Foundations of Mathematical Thinking · Senior Infants · Shapes Around Us · Autumn Term

Patterns and Repeating Sequences

Identifying patterns in sequences, finding the rule for the nth term, and generating terms.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Algebra - A.1
• NCCA: Junior Cycle - Algebra - A.2

About This Topic

Patterns and repeating sequences build early mathematical reasoning for Senior Infants. Children identify simple repeating units in sequences like red, blue, red, blue, predict what comes next, and create their own patterns with blocks or shapes. They answer key questions such as "What is the part that keeps repeating?" through exploration in the Shapes Around Us unit. These activities develop attention to detail and prediction skills essential for math.

This topic connects to NCCA Junior Cycle Algebra standards A.1 and A.2 by introducing rule-based thinking and sequence generation at a foundational level. Students notice patterns in everyday contexts, like clothing designs or playground arrangements, which strengthens observation and generalization. Logical progression from copying to inventing patterns fosters confidence and problem-solving.

Active learning benefits this topic because concrete manipulatives let children physically manipulate and test sequences, making abstract rules visible and interactive. Collaborative building encourages verbalizing the repeating unit, while movement-based patterns engage kinesthetic learners, ensuring all children grasp concepts through multiple senses.

Key Questions

1. What comes next in this pattern , red, blue, red, blue, __?
2. Can you make your own repeating pattern with these blocks?
3. What is the part that keeps repeating in this pattern?

Learning Objectives

• Identify the repeating unit within a given sequence of shapes or colors.
• Generate a repeating pattern of at least three units based on a given rule.
• Predict the next two elements in a sequence with a clear repeating unit.
• Create a novel repeating pattern using specified manipulatives.

Before You Start

Sorting and Classifying Objects

Why: Students need to be able to group objects by attributes like color or shape to recognize elements that can form repeating patterns.

Recognizing Similarities and Differences

Why: Identifying the repeating unit requires students to notice what stays the same within a sequence.

Key Vocabulary

pattern	A sequence of items that repeats in a predictable way.
sequence	A set of things, numbers, or events that follow one another in a particular order.
repeating unit	The smallest part of a pattern that, when repeated, creates the whole sequence.
predict	To say or estimate that something will happen in the future, based on what you know.

Watch Out for These Misconceptions

Common Misconception

Patterns only involve numbers or counting.

What to Teach Instead

Children often limit patterns to numerals from number work. Use color and shape manipulatives in small group builds to expand their view. Discussing diverse examples helps them identify repeating units across contexts, building flexible thinking.

Common Misconception

Any group of similar items forms a pattern.

What to Teach Instead

Students may see random repeats as patterns without a rule. Hands-on extension activities where predictions fail for non-repeating sets clarify the need for consistency. Peer sharing of successful rules reinforces true pattern structure.

Common Misconception

The repeating unit changes based on where you start.

What to Teach Instead

Shifting the starting point confuses some children. Circle activities rotating pattern starts, with physical rebuilding, reveal the fixed core unit. Group predictions highlight invariance, deepening understanding through trial.

Active Learning Ideas

Block Building: Repeating Chains

Pairs receive colored linking blocks in a starting pattern like two red, one blue. They copy it, add three more units by predicting, then explain the repeating part to their partner. Switch patterns for variety.

20 min·Pairs

Bead Necklaces: Color Sequences

Small groups thread beads following a card pattern such as yellow, green, yellow, green. They extend the necklace independently, then share and critique each other's repeating units with the group.

30 min·Small Groups

Human Patterns: Class Line-Up

Whole class forms a line, each child adding to a pattern by holding a colored card or striking a pose like clap-jump. Predict the next child's action before they join, discussing the core repeat afterward.

15 min·Whole Class

Clap and Draw: Sound Patterns

Individually, children listen to a teacher-clapped rhythm like clap-clap-stomp, draw symbols for it, then continue the sequence on paper. Pairs compare drawings and test extensions by clapping.

25 min·Individual

Real-World Connections

• Textile designers create fabric patterns by repeating motifs, like the classic polka dot or floral prints seen on clothing and home furnishings.
• Architects and builders use repeating patterns in tiling floors or arranging bricks to create visually appealing and structurally sound designs for buildings and public spaces.

Assessment Ideas

Quick Check

Present students with a sequence of 5-7 objects (e.g., colored blocks, shape cutouts) with a clear repeating unit. Ask: 'What comes next?' and 'What is the part that keeps repeating?' Observe their responses and ability to correctly identify the next element and the repeating unit.

Exit Ticket

Give each student a small bag of 3-4 different manipulatives (e.g., buttons, small toys). Ask them to create a pattern with at least two repetitions of a repeating unit and draw it on a provided worksheet. Collect the drawings to assess their ability to generate a pattern.

Discussion Prompt

Show a picture of a tiled floor or a patterned wallpaper. Ask: 'Can you find a part that repeats over and over again?' 'How do you know it's a pattern?' Facilitate a brief class discussion, encouraging students to point out the repeating unit and explain their reasoning.

Frequently Asked Questions

What hands-on activities teach repeating patterns to Senior Infants?

Use blocks, beads, and body movements for pattern building. Pairs extend block chains, small groups thread bead sequences, and whole class line-ups predict human patterns. These make rules tangible, encourage talk, and link to Shapes Around Us, aligning with NCCA algebra foundations.

How to address misconceptions in pattern sequences?

Common errors include thinking patterns are numbers only or lack fixed rules. Counter with diverse manipulatives and prediction tests in groups. Children rebuild shifted patterns to see core units persist, using peer discussion to refine ideas and build accurate models.

How can active learning help students understand patterns?

Active approaches with manipulatives let children touch, build, and test sequences, turning abstract repeats into concrete experiences. Collaborative extensions prompt explaining rules, while movement patterns engage bodies and voices. This multisensory method ensures retention, addresses varied learning styles, and sparks joy in discovery for Senior Infants.

How to assess pattern recognition in young learners?

Observe predictions during extensions, like "What comes next in red-blue-red-blue?" Note if they identify repeating units in creations. Use quick shares where children describe their patterns to peers. Rubrics track copying, extending, inventing, providing clear NCCA-aligned progress data.