Introduction to Patterns

Year Level

Year 7–10 (NSW)

Duration

45 minutes

Unit

Algebra in Everyday Life (Lesson 1 of 30)

Lesson Overview

In this lesson, students will explore number patterns found in nature and everyday contexts. They will identify, describe, and analyse simple numeric patterns, setting the foundation for algebraic thinking. This will engage their curiosity and help them connect mathematics with the real world.

NSW Curriculum Alignment

Content Descriptions (NSW Mathematics K-10 Syllabus):

AC9M7N01: Investigate and describe number patterns, including identifying the rule used to generate the pattern.
AC9M7A01: Use variables to represent numbers and write expressions to generalise patterns.
AC9M8N01: Analyse and apply patterns with linear and nonlinear relationships.
AC9M7PS01: Pose questions and explore mathematical problems in everyday contexts.

Proficiency Strands:

Understanding
Fluency
Problem Solving
Reasoning

Learning Objectives

By the end of this lesson, students will be able to:

Identify and describe simple numerical patterns found in natural and everyday settings.
Determine the rule that generates a given number pattern.
Express the pattern rule using simple algebraic notation (introduction to variables).
Recognise patterns as a foundation for algebraic thinking.
Work collaboratively and communicate their mathematical reasoning.

Resources

Whiteboard and markers
Pattern cards with number patterns related to nature (e.g., Fibonacci sequence, leaf arrangements, steps on stairs)
Worksheets with pattern sequences for individual and group activities
Natural objects (e.g., pine cones, shells, flower petals) for pattern observation

Lesson Structure

1. Introduction (5 minutes)

Begin with a question to the class: “Where have you seen number patterns in real life or in nature?”
Show images or actual natural objects demonstrating patterns (e.g., spirals on sunflower heads, arrangement of leaves).
Briefly explain that these patterns are not just pretty—they follow mathematical rules.
State learning objectives clearly.

2. Exploration and Pattern Identification (15 minutes)

Distribute pattern cards around the room. Each card shows a number pattern, some related directly to nature, others everyday (e.g., number of petals on flowers, steps in a staircase, seating arrangements).
In pairs, students rotate through different cards, describing the pattern and identifying what comes next.
Prompt students to articulate the rule in words (e.g., “add 2 each time” or “double the previous number”).
Walk around, ask probing questions to encourage deeper thinking (“What do you notice? How do you know this?”).

3. Introducing Algebraic Notation (10 minutes)

Gather students back and select 2-3 patterns from the cards to model writing an algebraic expression for the pattern.
Example: “Start with 3, then add 4 each step. We can say T(n) = 3 + 4(n – 1), where n is the step number.”
Model writing these expressions on the board and explain each part.
Have students attempt writing a simple algebraic expression for a pattern on their worksheet.

4. Application and Reasoning (10 minutes)

Give students a short worksheet with patterns that include numeric sequences and give space for writing rules and algebraic expressions.
Include one “real-world” scenario pattern — e.g., population growth of rabbits following a pattern seen in nature.
Students work independently but are encouraged to discuss and reason quietly in their pairs.
Teacher circulates to assist and prompt reasoning questions.

5. Conclusion and Reflection (5 minutes)

Round off with a 3-minute whole-class discussion: What was surprising about the patterns? How might this help with understanding algebra?
Reinforce that patterns are everywhere and algebra is a tool to describe and predict them.
Collect worksheets for informal assessment.

Assessment

Observation of pair discussions and verbal explanations during activity.
Review of worksheets to check understanding of pattern rules and ability to express these algebraically.
Informal questioning to assess student reasoning.

Differentiation Strategies

For students needing support, provide simpler patterns and structured sentence starters for describing rules.
For advanced students, challenge them to create their own number pattern and write the algebraic formula.
Use visual aids and natural objects to make abstract concepts more concrete.

Cross-Curricular Opportunities

Science: Connection to natural patterns in biology (e.g., Fibonacci in plants).
Technology: Recognising patterns in computing and coding.
Art: Patterns and symmetry in design and nature.

This lesson plan sets a solid groundwork for algebra through meaningful, age-appropriate engagement with patterns, fostering both conceptual understanding and enthusiasm for mathematics journey ahead.

Teaching Instructions