Repeating and Growing PatternsActivities & Teaching Strategies
Active learning helps students grasp repeating and growing patterns by making the abstract concrete. Moving, building, and discussing with peers turns pattern rules into something they can see and test right away. This hands-on work builds confidence before moving to abstract notation or symbols.
Learning Objectives
- 1Identify the repeating unit in a given visual or numerical pattern.
- 2Extend a given repeating or growing pattern by at least three elements.
- 3Create a repeating pattern using at least three distinct elements (shapes, colors, or numbers).
- 4Describe the rule for a given repeating pattern using clear and concise language.
- 5Formulate the rule for a growing pattern that increases by a constant amount.
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Partner Chain: Repeating Patterns
Pairs build paper chains with repeating units of two colors or shapes, like red-blue-red-blue. One student starts a five-link chain, the partner extends it by four links following the rule. Partners switch, describe the rule to each other, and compare chains.
Prepare & details
What comes next in this pattern: circle, triangle, square, circle, triangle, ...?
Facilitation Tip: During Partner Chain: Repeating Patterns, circulate and listen for students naming the core unit aloud before they add the next element.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Group Build: Growing Shape Towers
Small groups use linking cubes to construct towers where each level adds one more shape, alternating colors. They extend the pattern to five levels, sketch it, and write the rule. Groups share towers and predict the tenth level.
Prepare & details
How would you describe the rule of a repeating pattern?
Facilitation Tip: During Group Build: Growing Shape Towers, ask guiding questions like 'How many cubes will you add next?' to focus attention on the growth rule.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Class Hunt: Pattern Spotters
Whole class brainstorms pattern categories, then pairs search classroom and school for examples like window arrangements or number lines. They photograph or draw three patterns, note the rule, and share in a class gallery walk.
Prepare & details
Where can you find a pattern in your classroom or school?
Facilitation Tip: During Class Hunt: Pattern Spotters, carry a clipboard to model recording a rule immediately after students describe their findings.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Individual Create: Number Necklaces
Students string beads into growing patterns, starting with one bead, then two of another color, three of the first. They extend to six beads, label the rule on paper, and wear necklaces for peer review.
Prepare & details
What comes next in this pattern: circle, triangle, square, circle, triangle, ...?
Facilitation Tip: During Individual Create: Number Necklaces, provide number cards in advance so students focus on the necklace design rather than writing numbers.
Setup: Wall space or tables arranged around room perimeter
Materials: Large paper/poster boards, Markers, Sticky notes for feedback
Teaching This Topic
Teach patterns by starting with visuals and movement before symbols. Use multiple representations—shapes, colors, and numbers—so students connect the rule across formats. Avoid rushing to written rules; let students verbalize their thinking first. Research shows that students who describe patterns aloud before writing are more accurate and flexible in their rule application.
What to Expect
Successful learning looks like students confidently describing the core unit in repeating patterns, explaining how each step grows in growing patterns, and creating new examples with clear rules. Look for students using precise vocabulary and justifying their answers with evidence from the materials.
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 Partner Chain: Repeating Patterns, watch for students who insist patterns must involve numbers and ignore shape or color sequences.
What to Teach Instead
Use mixed materials like colored tiles and pattern blocks during Partner Chain. Ask partners to sort their core unit by shape, color, and number to show that rules can apply across types.
Common MisconceptionDuring Group Build: Growing Shape Towers, watch for students who assume towers always add one cube each step.
What to Teach Instead
Provide towers with varied growth rules (add one, add two, skip count by twos) and have groups sort them by rule type. Ask, 'How did your tower change from step to step?' to highlight different growth patterns.
Common MisconceptionDuring Class Hunt: Pattern Spotters, watch for students who claim classroom patterns are random with no describable rule.
What to Teach Instead
Ask students to sketch the pattern they find and label the core unit or growth step. Require them to share the rule with a partner before recording it, ensuring every pattern has a clear description.
Assessment Ideas
After Partner Chain: Repeating Patterns, present a mixed sequence of shapes and colors. Ask students to identify the next two elements and state the rule aloud to their partner before recording it on a mini whiteboard.
After Group Build: Growing Shape Towers, give students a card with a growing pattern of shapes. Ask them to draw the next step and write the rule in one sentence on the back of their tower cards.
During Class Hunt: Pattern Spotters, have students pair up to explain their findings to each other using sentence stems like 'This is a repeating pattern because...' or 'This is a growing pattern because...' before sharing with the class.
Extensions & Scaffolding
- Challenge early finishers in Partner Chain to create a repeating pattern with three alternating elements, then swap with a peer to extend it.
- Scaffolding for Group Build involves giving students a set number of cubes to add each time, like adding two cubes each step, so the rule is explicit.
- Deeper exploration involves having students compare their growing towers and categorize them by rule type (add one, add two, double), then present findings to the class.
Key Vocabulary
| Pattern | A sequence of elements that repeats or grows according to a predictable rule. |
| Repeating Pattern | A pattern where a specific unit or sequence of elements is repeated over and over. |
| Growing Pattern | A pattern where the number of elements increases or decreases by a consistent amount at each step. |
| Rule | The specific instruction or logic that defines how a pattern is formed or extended. |
| Element | An individual item within a pattern, such as a shape, color, or number. |
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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