Year 7
We've Got the Curriculum Covered
At TutorExel, our Year 7 Mathematics program builds a strong foundation in key skills. Lessons are tailored to your child’s pace and aligned with the Australian National Curriculum.
Tutoring is delivered through 1-on-1 or group online sessions, guided by expert tutors who focus on real progress.
TERM 1 – Number & Rational Foundations
S.No
Topic
What We Cover
1
Perfect Squares & Visual Patterns
Investigate squares of 1–20 using dot arrays and square grids. Explore patterns in square numbers, connections to area, and use of square notation. Compare growth between consecutive squares and recognise emerging numerical patterns.
2
Square Roots & Estimation
Explore the relationship between square numbers and their square roots. Estimate roots of non-perfect squares by locating numbers between two consecutive square numbers. Apply to contexts such as side lengths of square areas.
3
Prime Factors & Factor Trees
LeRepresent natural numbers as products of prime powers using factor trees, repeated division, and exponent notation. Investigate powers of 2, 3, and 5 and recognise numerical growth sequences.arn
4
LCM & HCF Using Prime Factorisation
Find lowest common multiples and highest common factors through comparison of prime factorizations. Apply to problems involving synchronisation, tiling patterns and grouping tasks.
5
Powers of 10 & Expanded Notation
Explore exponent notation for powers of 10 (10¹, 10², 10³…). Represent large numbers using place value expansions and scientific-style notations. Connect expanded notation with meaning in real contexts.
6
Rational Numbers on the Number Line
Represent fractions, mixed numbers and negative rational numbers on a number line. Use diagrams and number walls to explore equivalence, compare values and map intervals.
7
Fractions, Decimals, Percentages – Equivalence
Convert between fractions, decimals and percentages using diagrams, manipulatives and proportion reasoning. Reduce fractions using common divisors and justify equivalence visually and numerically.
8
Rounding & Estimation for Reasonableness
Round decimals to a required accuracy and determine appropriate rounding based on context. Use estimation to check reasonableness of calculations in real-life scenarios such as budgeting, material estimation and measurement.
9
Introduction to Integers & Ordering
Use number lines to compare and order integers, reinforcing vocabulary such as magnitude, sign and difference. Link integer ideas to elevation, temperature, bank balances and day-to-day contexts.
10
Term 1 Review & Assessment
Review square numbers, prime factors, rational numbers, estimation and integers. Apply skills to multi-step problems, reasoning tasks and term-end mastery checks.
TERM 2 – Number Operations, Ratios & Introductory Algebra
S.No
Topic
What We Cover
1
Adding & Subtracting Fractions (Conceptual Models)
Use fraction walls, rectangular arrays and diagrams to build conceptual understanding of adding/subtracting fractions. Explore common denominators through visual reasoning and decomposition of units into equal parts.
2
Fraction Operations in Real Contexts
Apply fraction addition/subtraction to recipes, measurement problems and scaling tasks. Use strategies with informal jottings, diagrams and digital tools to solve multi-step fraction problems efficiently.
3
Multiplying & Dividing Fractions
Develop strategies to multiply and divide fractions using arrays, algebra tiles and the commutative/associative properties. Explore situations such as finding 2/3 of 1/2 and modelling division through partitioning.
4
Operations with Decimals
Add, subtract, multiply and divide decimals using place-value reasoning, partitioning, and mental strategies. Solve problems in shopping, measurement, energy usage and everyday transactional contexts.
5
Percentages & Efficient Representations
Compare numerical forms (12.5%, 1/8, 0.125) to choose efficient strategies. Solve problems involving discounts, tax, increases/decreases and other financial contexts. Justify choice of representation.
6
Mathematical Modelling with Rational Numbers
Use additive and multiplicative reasoning in real-life modelling: profits/losses, credits/debits, altitude, recycling refunds and school data. Formulate models, choose representations and interpret results clearly.
7
Ratio Concepts: Part–Part & Part–Whole
Use diagrams, counters and manipulatives to interpret ratios. Connect ratios with fractions and solve problems involving comparison of quantities, colour-mixing, recipe scaling and proportional distribution.
8
Sharing & Applying Ratios
Divide quantities into ratios, solve capacity/mass/length ratio problems and apply ratios in construction, design and basic chemistry (mixture strengths). Justify solutions and interpret outcomes.
9
Algebraic Expressions & Translating Words to Symbols
Form algebraic expressions using constants, variables, operations and brackets. Translate verbal statements to algebraic form and recognise implied multiplication in terms like 3x and 4(y+2).
10
Using Formulas & Substitution
Substitute values into formulas from daily life (area, wages, densities). Evaluate unknowns in simple formula-based equations and link variables to measurable attributes in authentic contexts.
TERM 3 – Algebra, Equations, Graphs, Geometry & Measurement
S.No
Topic
What We Cover
1
Solving One-Variable Linear Equations (Concepts)
Explore the meaning of a solution by testing values through substitution. Use concrete materials and balance models to understand “keeping equations equal”. Introduce simple linear equations involving natural number solutions.
2
Solving Linear Equations (Algebraic Methods)
Apply inverse operations, backtracking and algebraic manipulation to solve equations such as 3x + 7 = 19. Verify by substitution and solve word problems requiring the formation of equations.
3
Understanding Graphs from Real Data
Interpret graphs representing speed, temperature, stock values and electricity usage. Describe relationships between variables, slopes, flat sections and changes. Tell the “story” behind each graph and link it to real contexts.
4
Creating Tables & Plotting Relations
Generate tables of values from linear functions and visually growing patterns. Plot ordered pairs on the Cartesian plane and describe the relationship between inputs and outputs. Identify linearity through equal differences.
5
Rules, Functions & Growing Patterns
Use diagrams and manipulatives to form linear growth patterns. Develop general rules using variables. Explore simple function machines using digital tools and predict values beyond the table.
6
Manipulating Formulas & Varying Variables
Use digital tools or spreadsheets to manipulate multi-variable formulas (e.g., volume = l×w×h). Investigate how changing one parameter affects the output. Conduct simple sensitivity analyses.
7
Area of Triangles, Rectangles & Parallelograms
Derive area formulas by decomposing and rearranging shapes. Understand perpendicular height in triangles and parallelograms. Solve real-world problems such as fabric cutting, garden design and material estimation.
8
Volume of Right Prisms
Build rectangular/triangular prisms using unit cubes to explore volume visually. Derive formulas for volume using base area × height. Apply to contexts such as tank capacity, buildings and packaging design.
9
Circles: Radius, Diameter & Circumference
Investigate the constant π through hands-on measurement with string and circular objects. Connect radius, diameter and circumference. Use formulas to solve measurement problems and discuss cultural significance of circles.
10
Angles, Parallel Lines & Transversals
Identify corresponding, alternate and co-interior angles when a transversal crosses parallel lines. Use dynamic geometry software to explore patterns. Apply angle sum of triangles (180°) and polygons to find unknown angles.
11
Mathematical Modelling With Ratios (Measurement Contexts)
Students use ratios to model real-world scenarios involving mixing, comparing quantities, and representing part–part or part–whole relations. They choose and justify appropriate models (fractions, ratio diagrams, bar models) and interpret solutions in context.
TERM 4 – Space, Statistics, Probability & Modelling
S.No
Topic
What We Cover
1
2D Representation of 3D Objects
Explore different 2D representations of objects including nets, isometric drawings and aerial views. Construct nets of cubes, prisms and pyramids; analyse which nets fold into valid 3D objects. Link to packaging, architecture and cultural mapping.
2
Drawing Views & Interpreting Isometric Diagrams
Use isometric and grid paper to draw front, top, side and back views of objects. Relate 2D sketches to 3D models and understand advantages/disadvantages of different representations in design and engineering.
3
Transformations: Translations & Reflections
Apply transformations on the Cartesian plane using digital tools. Perform translations and reflections, record coordinate changes and explore multiple ways to obtain the same transformation.
4
Rotations & Creating Transformation Patterns
Rotate shapes around a point on the Cartesian plane. Combine translations, reflections and rotations to produce artistic and mathematical patterns, including tessellations and cultural design motifs.
5
Classifying Shapes Using Algorithms
Design decision-tree algorithms to classify triangles based on sides and angles. Create flowcharts to sort quadrilaterals and polygons. Understand hierarchical relationships between kites, parallelograms, rectangles, squares and trapeziums.
6
Data Collection & Measures of Centre
Collect discrete and continuous numerical data through surveys or measurements. Calculate range, mean, median and mode. Explain how different measures describe data and how outliers influence results.
7
Stem–Leaf Plots, Dot Plots & Distribution Shapes
Create numerical data displays using software. Interpret symmetry, skewness and multimodal distributions. Compare mean and median across data sets and explain how graphical features reveal underlying trends.
8
Statistical Investigations (Plan, Collect, Analyse)
Conduct a full investigation: pose a question, gather data, represent information and interpret findings. Use real contexts such as reaction times, classroom energy usage or simple science experiments.
9
Probability, Sample Spaces & Predictions
Identify sample spaces for single-stage events (coins, dice, spinners). Assign probabilities, represent them on 0–1 scales and use them to predict relative frequencies. Link to real-world prediction models and AI/NLP frequency patterns.
10
Chance Experiments, Simulations & Term Review
Run repeated experiments and simulations using digital tools. Compare theoretical vs experimental probabilities. Understand the law of large numbers and investigate First Nations probability-based instructive games. Perform final term revision.
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