Mathematics · Grade 3

Active learning ideas

Geometric Patterns

Active learning works for geometric patterns because students need to see, touch, and manipulate shapes to understand how attributes create sequences. When they physically sort, build, and extend patterns, they internalize the concept of a repeating unit more deeply than with passive observation.

• Ontario Curriculum Expectations
• Ontario Curriculum: Mathematics (2020), Grade 3, Number B1.1
• Ontario Curriculum: Mathematics (2020), Grade 3, Number B1.2
• Ontario Curriculum: Mathematics (2020), Grade 3, Number B1. Number Sense

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Shape Pattern Stations

Prepare stations with attribute blocks, tangrams, and colored tiles. At each, students build a starter pattern, identify the core unit, and extend it by four elements. Groups rotate every 10 minutes and record descriptions.

Analyze the repeating elements in a geometric pattern.

Facilitation Tip

During Shape Pattern Stations, circulate to ask guiding questions like, 'What do you notice about the order of these shapes?' to prompt student reasoning.

What to look for

Provide students with a partial geometric pattern (e.g., square, circle, square, circle, ?). Ask them to draw the next two shapes and write one sentence describing the pattern's rule.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Inside-Outside Circle
• 25 min · Pairs

Partner Pattern Challenges

Pairs receive cards showing partial patterns; one partner hides the next three shapes and describes the rule verbally. The other builds the extension, then they switch and check accuracy.

Design the next three elements in a complex geometric pattern.

Facilitation Tip

During Partner Pattern Challenges, provide sentence stems for descriptions, such as, 'The pattern repeats every _____ because _____.' to support precise language.

What to look for

Display a complex geometric pattern on the board. Ask students to hold up fingers to indicate the number of elements in the repeating unit. Then, ask them to verbally describe the rule for the pattern.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 03

• Gallery Walk
• 35 min · Whole Class

Class Pattern Gallery Walk

Students create complex patterns on chart paper using shapes and attributes. Display around the room; class walks, predicts extensions, and votes on best verbal descriptions.

Explain how a geometric pattern can be described using words.

Facilitation Tip

During the Class Pattern Gallery Walk, assign each student a specific pattern to analyze and present, ensuring everyone participates.

What to look for

Present two different geometric patterns. Ask students: 'How are these patterns similar? How are they different? What makes each pattern unique?' Encourage them to use vocabulary like 'repeating unit' and 'attribute'.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Inside-Outside Circle
• 30 min · Individual

Individual Pattern Journals

Each student designs a geometric pattern with at least five repeats, notes attributes of the core unit, extends it twice, and writes a rule description.

Analyze the repeating elements in a geometric pattern.

Facilitation Tip

During Individual Pattern Journals, model how to label each step of the pattern with both a drawing and a written rule.

What to look for

Provide students with a partial geometric pattern (e.g., square, circle, square, circle, ?). Ask them to draw the next two shapes and write one sentence describing the pattern's rule.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Start with concrete examples using manipulatives before moving to abstract representations. Avoid rushing to numbers; emphasize shape attributes first. Research shows that students benefit from both building patterns and breaking them to test their understanding. Give students time to verbalize their thinking, as this clarifies their reasoning.

Students will recognize the core unit of a pattern, extend it logically, and describe its rule with clear language. They will also compare patterns and identify similarities and differences in their attributes.

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Watch Out for These Misconceptions

• During Shape Pattern Stations, watch for students who assume patterns must involve numbers rather than shapes.

  Provide mixed sets of colored tiles and pattern blocks at each station. Ask students to sort them by color, size, and shape, then have them compare how sequences form with each attribute. Highlight that the rule is the same, whether counting objects or following shape properties.

• During Partner Pattern Challenges, watch for students who believe any random repeat counts as a pattern.

  Give partners two sets of different manipulatives. Have one student build a sequence, and the other must identify if it forms a true pattern by checking for a consistent core unit. If it fails, they rebuild together, discussing where the rule breaks.

• During Class Pattern Gallery Walk, watch for students who rely solely on drawings to describe patterns.

  Require each student to write a sentence below their drawn pattern describing the rule. If descriptions are vague, prompt them to specify the attribute, such as, 'The pattern repeats the red triangle and blue square every two shapes.'

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Methods used in this brief

• Stations Rotation
• Inside-Outside Circle
• Gallery Walk