Grade 7 Math: Measurement unit
Students connect volume and capacity (1 mL = 1 cm³), use displacement to measure irregular objects, and convert between metric units of length, area and volume. They then study circles: how the radius, diameter and circumference are related, where pi comes from, how to draw circles and how to explain and use the area formula. Finally they use nets to find the surface area of cylinders and show that the volume of any prism or cylinder is the base area times the height. The unit ends with a two-day performance task designing a circular splash pool and its surroundings, and a unit test. The unit uses π = 3.14 throughout.
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 keys142 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“Design a Splash Pool Park”, with a rubric across all four achievement chart categories
- Unit test and answer key49 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: Volume and capacity | E2.1 |
| 3 | Lesson 2: Finding volume by displacement | E2.1 |
| 4 | Lesson 3: Converting length, area and volume | E2.2 |
| 5 | Lesson 4: Perimeter, area and volume with unit changes (quick check 1) | E2.2 |
| 6 | Lesson 5: Radius, diameter and pi | E2.3 |
| 7 | Lesson 6: Circumference problems | E2.3 |
| 8 | Lesson 7: Constructing circles | E2.4 |
| 9 | Lesson 8: Area of a circle (quick check 2) | E2.5 |
| 10 | Lesson 9: Area of a circle: problems | E2.5 |
| 11 | Lesson 10: Nets and surface area of cylinders | E2.6 |
| 12 | Lesson 11: Volume of prisms and cylinders (quick check 3) | E2.7 |
| 13 | Lesson 12: Finding a missing measurement | E2.7 |
| 14 | Performance task, day 1 | E2.1 to E2.7 |
| 15 | Performance task, day 2 | E2.1 to E2.7 |
| 16 | Review and catch-up | |
| 17 | Unit test | E2.1 to E2.7 |
Lesson 1: Volume and capacity
Learning goal: We are learning how volume and capacity are alike and different, and how millilitres connect to cubic centimetres.
Success criteria:
- I can explain the difference between volume and capacity.
- I can say that 1 mL takes up the same space as 1 cm³ and that 1 L is 1 000 cm³.
- I can switch between cm³, mL and L to solve problems.
Minds On (10 min)
- Hold up a 1 L carton and a solid wooden block. Ask students what could be measured about each one.
- Ask: "Which one can hold water, and which one only takes up space?"
- Let pairs share, then record the words volume (space taken up) and capacity (how much it can hold).
Action (35 min)
- Build a 10 cm by 10 cm by 10 cm cube with centimetre cubes (or show a picture) and note it holds 1 000 cm³. Pour 1 L of water into a see-through 10 cm cube box to show it is full.
- Show that 1 mL of water fills a 1 cm cube. Build the chain: 1 cm³ = 1 mL, 1 000 cm³ = 1 000 mL = 1 L.
- Students work through the worksheet, using a table to switch between units.
Consolidation (15 min)
- Discuss question 5: a vase has a thick glass base. Which is larger, its volume or its capacity?
- Exit: "Give one object that has volume but no capacity, and say why."
Volume and capacity
Show your work. 1 mL = 1 cm³ and 1 L = 1 000 mL.
- A fish tank is a rectangular prism 20 cm long, 10 cm wide and 5 cm tall. What is its volume? Assume thin walls.
- The tank in question 1 is filled to the top. How many millilitres of water does it hold?
- A juice box holds 250 mL. What is its capacity in cm³?
- A jug holds 2.5 L. What is its capacity in cm³?
- A glass vase has a thick solid glass base. Is its volume greater than, less than or equal to its capacity? Explain.
- A tank holds 3600 cm³ of water. How many litres is that?
- A fish tank measures 40 cm by 25 cm by 30 cm inside. How many litres of water does it hold when full?
- True or false: a brick has volume but no capacity. Explain your answer.
- A bottle holds 1.5 L. A paper cup holds 250 mL. How many cups can be filled from one full bottle?
Answer keys with worked steps are in the Teacher Guide.
Performance task: Design a Splash Pool Park
Your town is building a round splash pool. The pool is a cylinder with a diameter of 8 m and a depth of 0.5 m. A concrete walkway 1.5 m wide goes all the way around the pool, and a fence goes around the outside edge of the walkway. The town has a budget of $5000.00 for the walkway and fence. Use π = 3.14.
| Category | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| Knowledge and Understanding | Shows limited knowledge of circle and cylinder measures; uses formulas or unit changes with major errors. | Shows some knowledge; uses formulas and conversions with several errors. | Shows considerable knowledge; uses formulas and conversions correctly with minor errors. | Shows thorough knowledge; uses all formulas and conversions correctly and explains them. |
| Thinking | Plans and organizes the problem with limited effectiveness; the design in Part 5 does not meet the requirement. | Plans with some effectiveness; the design nearly meets the requirement and the budget check is incomplete. | Plans effectively; the design meets the requirement and the budget is checked correctly. | Plans with a high degree of effectiveness; the design is efficient and justified, with checks of reasonableness. |
| Communication | Presents work and the report with limited clarity; units and labels are often missing. | Presents work with some clarity; some units and labels are missing. | Presents work clearly with correct units, a labelled sketch and a clear table. | Presents work with great clarity and precision, using math language, labelled sketches and an organized report. |
| Application | Applies measurement ideas to the park with limited effectiveness. | Applies measurement ideas to the park with some effectiveness and some mistakes in context. | Applies measurement ideas to the park effectively; answers fit the situation. | Applies measurement ideas with a high degree of effectiveness and connects to real decisions such as cost and safety. |
Lessons in this unit
- Volume and capacityWe are learning how volume and capacity are alike and different, and how millilitres connect to cubic centimetres.E2.1
- Finding volume by displacementLearning to find the volume of an object by seeing how much water it pushes aside.E2.1
- Converting length, area and volumeWe are learning how metric units change for length, area and volume, and why the area and volume changes are bigger.E2.2
- Perimeter, area and volume with unit changesLearning to solve measurement problems where the units must be changed before we calculate.E2.2
- Radius, diameter and piWe are learning how a circle2019s radius, diameter and circumference are connected, and what pi means.E2.3
- Circumference problemsLearning to use C = π × d and C = 2 × π × r to solve problems, including finding the diameter or radius from the circumference.E2.3
- Constructing circlesLearning to draw circles when we are given the radius, diameter or circumference.E2.4
- Area of a circleWe are learning why the area of a circle is π × r × r and how to use it.E2.5
- Area of a circle: problemsLearning to solve problems with the area of circles, including finding the radius from an area and areas of combined shapes.E2.5
- Nets and surface area of cylindersLearning to picture a cylinder as a net and to add the areas of its parts to find the surface area.E2.6
- Volume of prisms and cylindersWe are learning why volume = area of the base × height for prisms and cylinders, and how to use it.E2.7
- Finding a missing measurementLearning to find the base area, height or radius of a prism or cylinder when we know the volume and one other measurement.E2.7
Ontario curriculum expectations covered
- E2.1
- Compare volume and capacity, and use the fact that 1 mL takes up 1 cm³ to solve problems, including displacement.
- E2.2
- Solve perimeter, area and volume problems that need a conversion between metric units.
- E2.3
- Use the links between radius, diameter and circumference to explain and use the circumference formula.
- E2.4
- Draw circles from a given radius, diameter or circumference.
- E2.5
- Show how radius, diameter and area are related, explain the area formula and use it to solve problems.
- E2.6
- Draw nets of cylinders and add the areas of the parts to find surface area.
- E2.7
- Show that volume of a prism or cylinder is base area times height and use it to find a missing base area, height or volume.
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?
E2.1, E2.2, E2.3, E2.4, E2.5, E2.6, E2.7 from Mathematics (2020), Strand E: Spatial Sense, part E2 Measurement (Grade 7).
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.