Numbers to a million
Grade 5 is where arithmetic starts to point at algebra. The numbers reach a million and the multiplication gets a second row, but the real change is a letter standing for a number that can change.
What Alberta asks for by the end of Grade 5
The subject: Mathematics
- Add and subtract numbers within 1 000 000, including decimals, using the standard written methods.
- Multiply three-digit numbers by two-digit numbers using the standard written method.
- Add and subtract fractions that have the same denominator.
- Write and evaluate algebraic expressions.
- Sort shapes using their symmetry.
- Calculate the area and perimeter of rectangles.
The fact sheet is a snapshot. Alberta's Grade 5 overview for parents also mentions changing improper fractions to mixed numbers and back, tests for divisibility, ratios, tables of values and the coordinate grid, so some of those are here too.
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 |
|---|---|
| Partial products | In 234 × 16, the two rows before the total: 234 × 6, and 234 × 10. Adding them is the answer. |
| Numerator, denominator | The top and bottom of a fraction. The denominator says what size the pieces are; the numerator says how many. |
| Common denominator | The same bottom number. Only fractions with one can be added by adding the tops. |
| Improper fraction, mixed number | 7/4 and 1 3/4: the same amount, written as quarters or as a whole and some quarters. |
| Algebraic expression | Numbers, operations and at least one letter: n + 7, 3 × n. It has a value once the letter has one. |
| Variable | The letter in an expression. It stands for a number that can change. |
| Evaluate | Work out an expression's value for a given number: n + 7 when n = 5 is 12. |
| Line of symmetry | A line a shape can be folded along so the halves match exactly. |
| Area and perimeter | The space inside a shape, in square units, and the distance around it. |
| Coordinates | A pair of numbers (x, y) that names a point on a grid: across first, then up. |
What to do at home
- Multiply the grocery bill — “Six boxes at $12 — and if it were 16 boxes?” Two-digit multiplication is easier to care about with a price attached.
- Cut a pizza into eighths — Three slices plus two slices is five eighths. Nobody would say five-sixteenths while holding the plate.
- Play the number machine — “I double your number and add 3.” Give them numbers until they can say the rule — that rule is an expression.
- Fold things in half — Leaves, letters, logos. Where does the fold make two matching halves? Some shapes have none.
- Fence the garden — With 24 m of fence, which rectangle holds the most ground? It is always the one closest to a square.
- Play battleship on graph paper — Calling out coordinates, across then up, is the coordinate outcome disguised as a game.
Sheets you can print for this
- Columns to a million — adding and subtracting, decimals too
- Multiplying by two digits — partial products
- Adding fractions — same denominator
- Letters for numbers — algebraic expressions
- Lines of symmetry — fold it, and finish it
- Area and perimeter — inside and around
- The coordinate grid — across, then up
The expectations above are paraphrased from Alberta Education's New K–6 curriculum fact sheets, which publish a snapshot of each grade rather than the complete program of studies. Alberta's full programs are at alberta.ca/curriculum.