Grade 7, Patterns and equations
Linear relations in tables
Fill in tables from an expression such as 3n + 2, then find the rule from a table.
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: Fill in the table
- Put each value of n into the expression. Write the result in the table.
- Level 2: With negative numbers
- Put each value of n into the expression. Write the result in the table.
- Level 3: Find the rule
- Find the rule that fits every row of the table.
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: Fill in the table
- 4n means 4 × n. For n = 0: 4 × 0 + 3 = 3.
- For n = 1: 4 × 1 + 3 = 7. For n = 2: 4 × 2 + 3 = 11.
Level 2: With negative numbers
- Different signs give a negative product. Same signs give a positive product.
- For n = −2: 3 × (−2) − 5 = −6 − 5 = −11.
- For n = −1: 3 × (−1) − 5 = −3 − 5 = −8. For n = 0: 3 × 0 − 5 = −5.
Level 3: Find the rule
- When n goes up by 1, the result goes down by 2: 5 − 7 = −2. So the rule starts −2n.
- Go back to n = 0. From n = 1 that is one row: 7 + 2 = 9. That is the number added, so the rule is −2n + 9.
- Check n = 3: −2 × 3 + 9 = 3.
Goes with
Reference sheets
One-page helpers a student keeps beside this sheet:
- Coordinates
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.7.c.5
The wording of each standard is on the Province's mathematics curriculum page.
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