Patterns and Relations

Overview

This opening lesson launches the 23-lesson unit by connecting visual, numerical, oral, and real-life patterns. Students use concrete materials and guided notes to describe what changes, identify a rule, and represent a relation in preparation for tables, graphs, expressions, and equations.

Learning intentions

• Students will describe patterns using words, numbers, diagrams, and actions.
• Students will identify the repeating or growing feature in a pattern.
• Students will continue simple numerical sequences using mental mathematics.
• Students will explain a pattern rule and connect it to a real-life situation.
• Students will begin distinguishing a pattern from its relation or rule.

Success criteria

• I can identify what changes and what stays the same.
• I can continue a visual or numerical pattern.
• I can describe a pattern rule in words.
• I can show my thinking with cubes, drawings, numbers, or an oral explanation.

Curriculum links

• Patterns and Relations — oral and written patterns and their corresponding relations.
• Patterns and Relations — tables of values, graphs, and conclusions from relations.
• Variables and Equations — representing expressions and equations in multiple ways.
• Mathematical processes — communication, connections, reasoning, visualization, problem solving, and mental mathematics and estimation.

Lesson structure (50 minutes)

1. 0–5 min · Engage with a pattern. Teacher displays the opening pattern challenge and briefly shows a suitable Numberock Grade 7 patterns video segment, pausing before the answer; students silently notice, sketch, or describe one pattern they see, then share with a partner. Ask: “Where do we see patterns outside mathematics?” Accept examples such as calendars, crops, building designs, music, clothing, and number sequences.

2. 5–12 min · Establish the learning focus. Teacher introduces the unit using the unit overview and learning intentions and distributes the visual guided-notes and pre-assessment sheet; students complete the first two prompts independently without concern about marks. Explain that today is a starting point: students may use pictures, cubes, numbers, or words, and the teacher is checking what support will be useful.

3. 12–22 min · Model pattern language. Teacher builds a growing pattern with linking cubes, recording the first four stages on the concrete-to-symbolic modelling slides and on the guided notes. Think aloud: “What changes? What stays the same? How could I tell someone the rule?” Students build each stage, compare stages, and use the sentence frame: “The pattern starts at ___ and ___ each time.” Model both a repeating pattern and a simple growing pattern, clarifying that a rule explains how the pattern is made.

4. 22–32 min · Collaborative pattern sort. Teacher gives each student a small set of colour-coded Mathology pattern cards and directs students to sort them using the sequence rule cards as optional visual prompts; students sort patterns into categories such as repeating, growing, or “not sure,” then justify one placement. Use a four-person structure: one student builds or points, one reads the card, one records, and one explains. Rotate roles once. Prompt rather than correct immediately: “What evidence from the next term supports your decision?”

5. 32–42 min · Independent pre-assessment and practice. Teacher directs students to complete the remaining items on the independent pattern sort and response tasks while circulating for individual evidence; students continue sequences, draw the next stage, identify what changes, and write or record a rule for one pattern. Include accessible options: reduced-number sequences, oral responses recorded by the teacher, or a cube model before writing. Do not reteach every item during this check; note misconceptions and strategies for future lessons.

6. 42–47 min · Share and connect representations. Teacher selects two contrasting examples and uses the discussion and representation slides to connect a picture, sequence, words, and a possible table of values; students explain how the representations describe the same relationship. Ask: “How do we know the rule works for every stage?” and “What information would a table or graph help us see?”

7. 47–50 min · Reflect and close. Teacher displays the closing reflection slide and asks students to complete the final reflection on the exit reflection box; students respond to “One pattern rule I can explain is…” and rate their confidence from 1 to 3. Collect all sheets and record brief observations against the three report-card evidence areas.

Resources

• the single lesson slide deck
• the visual guided-notes and pre-assessment sheet
• Mathology pattern cards
• Linking cubes
• Numberock Grade 7 patterns video segment
• Whiteboard, markers, and student pencils
• Colour-coded cards and highlighters
• Dyslexia-friendly large-print guided notes in a clear sans-serif font
• Optional audio/read-aloud directions

Assessment

• Knowledge and Understanding (K/U): Record whether each student identifies a repeating or growing pattern and describes what changes and stays the same. Progress is shown by moving from pointing or matching to an accurate verbal, pictorial, or written description.
• Mental Math (MM): Check whether students continue simple sequences accurately without relying on repeated counting. Progress is shown by identifying the change and predicting at least the next two terms.
• Problem Solving (PS): Note whether students explain and justify a pattern rule using cubes, drawings, numbers, or words. Progress is shown when the rule works for more than one stage and the student can connect two representations.
• Use the pre-assessment and confidence reflection to group students for the next lesson; record descriptive evidence in PowerSchool rather than a percentage grade.

Differentiation

• Provide colour-coded stages, arrows showing “what changes,” worked examples, and sentence starters: “The pattern repeats ___,” “Each time I ___,” and “I know because ___.”
• Read all directions aloud, allow students to explain orally or demonstrate with cubes, and provide large-print, uncluttered notes with a clear font and generous spacing.
• Offer reduced-number or two-stage options for students on modified programmes or with a mathematics disability; seat distractible students near materials and give them purposeful rotating roles.
• Extend ready students by asking them to create two different patterns with the same rule, or describe how their pattern could be represented in a table of values.