Linear Pattern Performance

Overview

In this 23rd lesson of the 26-lesson unit, students independently demonstrate how a linear pattern can be represented concretely, pictorially, numerically, graphically, and algebraically. The task consolidates prior work with tables of values, graphs, expressions, and pattern rules while giving the teacher an evidence checkpoint for reporting and next-step planning.

Learning intentions

Students will:

• Create and describe a linear pattern using tiles or another visual model.
• Record corresponding values in a table and plot them on a Cartesian plane.
• Write an algebraic expression for the pattern and explain what each part means.
• Solve and explain a related problem using their pattern.
• Reflect on their understanding, mathematical thinking, and independence.

Success criteria

• I can make a pattern that increases or decreases by a constant amount.
• I can show the same pattern with tiles, a table, a graph, and an expression.
• I can explain how my rule connects all four representations.
• I can solve a new problem using my rule and describe what I learned.

Curriculum links

• Patterns and Relations — oral and written patterns and their corresponding relations.
• Patterns and Relations — constructing tables of values, graphing relations, and drawing conclusions.
• Variables and Equations — representing and evaluating algebraic expressions.
• Mathematical processes — communication, connections, problem solving, reasoning, visualization, and mental mathematics and estimation.

Lesson structure (50 minutes)

1. 0–5 min · Reconnect and focus. Teacher displays the visual hook and task overview and asks, “How could one pattern tell a story in four different ways?” Students silently sketch or describe a familiar growing pattern, then share one possible rule with a partner.

2. 5–12 min · Review and model. Teacher briefly reviews a model such as “Figure 1 has 3 tiles, Figure 2 has 5 tiles, Figure 3 has 7 tiles,” explicitly connecting constant growth, a table, ordered pairs, a graph, and an expression such as (2n+1); play a short, teacher-selected review clip from the prepared linear-patterns search results if useful. Students identify the term number, constant difference, dependent value, and meaning of the expression, using the worked-example slides for visual reference.

3. 12–16 min · Explain the performance task. Teacher introduces the choice-based task and success criteria through the task instructions and visual rubric. Students choose one option: design a tile pattern, model a real-life linear situation, or use a teacher-provided starting pattern. Each student receives the linear-pattern performance task and reflection sheet and checks that their chosen pattern can be extended to at least five terms.

4. 16–35 min · Independent creation and practice. Teacher conferences briefly with each of the four students, prompting rather than completing the work; students use tiles or drawings to create the pattern, complete a table, plot integral-coordinate points, write and evaluate an expression, and solve the related problem on the performance task recording pages. Students who finish the core task may complete targeted Mathletics practice or select a relevant activity from the Mathology review menu, while the teacher records observations of accuracy, strategy use, and independence.

5. 35–44 min · Explain and submit. Teacher invites each student to give a brief oral or video explanation, using the visual rubric as a conference guide; students submit their written work and explain how the tile model, table, graph, expression, and answer are connected. The teacher may scribe, record the student, or accept a dyslexia-friendly typed, labelled, or audio submission. Students use the explanation prompts: “My rule is…”, “The constant change is…”, “This point means…”, and “I know my answer is reasonable because…”.

6. 44–50 min · Reflect and close. Teacher completes the evidence checkpoint and asks students to finish the reflection on the reflection and self-assessment page. Students rate their confidence, identify one successful representation and one next step, and answer: “What would change if the pattern started with a different number?” No new Friday instruction or assessment is assigned; the regular concept review is conducted by the EA.

Resources

• the linear-pattern review and performance-task deck
• the linear-pattern performance task and reflection sheet
• Algebra tiles, linking cubes, or square tiles
• Graph paper, pencils, rulers, coloured pencils, and erasers
• Prepared visual rubric for Knowledge and Understanding, Mental Math, Problem Solving, and independence
• Mathology linear-pattern review menu
• Mathletics access and headphones, as available
• Optional device for a short teacher-selected review video or oral/video submission

Assessment

• During conferencing, record evidence for Knowledge and Understanding: identifies constant change, completes a connected table and graph, writes an appropriate expression, and explains the meaning of the variable and constant.
• Record Mental Math and Estimation evidence: predicts or checks values, notices the constant difference, evaluates the expression accurately, and comments on whether the answer is reasonable.
• Record Problem Solving and independence evidence: selects or creates a viable pattern, applies the rule to a related problem, communicates a justification, persists with an appropriate scaffold, and completes the reflection. Use the submitted task, oral/video explanation, observations, and student reflection as the evidence checkpoint for PowerSchool descriptors.

Differentiation

• Provide a partially completed table, pre-drawn coordinate grid, colour-coded example, sentence starters, and a choice of starting patterns for students needing substantial support. Limit the number of terms while preserving the same mathematical ideas for students on modified programs.
• Use concrete tiles before drawings, then connect each representation one at a time. Check understanding after each step and provide a small visual checklist: tiles → table → points → graph → expression → problem.
• Offer enlarged templates, uncluttered dyslexia-friendly pages, a clear sans-serif font, extra spacing, reduced copying, oral directions, text-to-speech, scribing, speech-to-text, typed responses, or audio/video explanation.
• For distractible students, use a visible timer, a defined workspace, brief teacher check-ins, and a choice of two task contexts. Students who are ready may extend the pattern, justify why it is linear, or compare two expressions that represent the same relation.