Grade 7 Math: Number unit
Students work with numbers of all kinds: large whole numbers up to one billion, perfect squares and their roots, negative numbers, fractions, decimals and percents. They add, subtract, multiply and divide them, use exponents, and solve multi-step problems with the order of operations. In the performance task, "Plan the Fair Day", they use their number skills to plan crowds, supplies, fencing, cash and time for a school fair.
What's included
- Unit overviewBig ideas, expectations by code, learning goals and success criteria
- Day-by-day calendar20 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 keys115 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“Plan the Fair Day”, with a rubric across all four achievement chart categories
- Unit test and answer key45 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: Reading and writing numbers to one billion | B1.1 |
| 3 | Lesson 2: Perfect squares and square roots | B1.2 |
| 4 | Lesson 3: Comparing and ordering rational numbers | B1.3, B1.5 |
| 5 | Quick check 1 and review | B1.1–B1.3 |
| 6 | Lesson 4: Adding and subtracting integers | B2.4 |
| 7 | Lesson 5: Simplest form, GCF and LCM | B1.4, B2.6 |
| 8 | Lesson 6: Adding and subtracting fractions | B2.5 |
| 9 | Lesson 7: Multiplying and dividing fractions | B2.8 |
| 10 | Quick check 2 and review | B2.4–B2.8 |
| 11 | Lesson 8: Multiplying, dividing and rounding decimals | B2.9, B1.6 |
| 12 | Lesson 9: Fractions, decimals and percents | B1.7, B2.2 |
| 13 | Lesson 10: Mental math with percents | B2.3 |
| 14 | Quick check 3 and review | B2.9, B1.6, B1.7, B2.2, B2.3 |
| 15 | Lesson 11: Exponents and powers | B2.7 |
| 16 | Lesson 12: Order of operations and multi-step problems | B2.1 |
| 17 | Performance task, day 1: Plan the Fair Day | |
| 18 | Performance task, day 2: finish, report and share | |
| 19 | Review and test preparation | |
| 20 | Unit test |
Lesson 1: Reading and writing numbers to one billion
Learning goal: We are learning to read, write, compare and expand numbers up to one billion using place value and powers of ten.
Success criteria:
- I can say the value of any digit in a number up to one billion.
- I can write a large number in expanded form with powers of ten.
- I can compare and order large numbers and explain how I know.
Minds On (10 min)
- Show the numbers 48 300 000 and 483 000 000 side by side. Ask: "Which number is bigger, and how can you tell without counting digits one at a time?"
- Take two or three answers and record the strategies (count digits, compare the leftmost digit).
Action (35 min)
- Build a number on the place value chart one digit at a time. Group digits in threes with spaces, the way we write numbers in Canada.
- Model expanded form: each digit times the power of ten for its place. Link 10 × 10 × 10 to 10³.
- Compare numbers by lining up place values and starting at the left. Students do worksheet questions 1–6 in pairs.
Consolidation (15 min)
- Share question 5. Ask where we meet numbers this large (populations, distances, money in a national budget).
- Exit: "What is the value of the digit 4 in 142 603 975, and how do you know?"
Numbers to one billion
Show your work. Group digits in threes with spaces.
- Write 405 072 316 in expanded form using powers of ten.
- In the number 273 845 106, what is the value of the digit 7?
- Write the number shown in expanded form: 6 × 10⁸ + 2 × 10⁵ + 9 × 10³ + 4.
- Order these numbers from least to greatest: 48 300 000, 483 000 000, 48 030 000, 84 300 000.
- The population of a province is 38 250 000 (made-up). How many millions is that? (Write a decimal.)
- Ana says one billion is written as 10⁹ because it is a 1 followed by nine zeros. Is she correct? Explain.
- How many times as large as one million is one billion?
Answer keys with worked steps are in the Teacher Guide.
Performance task: Plan the Fair Day
Your class is planning a fair to raise money for the school library. The principal wants a plan with numbers that make sense. All the numbers below are made up for this task.
| Category | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| Knowledge and Understanding | Shows limited understanding of place value, fractions, integers or percents; many calculations are incorrect. | Shows some understanding; several calculations contain errors or steps are missing. | Shows considerable understanding; calculations are mostly correct with minor errors. | Shows thorough understanding; calculations are correct and efficient in every part. |
| Thinking | Uses a plan that rarely fits the problem; does not check whether answers make sense. | Uses a partly suitable plan; sometimes checks reasonableness. | Uses a suitable plan for each part and checks that answers make sense. | Chooses effective, efficient strategies, links the parts together, and justifies each choice. |
| Communication | Work is hard to follow; few units, symbols or steps shown. | Work is somewhat clear; some steps, units or symbols are missing or incorrect. | Work is clear; steps, units and symbols are mostly correct. | Work is clear, organized and precise; the report is persuasive and uses mathematical language well. |
| Application | Rarely connects the mathematics to the fair; the plan is not realistic. | Sometimes connects the mathematics to the fair; some choices do not fit the situation. | Connects the mathematics to the fair; choices such as rounding fit the situation. | Connects the mathematics to the fair in insightful ways; explains how choices affect the plan. |
Lessons in this unit
- Reading and writing numbers to one billionLearning to read, write, compare and expand numbers up to one billion using place value and powers of ten.B1.1
- Perfect squares and square rootsLearning to recognize perfect squares, find their square roots, and estimate other square roots.B1.2
- Comparing and ordering rational numbersLearning to compare and order positive and negative fractions and decimals, and to find numbers between two given numbers.B1.3, B1.5
- Adding and subtracting integersLearning to add and subtract positive and negative whole numbers using chips, number lines and equations.B2.4
- Simplest form, greatest common factor, lowest common multipleLearning to simplify fractions and to find the greatest common factor and lowest common multiple of numbers.B1.4, B2.6
- Adding and subtracting fractionsLearning to add and subtract fractions and mixed numbers by making equivalent fractions with a common denominator.B2.5
- Multiplying and dividing fractionsLearning to multiply and divide fractions by fractions using area models, number lines and equations.B2.8
- Multiplying, dividing and rounding decimalsLearning to multiply and divide with decimals on both sides of the sign and to round answers to a sensible place.B2.9, B1.6
- Fractions, decimals and percentsLearning to convert between fractions, decimals and percents and to recall common equivalents.B1.7, B2.2
- Mental math with percentsLearning to increase and decrease whole numbers by 1%, 5%, 10%, 25%, 50% and 100% in our heads and to explain our strategies.B2.3
- Exponents and powersLearning to write repeated multiplication as a power and to evaluate powers of whole numbers.B2.7
- Order of operations and multi-step problemsLearning to use the order of operations and the properties of operations to solve multi-step problems with whole numbers, decimals, fractions, ratios, rates and percents.B2.1
Ontario curriculum expectations covered
- B1.1
- Read, write, compare and expand whole numbers up to one billion with powers of ten, and talk about where such numbers appear.
- B1.2
- Recognize and show perfect squares, and find their square roots in different situations.
- B1.3
- Read, show, compare and order positive and negative fractions and decimals up to thousandths.
- B1.4
- Simplify fractions by using equivalent fractions when it helps.
- B1.5
- Find fractions and decimals that sit between any two given amounts.
- B1.6
- Round decimals to a tenth, a hundredth or a whole number, whichever suits the situation.
- B1.7
- Change between fraction, decimal and percent forms in a range of settings.
- B2.1
- Apply properties of operations, the order of operations and how operations relate to solve multi-step problems with whole numbers, decimals, fractions, ratios, rates and percents.
- B2.2
- Know common percent, fraction and decimal equivalents by heart.
- B2.3
- Use mental strategies to raise or lower a whole number by 1%, 5%, 10%, 25%, 50% or 100%, and explain them.
- B2.4
- Use objects, drawings and equations to show and solve problems that add or subtract integers.
- B2.5
- Add and subtract fractions, using equivalent fractions where needed, in a range of problems.
- B2.6
- Find the GCF of whole numbers no larger than 144, and the LCM of two or three whole numbers.
- B2.7
- Write and evaluate repeated multiplication of whole numbers using exponents.
- B2.8
- Multiply and divide a fraction by a fraction, using models and tools.
- B2.9
- Multiply and divide with decimals on both sides of the operation in everyday problems.
Questions about this unit
How long is this unit?
20 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, B1.5, B1.6, B1.7, B2.1, B2.2, B2.3, B2.4, B2.5, B2.6, B2.7, B2.8, B2.9 from Mathematics (2020), Strand B: Number (B1 Number Sense, B2 Operations).
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.