Mathematics · Year 7

Lesson 1

Write repeated multiplication in index notation and evaluate powers by identifying the base and the exponent.

⏱ 18 min · 11 questions

Lesson 2

Write whole numbers in expanded notation using powers of 10 and convert them back to standard form.

⏱ 17 min · 11 questions

Lesson 3

Connect perfect squares with their square roots and estimate the square roots of other numbers.

⏱ 18 min · 11 questions

Lesson 4

Write any whole number as a product of prime powers in index form using factor trees or repeated division.

⏱ 19 min · 11 questions

Lesson 5

Use prime factorisations to find the highest common factor and lowest common multiple and solve problems with them.

⏱ 20 min · 12 questions

Lesson 6

Round decimals to a sensible number of places and use estimation to check that answers are reasonable.

⏱ 18 min · 11 questions

Lesson 7

Use letters to stand for quantities in everyday formulas and substitute values to find an unknown.

⏱ 18 min · 11 questions

Lesson 8

Translate worded descriptions into algebraic expressions and read expressions back in words.

⏱ 18 min · 11 questions

Lesson 9

Evaluate algebraic expressions with brackets and powers by substituting values and applying the order of operations.

⏱ 18 min · 11 questions

Lesson 10

Use variables to express the commutative, associative and distributive laws and test whether statements are always true.

⏱ 19 min · 11 questions

Lesson 11

Use spreadsheet-style tables to change one variable in a formula while holding others constant and describe the effect.

⏱ 19 min · 11 questions

Lesson 12

Compare and order positive and negative integers on a number line in contexts such as temperature, elevation and money.

⏱ 17 min · 11 questions

Lesson 13

Add and subtract positive and negative integers, including subtracting a negative, using number lines and zero pairs.

⏱ 18 min · 11 questions

Lesson 14

Solve multi-step worded problems about temperatures, heights, lifts and money by writing them as integer calculations.

⏱ 18 min · 11 questions

Lesson 15

Place fractions, mixed numbers and decimals, including negative values, accurately on a number line.

⏱ 17 min · 10 questions

Lesson 16

Convert fractions, decimals and percentages into the same form so you can compare and order a mixed set of numbers.

⏱ 18 min · 10 questions

Lesson 17

Add and subtract fractions and mixed numbers whose denominators are not multiples of each other, using the lowest common denominator.

⏱ 19 min · 11 questions

Lesson 18

Multiply fractions and mixed numbers, cancelling common factors first to keep the numbers small.

⏱ 18 min · 11 questions

Lesson 19

Divide a fraction or mixed number by another fraction by multiplying by the reciprocal.

⏱ 18 min · 11 questions

Lesson 20

Write one quantity as a fraction and a percentage of another, converting to the same units first.

⏱ 17 min · 11 questions

Lesson 21

Share an amount in a given ratio by finding the total number of parts and the value of one part.

⏱ 17 min · 11 questions

Lesson 22

Solve ratio problems where one share is known by first finding the value of one part, then scaling up.

⏱ 18 min · 11 questions

Lesson 23

Solve one-step linear equations using inverse operations and check each solution by substituting it back in.

⏱ 16 min · 11 questions

Lesson 24

Solve two-step linear equations such as 3x + 5 = 26 by undoing operations in reverse order and checking by substitution.

⏱ 19 min · 11 questions

Lesson 25

Rearrange a parallelogram into a rectangle to explain why A = bh, then use the perpendicular height to find areas in suitable units.

⏱ 18 min · 10 questions

Lesson 26

Use A = ½bh for acute, right and obtuse triangles in any orientation, and work backwards to find a missing base or height.

⏱ 18 min · 10 questions

Lesson 27

Find the area of shapes built from rectangles, triangles and parallelograms by adding parts together or subtracting a part that is missing.

⏱ 20 min · 10 questions

Lesson 28

Find the volume of rectangular and triangular prisms using volume = area of cross-section × length.

⏱ 18 min · 10 questions

Lesson 29

Connect cubic units to millilitres and litres (1 cm³ = 1 mL, 1000 cm³ = 1 L, 1 m³ = 1000 L) to solve practical problems.

⏱ 18 min · 11 questions

Lesson 30

Discover π as the ratio of circumference to diameter and use C = πd or C = 2πr to find the distance around a circle.

⏱ 18 min · 11 questions

Lesson 31

Name the corresponding, alternate and co-interior angles made when a transversal crosses parallel lines, and state how they are related.

⏱ 18 min · 10 questions

Lesson 32

Find unknown angles in parallel-line diagrams step by step, giving a geometric reason for every step.

⏱ 20 min · 10 questions

Lesson 33

Use parallel lines to prove the angles of a triangle add to 180°, then find unknown interior and exterior angles.

⏱ 18 min · 10 questions

Lesson 34

Split a quadrilateral into two triangles to show its angles add to 360°, then find unknown angles.

⏱ 17 min · 10 questions

Lesson 35

Name triangles by their sides and their angles, and reason about which combinations are possible and which are impossible.

⏱ 17 min · 11 questions

Lesson 36

Classify quadrilaterals using their sides, angles and diagonals, and see how the special quadrilaterals form a family.

⏱ 20 min · 11 questions

Lesson 37

Draw and interpret the plan, front and side views of objects built from cubes, and use a plan with heights to count cubes.

⏱ 18 min · 9 questions

Lesson 38

Represent 3D objects made of cubes on isometric grid paper, and read isometric drawings to count cubes and picture other orientations.

⏱ 18 min · 9 questions

Lesson 39

Use coordinate rules to translate, reflect in the axes and rotate about the origin in all four quadrants.

⏱ 20 min · 10 questions

Lesson 40

Follow and design flowchart algorithms with yes/no decisions that sort polygons by their sides and angles.

⏱ 18 min · 10 questions

Lesson 41

Build a table of values from a rule or a growing pattern, and plot the points on the Cartesian plane, including negative values.

⏱ 18 min · 11 questions

Lesson 42

Read travel graphs and other real-life graphs to describe how one variable changes as another changes, including speeds and rest periods.

⏱ 18 min · 10 questions

Lesson 43

Tell discrete data from continuous data, and choose the mean, median or mode as the most useful measure of centre for a decision.

⏱ 18 min · 10 questions

Lesson 44

Describe the shape, centre and spread of a data display, identify outliers and explain how they affect the mean and the median.

⏱ 18 min · 10 questions

Lesson 45

Plan an investigation by posing a clear question, choosing variables and a fair collection method, and deciding how to display and summarise the data.

⏱ 18 min · 9 questions

Lesson 46

List the sample space of a single-stage event, write probabilities as fractions, decimals and percentages, and predict expected frequencies.

⏱ 18 min · 10 questions

Lesson 47

Calculate relative frequencies from experiments and simulations, and explain why they get closer to the theoretical probability as trials increase.

⏱ 18 min · 10 questions

Lesson 48

Solve practical money problems involving GST, discounts, best buys and ratio sharing, choosing the calculations and checking the results make sense.

⏱ 20 min · 10 questions