Linear Equations Assignment Year 8 Mathematics 2025

Linear Equations Assignment Year 8 Mathematics 2025

Linear equations are essential for understanding relationships between variables in mathematics. This assignment for Year 8 students focuses on modeling real-life situations using linear equations, particularly in contexts like event planning. Students will explore cost calculations involving fixed and variable expenses, using digital tools to graph and analyze their findings. The assignment encourages problem-solving and reasoning skills, allowing students to apply mathematical concepts to practical scenarios. Ideal for students looking to enhance their understanding of algebra and its applications in everyday life.

Key Points

  • Explores linear equations through real-world applications in event planning.
  • Encourages Year 8 students to use digital tools for graphing and analysis.
  • Focuses on cost calculations involving fixed and variable expenses.
  • Develops problem-solving and reasoning skills in mathematical contexts.
  • Gurtaj Sohi
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Mathematics Faculty
Year 8
Term 2: Linear Equations
the best we can be . . .
Name:
Form
Class:
Teacher:
Handed out:
Thursday, Week 4
Mode:
Assignment
Draft due:
Friday, Week 5
Final due:
Friday, Week 7
Context: Use linear equations to model the costing of an event
Content Descriptors
Number and Algebra:
• graph linear relations on the Cartesian plane using digital
tools where appropriate; solve linear equations and one-
variable inequalities using graphical and algebraic
techniques; verify solutions by substitution (AC9M8A02)
• Use mathematical modelling to solve applied problems
involving linear relations, including financial contexts;
formulate problems with linear functions, choosing a
representation; interpret and communicate solutions in
terms of the situation, reviewing the appropriateness of the
model (AC9M8A03)
• experiment with linear functions and relations using digital
tools, making and testing conjectures and generalising
emerging patterns (AC9M8A03)
Proficiencies:
• Understanding includes connecting
rules for linear relations with their
graphs
• Fluency includes calculating
accurately with simple decimals,
factorising and simplifying basic
algebraic expressions
• Problem-solving includes
formulating and modelling practical
situations
• Reasoning includes justifying the
result of a calculation or estimation
as reasonable
Cognitive Verbs: Knowledge Utilisation: Problem Solve
Explain
Demonstrate
Calculate
Predict
Apply
Identify
Compare
Determine
Sketch
Analyse
Design
Justify
Prove
Evaluate
Conjectures
Problem Solving
Modelling Task
(PSMT) Conditions
• 0.5 lesson – Reading and interpreting task
• Total of nine class lessons
• 1 lesson feedback
• Calculators allowed
• Show all working
Assessable Elements
Grade
Understanding and Fluency
Problem Solving and Reasoning
Context
Linear relationships are a way to understand and represent how things in real life are connected.
We use them when we have two sets of information, which we call 𝑥 and 𝑦 values.
By exploring these values, we can figure out how they relate to each other in a straight line. Once
we know the relationship, we can use it to solve math problems or answer questions about real-
life situations.
Linear relationships can be seen in various real-world examples:
• Tradespeople use a combination of fixed charge out fees and hourly rates to determine
their quotes for services.
• Travel agents calculate travel costs by considering a fixed price for a flight and a daily
accommodation rate.
• Companies like E-bikes and E-scooter (such as Lime Scooters) charge a fixed price to unlock
their devices and additional costs based on the duration of use.
• People planning parties need to factor in fixed charges for venue hire and catering costs
per person attending.
Task
In this PSMT, you will use digital tools to explore linear functions and their connection to party
planning. By experimenting with different variables like the cost per head and one-off/fixed
expenses, you will observe how these variables affect the total cost of the party.
Using the data from the investigation you will make conjectures (predictions), test hypotheses,
and identify patterns and use this knowledge to plan and justify an end of Year Class Party.
The goal is to use digital tools (Desmos) to investigate and determine a party option that includes
both the cost per head and one-off/fixed expenses that fit within your budget limitations and
criteria.
Your party options should meet the following criteria:
• Include at least one per-head cost, such as catering or activity fees like laser zone.
• Incorporate a one-off/fixed cost that remains the same regardless of the number of
attendees. For example, renting a boat, hall, bus, or arranging entertainment like a DJ,
band, face painting, jukebox, or fire twirlers.
• Cater for a class size of 25 students
• Must stay within a budget of $900
You will need to present your findings using tables, graphs, and algebraic formulas to make well-
informed choices based on comprehensive analysis and explain why your party option is a
preferred choice.
We Do
Your teacher has drafted a proposed End of Year Class Party at the Roller drome to reward all
the students and has selected the Discount Party option and has also included a photobooth.
Cost per head
One-off/fixed cost
Photobooth - $100
Write a worded statement to represent this
party option:
Write an algebraic formula for this party
option:
Using the data above complete the total cost for
the party
Using Desmos screen shot and insert the
graph for the party cost
Number of People
Attending
(x -variable)
Total Cost of Party ($)
(y-variable)
y = m x + c
0
0 x 22 + 100 =
1
1 x 22 + 100 =
2
2 x 22 + 100 =
3
3 x 22 + 100 =
4
4 x 22 + 100 =
5
5 x 22 + 100 =
10
10 x 22 + 100 =
25
25 x 22 + 100 =
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End of Document
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FAQs of Linear Equations Assignment Year 8 Mathematics 2025

What are the key concepts covered in the linear equations assignment?
The assignment covers essential concepts of linear equations, including how to model real-life scenarios such as budgeting for events. Students learn to graph linear functions and solve equations using both graphical and algebraic techniques. The focus is on understanding the relationship between variables, particularly in financial contexts, which is crucial for effective decision-making in real-world situations.
How does the assignment help students apply linear equations to real-life situations?
By engaging in tasks that involve planning an event, students apply linear equations to calculate total costs based on fixed and variable expenses. This practical application helps them understand how mathematical modeling can solve real problems, such as budgeting for a party. The assignment encourages students to think critically about how changes in costs affect overall expenses, reinforcing their understanding of linear relationships.
What skills will students develop through this linear equations assignment?
Students will develop critical problem-solving and reasoning skills as they work through the assignment. They will learn to formulate and test hypotheses based on their findings, analyze data using digital tools, and communicate their solutions effectively. Additionally, the assignment fosters mathematical fluency by requiring accurate calculations and the ability to interpret graphs, which are vital skills in both academic and real-world contexts.
What tools are recommended for completing the linear equations assignment?
Students are encouraged to use digital tools such as Desmos for graphing linear equations and analyzing data. These tools facilitate a deeper understanding of the relationship between variables by allowing students to visualize their findings. The use of technology enhances their learning experience and prepares them for more advanced mathematical concepts in the future.
How is the assignment structured for Year 8 students?
The assignment is structured to guide Year 8 students through a series of tasks that build on their understanding of linear equations. It includes reading and interpreting tasks, feedback sessions, and opportunities to experiment with different variables in real-world contexts. This structured approach ensures that students not only grasp theoretical concepts but also apply them practically, enhancing their overall learning experience.

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