Representing One Pattern

Overview

In this ninth lesson of the Linear Patterns and Algebra unit, students connect one linear pattern across a diagram, table, words, and an emerging algebraic rule. Concrete visual stations, guided notes, oral rehearsal, and independent practice strengthen retention and prepare students to describe how representations agree.

Learning intentions

Students will:

• represent a linear pattern with a diagram, table, words, and a rule;
• identify the constant change and starting value;
• translate accurately from one representation to another;
• use mathematical language to explain why representations show the same pattern.

Success criteria

• I can extend a pattern and identify how it changes.
• I can complete a table and describe the pattern in words.
• I can write an emerging rule using a variable, such as “multiply the position by ___, then add ___.”
• I can check that my diagram, table, words, and rule agree.

Curriculum links

• Patterns and Relations — understanding oral and written patterns and their corresponding relations.
• Patterns and Relations — constructing tables of values from relations, graphing values, and analysing patterns.
• Patterns and Relations — evaluating expressions when the value of a variable is given.
• Mathematical processes — communication, connections, reasoning, problem solving, visualization, and mental mathematics and estimation.

Lesson structure (50 minutes)

1. 0–5 min · Hook and retrieval. Display a growing pattern such as 3, 5, 7, 9 and ask, “How could four different descriptions prove this is the same pattern?” Open the hook and retrieval slides and have students silently predict the next two terms before sharing. Teacher records student language without correcting it immediately.

2. 5–13 min · Explicit teaching. Use a visual pattern, such as figures made from matchsticks or tiles, and model how to record figure number, number of objects, and constant change in the worked-example slides. Students complete the reduced-copy guided notes as the teacher models the diagram, table, words (“start at 2 and add 3 each time”), and emerging rule (“3n − 1”), with frequent oral rehearsal using the sentence frame: “When the position is __, the total is __ because __.”

3. 13–28 min · Visual station rotation. Set up three short stations for the four students; rotate after five minutes, with one student working independently when needed. At the diagram station, students build and extend a pattern using the sequence rule cards and sketch the next figure; at the table-and-words station, students complete a table and describe the change; at the media station, students view a brief teacher-selected clip from the provided linear-pattern search results and identify the representations shown. Station instructions and a timer appear in the station instruction slides. Teacher circulates, prompts “What stays the same?” and “What changes?”, and records misconceptions.

4. 28–38 min · Guided translation. Bring students together and model one shared example: a pattern begins with 4 objects and increases by 3 for each new position. Co-construct the diagram, table, words, and rule in the four-square representation organiser and display the corresponding prompts in the guided-practice slides. Students explain each connection to a partner, then solve a second example with teacher questioning rather than immediate answers.

5. 38–46 min · Independent practice. Students complete the remaining translation tasks on the independent pattern practice and then practise selected related questions in Mathletics. Each student must translate at least one pattern in two directions, such as table to words and rule to table. Teacher conferences briefly with each student, checking position number, constant change, accurate substitution, and reasonable answers.

6. 46–50 min · Evidence checkpoint and exit. Students complete the final four-square check on the four-square representation organiser, circling any representation that does not agree and correcting it. Use the plenary and reflection slides to ask, “How can one representation help you check another?” Students state one connection orally and submit the organiser.

Resources

• the complete representing-patterns slide deck
• the guided notes, four-square organiser, and practice worksheet
• the sequence rule cards
• Mathology visual pattern materials and manipulatives
• Mini-whiteboards, markers, linking cubes or tiles
• Student devices and headphones for a short teacher-selected video clip
• Mathletics access
• Timer and teacher observation checklist

Assessment

• Knowledge and Understanding: During modelling and station work, document whether each student identifies the starting value, constant change, position number, and relationship among the four representations. Progress is indicated by completing a table and explaining the rule with no more than one prompt.
• Mental Math: Ask students to continue sequences, identify the next term, and mentally use the constant change. Progress is indicated by correctly predicting at least two terms and explaining the additive change.
• Problem Solving: Assess the four-square organiser and independent practice. Progress is indicated by translating a pattern between at least two representations, checking agreement, and correcting an error with a clear explanation.
• Record observations using the PowerSchool descriptors for Knowledge and Understanding, Mental Math, and Problem Solving; retain the organiser as work evidence.

Differentiation

• Provide reduced-copy notes, enlarged high-contrast examples, colour-coded columns, tactile objects, and one representation at a time for students with dyslexia, a math disability, or foundational gaps. Read instructions aloud and allow oral responses before writing.
• Use sentence starters: “The pattern increases by…,” “The position tells me…,” and “I know the rule matches because….” Pair students strategically and assign brief roles to reduce distraction and off-topic attention.
• Offer frequent retrieval pauses, worked examples, a visible “first–next–check” routine, and a quiet station or headphones for students who need reduced stimulation.
• For students ready for challenge, ask them to create a pattern with a specified constant change, write an emerging rule, and prove it works for the first five positions.