Integers on the Line
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.
NEED SOME LESSON PLANS
Overview
Today’s lesson develops Year 7/8 integer skills by using a number line to compare, order, and solve addition and subtraction problems with integers. It builds toward later work modelling changes in context (e.g., gains/losses).
Learning intentions
- Students will compare and order integers using less-than/greater-than language.
- Students will solve addition and subtraction problems involving integers.
- Students will justify their answers using a number line and correct integer language (sign, magnitude, difference).
- Students will check reasonableness by considering direction and size of change.
Success criteria
- I can say which integer is smaller or larger and write the correct inequality.
- I can use a number line to find the value of an integer sum or difference.
- I can explain whether my answer should be positive or negative and why.
- I can correct one mistake by re-checking my steps on the number line.
Curriculum links
- Number — AC9M7N07 compare, order and solve problems involving addition and subtraction of integers.
- Number — apply less-than/greater-than notation and language when comparing integers.
- Number — add and subtract integers using a number line and discuss magnitude/sign.
Lesson structure (45 minutes)
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0–5 min · Hook (everyday context). Teacher writes: “Temperature drops from -2°C to -7°C. How much did it drop?” and asks students to vote: did it change by +5 or -5? Students think-pair-share, then indicate their vote.
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5–12 min · Quick direct teach (comparing integers). Teacher models comparing -5 and +2 on a number line; explicitly links “negative is less than positive” to order on the line, then introduces notation: -5 < +2. Students copy a worked comparison and complete two oral prompts: -3? -6, +1? -4 (students respond with <, >, or =).
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12–22 min · Worked examples (add/subtract with number line). Teacher demonstrates two types:
- Example A: -2 + 5. Start at -2, move 5 right to land on +3.
- Example B: -6 − 3. Explain that subtracting 3 means move 3 left (to -9). Students record the two steps and underline the direction of movement (right for add positive; left for subtract positive).
- 22–34 min · Guided practice (mini-stations). Teacher divides class into 3 rapid stations (rotate every ~4 minutes), with a short teacher prompt at each station:
- Station 1: Inequalities (write < or >): -8 __ -3; +4 __ -1; -2 __ -2.
- Station 2: Add: -7 + 2; +6 + (-9); -3 + (-5).
- Station 3: Subtract: -4 − 6; +5 − 9; -10 − (-3). Students complete the task sheets using number lines; they must show at least one number line per station.
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34–42 min · Whole-class problem solving (explain reasoning). Teacher projects a problem: “A video game score changes from -12 to -5. What is the difference in score?” and asks students to connect sign + direction to the change (move right 7). Students explain using sentence frames: “Because we move ___, the change is +/− ___, so the difference is ___.”
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42–45 min · Exit ticket (assessment of understanding). Teacher collects:
- (1) Write an inequality: -6 __ -2
- (2) Calculate: -3 + 8
- (3) Calculate: -5 − 7 (include one number line sketch) Students complete independently.
Resources
- Printed number line worksheets (from at least -20 to +20).
- Inequality cards or a mini-whiteboard set for <, >, = responses.
- Station activity sheets (3 short sets per student).
- Projector/interactive display for worked examples.
- Sentence starters for explaining: “Starting at…, moving… land on…”
- Timer for rotations.
- Markers/pencils, rulers for drawing number lines neatly.
Assessment
- Teacher listens during Hook and Station 1 responses for common misconceptions (e.g., thinking negative + positive is always negative).
- During guided practice, check that students correctly interpret subtracting as moving left on the number line.
- Exit ticket confirms: inequality accuracy, correct sum/difference, and ability to justify with a number line/direction.
Differentiation
- Support: Provide a “direction reminder” strip (add positive → right; subtract positive → left) and partially drawn number lines for students who need scaffolding.
- Support for language: Offer word banks for sign (positive/negative), magnitude (size), difference (how far apart), and translate “−” into “move left”.
- Extension: Challenge students with mixed-sign ordering tasks, e.g., “Order: -9, +2, -1, +6” then write two inequalities and one subtraction check on a number line.
- EAL/SEN: Allow oral explanation before writing; use consistent sentence frames and model one example with the class before stations.
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