Integer Journeys
Maths • 45 • 25 students • Created with AI following Aligned with Australian Curriculum (F-10)
Free PDF · we'll email you a copy
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).
-
Numeracy
-
Digital Literacy
-
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.
-
discounts definitions
-
What is a percentage?
-
Relationship between fractions, decimals and percentages
-
Visual representations using hundred grids
-
Some practical asm for students to practice
-
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.
NEED 3-4 LESSON PLANS FOR YEAR 7
Overview
Students use number lines and integer language to compare, order, and solve addition and subtraction problems involving integers in realistic contexts (e.g., temperature changes or account balances). This lesson builds on students’ understanding of negative numbers by focusing on magnitude, sign, and efficient strategies.
Learning intentions
- Students will compare and order integers using less-than and greater-than reasoning.
- Students will represent integer addition and subtraction on a number line.
- Students will solve word problems involving addition and subtraction of integers and justify their steps.
- Students will check reasonableness of answers using the context (sign and magnitude).
Success criteria
- I can explain what a negative sign means in a situation (e.g., below zero).
- I can mark and compare integers on a number line using correct inequality statements.
- I can solve integer addition/subtraction problems using a number line or equivalent method.
- I can describe how my answer matches the context (e.g., “a drop means the result is negative”).
Curriculum links
- Number — AC9M7N07 (compare, order and solve problems involving addition and subtraction of integers; including using number line reasoning and inequality language such as less-than/greater-than).
- Numeracy (ACARA) — working with signs, magnitude, and interpreting solutions in context.
- Critical and Creative Thinking (ACARA) — choosing a strategy and justifying the reasonableness of results.
Lesson structure (45 minutes)
-
0–5 min · Hook (context + quick think). Teacher displays two brief scenarios: “Morning temperature is 3°C. It drops 8°C.” and “Your account starts at -$25. You earn $40.” Students write the likely sign of each answer (positive/negative) and share with a partner.
-
5–12 min · Direct teach (integer language + inequalities). Teacher models how to compare integers using the number line and the meaning of inequalities, e.g., -5 is less than +2, and shows how to write (−5) < (+2). Students complete 3 quick items: write < or > between pairs such as -7 and -2, and -1 and -6, then check with a partner.
-
12–23 min · Teaching focus (add/subtract on a number line). Teacher demonstrates two examples:
- (-3) + (-6): move left 6 from -3 to reach -9.
- (+5) − (+8): subtraction as “how far to the left” (equivalently, (+5) + (−8)) to reach -3. Students use their own number lines to model 4 similar problems (teacher selects):
- (+2) + (−7)
- (−4) + (+9)
- (−6) − (−3)
- (+8) − (−5)
- 23–33 min · Guided practice (word problems with justification). Teacher provides a structured template on the board: “Start → Operation → Direction on number line → Final answer → Context check (sign + magnitude).” Students work in pairs on 3 problems:
- Temperature: “It is -2°C. It rises 6°C. What is the new temperature?”
- Elevation: “The trail is 120 m above sea level. The point is 35 m below that. What is the elevation?”
- Finance: “You owe $18 (-$18). You pay $25 (+25). What is your new balance?” Teacher circulates, prompting students to say the direction (left/right) and explain sign.
-
33–41 min · Independent application (compare and order). Students receive a set of 10 integers (mixed signs). Task: order them from least to greatest and write two inequality statements correctly (e.g., “-4 < -1” and “0 < 3”). Teacher reminds: most negative is least; positives increase to the right. Students submit their ordered list and two inequalities.
-
41–45 min · Exit ticket (quick check). Individually students answer:
- (−9) + (−4) =?
- Which is greater: (−2) or (−7)?
- One-sentence context check for their addition answer (“Because the result is …, it makes sense that …”).
Resources
- Whiteboard and markers
- Printed number line handouts (e.g., -20 to +20) for modelling
- Integer word problem cards (temperature/elevation/finance)
- Inequality notation reminder strip: <, >, = plus example
- Student workbooks or loose-leaf
- Timer for transitions
- Optional: class digital poll tool for the hook (no requirement)
Assessment
- Formative during guided and independent tasks: listen for correct direction (left/right) and correct inequality language.
- Check student number line accuracy (landing point) and whether the written final answer matches the context sign.
- Exit ticket marking against: correct computation, correct inequality, and at least one justification statement linked to context.
Differentiation
- Support: provide sentence starters for justification (“I moved left because I added a negative…”; “The inequality shows that…”). Offer partially completed number lines for the first two guided problems.
- Support for EAL/SEN: allow verbal justification first, then students write a shortened solution (Start/Operation/Answer/Check).
- Extension: ask students to create their own word problem that results in a negative answer and swap with a partner to solve and verify using a number line.
- Challenge in ordering: include integers that test common misconceptions (e.g., -10 vs -2, 0 in the set).
Create Your Own AI Lesson Plan
Join thousands of teachers using Kuraplan AI to create personalized lesson plans that align with Aligned with Australian Curriculum (F-10) in minutes, not hours.
Created with Kuraplan AI
Generated using openai/gpt-5.4-nano
🌟 Trusted by 1000+ Schools
Join educators across Australia