Grade: 5-6

Duration: 60 minutes

Class Size: 8 Students

Unit: Mastering Algebraic Foundations

Lesson 1 of 5

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Curriculum Alignment: Ontario Mathematics Curriculum 2023 (Grade 5-6)

Overall Expectation:

• Patterning and Algebra
  • Algebra Strand: Model and represent mathematical situations using expressions involving variables (Numbers, Grades 4–6, Patterning and Algebra, Strand C, Overall Expectations 3)**

Specific Expectations:

• Use concrete materials and diagrams to represent and determine the values of algebraic expressions, including simple monomials, in one variable (Grade 6, Strand C3.2)
• Describe, extend, and create repeating patterns and growing patterns involving whole numbers and variables (Grade 5, Patterning and Algebra, Strand C2.1)

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Learning Objectives

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

1. Identify and describe the components of algebra tiles: unit tiles (constants), x-tiles (variables), and x²-tiles (variable squared units).
2. Represent algebraic expressions visually using algebra tiles.
3. Understand how algebra tiles correspond to variables and constants in expressions.
4. Develop a conceptual understanding of using manipulatives to simplify and combine algebraic terms.

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Materials Needed

• Sets of physical algebra tiles for each student or pair (including unit squares, rectangular x-tiles, and large square x²-tiles)
• Whiteboard and markers
• Large visual images of algebra tiles projected or displayed
• Student math notebooks
• Chart paper with sample algebraic expressions
• Timer or stopwatch
• Sticky notes and coloured markers

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Lesson Structure

1. Engage (10 minutes) — Introduction to Visual Variables

• Hook: Display a simple expression on board: 3 + x + x², with a sketch of different tiles next to values. Ask students if they can guess what each tile might represent.
• Lead a brief discussion: “What do you think variable x means? Can we see it?”
• Connect to Real Life: Explain that algebra tiles help us see variables and constants, turning abstract letters into pictures we can move and touch.

Curriculum Connection: Builds foundational understanding for representing expressions concretely (Grade 6, Strand C3.2).

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2. Explore (20 minutes) — Hands-On Activity: Building Expressions

• Introduce Components:

  • Unit tile = 1 (constant)
  • x-tile = x (length)
  • x²-tile = x * x (area)

• Give each student/pair a complete set of algebra tiles.

• Call out expressions such as:

  • 2 + x
  • x + x²
  • 3 + 2x + x²

• Students use tiles to form these expressions physically on their desks.

• Encourage students to describe the parts as they build the expression aloud.

• Challenge: Show an expression on chart paper without variables (e.g. 2 + 3), then with variables (e.g. 1 + 2x). Have students build both and compare.

Curriculum Connection: Representing and modelling expressions concretely develops understanding of variables and constants (Grade 6).

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3. Explain (10 minutes) — Guided Discussion and Symbolic Representation

• Using student models on desks, show how tile placement corresponds to terms in expressions.

• On whiteboard, translate the tile groups into algebraic notation.

• Emphasise the difference between constants and variable terms, and introduce the notation for combining “like terms” visually.

• Ask:

  • How many unit tiles do you see?
  • How many x tiles?
  • Is there an x² tile?

• Write the algebraic expression together on the board.

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4. Elaborate (10 minutes) — Group Quick Matching Game

• Prepare sticky notes with different algebraic expressions and separate sticky notes with sets of algebra tile pictures/diagrams.

• In pairs, students match expressions to the correct tile representation.

• Rotate pairs and repeat with varied expressions increasing complexity (only up to single variables and constants).

• Prompt: What happens when you add more x tiles? Or remove one unit tile?

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5. Evaluate (5 minutes) — Exit Ticket

• Give students a simple drawing of algebra tiles representing an expression.
• Task: Write the algebraic expression shown by the tiles (for example, 3 + 2x).
• Collect these to monitor individual understanding for adjustment in next lessons.

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6. Consolidate (5 minutes) — Reflect and Connect

• Quick round-table sharing: Each student says one new thing they learned about algebra tiles.
• Teacher summarises key messages: Algebra tiles turn letters into pictures, helping us “see” math.

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Differentiation and Support

• For students needing support: Use larger, tactile tiles; provide one-on-one support during hands-on tasks.
• For advanced learners: Challenge them to create their own expressions with tiles and explain their meaning orally or in writing.

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Assessment for Learning

• Observation during hands-on activities and group game
• Student explanations and participation in discussions
• Exit ticket written response

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Teacher Reflection Notes (Post-Lesson)

• Did students successfully connect tiles to algebraic notation?
• Were all students engaged with the hands-on materials?
• Identify any misconceptions (e.g., misunderstanding x² tiles) for reteaching in Lesson 2.
• Plan for incorporating technology or virtual algebra tile apps next lessons for reinforcement.

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Additional Ideas to “Wow” Teachers

• Introduce a digital interactive whiteboard simulation of algebra tiles for those with access to tablets or computers.
• Create a classroom “Algebra Tile Gallery” where students post their creative expressions and explain them visually.
• Use real-world examples (e.g., area models of gardens, or tiled floors) to connect algebra tiles to spatial reasoning.

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End of Lesson 1 Plan – “Introduction to Algebra Tiles”