Patterns and Repeating DesignsActivities & Teaching Strategies
Active learning lets students test rules with their hands and eyes, not just listen to explanations. For patterns and tessellations, movement and trial build spatial logic faster than worksheets alone.
Learning Objectives
- 1Identify repeating elements in given shape and colour patterns.
- 2Extend given patterns by accurately predicting and adding the next three elements.
- 3Create a repeating pattern using at least two different 2D shapes.
- 4Describe the rule of a simple repeating pattern using shape names or colour names.
- 5Demonstrate how specific 2D shapes can tessellate a surface without gaps or overlaps.
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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.
Prepare & details
What comes next in this shape or colour pattern?
Facilitation Tip: In the Pattern Extension Relay, circulate with a timer and call out the next step only after pairs have shown their answer to you.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
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.
Prepare & details
How can you make your own repeating pattern using shapes or colours?
Facilitation Tip: During the Tessellation Challenge, provide scissors so groups can trim shapes to test fits on grid paper before gluing.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
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.
Prepare & details
Can you describe the rule in a pattern and continue it correctly for three more items?
Facilitation Tip: For the Repeating Pattern Chain, hand each student a single card so the whole class must decide order together.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
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.
Prepare & details
What comes next in this shape or colour pattern?
Facilitation Tip: With Design Your Tessellation, give colored pencils and dot paper so students can rotate shapes before drawing final lines.
Setup: Flexible workspace with access to materials and technology
Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials
Teaching This Topic
Teach by doing first: let students extend a pattern with real objects before they draw or write rules. Avoid showing finished answers early; instead, ask, 'What could come next?' to keep thinking open. Research shows physical pattern blocks reduce guessing and build stronger reasoning than screen-based drills.
What to Expect
Successful learners will speak in rules, spot errors in sequences, and adjust shapes until they fit together without gaps. They will explain their thinking clearly to peers during each task.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring Tessellation Challenge, watch for students assuming all shapes can tile without testing.
What to Teach Instead
Hand each group circles and irregular pentagons alongside squares; ask them to try fitting them on grid paper and observe the gaps before moving to regular shapes.
Common MisconceptionDuring Repeating Pattern Chain, watch for students describing patterns as random or just pretty.
What to Teach Instead
Pause the chain after three turns and ask a student to state the rule aloud; if unclear, have the class test predictions using the next card to reveal the pattern's consistency.
Common MisconceptionDuring Design Your Tessellation, watch for students arranging shapes only in straight rows.
What to Teach Instead
Provide curved templates or let students rotate triangles to form spirals; display finished designs to show that tessellations can curve and shift while still covering the surface.
Assessment Ideas
After Pattern Extension Relay, hand each student a worksheet with three incomplete patterns and ask them to draw the next three elements and write the rule for one pattern.
During Tessellation Challenge, circulate and ask each group to point to the shapes they are using and explain how they fit together without gaps.
After Repeating Pattern Chain, show images of tiled floors or patterned wallpaper and ask students to describe the repeating part, the shapes used, and whether the shapes fit perfectly.
Extensions & Scaffolding
- Challenge: Ask early finishers to create a pattern with two changing features, like shape and color, and write the rule for a partner to follow.
- Scaffolding: Provide a bank of shape cut-outs and a strip of paper; students arrange and glue shapes one at a time to reduce cognitive load.
- Deeper exploration: Introduce pentagons and octagons in small groups and ask them to rotate shapes to find partial fits, then discuss why regular hexagons tile perfectly but these do not.
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. |
Suggested Methodologies
Planning templates for Foundations of Mathematical Thinking
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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Examine the characteristics of three-dimensional objects and calculate their surface area, focusing on cubes, cuboids, and cylinders.
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3D Shapes in the Environment
Investigate how 2D nets fold to form 3D shapes and design nets for simple solids.
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Position and Direction
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