Overarching Idea (OI)

Patterns in arithmetic sequences can be described, represented, and analysed using tables, coordinate grids, and simple algebraic expressions to solve problems involving missing terms and term positions.

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Guiding Question (GQ)

How can we use patterns in arithmetic sequences to predict terms, represent sequences visually, and solve problems?

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Curriculum Alignment

Alberta Mathematics Curriculum (Grade 5 - Number)

• Learning Outcome 5-5: Investigate, describe, and apply the concept of a term-to-term rule to solve problems involving patterns and sequences.
• Competency Focus: Reasoning and analyzing; Understanding and solving; Communicating

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Learning Objectives (LO)

By the end of this 60-minute lesson, students will be able to:

1. Relate terms to their position within an arithmetic sequence (K1)
2. Represent arithmetic sequences using tables and coordinate grids (U1)
3. Describe the linear relationship within arithmetic sequences in their own words (U1)
4. Write simple algebraic expressions to represent the nth term of an arithmetic sequence (S/P1)
5. Solve problems involving missing terms and identify term positions in sequences (S/P1)

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Lesson Breakdown

Materials Needed

• Whiteboard and markers
• Chart paper with arithmetic sequence examples
• Graph paper (1 per student)
• Sequence cards (term numbers and values)
• Printed worksheets (tables, coordinate grids, word problems)
• Sticky notes
• Document camera or projector

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Time and Activities

0 – 10 min: Engagement & Introduction

• Begin with a quick warm-up pattern game on the board: e.g., write 2, 5, 8, 11,... and ask students what the next term is and why.
• Ask: How do you know what number comes next? Collect responses to highlight “constant difference.”
• Introduce the term "Arithmetic Sequence" and use Alberta-specific language from curriculum: term-to-term rule.
• Display various simple sequences highlighting a constant increase/decrease.

Teacher notes: Emphasize relating each term number to its value (e.g., term 1 is 2, term 2 is 5, etc.).

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10 – 25 min: Exploration & Representation

• Hand out graph and lined paper.
• Activity 1 (Individual): Given the sequence 3, 6, 9, 12,... students create a table with term number (n) and term value (Tₙ).
• Activity 2 (Pairs): Plot these points on coordinate grids where x = term number, y = term value, e.g., (1,3), (2,6), (3,9),...
• Lead a class discussion connecting the visual linear pattern (straight line) with the sequences.

Prompt: What do you notice about how the points are arranged?

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25 – 40 min: Connection to Algebra & Problem Solving

• Model writing the algebraic expression for the nth term using the pattern: Tₙ = 3n (since term increases by 3 each time, starting from 3).
• Work through a guided example: Find the 10th term and Find the term when the value is 24.
• Distribute worksheet with missing term problems and term-to-term problems (e.g., fill in blanks, find term position from value).
• Circulate to assist and encourage use of tables, equations, graphs to solve.

Teacher notes: Scaffold writing expressions by relating to rule and first term explicitly.

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40 – 55 min: Creative Application & Reasoning

• In small groups, students design their own arithmetic sequence with a chosen term-to-term difference (positive or negative) and first term.
• Each group creates:
  • A table of the first 8 terms
  • A coordinate grid plot
  • The algebraic expression for their sequence
• Groups write one word problem involving their sequence for peers to solve.
• Groups exchange problems and solve each other's sequences, showing all work.

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55 – 60 min: Reflection and Assessment

• Exit Ticket: On sticky notes, students write:
  • One new thing they learned about arithmetic sequences
  • One question or difficulty they encountered
• Collect sticky notes, quickly review common points & clarify misconceptions if time permits.

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Assessment

• Formative: Observation during pair/ group activities, worksheet completion, and teacher questioning.
• Summative: Exit tickets assessing self-reflection and comprehension of key concepts.
• Optional Extension: Use mental math quizzes on term position and missing terms for fast finishers.

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Differentiation Strategies

• For learners needing support: Use concrete manipulatives such as counters or blocks to physically build sequences. Emphasize verbal explanation before writing expressions.
• For advanced students: Challenge with sequences involving subtraction or larger term-to-term differences and introduce sequences with a fractional increment. Encourage explaining the reasoning behind algebraic expressions.

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Teacher’s Tips

• Encourage students to use precise mathematical language: “term,” “term-to-term rule,” “constant difference,” “linear relationship.”
• Use real-world examples (like seats in rows, stairs) to relate sequences to familiar contexts for deeper understanding.
• Celebrate creativity in sequence creation—this promotes ownership and deeper engagement.

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References to Alberta Curriculum Terminology and Outcomes

• Number and Patterns: Develop understanding of number patterns and relations (Gr 5, 5-5).
• Representation: Use tables, graphs, and expressions to organise and communicate mathematical ideas.
• Problem Solving: Situate problems in real life to develop reasoning (use of patterns in problem contexts).

This lesson plan is designed to develop students’ conceptual understanding, communication skills, and algebraic thinking in line with Alberta’s standards and ensures a rich, engaging 60-minute learning experience.