Below zero and beyond
Grade 6 is where numbers go below zero, repeated multiplication gets a short form, and a letter becomes an unknown to find rather than a value to plug in. It all has to work without a calculator in June.
What Alberta asks for by the end of Grade 6
The subject: Mathematics
- Compare and order positive and negative numbers, and add them.
- Solve problems with the standard written methods, including multiplying and dividing decimals by whole numbers.
- Analyze numbers using prime factorization and powers.
- Relate fractions to division, add and subtract fractions, and multiply fractions and whole numbers.
- Use equivalent ratios, rates, unit rates and percents.
- Simplify expressions and solve equations with one or two operations.
- Relate shapes through symmetry and congruence, and locate and move shapes in the Cartesian plane.
- Find the area of parallelograms and triangles, and the volume of rectangular prisms.
- Describe how one quantity depends on another, with tables, rules and graphs.
- Investigate relative frequency through experiments.
Symmetry, congruence and tessellations — including First Nations and Métis star blanket designs — are part of Grade 6 too, though not on a sheet here yet. The achievement test has two parts, and neither allows a calculator. Part A is 15 quick number questions in 30 minutes; Part B is 40 questions from the whole course in 75 minutes, 80% of the mark.
The words, first
These are the terms a teacher will use at a parent interview, defined before anything below uses them.
| Word | What it means |
|---|---|
| Integer | A whole number or its negative: …, −2, −1, 0, 1, 2, … |
| Opposite | The same distance from zero on the other side: −6 and 6. |
| Power, base, exponent | 2⁵ is a power. The base, 2, is multiplied by itself; the exponent, 5, says how many times: 2 × 2 × 2 × 2 × 2 = 32. |
| Prime, composite | A prime has exactly two factors, 1 and itself: 2, 3, 5, 7, 11. A composite has more. |
| Prime factorization | A number written as primes multiplied together: 60 = 2² × 3 × 5. |
| Common denominator | A shared bottom number, so fractions with different ones can be added: 1/2 + 1/3 = 3/6 + 2/6. |
| Ratio | A comparison of two amounts: 1 part juice to 4 parts water is 1 : 4. |
| Rate, unit rate | A comparison of different kinds of amounts, like kilometres and hours. A unit rate is per one: 75 km per hour. |
| Equation | Two expressions with an equals sign between them: 2 × n + 3 = 17. Solving it means finding n. |
| Cartesian plane | The coordinate grid with both axes going below zero, making four quadrants. |
| Independent, dependent variable | In a function, the quantity you choose or that changes on its own (time), and the one that depends on it (height). |
| Relative frequency | How often something happened as a fraction of all the tries: 12 reds in 40 spins is 12/40, or 30%. |
| Volume | The space inside a 3-D object, in cubic units: length × width × height for a box. |
What to do at home
- Read the thermometer out loud — In January: −12 today, −18 tomorrow. Which is colder, and by how much? Count it on a number line if needed.
- Play doubling — 1, 2, 4, 8, 16… Each step is another power of 2. How many doublings to pass 1000?
- Split the bill — At a restaurant, divide a real total by the number of people. Decimals are easier to care about with money.
- Double a recipe — or half it — ¾ cup times 2, ⅔ cup halved. Fractions times whole numbers is a Grade 6 outcome.
- Think of a number — “I doubled it and added 3 and got 17.” Working backwards is solving an equation.
- Practise without a calculator — Both math tests in June are calculator-free, so the written methods have to be solid. A few questions a day beats a cram.
Sheets you can print for this
- Below zero — negative numbers
- Powers and primes — exponents and prime factors
- Decimals: multiply and share — without a calculator
- Different denominators — adding, subtracting and multiplying fractions
- Rates and ratios — comparing amounts
- Solve for n — equations
- Four quadrants — the cartesian plane
- Area and volume — flat and solid
- Rules and tables — functions: one quantity depends on another
- How often? — relative frequency
- Part A warm-up — 15 number questions, 30 minutes, no calculator
The expectations above are paraphrased from Alberta Education's Grade 6 programs of study, published on new LearnAlberta.