Building Expressions with Tiles

Overview

In this 50-minute lesson, Grade 7 students use algebra tiles to represent and interpret linear expressions such as (x+3) and (2x+4). The lesson builds from concrete models to symbolic notation and connects with prior learning about variables, terms, and numerical patterns.

Learning intentions

Students will:

• Represent linear expressions with algebra tiles.
• Connect a tile model to symbolic notation.
• Identify the variable, coefficient, and constant in an expression.
• Explain how different representations can show the same mathematical relationship.
• Practise communicating mathematical thinking using diagrams and equations.

Success criteria

• I can build an expression using (x)-tiles and unit tiles.
• I can write the matching expression for a tile model.
• I can identify the variable, coefficient, and constant.
• I can explain how I know my model and expression match.

Curriculum links

• Patterns and Relations — oral and written patterns and their corresponding relations.
• Patterns and Relations — representing relationships using tables, graphs, and symbolic forms.
• Variables and algebraic representations — evaluating and interpreting expressions.
• Mathematical processes — communication, connections, visualization, reasoning, and problem solving.

Lesson structure (50 minutes)

1. 0–5 min · Attention hook and retrieval. Display the opening visual and retrieval questions showing two groups of identical mystery tiles and ask, “How could we describe this without counting every tile?” Students briefly recall the meanings of variable, term, coefficient, and constant using guided notes or verbal responses. Record key ideas on the board: (x) represents an unknown quantity, a coefficient tells how many (x)-tiles, and a constant is a number without a variable.

2. 5–13 min · Explicit teaching with concrete models. Use the algebra-tile vocabulary and worked-example slides and physical tiles to model (x+3), then (2x+4). Think aloud: one (x)-tile represents (x), two (x)-tiles represent (2x), and four unit tiles represent (+4). Students build each example beside the teacher and say the expression aloud. Emphasize that the plus sign means the quantities are combined; it does not mean the tiles must be physically joined.

3. 13–18 min · Visual demonstration and check for understanding. Show a short, teacher-selected algebra-tiles writing-expressions video from the prepared classroom search result, pausing before each answer. Students use thumbs up/down or mini-whiteboards to predict the expression, then explain one choice to a partner. Revisit any misconception, especially confusing (2x) with (x+2).

4. 18–30 min · Guided Mathology practice. Complete the relevant hands-on Mathology activity with students in pairs. Distribute the Algebra Tiles: Linear Expressions Pack for additional labelled tile models and prompts. Call out an expression, such as (x+5), (3x+1), or (2x+6); students build it, sketch it, and write the symbolic expression on the Building Expressions with Tiles worksheet. Rotate roles: builder, recorder, checker, and explainer. With four students, provide immediate feedback after each model.

5. 30–42 min · Independent practice and targeted support. Students complete the remaining worksheet matching tasks, moving between tile models, drawings, and expressions. Then they practise selected questions in Mathletics. Confer individually: ask, “How many (x)-tiles do you see?” and “What number of unit tiles remains?” Students requiring reduced workload complete (x+2), (x+4), (2x+1), and (2x+3); other students complete expressions with up to four (x)-tiles and eight unit tiles.

6. 42–48 min · Evidence checkpoint. Give each student two prompts: build and label (x+3) and (2x+4), then write the matching expressions. Students circle the variable, underline the coefficient, and box the constant. Each student explains one model orally while the teacher records evidence of accurate construction, notation, and vocabulary.

7. 48–50 min · Exit reflection. Re-display the closing reflection slide. Students complete the final worksheet prompt: “A model has three (x)-tiles and five unit tiles. Write the expression and identify its coefficient and constant.” They add a confidence rating from 1–4 and hand in the worksheet.

Resources

• the complete Building Expressions with Tiles slide deck
• the Building Expressions with Tiles worksheet
• the Algebra Tiles: Linear Expressions Pack
• Physical algebra tiles or teacher-made tile sets
• Mini-whiteboards, markers, and erasers
• Mathology hands-on lesson materials
• Student devices and Mathletics
• Projector or interactive display
• Guided notes and vocabulary reference cards

Assessment

• Knowledge and Understanding: Observe whether students correctly identify variables, coefficients, constants, and terms. Progress is indicated when a student accurately builds (x+3) and (2x+4), labels the parts, and writes the matching notation.
• Mental Math: During retrieval and quick prediction checks, listen for efficient recognition of one, two, three, and four groups of (x), and accurate counting of unit tiles without relying on repeated recounting. Record whether the student responds accurately and explains the quantity represented.
• Problem Solving: Review worksheet matching tasks and the checkpoint. Progress is indicated when students select or construct a model, connect it to an expression, and justify why the representations match.
• Use brief PowerSchool-aligned notes under Knowledge and Understanding, Mental Math, and Problem Solving, including the level of prompting required.

Differentiation

• Provide prebuilt examples, colour-coded tiles, enlarged visual models, and sentence starters: “I see ___ (x)-tiles, so the coefficient is ___.”
• Allow students with dyslexia or reading difficulties to access uncluttered worksheets, large sans-serif print, increased spacing, read-aloud instructions, and oral responses. Pair symbols with pictures and avoid unnecessary text.
• For students on modified programmes or with significant gaps, use only one or two (x)-tiles and up to four unit tiles; provide a completed example and check after each step.
• Use tactile tiles, repeated modelling, and frequent retrieval. Seat distractible students near the demonstration area and assign purposeful roles such as builder or checker.
• Challenge confident students to build and write (3x+7), compare (x+5) and (2x+3), or create two different models and explain whether they are equivalent.