Understanding Growing Patterns In Mathematics
Recognizing Growing Patterns in Numbers and Objects
Growing patterns show change in a sequence of numbers, shapes, or objects. The changes follow a consistent rule, and the rule describes how the pattern grows. Examples of growing patterns include:
- Numerical growing pattern: 2, 4, 6, 8 (increases by 2)
- Geometric growing pattern:
The growing pattern above increases by one circle between the triangles each time.
Why Are Growing Patterns Important?
Recognizing Growing Patterns
Describing how a pattern grows gives students a way to identify rules and relationships. This skill lays the foundation for problem-solving in math by helping students recognize predictable changes. Examples include:
- Measurement: Predicting how a growing chain of blocks changes in length as more blocks are added.
- Skip Counting: Using a growing pattern to learn counting by 2s, 5s, or 10s.
- Geometry: Describing how a shape (like a triangle or staircase) grows step by step in a repeating design.
Developing Mathematical Reasoning Through Explanation of Growing Patterns
Identifying a growing pattern is an important first step, but defining and explaining the rule is just as critical. When students articulate the rule, they deepen their understanding of the pattern’s structure and develop the ability to describe relationships between numbers or objects.
This matters because:
1. It encourages precision: Verbalizing the rule helps students think carefully about how the pattern changes.
2. It builds problem-solving skills: Explaining the rule enables students to extend patterns and make predictions.
3. It supports communication: Math is a language, and describing patterns builds the skills needed for clear mathematical communication.
Teaching Strategies for Growing Patterns
Using Manipulatives to Explore Growing Patterns
Introduce growing patterns with hands-on tools like counters, Unifix cubes, or pattern blocks.
For instance, have students create growing patterns by adding one block or counter to each step. One approach could be to start with one cube, then add two, then three, creating a growing staircase.
You can also ask students to describe the rule for the pattern and predict what comes next.
Representing Growing Patterns on a Number Line or Chart
Help students visualize growing patterns by recording them on a number line or chart.
For example, write a number pattern (e.g., 2, 4, 6, 8,10) on a chart. Students can then:
- Mark the points on a number line to show how the pattern increases.
- Use arrows or “hops” to demonstrate the consistent change between numbers.
Ask, “What is the rule for this pattern?” and “What would the next number be?”
Building Vocabulary for Describing Growing Patterns
Encourage students to use clear and precise language when describing growing patterns and defining their rules. Providing a consistent vocabulary helps students articulate their thinking and supports mathematical communication.
Tips for Encouraging Language Use Around Growing Patterns:
Introduce Key Terms: Use words like “grow,” “pattern, “increase,” “add,” and “rule” during instruction and encourage students to use this language.
Model Descriptions: Demonstrate how to describe a growing pattern. For example: “This pattern grows because we add 2 each time.”
Ask Open-Ended Questions: Prompt students to explain their reasoning with questions like:
- “What happens in each step?”
- “How can you describe the rule for this growing pattern?”
- “What words can we use to explain how the pattern grows?”
