Fibonacci and Patterns

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ST Name/ Ainm:

Caoimhe Blaney

ST Number:

40035443

Class Level:

6th Class

Date:

14th May 2025

Subject:

Mathematics

Time:

10:10

Duration of Lesson:

40 minutes

Number of Pupils:

21

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Strand(s):

Algebra; Number

Strand Unit(s)/ Element(s):

Rules and properties; pattern and sequences.

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Learning Outcome(s) (from IE Curriculum):

• Number strand: Recognise, describe and generate increasing and decreasing sequences and patterns including those found in real-life contexts (N.4).
• Algebra strand: Explore patterns and relationships in number and geometric sequences and describe them using words, diagrams, and symbols (A.1).
• Competency focus: Using Mathematics – developing an understanding of patterns and relationships in numbers, enhancing mathematical reasoning and problem-solving skills.

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Content Objectives

• Identify and explain generalisations seen in Fibonacci’s number sequence and triangular numbers as they arise in mathematical patterns.
• Represent these mathematical sequences in multiple ways: verbal, diagrammatic, and symbolic.

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Learning Objectives

The child should be enabled to:

1. Describe the Fibonacci sequence and identify its pattern.
2. Determine triangular numbers by examining the pattern in "The Twelve Days of Christmas" carol.
3. Link the concept of sequences to real-life and cultural examples, fostering curiosity and numeracy connections.

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Assessment / Measúnú

1. Method: Teacher Observation during discussions & pair-work activities.
2. Assessment of: Students’ ability to identify patterns in sequences and articulate their reasoning.
3. To be recorded: KWL chart (What I Know, What I Want to Know, What I Learned) and final reflections during plenary.

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Teacher Questioning

Lower order questions (Closed)

1. What is the first number in the Fibonacci sequence?
2. How do you get the next number in the Fibonacci sequence?
3. Can you count how many gifts are given on the third day in "The Twelve Days of Christmas"?

Higher order questions (Open)

1. Why do you think the Fibonacci sequence appears in nature and art?
2. Can you find a rule to calculate the next triangular number without adding all previous numbers?
3. How might understanding these patterns help in other areas of maths or daily life?

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Language Development Opportunities

• Introduce key mathematical vocabulary: sequence, pattern, sum, triangular number, Fibonacci, generalisation, term.
• Encourage verbal explanations and peer discussions using sentence starters: “I notice that...”, “The pattern is... because...”, “This number is... because it follows...”.

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Literacy Development Opportunities

• Use the lyrics from "The Twelve Days of Christmas" to extract numeric patterns.
• Students will write short explanations or summaries of the Fibonacci pattern or triangular numbers in their own words.
• Label diagrams representing sequences.

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Oral Language

• Collaborative pair discussions interpreting patterns.
• Whole class sharing of findings and prompts to use mathematical language fluently.

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Teaching Methodologies

• Primary: Active Learning, Talk and Discussion, Collaborative/Co-operative Learning
• Using cognitively challenging tasks with emphasis on mathematical modelling, promoting maths talk, and encouraging curiosity and playfulness in learning sequences.

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Introduction (5 minutes)

• Stimulus: Show a colourful spiral image of sunflower seeds and a short animated video illustrating the Fibonacci sequence in plants and shells.
• Elicit Prior Knowledge: Ask, “Have you ever noticed patterns like this in nature or art?” and “What do you already know about number patterns?”
• Share Learning Intention: Display and read out – “Today we will explore a fascinating sequence called Fibonacci’s numbers and discover how patterns appear in a famous Christmas carol.”
• WALT: We Are Learning To understand Fibonacci’s sequence and find patterns in ‘The Twelve Days of Christmas’ carol.

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Development (30 minutes)

Part 1: Introducing Fibonacci Sequence (15 minutes)

• Write the Fibonacci sequence on the board: 0, 1, 1, 2, 3, 5, 8, 13...
• Explore how each number is a sum of the two preceding numbers; represent this with arrows and visuals.
• Discuss real-life examples: sunflowers, pinecones, snail shells.
• Activity: In pairs, students create a visual diagram (using coloured counters or drawing spirals) to model the sequence.
• Teacher circulates, asking guided questions to check understanding (e.g., “How did you find this number?”)

Part 2: Triangular Numbers & The Twelve Days of Christmas (15 minutes)

• Explain triangular numbers as numbers that can form equilateral triangles with dots.
• Relate to “The Twelve Days of Christmas” carol – how many gifts in total each day? (1 gift on the first day, 3 total on the second, etc.)
• Provide the first 5 verses of the carol on handouts or whiteboard.
• Activity: Students work in pairs to add the gifts for each day, noticing the pattern creating triangular numbers (1, 3, 6, 10, 15…).
• Students draw dots or use manipulatives to visualise these triangular numbers.
• Class discussion focusing on verbal and symbolic representation of the pattern and a formula if possible (e.g., n(n+1)/2).

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Conclusion (5 minutes)

Cognitive

• Recap key ideas: “What is special about Fibonacci numbers? How do triangular numbers relate to the twelve days?”
• Use KWL chart: “What did you learn today?”

Social

• Allow pairs to share their patterns and explain their reasoning to the class briefly.
• Praise collaborative learning and language use.

Transition (if appropriate)

• Link to next topic: “Next time, we will apply sequences to problem-solving situations and explore how formulas work!”

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Universal Design for Learning (UDL)

Pupil(s)	Reason(s)	Method(s)	Additional Comments
Student 1	Autism	Invitation to participate, SNA support, individual work	Ensures personalised access and comfort
Students 2,3,4,5	EAL	Word banks, iPad translation tools	Supports language development and comprehension
Students 6,7,8,9	Dyslexia	Extended time, simplified worksheets	Reduces pressure, scaffolds learning

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The Learning Environment & Resources

• Students seated in pairs mixing ability levels for peer support.
• Visual displays including Fibonacci spiral, triangular numbers diagram on whiteboard/interactive whiteboard (IWB).
• Visual timer on display to help focus on time-management for each activity.
• Teacher circulates for on-the-spot formative assessment and assistance.
• Resources: Maths copies, pencils, rubbers, rulers, counters or coloured dots, pre-drawn triangular numbers diagram on graph paper, poem excerpt printed.
• Use of the Busy at Maths 6th Class book for reinforcement.

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This lesson uniquely links mathematical concepts with natural patterns and cultural references, encouraging deep understanding and excitement for maths through discovery and discussion, grounded firmly in the Irish curriculum's emphasis on pattern recognition, problem solving, and cooperative learning.