MathsFreePrintable

Growing Patterns Stations

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.

Growing Patterns Stations worksheet preview
Name:Date:

Growing Patterns Stations

At each station, investigate the growing dot pattern. Each new shape adds one more row of dots. Use the pattern to predict, describe and generalise. You may use n for the shape number.

Station 1: Notice and predict

Study the first four shapes. The dots are arranged in rows.

Shape 1 ●

Shape 2 ● ● ●

Shape 3 ● ● ● ● ● ●

Shape 4 ● ● ● ● ● ● ● ● ● ●

1.How many dots are in Shapes 1, 2, 3 and 4? Write the four totals in order.
2.How many dots will Shape 5 have? Explain what is added to make the next shape.
3.Choose the number of dots in Shape 6.
  • 18
  • 21
  • 24
  • 36

Station 2: Find the rule

Look for how the totals change as the shape number increases.

4.Complete the sequence of totals: 1, 3, 6, 10, __, __. Write the next two totals.
5.True or false? The pattern adds the same number of dots each time. Explain your choice.
6.Match each shape number to its total number of dots.
  • Shape 3
  • Shape 4
  • Shape 5
  • 10 dots
  • 15 dots
  • 6 dots
7.A student says Shape 10 has 10 dots because its shape number is 10. Is the student correct? Work out the correct total.

Station 3: Generalise and create

Use algebra to describe the pattern for any shape number.

8.Let n stand for the shape number. Which expression gives the total number of dots in Shape n?
  • n + 1
  • 2 × n
  • n × (n + 1) ÷ 2
  • n × n
9.Use the expression you selected in the previous question to check the number of dots in Shape 4. Show your substitution and calculation.
10.A display needs 36 dots arranged in this pattern. Which shape number is it? Explain how you know.
11.Create a different growing pattern that starts with 2 dots and adds 3 dots each time. Write the first four totals and describe the rule.

3 printable pages

  • Growing Patterns Stations, page 1 of 3: Station 1: Notice and predict, Station 2: Find the rule

    Page 1

  • Growing Patterns Stations, page 2 of 3: Station 3: Generalise and create

    Page 2

  • Growing Patterns Stations, page 3 of 3: 11. Create a different growing pattern that starts with 2 dots and adds 3 dots each time.…

    Page 3

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