Number Patterns Exploration

Overview

This 60-minute lesson engages 5th grade students in exploring number patterns through tables and writing corresponding equations. The activities align with Ontario Curriculum Expectations for Grade 5 Mathematics, Number Sense and Numeration, Patterns and Algebra (5NA1, 5NA2, 5NA3). Students will develop skills to recognize patterns, extend them, and express relationships algebraically using variables, fostering early algebraic thinking.

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Curriculum Connections

Ontario Curriculum – Grade 5 Mathematics Expectations:

• 5NA1: Identify, describe, extend, and create a variety of numeric and geometric patterns, using tables, charts, and diagrams.
• 5NA2: Represent growing patterns using variables and expressions.
• 5NA3: Model and solve problems involving numeric patterns (e.g., using equations to express relationships).
• Mathematical Processes: Reasoning and proving, connecting, representing, communicating

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Learning Goals

By the end of this lesson, students will be able to:

• Interpret number patterns presented in table format.
• Describe how the pattern changes from one row to the next.
• Write algebraic expressions or equations to represent number patterns using a variable.
• Explain their reasoning clearly using mathematical vocabulary.

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Materials Needed

• Whiteboard and markers
• Student individual mini whiteboards or lined paper
• Pre-prepared pattern tables printed or projected (e.g., input-output tables)
• Colourful pattern cards (optional)
• Sticky notes and markers
• Chart paper for group work

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Lesson Structure

1. Introduction (10 minutes)

• Warm-up Discussion:
  Begin by showing a simple numeric pattern (e.g., 2, 4, 6, 8...) and ask students to describe what they notice — what comes next and why?
  Prompt: "How does this pattern grow?"
• Introduce the concept that patterns can be shown in tables with input and output values.
• Display a simple input-output table:

Input (n)	Output
1	3
2	5
3	7
4	9

• Pose the question: "Can we find a rule that connects the input (n) to the output?"
• Guide the class to notice the pattern in output increasing by 2 each time.

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2. Guided Learning: Writing Equations From Tables (20 minutes)

• Step 1: Explore a Table Together
  Present a new table:

Input (n)	Output
1	4
2	7
3	10
4	13

• Work as a class to find the rule connecting input and output aloud.
  Encourage students to use language like “For each increase of 1 in n, the output increases by 3.”

• Introduce the variable ( n ) for input and algebraic expressions: "Output = 3 × ( n ) + 1" (or other discovered rules).

• Write the corresponding equation on the board and explain each part of the equation.

• Step 2: Paired Practice
  Students work in pairs with a unique table each. They will:

  • Identify the pattern in output values.
  • Extend the table for 2 more rows.
  • Write an equation expressing the output in terms of ( n ).

• Teacher circulates, asks probing questions, and supports students struggling to form the equations.

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3. Independent Application (15 minutes)

• Provide individual students with a new table (differentiated levels) and ask them to:

  • Describe the pattern in words.
  • Extend the table by adding 3 new rows.
  • Write an equation representing the rule.

• Students will write their work on mini whiteboards or paper.

• Include one "challenge" table that introduces a different operation such as subtraction or multiplication/division for advanced learners.

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4. Sharing and Reflecting (10 minutes)

• Invite students to share their equations and explain their thinking.

• Use chart paper to record some different equations and compare them.

• Ask reflective questions:

  • "What did you notice about the pattern?"
  • "How does the equation help you predict outputs?"
  • "Can one equation apply to different tables?"

• Highlight the connection between recognizing a pattern and representing it algebraically.

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5. Assessment and Consolidation (5 minutes)

• Conduct a quick formative assessment by presenting a new short table and asking students individually to write the equation connecting input and output.

• Collect their responses using sticky notes posted on the whiteboard or verbally explain.

• Provide immediate feedback, clarifying misunderstandings and reinforcing correct concepts.

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Differentiation Strategies

• For students needing extra support:
  Provide tables where outputs increase by a constant and allow use of counters/tiles to visualise the pattern.
• For advanced learners:
  Introduce patterns involving two-step rules (e.g., output = 2n + 3), or explore patterns involving non-linear relationships.

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Extensions and Home Connections

• Encourage students to create their own number pattern tables at home and write the rule as an equation.
• Suggest exploring patterns in daily life (e.g., stairs, calendar dates, rhythms) and bring examples to class.

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Teacher’s Notes

• Emphasize using correct mathematical vocabulary: input, output, pattern, rule, variable, equation.
• Encourage verbal explanations to strengthen mathematical communication.
• Use this lesson as a springboard for later topics, connecting to proportional reasoning and algebraic expressions.

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This lesson plan aligns tightly with Ontario’s expectations for Grade 5 Pattern and Algebra learning and builds foundational algebra skills by blending pattern recognition with numeric expressions that deepen mathematical reasoning in an engaging, collaborative way.