Evidence in Linear Patterns

Overview

In this penultimate unit lesson, students review how evidence has been collected across linear-pattern and algebra activities, then complete a short performance task similar to the summative assessment. The teacher models expectations, observes each student’s independent work, and records progress in Knowledge and Understanding, Mental Math, and Problem Solving.

Learning intentions

Students will:

• identify and describe the relationship in a linear pattern;
• represent one relationship with figures, a table, a graph, and an expression;
• use a rule to find an unknown term and solve a simple equation;
• check an answer and explain thinking using words, symbols, pictures, or voice.

Success criteria

• I can identify the relationship.
• I can use a rule.
• I can check my answer.
• I can explain my choice.

Curriculum links

• Patterns and Relations — demonstrate understanding of oral and written patterns and their corresponding relations.
• Patterns and Relations — construct and analyse tables and graphs from a relation.
• Patterns and Relations — evaluate expressions and solve simple linear equations.
• Mathematical processes — communicate, make connections, reason, estimate mentally, and solve problems.

Lesson structure (50 minutes)

1. 0–5 min · Engage and retrieve. Open the hook and retrieval slides with the question, “A pattern starts 4, 7, 10, 13. How could you convince someone that the next term is 16?” Students use mini-whiteboards to write or draw the rule, then explain it to a partner. Teacher listens for “add 3,” “constant increase,” and use of appropriate symbols.

2. 5–12 min · Clarify evidence and criteria. Display the success-criteria and evidence slides. Teacher explains that today’s work is practice evidence, not a surprise test, and introduces the three gradebook areas: Knowledge and Understanding (what the student knows and represents), Mental Math (efficient calculation or reasonable estimation), and Problem Solving (choosing a strategy, persevering, checking, and explaining). Students help sort sample responses into “secure,” “developing,” or “needs support,” justifying one decision.

3. 12–18 min · Model the performance task. Teacher builds or draws the first three terms of a pattern such as 3, 5, 7 tiles and thinks aloud: “The pattern grows by 2. The table shows term number and total. The rule is 2n + 1.” Model plotting ordered pairs, finding a later term, and checking by substitution. Refer to the sequence rule cards as a visual prompt, without giving students the task answer. Students identify where the model shows knowledge, mental calculation, and problem solving.

4. 18–35 min · Individual evidence task. Distribute the linear-pattern evidence task. Students complete the core task independently: build or draw the first three terms of a linear pattern; complete the table; plot ordered pairs; write an expression and rule for any term; solve a simple equation such as 3x + 2 = 14; and solve one real-world problem involving cost, distance, saving, or production. Directions are concrete: “Build or draw,” “Complete the table,” “Circle the rule,” “Show one check,” and “Explain your thinking.” Teacher conferences briefly with each student, recording prompting level and evidence in the rubric.

5. 35–43 min · Explain and check. Students choose one representation and explain how it connects to another. They complete the prompt, “I know my rule works because…” and check one calculation by substitution, a second method, or estimation. Students may give a spoken explanation to the teacher, use a voice recording, or ask the teacher to scribe. Teacher notes transfer between representations, vocabulary, symbols, persistence, and accuracy.

6. 43–50 min · Reflect and plan next steps. Revisit the reflection and plenary slides. Each student shares one success and one next step, using the success criteria. Teacher collects the worksheet and completes a brief evidence record: Knowledge and Understanding, Mental Math, Problem Solving, independence, and required accommodations. Students identify which skill they will practise before the summative performance task.

Resources

• the linear-pattern assessment deck
• the linear-pattern evidence task
• the sequence rule cards
• Linking cubes, square tiles, or counters
• Graph paper and pencils
• Mini-whiteboards and markers
• Calculator, when calculation is not the assessed outcome
• Three-level evidence rubric and teacher observation record

Assessment

• During retrieval, modelling, and conferencing, check whether students identify constant growth, use vocabulary such as term, rule, variable, and expression, and connect figures, tables, graphs, and symbols.
• Record separate progress indicators: Knowledge and Understanding: accurately represents and describes the relationship; Mental Math: calculates efficiently or estimates reasonably and explains the check; Problem Solving: selects a strategy, persists, transfers representations, and explains the solution.
• Collect the worksheet as formative evidence. Mark each area as secure, developing, or requiring targeted instruction, noting the level of prompting and any accommodation used.

Differentiation

• Provide a partially completed table, pre-drawn axes, a pattern with a smaller constant increase, and sentence starters: “The pattern changes by…,” “My rule is…,” and “I checked by…”. Allow manipulatives throughout.
• For students with a math disability or significant gaps, read directions aloud one step at a time, highlight key information, model one example, reduce the number of terms, and accept oral, drawn, or video explanations. Scribe when needed.
• Use dyslexia-friendly formatting: clear sans-serif font, large spacing, short numbered directions, uncluttered pages, high contrast, and no unnecessary copying. Pair spoken directions with visual examples.
• For students ready for challenge, ask them to create a different linear pattern with the same rule structure, prove the rule works for a distant term, or explain why a non-linear pattern does not fit the rule.