Grade 7 Math: Geometry and Transformations unit
Students start by sorting prisms, pyramids and cylinders by their bases, faces, edges, vertices and symmetry, then draw top, front, side, perspective and isometric views and make scale drawings. They then move shapes on a Cartesian plane with translations, reflections and rotations, predict the results, and finish with dilations and similar shapes. In the performance task they plan a community plaza: a mosaic tile pattern, planters, a bench and a scaled plan.
What's included
- Unit overviewBig ideas, expectations by code, learning goals and success criteria
- Day-by-day calendar18 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 keys121 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“Community Plaza Plan”, with a rubric across all four achievement chart categories
- Unit test and answer key48 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: Prisms and cylinders | E1.1 |
| 3 | Lesson 2: Pyramids | E1.1 |
| 4 | Lesson 3: Symmetry of solids (Quick check 1) | E1.1 |
| 5 | Lesson 4: Top, front and side views | E1.2 |
| 6 | Lesson 5: Scale drawings | E1.2 |
| 7 | Lesson 6: Perspective and isometric views (Quick check 2) | E1.2 |
| 8 | Lesson 7: Translations on the Cartesian plane | E1.4 |
| 9 | Lesson 8: Reflections | E1.4 |
| 10 | Lesson 9: Rotations about the origin | E1.4 |
| 11 | Lesson 10: Combining transformations (Quick check 3) | E1.4 |
| 12 | Lesson 11: Dilations | E1.3 |
| 13 | Lesson 12: Similar shapes | E1.3 |
| 14 | Catch-up and conferencing day (reteach from quick checks) | All |
| 15 | Performance task: Community Plaza Plan (part 1) | E1.3, E1.4 |
| 16 | Performance task: Community Plaza Plan (part 2) | E1.1, E1.2 |
| 17 | Review: stations and practice test | All |
| 18 | Unit test | All |
Lesson 1: Prisms and cylinders
Learning goal: We are learning to sort prisms and cylinders by their bases, faces, edges and vertices.
Success criteria:
- I can name a prism from the shape of its base.
- I can count the faces, edges and vertices of a prism.
- I can tell a right prism from an oblique prism.
- I can explain how a cylinder is like a prism and how it is different.
Minds On (10 min)
- Show a box of tissues, a can of soup and a triangular chocolate box. Ask: "What do all three objects have in common, and what is different about them?"
- Students share with a partner, then the class builds a list of words on the board (flat, curved, bases, faces).
Action (35 min)
- Hand out models. Students record the shape of the two bases and the number of faces, edges and vertices for each prism, then look for the pattern when the base has n sides.
- Introduce the words: a cylinder has two parallel, matching bases joined by parallel lines; a prism is a cylinder whose bases are polygons and whose side faces are parallelograms. A prism is named for its base.
- Compare a right prism (sides meet the bases at right angles) with an oblique prism (sides lean). Students complete the worksheet.
Consolidation (15 min)
- Build a class chart: base shape, faces, edges, vertices. Discuss the pattern F = n + 2, E = 3n, V = 2n.
- Discuss question 6: why is a soup can a cylinder but not a prism?
- Exit: "A prism has a base with 7 sides. How many vertices does it have?"
Prisms and cylinders
Show your work. A prism with an n-sided base has n + 2 faces.
- A prism has a pentagon for each base. How many faces does the prism have?
- How many edges does a hexagonal prism have?
- How many vertices does an octagonal prism have?
- A prism has 15 edges. What shape are its bases? Name the prism.
- Look at the side views of the two prisms. Which is a right prism and which is oblique? How can you tell?
- A soup can is a cylinder. Explain why it is not a prism.
- Check Euler's rule on a pentagonal prism: faces + vertices − edges. What do you get?
Answer keys with worked steps are in the Teacher Guide.
Performance task: Community Plaza Plan
The town is building a small plaza. You are on the design team. You will design a tile pattern for the floor, a sign for the entrance, plant boxes and a bench, and you will draw the plan to scale.
| Category | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| Knowledge and Understanding | Finds some images with errors and gives few correct counts for the solids. | Finds most images and counts with some errors; shows partial understanding of each idea. | Finds nearly all images, counts and views correctly and shows understanding of each idea. | Finds all images, counts and views correctly, with precise use of rules and properties. |
| Thinking | Plans with limited steps; makes little use of transformation rules. | Uses some rules to plan and check; sometimes needs help to sequence steps. | Uses rules to plan and check the pattern, the sign and the plan with logical steps. | Uses rules to predict, check and justify, and finds efficient or creative ways to combine transformations. |
| Communication | Drawings and labels are unclear; little correct use of mathematical language. | Drawings and labels are partly clear; some correct mathematical language. | Drawings are clear and labelled; the explanation uses correct language and notation. | Drawings and explanation are very clear and use precise language and notation throughout. |
| Application | Applies concepts to the plaza with limited success; scale or similarity are rarely correct. | Applies concepts to the plaza with some success; scale and similarity are partly correct. | Applies concepts to the plaza effectively; scale and similarity are correct. | Applies concepts to the plaza effectively and with insight; the design is well justified. |
Lessons in this unit
- Prisms and cylindersLearning to sort prisms and cylinders by their bases, faces, edges and vertices.E1.1
- PyramidsLearning to describe pyramids by their base, apex, faces, edges and vertices.E1.1
- Symmetry of solidsLearning to find plane symmetry and rotational symmetry in prisms, pyramids and cylinders.E1.1
- Top, front and side viewsLearning to draw and read the top, front and side views of buildings made of cubes.E1.2
- Scale drawingsLearning to read and make scale drawings of objects and rooms.E1.2
- Perspective and isometric viewsLearning to draw and read perspective and isometric views of objects.E1.2
- Translations on the Cartesian planeLearning to slide shapes on a coordinate grid and to predict where they land.E1.4
- ReflectionsLearning to flip shapes across a line on a coordinate grid and to predict where they land.E1.4
- Rotations about the originLearning to turn shapes about the origin and to predict where they land.E1.4
- Combining transformationsLearning to combine transformations and predict the final image.E1.4
- DilationsLearning to enlarge and reduce shapes using a scale factor and a centre of dilation.E1.3
- Similar shapesLearning to tell when two shapes are similar and to use the scale factor to find missing sides.E1.3
Ontario curriculum expectations covered
- E1.1
- Describe and sort cylinders, pyramids and prisms by their properties, including plane symmetry and rotational symmetry.
- E1.2
- Draw top, front, side and perspective views of objects and spaces, using sensible scales.
- E1.3
- Enlarge and reduce shapes with dilations and describe how the image is similar to the original.
- E1.4
- Describe and perform slides, flips and turns of shapes on a coordinate grid, and predict where the image will land.
Questions about this unit
How long is this unit?
18 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.