MathsFreePrintable

Linear Patterns Exploration

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.

Download now

Name:Date:

Linear Patterns Exploration

Study how each sequence changes. Show your thinking where you can.

Pattern Tables

1.A sequence has 3 tiles in position 1, 7 tiles in position 2, 11 tiles in position 3, and 15 tiles in position 4. Describe the rule for moving from one position to the next.

2.A sequence starts with 6 counters in position 1 and 10 counters in position 2. It increases by the same amount each time. How many counters are in positions 3, 4, and 5?

3.What is the constant change in the sequence 6, 10, 14, 18, 22?

Predicting and Explaining

4.A tile pattern begins with 3 tiles and gains 4 tiles at each new position. How many tiles will position 9 have? Explain how you worked it out.

5.Choose the statement that best describes a linear pattern.

The amount added or subtracted stays the same between consecutive terms.
The numbers must get larger by different amounts.
Every pattern begins at 1.
A linear pattern cannot include shapes.

Visual Patterns

Term 1: ●

Term 2: ●●

Term 3: ●●●

Term 4:

Term 5:

6.Create your own linear pattern using dots, shapes, or symbols. Show at least four terms.

7.Write a sentence explaining the constant change in the pattern you created.

True or False

8.For each statement, decide whether it is true or false.

TrueFalse

If position 3 has 14 counters and the rule is “add 5”, position 4 has 19 counters.

Every linear pattern must start with 1.

The equals sign means that the values on its two sides are the same.

If you know a linear pattern's rule and starting point, you can work out a later term.

Pattern Vocabulary

9.Match each pattern word to its meaning.

Term
Position
Rule
Element

A basic shape or symbol used to build a visual pattern
One item or value in a sequence
A description of how to make or continue the pattern
Where a term occurs in the sequence

Problem Solving

10.A kapa haka group practises lining up in rows. Row 1 has 5 people, row 2 has 8, and row 3 has 11. If the pattern continues, how many people will be in row 6?

11.Explain why your answer for row 6 follows the pattern 5, 8, 11, ...

12.For the row pattern 5, 8, 11, ..., write a number sentence showing the number of people in row 4 as the row 1 amount plus the increases.