Percent and Irrational Sprint
Maths • 45 • 25 students • Created with AI following Aligned with Australian Curriculum (F-10)
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Teaching Instructions
Lesson Sequence Planning Template
This template is for use during your group workshop to complete a 5–6 lesson sequence planning task. Work collaboratively to fill out each section using the Australian Curriculum and subject-appropriate resources. Be sure to save your work as you go in a group/shared document.
Group members:
Rachel Ho – 2403761
Tue Minh Nguyen -
Section 1: Curriculum Details
Learning Area/subject:
Mathematics
Year Level/Band: 8
Achievement Standard:
Content Descriptors 2–3: (cut and paste from AC)
cut and paste from AC then highlight/bold the sentence statements that are relevant to this sequence.
By the end of Year 8, students recognise irrational numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students solve problems involving the 4 operations with integers and positive rational numbers. They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts. Students apply algebraic properties to rearrange, expand and factorise linear expressions. They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically. Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context. They make and test conjectures involving linear relations using digital tools.
Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms. They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angle triangles. Students use formulas to solve problems involving the area and circumference of circles. They solve problems of duration involving 12- and 24-hour cycles across multiple time zones. Students use 3 dimensions to locate and describe position. They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity. Students apply the properties of quadrilaterals to solve problems.
They conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range. Students represent the possible combinations of 2 events with tables and diagrams, and determine related probabilities to solve practical problems. They conduct experiments and simulations using digital tools to determine related probabilities of compound events.
- Number – AC9M8N5
Use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model
- Measurement - AC9M8M05
Recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure
- Measurement – AC9M8M07
Use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model
- AC9M8N04
use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate
General Capabilities 1-2: (the icons for these will be shown under the content descriptions you have selected).
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Numeracy
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Digital Literacy
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Critical and Creative Thinking
Section 2: Lesson Sequence Overview (5–6 Lessons)
Lesson #
Lesson Title
Learning Intention
Activity Description
Authentic Resources
Lesson 1
Understand rational numbers and percentages
-> focus on Conceptual knowledge
We are learning to understand percentages and represent them as fractions and decimals.
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discounts definitions
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What is a percentage?
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Relationship between fractions, decimals and percentages
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Visual representations using hundred grids
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Some practical asm for students to practice
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e.g: Convert 25%....
Application
Questions:
What does "30% OFF" actually mean?
Which discount looks larger?
Warm-up (5 min)
Brainstorm: "Where do we see percentages in everyday life?"
Explicit teaching (15 min)
Meaning of percentages
Relationship between fractions, decimals and percentages
Visual models (100 grids, bar models)
Guided practice (15 min) Students convert between:
fractions
decimals
percentages
Application (20 min) Students explore real supermarket catalogues and identify percentage discounts.
Example:
20% OFF
50% OFF
75% OFF
Discuss what each discount actually means.
PowerPoint
Hundred grids
Fraction strips
Coles catalogue
Woolworths catalogue
Calculator
Lesson 2
Calculate percentages and discounts in Real life situations
-> apply Mathematical skills
We are learning to calculate percentage discounts and determine sale prices.
Teacher modelling Finding:
10%
25%
50%
Any percentage
Guided practice Students solve scaffolded examples.
Independent application
Students compare prices from:
Coles
Woolworths
Big W
Questions:
Which store is cheaper?
Which sale saves more money?
Students explain their reasoning.
Resources
Calculators
Supermarket catalogues
Google Sheets
Discount worksheet
Lesson 3
Understand rates and unit pricing
compare products using unit rates.
Teacher introduces:
What is a rate?
Cost per kg
Cost per litre
Worked examples.
i am looking for some more options of lessons plans
Overview
Students connect percentages to rational representations and use practical modelling to solve discount problems. The lesson also includes a short number-system focus (irrational numbers) to strengthen Year 8 “real number” understanding while keeping the main modelling work centred on percentages and rational numbers.
Learning intentions
- Students will interpret “% off” as a fraction and as a decimal (hundredths).
- Students will model and solve practical discount problems using efficient strategies.
- Students will recognise that some numbers (like square roots and (π)) are irrational and cannot be written exactly as terminating/recurring decimals.
- Students will communicate solutions in terms of the situation and check the reasonableness of their results.
Success criteria
- I can convert a percentage to a fraction over 100 and to a decimal.
- I can calculate a sale price from an original price and a percentage discount.
- I can explain which discount saves more and why, using my numbers and models.
- I can identify when a decimal is terminating/recurring and explain why an irrational number is different (e.g. (π)).
Curriculum links
- Number — AC9M8N05: Use mathematical modelling to solve practical problems involving rational numbers and percentages; formulate, calculate efficiently, interpret and review in context.
- Number — AC9M8N03: Recognise terminating and recurring decimals using digital tools as appropriate.
- Number — AC9M8N01: Recognise irrational numbers in applied contexts, including square roots and (π).
- Critical and creative thinking: reason about and verify strategies when interpreting discounts and checking results.
Lesson structure (45 minutes)
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0–5 min · Hook (supermarket prompt). Teacher shows two sale signs: “30% OFF” and “25% OFF” on the same item price, and asks: which saves more money and how do you know? Students answer with a quick estimate first, then justify with one sentence using “fraction/decimal” words.
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5–14 min · Direct teach (percent ↔ rational forms). Teacher explicitly models: “30% off” means paying 70%, and 70% = ( \frac{70}{100} ) = 0.70. Teacher demonstrates using a 100 grid/bar model and connects percentage to rational number reasoning. Students complete 3 quick conversions on mini-whiteboards:
- 25% as a decimal
- 40% as a fraction over 100
- “Pay 85%” written as a decimal
- 14–27 min · Guided practice (discount modelling). Teacher works through one example together (e.g. $48 with 25% off), showing an efficient strategy: discount amount = original × 0.25, then sale price = original − discount, and also the alternative “pay 75%”. Students then solve two similar problems in pairs on a worksheet:
- Item A: $36 at 30% off
- Item B: $55 at 20% off Students must show both a fraction/decimal link and a calculation, then circle which method they found most efficient.
- 27–35 min · Number focus (terminating/recurring vs irrational). Teacher introduces a short diagnostic:
- “What do you notice?” (1/4 = 0.25) (terminating), (1/3 = 0.333...) (recurring), (π \approx 3.141\ldots) (irrational). Teacher asks students to classify: “Terminating, recurring, or irrational?” for three values: ( \sqrt{2}), (0.125), and (3.141) (not claiming exactness—use “irrational in decimal expansion”). Students use a decision rule in their books: terminating/recurring relates to fractions with appropriate denominators; irrational numbers like ( \sqrt{2}) and (π) do not end or repeat.
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35–43 min · Application task (choose best offer, explain). Teacher presents a practical scenario: “Two offers for the same $80 headphones: Offer 1 is 25% off. Offer 2 is ‘pay $60’.” Students model each option, compare savings, and write a short explanation that uses percent/decimal reasoning and references which offer saves more and by how much.
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43–45 min · Exit ticket (reasonableness check). Students answer:
- Convert 18% to a decimal.
- If something costs $50, what is the approximate sale price with 18% off? (Exact value accepted if correct; students must show quick method.)
Resources
- Supermarket-style discount cards/signs (30% off, 25% off, etc.)
- Hundred grid or bar model handouts
- Mini-whiteboards and markers
- Worksheet with 2–3 conversion items and 2 guided discount problems
- Scenario card for the “two offers” comparison
- Calculator for checking only (where appropriate)
- Short classification set for terminating/recurring/irrational (printed)
- Digital timer (to keep the modelling pace)
Assessment
- Formative during hook and conversion checks (teacher listens for correct “% to 0.xx and /100” links).
- Guided practice observation: look for correct discount strategy and clear representation (fraction/decimal + calculation).
- Exit ticket: conversion accuracy and approximation/sale price method.
Differentiation
- Support: provide sentence starters (“25% off means pay ___%”, “0.25 of the price is the discount”, “I checked by comparing discount amounts”). Offer an extra worked example step on the worksheet margin.
- Support: allow use of a 100 grid for any student who struggles to convert percentages to decimals.
- Extension: give a challenge where discounts are not whole numbers (e.g. 12.5% off) and students choose between “multiply by (1 − p)” or “find discount then subtract”.
- EAL/SEN: keep scenarios simple, use consistent wording (“saves more money”, “sale price”, “original price”), and allow students to show reasoning with labelled models (not only written sentences).
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