MathsFreePrintable

Linear Pattern Equation Formulation

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Linear Pattern Equation Formulation worksheet preview

Linear Pattern Equation Formulation

Linear patterns and equations illustration

📊 Part 1: Identifying Linear Patterns

1. Look at this pattern: 5, 8, 11, 14, 17, ...

What is the constant difference? ____

The equation is 3n + 2

The equation is 5n

The equation is n + 3

The equation is 2n + 3

2. For the pattern 12, 15, 18, 21, 24, ...

Complete the table:

Term number (n): 1, 2, 3, 4, 5

Term value: 12, ___, ___, ___, ___

The equation for this pattern is: ________________

3. Which of these scenarios would create a linear pattern?

Saving $5 each week

Doubling your money each month

Walking 2 kilometres each day

Temperature increasing by 3°C each hour

✏️ Part 2: Real-World Equation Formulation

4. Sarah starts with $20 and saves $8 each week.

Let w = number of weeks

Write an equation for her total savings: S = ________________

How much will she have after 6 weeks? $______

5. A plant is 15cm tall and grows 4cm each month.

Let m = number of months

Write an equation for the plant's height: H = ________________

6. Tom climbs stairs at a rate of 25 steps per minute. He starts at ground level.

Write an equation for the total steps climbed after t minutes:

Steps = ________________

Explain your reasoning:

7. Extension: A water tank starts with 200 litres and loses 15 litres each hour.

Write an equation for the water remaining after h hours:

Water = ________________

When will the tank be empty? Show your working:

🎯 Part 3: Pattern Creation and Reflection

8. Create your own linear pattern that starts with 7 and has a constant difference of 6.

Pattern: 7, ___, ___, ___, ___

Equation: ________________

9. Look at this Māori tukutuku pattern sequence:

If a tukutuku panel uses 4 triangles in row 1, 7 triangles in row 2, and 10 triangles in row 3...

Write an equation for the number of triangles in row n: ________________

How many triangles would be in row 8? ______

10. Reflection: Explain in your own words how to write an equation from a linear pattern.

About This Worksheet

Free in Kuraplan

Sign up free, grab the PDF, and customize it for your class.

Print-Ready

Formatted for standard paper. Clean layout, easy to read.

AI-Generated

Created with Kuraplan's AI, designed for real classroom use.

For Teachers & Parents

Use in classrooms, for homework, tutoring, or homeschool.

Need a custom version of this worksheet?

Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.

Generate Custom Worksheets — Free
No credit card Curriculum-aligned Under 60 seconds