Foundations of Mathematical Thinking · 2nd Year · Operations and Algebraic Patterns · Autumn Term

Creating Our Own Patterns

Students design and describe their own repeating and growing patterns using various materials.

• NCCA Curriculum Specifications
• NCCA: Primary - Algebra
• NCCA: Primary - Communicating and expressing

About This Topic

Creating Our Own Patterns invites students to design repeating and growing patterns using everyday materials like beads, blocks, or colored tiles. They begin with repeating patterns, such as alternating two shapes in an ABAB sequence, and progress to growing patterns where the number of elements increases by a consistent amount, like adding one more circle each step. Students describe their patterns verbally and record the rule they followed, such as 'red, blue, repeat' or 'two squares, then three, then four.'

This topic supports NCCA Primary Algebra standards by developing early algebraic reasoning through pattern recognition and extension. It also aligns with Communicating and Expressing objectives, as students explain their designs and compare them to peers' work, answering key questions like 'How is your pattern the same or different from your partner's?' Such activities build confidence in articulating mathematical ideas and sharpen comparison skills essential for operations.

Active learning benefits this topic greatly because students construct patterns hands-on, experiment with rules, and immediately see results. Pair and group discussions during creation and sharing refine understanding, as peers question and replicate patterns, turning abstract rules into concrete, shared knowledge that sticks.

Key Questions

1. Can you create your own repeating pattern using two different shapes?
2. How is your pattern the same or different from your partner's?
3. What rule did you use to make your pattern?

Learning Objectives

• Design repeating patterns using at least two different attributes (e.g., color, shape, size).
• Describe the rule of a created repeating pattern using precise mathematical language.
• Compare and contrast their own created patterns with those of their peers, identifying similarities and differences in rules and attributes.
• Create a growing pattern where the number of elements increases by a consistent amount.
• Explain the rule governing a growing pattern, articulating the consistent change between steps.

Before You Start

Sorting and Classifying Objects

Why: Students need to be able to identify and group objects based on shared attributes like color, shape, or size to use these attributes in pattern creation.

Counting and Number Recognition

Why: Understanding quantity is fundamental for creating growing patterns where the number of elements changes consistently.

Key Vocabulary

Repeating Pattern	A pattern that follows a sequence that repeats itself exactly, such as ABAB or ABCABC.
Growing Pattern	A pattern where the number of elements increases or decreases by a consistent amount at each step.
Attribute	A characteristic or feature of an object, such as its color, shape, or size, used to create patterns.
Rule	The specific instruction or logic that defines how a pattern is made or extended.

Watch Out for These Misconceptions

Common Misconception

Patterns must always repeat the exact same sequence forever.

What to Teach Instead

Repeating patterns follow a core unit like ABAB, but growing patterns change by adding elements. Hands-on extension activities, where students add to a partner's pattern, reveal the difference, as groups test and adjust rules together during peer review.

Common Misconception

Any random arrangement of shapes counts as a pattern.

What to Teach Instead

Patterns require a predictable rule. When students describe and replicate peers' designs in pairs, inconsistencies emerge, prompting clarification. Group sharing sessions help, as collective feedback refines vague ideas into precise rules.

Common Misconception

Growing patterns repeat a fixed unit like repeating ones.

What to Teach Instead

Growing patterns expand systematically, such as doubling each time. Building chains collaboratively shows the progression, and predicting next steps aloud corrects confusion through trial and class discussion.

Active Learning Ideas

Pairs: Shape Swap Patterns

Partners take turns creating a repeating pattern with two shapes on a strip of paper, then describe the rule without showing it. The listener recreates the pattern and checks accuracy. Switch roles after 10 minutes.

30 min·Pairs

Small Groups: Growing Bead Chains

Each group uses string and beads to build a growing pattern, starting with one bead type and adding more each time per the rule. Groups extend each other's chains and present the final rule to the class.

45 min·Small Groups

Whole Class: Pattern Prediction Game

Display student patterns on the board. Class predicts the next three elements as a group, with creator confirming the rule. Vote on predictions to build consensus.

25 min·Whole Class

Individual: Material Mix Patterns

Students select from a tray of objects to create one repeating and one growing pattern on paper. Label the rule and share one with a neighbor for feedback.

20 min·Individual

Real-World Connections

• Textile designers create repeating patterns for fabrics used in clothing and home furnishings, like the geometric prints found on curtains or the floral motifs on dresses. They must clearly define the repeating unit and how it is applied across the material.
• Architects and builders use patterns in construction, from the repeating brickwork on a wall to the arrangement of tiles in a mosaic. Understanding how patterns grow or repeat is essential for structural integrity and aesthetic design.

Assessment Ideas

Quick Check

Provide students with a collection of manipulatives (e.g., colored blocks, buttons). Ask them to create a repeating pattern using two different attributes, like color and shape. Observe their creations and ask them to state the rule aloud, for example, 'Red square, blue circle, red square, blue circle.'

Discussion Prompt

Have students work in pairs to create a growing pattern. After they have designed it, ask: 'How many items are in your first step? How many in your second? What is the rule that makes your pattern grow?' Then, prompt them to compare their pattern to their partner's: 'What is the same about your patterns? What is different?'

Peer Assessment

Students create a visual representation of their repeating or growing pattern on paper, including a written rule. They then exchange their work with a classmate. The classmate's task is to try and replicate the pattern based on the rule and then provide one specific piece of feedback, such as 'Your rule clearly explains how to make the next step.'

Frequently Asked Questions

How do you teach students to create their own patterns in 2nd year?

Start with familiar repeating patterns using two colors or shapes, then introduce growing ones by adding units. Provide materials like linking cubes or pattern cards. Guide with questions: 'What rule makes this repeat?' Have students swap and recreate partners' patterns to practice description and verification, building both creation and communication skills over 3-4 lessons.

What materials work best for pattern creation activities?

Use accessible items like colored beads, attribute blocks, buttons, or paper cutouts in varied shapes and colors. These allow tactile manipulation and sorting by attributes. Trays with limited options prevent overwhelm, while string or strips encourage linear patterns. Rotate materials weekly to maintain engagement and connect to classroom themes.

How does active learning help with creating patterns?

Active learning engages students through hands-on building, where they test rules immediately and adjust based on results. Pair replication ensures rules are clear, as partners expose ambiguities. Group galleries let students view diverse examples, sparking ideas and peer teaching. This approach makes pattern rules memorable, reduces errors, and boosts confidence in algebraic thinking.

What are common challenges when students describe pattern rules?

Students often use vague terms like 'it goes like this' instead of precise rules. Address by modeling descriptions first, then requiring written labels. Peer challenges during swaps highlight gaps, with prompts like 'How can I make the next part?' Repeated sharing builds precise language aligned with NCCA Communicating standards.