The Big Catch

Overview

Lesson Title: The Big Catch: Analysing Patterns and Relationships
Unit: Algebraic Fishing Adventures (Lesson 5 of 8)
Year Level: Year 8
Duration: 45 minutes
Class Size: 1 student
Australian Curriculum Alignment:
Mathematics – Year 8
ACMNA193: Extend and apply the distributive law to the expansion of algebraic expressions
ACMNA194: Factorise algebraic expressions by identifying and using common factors
ACMNA190: Plot linear relationships on the Cartesian plane with and without the use of digital technologies
ACMNA191: Solve linear equations using algebraic and graphical techniques

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Learning Intentions

By the end of the lesson, the student will be able to:

• Identify and describe numerical patterns in real-world contexts (fishing data).
• Represent patterns using algebraic expressions and equations.
• Analyse these patterns to identify relationships and trends.
• Use discovered patterns to make predictions about future outcomes.

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Success Criteria

The student will:

• Accurately identify a pattern from a fishing data set.
• Construct an algebraic expression that models the pattern.
• Justify their mathematical reasoning using appropriate terminology.
• Use their algebraic model to make a logical prediction.

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Lesson Hook (5 minutes)

Activity:
Pose a scenario to set the context:

"Imagine you're a marine biologist studying fish populations along the east coast of Australia. You’ve been collecting data about how many fish are caught each day over time. Your job today is to predict how many fish might be caught tomorrow based on patterns in this data."

Visual Cue:
Provide the student with a laminated card showing a stylised map of Australian coastal regions with fictional data on average fish catches over a week. Introduce the term trend and relate it to what scientists use in the real world.

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Introduction to New Learning (10 minutes)

Mini-lesson:

• Review what algebraic expressions are and how they are used to represent real-life relationships.
• Specifically focus on numeric patterns becoming algebraic expressions, then equations.
• Show example:
  • Monday: 5 fish, Tuesday: 7, Wednesday: 9, Thursday: 11...
  • Ask: “What’s happening here?”
  • Guide towards recognition of common difference (+2), and express the pattern algebraically as:

    Fish caught on day n = 3 + 2n

Hands-on Note-Taking:
The student creates a visual fishing journal (a foldable or interactive notebook section), adding this pattern with drawings representing fish for each day.

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Guided Practice (10 minutes)

Activity: "Fishing Data Dive"

Provide the student with a fishing log containing fictional data of fish caught by a sustainable fishing crew over a fortnight. Example data points (simplified):

Day	Fish Caught
1	4
2	8
3	12
4	16
5	20

Task:

• Identify the pattern.
• Determine the rule (multiplicative reasoning - e.g., Fish = 4n).
• Write an algebraic expression.
• Predict how many fish will be caught on Day 8.

Teacher Prompts:

• “If this pattern continues, what would Day 10 look like?”
• “Can you explain how you know this using algebra?”

Differentiation Support:

• Use fish cut-outs and number lines for visual reinforcement if needed.
• Offer sentence stems like “The number of fish caught increases by...” or “I can model this using...”

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Independent Application (10 minutes)

Activity: "Forecast the Future Catch"

The student is given a new data set with a slightly irregular pattern – e.g., introduces a fixed starting number that’s not zero, or includes a repeating element.

Day	Fish Caught
1	10
2	13
3	16
4	19
5	22

Task:

• Determine the relationship.
• Write an algebraic expression for the number of fish caught on day n.
• Graph the relationship using Cartesian coordinates (on grid paper).
• Predict the number of fish on Day 10.

Focus Questions:

• “Can you graph this pattern?”
• “What does this tell you about what might happen over time?”

Encourage reflection on whether the pattern is always linear.

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Consolidation & Reflection (5 minutes)

Activity: "Fish Tales Wrap-Up"

The student completes a quick reflection prompt (write or speak):

“Today I discovered that patterns in data can be written using algebra. One thing I noticed was…, and I used algebra to…”

Then, draw a quick comic strip (2-block) showing themselves as a "data detective" predicting tomorrow’s catch using maths.

Teacher Checkpoint:
Use this opportunity to correct misconceptions or highlight strong reasoning skills.

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Extension / Homework (Optional)

Task:
Collect some kind of numerical pattern in the student’s own life (could be steps walked per day, number of glasses of water, minutes of video watched), identify a pattern over a few days, and write an algebraic expression to model it.

Prepare to share next lesson.

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Assessment Strategies

• Formative Assessment through think-alouds, whiteboarding during guided practice.
• Anecdotal Records: Note the student’s use of mathematical vocabulary and reasoning.
• Work Sample: Collect the algebraic expressions and graph created in the independent application.
• Exit Slip/Reflection to assess understanding and application of today’s concepts.

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Resources & Materials

• Fictional fishing data cards (laminated)
• Number lines and fish cut-outs
• Grid paper and coloured pencils
• Visual fishing-themed student journal or foldable
• Whiteboard and markers
• Fish Tales reflection sheet

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Teacher Notes

• Lean into the narrative of the unit – students love the idea of ‘fishing adventures’ and the high-seas context makes algebra feel purposeful.
• Encourage pattern spotting as a real-world “scientific skill.”
• Build anticipation for next lesson: "What happens when the pattern doesn’t make sense? What then?"

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Coming Up Next...

Lesson 6: Nets and Variables
Students will explore how constraints affect fish catch predictions using inequality statements and graphs.

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This lesson ensures that the student not only masters the mathematical content but also engages with real-world context and applies critical thinking skills. With a strong narrative thread and interactive resources, it inspires deeper interest in algebra through a uniquely Australian lens.