Grade 6 Math: Number unit
Students read and compare whole numbers to one million, integers, decimals and fractions, and move between fractions, decimals and percents. They use divisibility rules and prime factors, and they add, subtract, multiply and divide with whole numbers, decimals and fractions. They also work with ratios, rates and percents. The unit ends with a two-day performance task in which students plan and report on a snack stall using made-up numbers.
What's included
- Unit overviewBig ideas, expectations by code, learning goals and success criteria
- Day-by-day calendar16 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 keys130 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“Number Night Snack Stall”, with a rubric across all four achievement chart categories
- Unit test and answer key38 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: Whole numbers to one million | B1.1 |
| 3 | Lesson 2: Integers on number lines | B1.2 |
| 4 | Lesson 3: Decimals to thousandths | B1.4 |
| 5 | Lesson 4: Rounding decimals and matching fractions to decimals (then Quick check 1) | B1.5, B1.6 |
| 6 | Lesson 5: Comparing and ordering integers, decimals and fractions | B1.3 |
| 7 | Lesson 6: Divisibility rules and prime factors | B2.2, B2.6 |
| 8 | Lesson 7: Mental math with percents | B2.3 |
| 9 | Lesson 8: Adding, subtracting and dividing decimals (then Quick check 2) | B2.4, B2.11 |
| 10 | Lesson 9: Adding and subtracting fractions | B2.5 |
| 11 | Lesson 10: Multiplying and dividing by decimal tenths | B2.7, B2.8 |
| 12 | Lesson 11: Multiplying and dividing whole numbers by fractions | B2.9, B2.10 |
| 13 | Lesson 12: Ratios, rates and percents (then Quick check 3) | B2.12, B2.1 |
| 14 | Performance task, day 1 | B1, B2 |
| 15 | Performance task, day 2 | B1, B2 |
| 16 | Unit test | B1, B2 |
Lesson 1: Whole numbers to one million
Learning goal: We are learning to read, write and show whole numbers up to 1 000 000 and to say where we see numbers this large.
Success criteria:
- I can say the value of each digit in a six-digit number.
- I can write a number in standard, expanded and word form.
- I can place and compare numbers up to 1 000 000.
Minds On (10 min)
- Show the numbers 98 765 and 101 234 on the board. Ask: "Which number is greater, and how can you tell without counting every digit?"
- Collect two or three strategies (number of digits first, then the leftmost digit).
Action (35 min)
- Build a six-digit number with digit cards on a place value chart. Name each digit’s value aloud (hundred thousands, ten thousands, thousands, hundreds, tens, ones).
- Model standard, expanded and word form for one number. Show a number line from 0 to 1 000 000 with marks every 100 000 and place numbers on it.
- Students complete the worksheet in pairs.
Consolidation (15 min)
- Discuss question 7: where do we see numbers this big (populations, prices of houses, distances, website visits)?
- Exit: "What is the value of the digit 8 in 482 593, and how do you know?"
Whole numbers to 1 000 000
Write numbers with a space between groups of three digits. Show your thinking.
- What is the value of the digit 8 in 482 593?
- Write 305 070 in expanded form.
- What number is 6 × 100 000 + 2 × 10 000 + 7 × 100 + 4 × 10 + 9 × 1?
- Write 205 340 in words.
- How much greater is 101 234 than 98 765?
- Which is closer to 1 000 000: 989 500 or 1 010 000? Show how you know.
- Name two places in everyday life where numbers close to one million are used.
- Point A shows a number on this number line. Each small mark is 100 000. What number is A?
- Point B is halfway between two small marks (each small mark is 100 000). What number is B?
Answer keys with worked steps are in the Teacher Guide.
Performance task: Number Night Snack Stall
Your class is running a snack stall at a made-up school event called Number Night. You will make 120 bags of trail mix, sell them over two days, and report to the principal on how the stall did. Use the made-up numbers below, show your calculations, and explain your choices.
| Category | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| Knowledge and Understanding | Shows limited understanding of ratio, percent, place value and divisibility; calculations have many errors. | Shows some understanding; most calculations are correct but with errors in decimals, fractions or prime factors. | Shows considerable understanding; calculations are correct with only minor slips. | Shows thorough understanding; all calculations are accurate and efficient, including rounding and prime factors. |
| Thinking | Uses planning and checking with limited effectiveness; does not estimate. | Uses planning and checking with some effectiveness; estimates, but does not use them to check. | Uses planning and checking with considerable effectiveness; uses estimates to judge answers. | Uses planning and checking with a high degree of effectiveness; finds and fixes errors and justifies choices. |
| Communication | Communicates with limited clarity; steps and units are missing. | Communicates with some clarity; some steps, units and math words are used. | Communicates with considerable clarity; steps, units and math words are clear. | Communicates with a high degree of clarity and precision; a reader can follow every step. |
| Application | Makes limited connections between the numbers and the stall decisions. | Makes some connections; the report names a decision with little reasoning. | Makes considerable connections; the report makes sensible choices backed by the numbers. | Makes strong connections; the report makes insightful choices and suggests thoughtful improvements. |
Lessons in this unit
- Whole numbers to one millionLearning to read, write and show whole numbers up to 1 000 000 and to say where we see numbers this large.B1.1
- Integers on number linesLearning to read and show integers on horizontal and vertical number lines and to use integers to describe real situations.B1.2
- Decimals to thousandthsLearning to read, show, compare and sort decimals that go out to the thousandths place.B1.4
- Rounding decimals and matching fractions to decimalsLearning to round decimals, including repeating ones, and to show that a fraction and a decimal can name the same amount.B1.5, B1.6
- Comparing and ordering integers, decimals and fractionsLearning to compare and order integers, decimals and fractions, on their own and mixed together.B1.3
- Divisibility rules and prime factorsLearning to use divisibility rules and to write a composite number as a product of prime numbers.B2.2, B2.6
- Mental math with percentsLearning to find 1%, 5%, 10%, 15%, 25% and 50% of a number in our heads and to explain our strategy.B2.3
- Adding, subtracting and dividing decimalsLearning to estimate, add and subtract whole numbers and decimals, and to divide decimals by whole numbers up to 10.B2.4, B2.11
- Adding and subtracting fractionsLearning to add and subtract fractions and mixed numbers with like and unlike denominators.B2.5
- Multiplying and dividing by decimal tenthsLearning to multiply and to divide numbers with three digits by tenths such as 0.3 and 0.4.B2.7, B2.8
- Multiplying and dividing whole numbers by fractionsLearning to find a fraction of a whole number and to find how many times a fraction fits into a whole number.B2.9, B2.10
- Ratios, rates and percentsLearning to solve problems with ratios, rates and percents and to choose the operations for multi-step problems.B2.12, B2.1
Ontario curriculum expectations covered
- B1.1
- Read, write and show whole numbers up to a million and describe where such numbers appear.
- B1.2
- Read and show integers using horizontal and vertical number lines and other tools.
- B1.3
- Compare and order integers, decimals and fractions on their own or mixed together.
- B1.4
- Read, model, compare and sort decimals with as many as three places.
- B1.5
- Round terminating and repeating decimals to a whole number, tenth or hundredth.
- B1.6
- Show how fractions and decimals up to thousandths name the same amounts.
- B2.1
- Use properties of operations and links between operations to solve multi-step problems with whole numbers, decimals, fractions, ratios, rates and percents.
- B2.2
- Use divisibility rules for 2, 3, 4, 5, 6, 8, 9 and 10.
- B2.3
- Find 1%, 5%, 10%, 15%, 25% and 50% of whole numbers mentally and describe the method.
- B2.4
- Add and subtract whole numbers and decimals, estimating and using written methods.
- B2.5
- Add and subtract fractions with the same or different denominators using models and tools.
- B2.6
- Write composite numbers as products of primes, including with factor trees.
- B2.7
- Multiply numbers with three digits by tenths, using written methods.
- B2.8
- Divide three-digit whole numbers by decimal tenths, handling remainders sensibly.
- B2.9
- Find a proper fraction of a whole number using tools and strategies.
- B2.10
- Find how many proper fractions fit into a whole number using tools and strategies.
- B2.11
- Divide decimals with as many as three places by one-digit whole numbers and 10.
- B2.12
- Solve problems with ratios, percents and rates using tools and strategies.
Questions about this unit
How long is this unit?
16 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, B2.1, B2.2, B2.3, B2.4, B2.5, B2.6, B2.7, B2.8, B2.9, B2.10, B2.11, B2.12 from Mathematics (2020), Strand B: Number (B1 Number Sense, B2 Operations), Grade 6.
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.