Grade 8 Math: Number unit
Students work with the whole real number system. They write huge and tiny numbers in scientific notation, sort rational and irrational numbers, estimate square roots, and move flexibly between fractions, decimals and percents (including percents above 100% and below 1%). They compute with integers and fractions, follow the order of operations, and use rates, proportions and percents to solve everyday multi-step problems such as discounts and HST. The unit ends with a class trip budget.
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 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“Class Trip Budget”, with a rubric across all four achievement chart categories
- Unit test and answer key31 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: Scientific notation | B1.1 |
| 3 | Lesson 2: Rational and irrational numbers | B1.2 |
| 4 | Lesson 3: Squares and square roots (Quick check 1) | B1.3, B2.2 |
| 5 | Lesson 4: Fractions, decimals and percents | B1.4 |
| 6 | Lesson 5: Mental math with powers of ten | B2.3 |
| 7 | Lesson 6: Adding and subtracting integers | B2.4 |
| 8 | Lesson 7: Multiplying and dividing integers (Quick check 2) | B2.7 |
| 9 | Lesson 8: Adding and subtracting fractions | B2.5 |
| 10 | Lesson 9: Multiplying and dividing fractions | B2.6 |
| 11 | Lesson 10: Order of operations with rational numbers (Quick check 3) | B2.1 |
| 12 | Lesson 11: Rates, ratios and proportions | B2.8 |
| 13 | Lesson 12: Discounts, HST and percent change | B2.1, B1.4 |
| 14 | Catch-up and conferencing day (reteach from quick checks) | All |
| 15 | Performance task: Class Trip Budget (part 1) | B1.4, B2.1, B2.8 |
| 16 | Performance task: Class Trip Budget (part 2) | B2.5, B2.6, B2.1 |
| 17 | Review: stations and practice test | All |
| 18 | Unit test | All |
Lesson 1: Scientific notation
Learning goal: We are learning to use scientific notation to write and compare huge and tiny numbers.
Success criteria:
- I can write a number in scientific notation and in standard form.
- I can compare numbers written in scientific notation.
Minds On (10 min)
- Show: "Canada has about 41 000 000 people. The world has about 8 100 000 000." Ask: "About how many Canadas would fit in the world population?"
- Students estimate in pairs, then share strategies.
Action (35 min)
- Introduce scientific notation: a number from 1 to less than 10, times a power of ten.
- Model large numbers (45 000 000 = 4.5 × 10⁷) and small numbers (0.000 36 = 3.6 × 10⁻⁴).
- Show how to compare: first compare the powers of ten, then the leading numbers.
- Students complete the worksheet in pairs.
Consolidation (15 min)
- Return to the Minds On question and solve it with scientific notation.
- Exit: "Write a number from science or the news in scientific notation and explain what it describes."
Scientific notation
Show how many places the decimal point moves.
- Write 45 000 000 in scientific notation.
- Write 0.000 36 in scientific notation.
- Write 2.07 × 10⁵ in standard form.
- Canada has about 41 000 000 people and the world has about 8.1 × 10⁹. About how many times larger is the world population? Round to the nearest whole number.
- Order from least to greatest: 3.2 × 10⁻³, 4.1 × 10⁻⁴, 2.9 × 10⁻³.
- Ava says 23 × 10⁴ is in scientific notation. Is she correct? Explain.
Answer keys with worked steps are in the Teacher Guide.
Performance task: Class Trip Budget
Your class of 28 students and 4 adult supervisors is going on a trip to a science centre. A bus costs $1150 plus 13% HST. Tickets are $34.50 each for everyone, with a 15% group discount, plus 13% HST. Lunch is 8 pizzas at $18.99 each, plus 13% HST. The adults do not pay; the students share the total cost. The class wants to raise 3/5 of the total by selling chocolate bars for $3 each, and the class keeps 40% of each sale as profit.
| Category | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| Knowledge and Understanding | Few calculations with percents, rates and fractions are correct. | Some calculations are correct; several errors. | Most calculations are correct; minor errors. | All calculations are correct and accurate. |
| Thinking | Plans the budget with limited success; steps missing. | Plans the budget with some success; some steps missing. | Plans the budget in a logical order with considerable success. | Plans an efficient approach and checks that answers are reasonable. |
| Communication | Work is hard to follow; units and labels often missing. | Work is somewhat clear; some labels missing. | Work is clear and labelled; money is shown correctly. | Work and recommendation are clear, organized and convincing. |
| Application | Connects the math to the trip with limited effectiveness. | Connects the math to the trip with some effectiveness. | Uses the math to make sensible decisions about the trip. | Uses the math to make and justify thoughtful decisions (e.g. rounding bars up, comparing options). |
Lessons in this unit
- Scientific notationLearning to use scientific notation to write and compare huge and tiny numbers.B1.1
- Rational and irrational numbersLearning to tell rational and irrational numbers apart and to order them.B1.2
- Squares and square rootsLearning to recall perfect squares and to estimate and calculate square roots.B1.3, B2.2
- Fractions, decimals and percentsLearning to change between fractions, decimals and percents, including percents above 100% and below 1%.B1.4
- Mental math with powers of tenLearning to multiply and divide by powers of ten in our heads and explain how.B2.3
- Adding and subtracting integersLearning to add and subtract integers using models and strategies.B2.4
- Multiplying and dividing integersLearning to multiply and divide integers and explain the sign rules.B2.7
- Adding and subtracting fractionsLearning to add and subtract fractions and mixed numbers, including negative fractions.B2.5
- Multiplying and dividing fractionsLearning to multiply and divide fractions, whole numbers and mixed numbers.B2.6
- Order of operations with rational numbersLearning to use the order of operations with integers, fractions and decimals.B2.1
- Rates, ratios and proportionsLearning to compare rates and use proportional reasoning to find missing values.B2.8
- Discounts, HST and percent changeLearning to solve multi-step percent problems about money.B2.1, B1.4
Ontario curriculum expectations covered
- B1.1
- Show and compare huge and tiny numbers, including in scientific notation, and explain where they appear in daily life.
- B1.2
- Sort, compare and order rational and irrational numbers in real situations.
- B1.3
- Estimate and find square roots in context.
- B1.4
- Switch between fractions, decimals and percents, including percents above 100% and below 1%, to solve problems.
- B2.1
- Use operation properties and the order of operations to solve multi-step problems with rational numbers, ratios, rates and percents.
- B2.2
- Know common perfect squares and their square roots.
- B2.3
- Use mental math to multiply and divide by powers of ten and explain how.
- B2.4
- Add and subtract integers in context.
- B2.5
- Add and subtract fractions in context.
- B2.6
- Multiply and divide fractions, whole numbers and mixed numbers in context.
- B2.7
- Multiply and divide integers in context.
- B2.8
- Compare proportional situations, find missing values, and reason proportionally to solve problems.
- 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?
B1.1, B1.2, B1.3, B1.4, B2.1, B2.2, B2.3, B2.4, B2.5, B2.6, B2.7, B2.8 from Mathematics (2020), Strand B: Number.
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.