Grade 5, Patterns and equations
Equations with a variable
Find the number a letter stands for, as in 4 + x = 15.
Three levels
One skill, rising difficulty
Each sheet carries one level. The three are the same skill at rising difficulty, each named for what it practises.
- Level 1: Add and subtract
- Find the number that makes each equation true.
- Level 2: Multiply and divide
- Find the number that makes each equation true.
- Level 3: Mixed, the variable on either side
- Find the number that makes each equation true.
Worked example
How the sheet explains it
The helper printed at the top of each sheet: one solved example and the steps a student follows, before the first question. Every number sentence in it is proven by the same checker as the answer key.
Level 1: Add and subtract
n + 18 = 45 n = 27
- Undo adding 18 by subtracting: 45 − 18 = 27.
- Check: put 27 in for n. 27 + 18 = 45.
- If a number is taken away from the letter, as in n − 6 = 9, undo it by adding: 9 + 6 = 15.
- If the letter is taken away, as in 20 − n = 13, subtract the answer: 20 − 13 = 7.
Level 2: Multiply and divide
8 × n = 56 n = 7
- Undo × 8 by dividing: 56 ÷ 8 = 7.
- Check: put 7 in for n. 8 × 7 = 56.
- If the letter is divided, as in n ÷ 4 = 6, undo it by multiplying: 6 × 4 = 24.
- If you divide by the letter, as in 32 ÷ n = 8, divide by the answer: 32 ÷ 8 = 4.
Level 3: Mixed, the variable on either side
48 = y + 19 y = 29
- The letter is on the right. It means the same as y + 19 = 48.
- Undo adding 19 by subtracting: 48 − 19 = 29.
- Check: 29 + 19 = 48.
- When the letter comes after − or ÷: 20 − n = 13 gives n = 20 − 13 = 7, and 32 ÷ n = 8 gives n = 32 ÷ 8 = 4.
Goes with
Reference sheets
One-page helpers a student keeps beside this sheet:
- Solving equations
Every reference, facts and support sheet is listed in the worksheet catalogue.
In the BC curriculum
Content standards
The British Columbia content standard this skill is written for, by the codes used across this site:
- bc.math.5.c.11
The wording of each standard is on the Province's mathematics curriculum page.
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