Growing PatternsActivities & Teaching Strategies
Active learning works well for growing patterns because students need to see and build the steady increase themselves, not just hear about it. When children manipulate objects, the jump from 3 to 5 blocks or from 1 to 2 beads becomes clear in their hands before it appears on paper.
Learning Objectives
- 1Identify the growth rule in a given visual or numerical growing pattern.
- 2Compare and contrast repeating patterns with growing patterns.
- 3Construct the next two steps of a growing pattern based on its identified rule.
- 4Explain the rule of a growing pattern using clear mathematical language.
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Pairs: Block Chain Builder
Partners take turns adding to a chain of unifix cubes following a rule like 'add two each time.' They describe the rule after five steps and predict the tenth step. Switch roles and compare predictions.
Prepare & details
Differentiate between a pattern that repeats and one that grows.
Facilitation Tip: During Block Chain Builder, circulate with a chart that lists possible growth rules so you can nudge pairs who are stuck on ‘What comes next?’
Setup: Tables with large paper, or wall space
Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map
Small Groups: Shape Garden Growth
Each group gets pattern cards with growing flower shapes. They copy the first three terms on grid paper, identify the rule, and draw the next two. Discuss as a class what rules they found.
Prepare & details
Analyze the 'growth rule' in a numerical or visual pattern.
Facilitation Tip: Shape Garden Growth runs best when you limit each group to two colors and one shape so the growth in quantity stands out against the constant visual elements.
Setup: Tables with large paper, or wall space
Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map
Whole Class: Human Number Line
Students line up to form a growing pattern by adding one more child each round, such as groups of 2, 3, 4. The class calls out the rule and predicts the next group size before adding.
Prepare & details
Construct the next two steps in a given growing pattern.
Facilitation Tip: For the Human Number Line, place a large number line on the floor and have students physically step forward by the agreed amount to feel the increase in their bodies.
Setup: Tables with large paper, or wall space
Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map
Individual: Bead Necklace Extension
Students string beads in a growing pattern provided on cards, like 1 bead, 2 beads, 4 beads. They continue independently and write the rule in words.
Prepare & details
Differentiate between a pattern that repeats and one that grows.
Setup: Tables with large paper, or wall space
Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map
Teaching This Topic
Start with repeating patterns for contrast, then introduce growing patterns using the same vocabulary: ‘This one adds two more each time.’ Avoid calling any pattern ‘easy’ or ‘hard’; instead, praise clear descriptions of the rule. Research shows that when students articulate the rule themselves, their transfer to new contexts improves.
What to Expect
Successful learning looks like students describing the rule aloud, building or drawing the next two steps, and using the same rule when the materials change. Expect them to explain why the pattern grows rather than repeats, and to compare a growing pattern to a repeating one in their own words.
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 Block Chain Builder, watch for students who loop back to the first shape instead of adding more.
What to Teach Instead
Hand them a second strip of paper labeled ‘Step 1, Step 2, Step 3’ and ask them to rebuild the chain exactly before drawing the next two steps.
Common MisconceptionDuring Shape Garden Growth, watch for students who change the amount added each step without noticing.
What to Teach Instead
Have them rebuild the garden with color-coded sticks and ask them to count the new pieces only; the consistency will become visible.
Common MisconceptionDuring Bead Necklace Extension, watch for students who treat the visual picture as a repeating pattern.
What to Teach Instead
Cover all but the first two beads with paper, then slowly reveal each new bead while saying ‘Now we have one more than before,’ to highlight growth.
Assessment Ideas
After Block Chain Builder, give each student a half-sheet with a growing pattern drawn in blocks and ask them to draw the next two steps and write the rule below.
During Human Number Line, stop the line after three steps and ask each student to whisper the next number to a partner, then listen for correct use of the growth rule.
After Shape Garden Growth, hold a gallery walk and ask students to point to one growing pattern and explain to a partner how it differs from a repeating pattern they see.
Extensions & Scaffolding
- Challenge pairs who finish early to invent a new growing pattern using the same blocks, then swap with another pair to solve it.
- Scaffolding: Provide a sentence stem ‘The pattern grows by ___ each time’ and a number line strip for students who struggle to count on.
- Deeper exploration: Ask students to predict the 10th step of their pattern and justify their answer using repeated addition or counting on.
Key Vocabulary
| Growing Pattern | A sequence where the number of items or the value increases or decreases by a consistent amount at each step. |
| Repeating Pattern | A sequence where a specific unit or set of items is repeated over and over again. |
| Growth Rule | The specific instruction that describes how the pattern changes from one step to the next, for example, 'add 2' or 'take away 1'. |
| Term | A single element or step within a pattern sequence. |
Suggested Methodologies
Planning templates for Mathematics
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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