Grade 8 Math: Measurement unit
Students measure the world at every scale, from nanometres to gigametres. They read and make scale drawings, find unknown angles with angle properties, calculate perimeter, area, volume and surface area of composite shapes and objects (including circles and cylinders), and discover and apply the Pythagorean theorem. The unit ends with a schoolyard garden design task that pulls every skill together.
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
- Student worksheets with answer keys112 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“Schoolyard Garden”, with a rubric across all four achievement chart categories
- Unit test and answer key33 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: Metric prefixes, very big and very small | E2.1 |
| 3 | Lesson 2: Powers of ten and converting units | E2.1 |
| 4 | Lesson 3: Scale drawings and actual lengths | E1.3 |
| 5 | Lesson 4: Scale, area and redrawing at a new ratio (Quick check 1) | E1.3, E2.1 |
| 6 | Lesson 5: Angles on lines and around points | E2.2 |
| 7 | Lesson 6: Parallel lines and transversals | E2.2 |
| 8 | Lesson 7: Angles in polygons (Quick check 2) | E2.2 |
| 9 | Lesson 8: Perimeter and area of composite shapes and circles | E2.3 |
| 10 | Lesson 9: Volume of prisms and cylinders | E2.3 |
| 11 | Lesson 10: Surface area of prisms and cylinders (Quick check 3) | E2.3 |
| 12 | Lesson 11: Discovering the Pythagorean relationship | E2.4 |
| 13 | Lesson 12: Using the Pythagorean theorem | E2.4 |
| 14 | Catch-up and conferencing day (reteach from quick checks) | All |
| 15 | Performance task: Schoolyard Garden (part 1) | E1.3, E2.2, E2.3 |
| 16 | Performance task: Schoolyard Garden (part 2) | E2.3, E2.4 |
| 17 | Review: stations and practice test | All |
| 18 | Unit test | All |
Lesson 1: Metric prefixes, very big and very small
Learning goal: We are learning to describe very large and very small measurements with metric prefixes.
Success criteria:
- I can name the prefixes from pico to tera and their values.
- I can convert a measurement such as 4.5 MW into watts.
Minds On (15 min)
- Show three images: a hard drive labelled 2 TB, a wind turbine rated 3 MW, and a microscope image of bacteria labelled 2 µm.
- Ask: "What do T, M and µ mean? Which is biggest? Smallest?" Think-pair-share for 3 minutes.
- Record ideas on chart paper without correcting yet.
Action (30 min)
- Build the prefix ladder together: tera (10¹²), giga (10⁹), mega (10⁶), kilo (10³), base unit, milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹), pico (10⁻¹²).
- Model: each step of three places is ×1000. Moving to a smaller unit makes the number bigger.
- Work through 4.5 MW = 4 500 000 W and 2 µm = 0.000 002 m together.
- Students complete the worksheet in pairs. Circulate and ask the prompts below.
Consolidation (15 min)
- Pairs share question 6 (nanometres in a millimetre) and compare strategies.
- Revisit the Minds On chart and correct any ideas.
- Exit: "Write one measurement from your life that uses a prefix, and convert it to the base unit."
Metric prefixes
Show your work. Write very large or very small answers in standard form and with an exponent.
- Fill in the value of each prefix as a power of ten: tera, giga, mega, kilo, milli, micro, nano, pico.
- How many bytes are in 1 gigabyte (metric)?
- A wind turbine produces 4.5 megawatts. How many watts is that?
- A bacterium is 2 micrometres long. How long is it in metres?
- Which is larger: 750 megabytes or 0.8 gigabytes? Explain.
- A computer chip has parts that are 5 nanometres wide. How many 5 nm parts fit side by side across 1 millimetre?
- Why do scientists use prefixes such as giga and nano instead of writing out all the zeros?
Answer keys with worked steps are in the Teacher Guide.
Performance task: Schoolyard Garden
The school council is turning an empty 18 m by 12 m rectangle of the schoolyard into a garden. The plan includes a circular pond with a diameter of 3 m, two cylindrical raised planters (radius 0.5 m, height 0.6 m), one rectangular raised bed (4 m long, 1.2 m wide, 0.4 m tall), a flower bed shaped like a trapezoid (parallel sides 3 m and 2 m, 1.5 m apart), and a straight stepping-stone path from one corner to the opposite corner. Everything else will be grass. The council needs a plan and a materials list. Use 3.14 for π.
| Category | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| Knowledge and Understanding | Uses few formulas and properties correctly; many calculation errors. | Uses some formulas and properties correctly; several errors. | Uses most formulas and properties correctly; minor errors. | Uses all formulas and properties correctly and accurately. |
| Thinking | Breaks the garden into parts with limited success; plan is incomplete. | Breaks the garden into parts with some success; some steps missing. | Breaks the garden into parts and plans the steps with considerable success. | Plans an efficient, complete approach and checks that answers are reasonable. |
| Communication | Scale drawing and work are hard to follow; units often missing. | Scale drawing and work are somewhat clear; some units missing. | Scale drawing is accurate and labelled; work is clear with units. | Scale drawing is precise and fully labelled; work and recommendation are clear and convincing. |
| Application | Connects measurement to the garden with limited effectiveness. | Connects measurement to the garden with some effectiveness. | Uses measurement to make sensible decisions about materials. | Uses measurement to make and justify thoughtful decisions (e.g. rounding up seed, choosing the scale). |
Lessons in this unit
- Metric prefixes, very big and very smallLearning to describe very large and very small measurements with metric prefixes.E2.1
- Powers of ten and converting unitsLearning to use powers of ten to convert between metric units.E2.1
- Scale drawings and actual lengthsLearning to use a scale to find actual lengths and drawing lengths.E1.3
- Scale, area and redrawing at a new ratioWe are learning how a scale affects area and how to redraw a plan at a different scale.E1.3, E2.1
- Angles on lines and around pointsLearning to calculate unknown angles on straight lines, at right angles, around a point and where lines cross.E2.2
- Parallel lines and transversalsLearning to find angles formed when a transversal crosses parallel lines.E2.2
- Angles in polygonsLearning to find the sum of interior angles of any polygon and use it to find unknown angles.E2.2
- Perimeter and area of composite shapes and circlesLearning to find perimeter and area of shapes made from rectangles, triangles, trapezoids and circles.E2.3
- Volume of prisms and cylindersLearning to find the volume of prisms, cylinders and composite objects.E2.3
- Surface area of prisms and cylindersLearning to find the surface area of prisms and cylinders, including open containers.E2.3
- Discovering the Pythagorean relationshipLearning to describe the relationship between the sides of a right triangle.E2.4
- Using the Pythagorean theoremLearning to use the Pythagorean theorem to solve real problems.E2.4
Ontario curriculum expectations covered
- E1.3
- Use scale drawings to find actual lengths and areas, and redraw scale drawings at different ratios.
- E2.1
- Describe huge and tiny metric measurements (from pico- up to tera-) using models, place value and powers of ten.
- E2.2
- Solve problems with angle properties: intersecting lines, parallel lines cut by a transversal, and polygons.
- E2.3
- Use formulas to solve problems about the lengths, areas, volumes and surface areas of shapes and objects built from simpler parts, including circles and cylinders.
- E2.4
- Describe the Pythagorean relationship with geometric models and use it to find an unknown side of a right triangle.
- A1
- Every lesson builds in the strand A skills: problem solving, reasoning, communicating, representing, and coping with challenges.
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?
E1.3, E2.1, E2.2, E2.3, E2.4 from Mathematics (2020), Strand E: Spatial Sense.
What format are the files?
Each unit comes as a Teacher Guide and Student Pages, both as editable Word files and print-ready PDFs. The Word files open in Google Docs, 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.