Distributive Property Models

Overview

In this 50-minute Grade 7 lesson, students connect multiplication of whole-number expressions to area models, arrays, and algebra tiles. Building on prior work with variables, terms, and simple linear expressions, students use concrete and pictorial representations before expanding expressions symbolically.

Learning intentions

Students will:

• Model an expression using a rectangular array or algebra tiles.
• Use the distributive property to split a rectangle into smaller parts.
• Expand simple expressions such as (3(x+2)) and (4(x+5)).
• Explain why an area model and its expanded expression are equivalent.
• Check an expression by substituting a simple value for the variable.

Success criteria

• I can build or draw a rectangle to represent an expression.
• I can split the rectangle into parts and label each area.
• I can write the matching expanded expression.
• I can explain how the model proves that both expressions are equivalent.

Curriculum links

• Patterns and Relations — oral and written patterns and their corresponding relations.
• Patterns and Relations — representing relations using tables, graphs, and symbolic forms.
• Variables and Equations — evaluating expressions when the variable is given a value.
• Mathematical processes — communication, connections, problem solving, reasoning, visualization, and mental mathematics and estimation.

Lesson structure (50 minutes)

1. 0–5 min · Attention hook and retrieval. Teacher displays a large rectangle labelled (x+3) on one side and (2) on the other using the opening array challenge. Ask, “How could we find the total area without treating (x+3) as one unknown block?” Students silently sketch an idea, then explain it to a partner; teacher briefly reviews variable, coefficient, term, and area.

2. 5–13 min · Explicit modelling. Teacher uses a large visual array and the algebra tiles linear expressions pack to build (3(x+2)): three rows each containing one (x)-tile and two unit tiles. Teacher records (3(x+2)=3x+6), connecting each part of the model to its area. Students build the same model, touch or point to each section, and repeat the explanation: “The 3 multiplies every term inside the brackets.”

3. 13–22 min · Guided Mathology activity. Teacher follows the selected Mathology hands-on task, pausing after each example to ask, “What are the two smaller rectangles?” and “What does each area represent?” Use the worked-example and activity-instruction slides to show (2(x+4)) and (5(x+1)). Students work in pairs, physically grouping tiles or drawing on grid paper, then record the factored and expanded forms. Rotate partners using a brief movement prompt so students change places without creating off-task transitions.

4. 22–28 min · Visual explanation and check. Teacher shows a short, pre-screened segment from the prepared distributive-property video search, stopping before the symbolic answer when possible. Students hold up or point to the matching parts of their own models. Teacher asks each student to explain one multiplication step; misconceptions are corrected immediately using the large array.

5. 28–40 min · Guided and independent practice. Teacher completes the first two questions on the distributive property area-model worksheet, including a simplified one-factor version such as (2(x+3)), then assigns the remaining questions at an appropriate level. Students draw or use tiles first, expand expressions, and check selected answers in Mathletics when finished. Suggested practice: (3(x+4)), (4(x+2)), (2(x+7)), and (5(x+3)). Students who are ready may expand (3(2x+1)) with teacher support.

6. 40–47 min · Evidence checkpoint. Teacher gives each student the expression (4(x+2)), or (2(x+5)) for students using the modified version. Each student independently draws or builds one area model, labels both smaller areas, writes the matching expanded expression, and explains the connection orally or in writing. Teacher records evidence for Knowledge and Understanding and Problem Solving.

7. 47–50 min · Plenary and exit response. Teacher returns to the opening question on the reflection and exit prompt slide. Students complete: “The expression ___ is equivalent to ___ because …” and rate confidence from 1 to 3. Collect responses to identify who needs reteaching during the next review session.

Resources

• the distributive property visual lesson deck
• the distributive property area-model worksheet
• the algebra tiles linear expressions pack
• Large coloured algebra tiles or magnetic tiles
• Large visual arrays and chart paper
• Grid paper, pencils, highlighters, and mini-whiteboards
• Mathology hands-on activity materials
• Student devices and Mathletics
• Pre-screened classroom video segment

Assessment

• Knowledge and Understanding: During modelling and guided practice, students identify the factors, terms, and areas in an array. Progress is shown when a student correctly matches a model such as (3(x+2)) with (3x+6), using accurate labels.
• Mental Math: Students mentally identify repeated groups and calculate unit areas or simple products such as (3\times2) and (4\times5). Progress is shown through quick responses, tile grouping, and reasonable checks before recording.
• Problem Solving: At the evidence checkpoint, students independently represent an expression, expand it, and justify equivalence. Progress is shown by a complete area model, matching expanded expression, and a logical explanation.
• Use student work and exit responses to update PowerSchool descriptors for Knowledge and Understanding, Mental Math, and Problem Solving.

Differentiation

• Provide large colour-coded arrays, labelled tiles, pre-drawn rectangles, grid paper, and a multiplication reference for students who need foundational support.
• Use the sentence frames “I see ___ groups of ___,” “The first area is ___,” and “The expression is equivalent because ___.”
• Offer the simplified one-factor pathway with expressions of the form (a(x+b)); reduce the number of questions while maintaining repeated modelling and immediate feedback.
• Support dyslexic learners with a clear sans-serif worksheet, enlarged print, generous spacing, minimal text, read-aloud instructions, colour coding, and the option to respond orally or point to a model.
• Pair students strategically and assign concrete materials or a recorder role to reduce distraction. Extend confident students by asking them to compare (3(x+4)) and (3x+12), then verify equivalence by substituting (x=2).