Foundations of Mathematical Thinking · 1st Class · Exploring 2D Shapes · Spring Term

Patterns and Repeating Designs

Investigate shapes that can tessellate (tile a surface without gaps) and create tessellating patterns.

• NCCA Curriculum Specifications
• NCCA: Primary - Shape and Space
• NCCA: Primary - Patterns

About This Topic

Patterns and repeating designs guide 1st Class students to identify, extend, and create sequences using shapes and colours, while tessellations reveal how specific 2D shapes tile surfaces without gaps or overlaps. Students tackle key questions such as "What comes next in this pattern?" and "How can you make a repeating design?", directly supporting NCCA Primary Shape and Space and Patterns strands. They articulate simple rules, like alternating triangle and square, and extend patterns for several steps.

This topic lays groundwork for algebraic reasoning through prediction and rule description, while tessellation work sharpens spatial visualization and geometric intuition. Connections to art and everyday designs, such as floor tiles or clothing prints, make patterns relevant and spark curiosity about mathematics in the world around them.

Active learning excels with this content because students manipulate physical shapes to test tessellations or build patterns collaboratively. Trial and error with cut-outs or interlocking tiles helps them internalize rules kinesthetically, fostering persistence and deeper retention over rote memorization.

Key Questions

1. What comes next in this shape or colour pattern?
2. How can you make your own repeating pattern using shapes or colours?
3. Can you describe the rule in a pattern and continue it correctly for three more items?

Learning Objectives

• Identify repeating elements in given shape and colour patterns.
• Extend given patterns by accurately predicting and adding the next three elements.
• Create a repeating pattern using at least two different 2D shapes.
• Describe the rule of a simple repeating pattern using shape names or colour names.
• Demonstrate how specific 2D shapes can tessellate a surface without gaps or overlaps.

Before You Start

Identifying 2D Shapes

Why: Students need to be able to recognize and name basic 2D shapes before they can use them in patterns or tessellations.

Colour Recognition

Why: Students must be able to identify and differentiate colours to create and extend colour patterns.

Key Vocabulary

pattern	A repeating sequence of shapes, colours, or objects that follows a specific rule.
repeating unit	The smallest part of a pattern that repeats over and over again.
tessellate	To tile a flat surface with one or more geometric shapes, leaving no gaps or overlaps.
2D shape	A flat shape with length and width, such as a square, triangle, or hexagon.

Watch Out for These Misconceptions

Common Misconception

All shapes can tessellate a surface.

What to Teach Instead

Hands-on trials with circles or irregular shapes show gaps form, while regular polygons succeed. Small group experimentation and peer sharing clarify that equal sides and angles enable perfect fits.

Common Misconception

Patterns follow no specific rule, just look nice.

What to Teach Instead

Prediction games require stating and testing rules, like ABAB, revealing consistency matters. Collaborative extensions help students spot errors and refine their thinking through discussion.

Common Misconception

Tessellations use shapes in straight lines only.

What to Teach Instead

Rotating and flipping shapes during station work demonstrates curved arrangements work too. Visual models from group posters correct this, building flexibility in spatial reasoning.

Active Learning Ideas

Pairs: Pattern Extension Relay

Partners take turns extending a teacher's starter pattern with coloured blocks or beads, saying the rule aloud before passing. Switch roles after three extensions. Pairs compare final patterns and explain differences.

20 min·Pairs

Small Groups: Tessellation Challenge

Provide paper, scissors, and shape templates like equilateral triangles, squares, and hexagons. Groups cut and arrange shapes to cover surfaces without gaps, rotating or flipping as needed. Record successful combinations on charts.

30 min·Small Groups

Whole Class: Repeating Pattern Chain

Teacher models a simple shape or colour pattern on the board. Each student adds one element following the rule, standing to share. Class votes on accuracy and extends collectively.

25 min·Whole Class

Individual: Design Your Tessellation

Students select 2-3 shapes from a kit and create a personal repeating design on grid paper. Label the tiling rule and colour for display. Share one discovery with the class.

15 min·Individual

Real-World Connections

• Tiling professionals use specific shapes like squares and hexagons to create decorative and functional floors and walls in homes and public buildings, ensuring the tiles fit together perfectly.
• Textile designers create repeating patterns for fabrics used in clothing, upholstery, and curtains, often using geometric shapes or motifs that are repeated across the material.
• Architects and artists use tessellations to design mosaics and decorative facades, considering how shapes fit together to create visually appealing and stable structures.

Assessment Ideas

Exit Ticket

Provide students with a worksheet showing three incomplete patterns. Ask them to draw the next three elements for each pattern and write the rule for one of them (e.g., 'blue circle, red square, blue circle, red square').

Quick Check

Hold up a set of 2D shape cut-outs (squares, triangles, hexagons). Ask students to select shapes that can tessellate and demonstrate how they fit together on their desks. Ask: 'Which shapes fit together without any spaces?'

Discussion Prompt

Show students images of tiled floors or patterned wallpaper. Ask: 'What patterns do you see? Can you describe the repeating part? What shapes are used? Do the shapes fit together perfectly?'

Frequently Asked Questions

How to teach tessellations in 1st class Ireland?

Start with familiar shapes like squares on floors, then provide templates for triangles and hexagons. Guide students to cut, arrange, and test tilings on paper. Link to NCCA Shape and Space by emphasizing no-gaps rule, using class murals to display successes and reinforce spatial skills over 2-3 lessons.

Activities for repeating patterns 1st class?

Use beads, blocks, or paints for chain-building relays in pairs, where students extend and verbalize rules. Whole-class board patterns let everyone contribute. These build prediction from NCCA Patterns strand, with displays celebrating creative designs that follow ABAB or ABC rules accurately.

How can active learning help patterns and tessellations?

Active approaches like manipulating tiles or extending patterns in groups make rules tangible through touch and talk. Students discover tessellation properties via trial-and-error, reducing frustration and boosting confidence. Collaborative sharing corrects errors on the spot, aligning with NCCA emphasis on exploration for lasting mathematical understanding.

NCCA standards for shape patterns 1st class?

NCCA Primary Mathematics specifies recognizing, continuing, and creating patterns with shapes and colours in Shape and Space. Students describe rules and extend for three items, as in key questions. Tessellations support spatial strand by exploring shape properties, integrated in Spring term Exploring 2D Shapes unit for holistic development.