartesian plane.E1.3
- Translations on the planeLearning to describe and perform translations of points and shapes on a coordinate plane.E1.3, E1.4
- Reflections on the planeLearning to reflect shapes in the x-axis and the y-axis and to predict the image.E1.4
- Rotations about the originLearning to rotate shapes by multiples of 90° about the origin, clockwise and counterclockwise.E1.4
- Combining and predicting transformationsLearning to combine translations, reflections and rotations and to predict the final image.E1.4
Ontario curriculum expectations covered
- E1.1
- Make and use property lists for different quadrilaterals, covering sides, angles, diagonals, line symmetry and rotational symmetry.
- E1.2
- Build a cube object when its top, front and side views are given.
- E1.3
- Plot and read points in all four quadrants, and describe the translation between two points.
- E1.4
- Perform and describe slides, flips and turns (up to 360°) of shapes on a grid, alone and in combination, and predict the image.
Questions about this unit
How long is this unit?
17 school days: 12 lessons plus a diagnostic, a catch-up day, a two-day performance task, a review day and the unit test.
Which expectations does it cover?
E1.1, E1.2, E1.3, E1.4 from Mathematics (2020), Strand E: Spatial Sense, E1 Geometric and Spatial Reasoning.
What format are the files?
Each unit comes as a Teacher Guide and Student Pages, both as editable Word files and print-ready PDFs, plus a PowerPoint deck of lesson slides. The Word files open in Google Docs and the slides open in Google Slides, so you can change anything.
Can I share it with my colleagues?
A single licence is for one teacher's classes. For a grade team, the team licence covers up to 5 teachers at one school for $49.99.
What if it isn't right for my class?
Email help@unitplans.ca within 7 days of buying for a full refund.