📐

Grade 7 Mathematics

Strengthen your mathematical reasoning and problem-solving.

Unit Outline

Number August – October 2025

Ratios & Proportions — Scaling, Sharing & Rates

We are learning to simplify ratios, share quantities, work with direct proportion, and use scale drawings.

Key Concept: Relationships

Related Concepts: Equivalence, Quantity

Global Context: Globalisation and Sustainability

"Understanding proportional relationships helps us compare, scale, and distribute quantities fairly."

Your Learning Journey

Simplifying Ratios Write ratios in their simplest form

Sharing in a Ratio Divide quantities into given ratios

Proportion Problems Solve problems using the unitary method

Direct Proportion Recognise and use y = kx relationships

Scale Drawings Use map scales and scale factors in real-world contexts

Assessment Criteria

All MYP Mathematics assessments are marked against four criteria (A–D), each scored 1–8. Here is what each level looks like.

Knowing and Understanding

Select and apply mathematical techniques to solve problems.

1–2

Attempts to use mathematical knowledge but with frequent errors.

3–4

Applies mathematical knowledge to solve routine problems. Some errors in complex situations.

5–6

Selects and applies appropriate mathematical knowledge to solve problems accurately.

7–8

Selects and applies mathematical knowledge with precision in both familiar and unfamiliar situations.

Investigating Patterns

Select and apply mathematical problem-solving techniques, describe patterns, and make generalisations.

1–2

Identifies simple patterns when given guidance.

3–4

Applies problem-solving techniques, describes patterns, and attempts a general rule.

5–6

Applies techniques to find patterns, describes and verifies general rules.

7–8

Discovers complex patterns, proves general rules, and justifies conclusions with mathematical reasoning.

Communicating

Use correct mathematical language, notation, diagrams, and conventions.

1–2

Shows some working. Uses basic mathematical language.

3–4

Shows working with some organisation. Uses some mathematical notation correctly.

5–6

Shows clear, well-organised working. Uses correct notation and diagrams consistently.

7–8

Communicates mathematical thinking with precision, clarity, and sophisticated use of notation.

Applying Mathematics in Real Life

Transfer mathematical knowledge to real-life situations and discuss the degree of accuracy.

1–2

Identifies a real-life context but struggles to apply mathematics to it.

3–4

Applies mathematics to a real-life situation and discusses the result.

5–6

Models a real-life situation mathematically, discusses accuracy, and draws conclusions.

7–8

Creates sophisticated mathematical models for real-life problems, critically evaluates accuracy and limitations.

Lesson Slides

1 Introduction to Ratio ⬇ Download 2 Equivalent Ratios & Simplifying ⬇ Download 3 Proportion Problems ⬇ Download 4 Direct Proportion ⬇ Download 5 Scale Drawings & Maps ⬇ Download 6 📚 Full Revision (all topics) ⬇ Download

Worksheets

📖 Revision Booklet ⬇ Download 📝 Introduction to Ratio ⬇ Download 📝 Equivalent Ratios ⬇ Download 📝 Proportion Problems ⬇ Download 📝 Direct Proportion ⬇ Download 📝 Scale Drawings ⬇ Download 💻 Full Revision Worksheet (Fillable) ⬇ Download 🤖 Upload → Get Instant Feedback 🤖 Open

Review Games

⚖️ Ratio & Proportion Review

14 questions · Multiple choice · Shuffled each time

↗ New Tab

Join Dots — Ratios & Proportions

14 questions · Multiple choice · Shuffled each time

↗ New Tab

Videos

🎬🎬 Proportional Reasoning (Math Antics)↗ 🎬🎬 Map Scales Explained (BBC Bitesize)↗ 🎬🎬 Scale Drawings (Math Antics)↗

Key Vocabulary

Essential terms for this unit. Use these to build your mathematical vocabulary.

Ratio & Proportion

⚖️ Ratio 比

A comparison of two quantities using a colon. e.g. 3:5 means '3 to 5'.

✂️ Simplify 化简

Divide both parts of a ratio by their HCF. e.g. 12:8 = 3:2.

🟰 Equivalent Ratio 等值比

Ratios with the same value. 2:3 = 4:6 = 6:9 (multiply both parts by the same number).

📊 Proportion 比例

A statement that two ratios are equal. Also: a part expressed as a fraction of the whole.

📈 Direct Proportion 正比例

As one quantity increases, the other increases at the same rate. y = kx.

🔑 Constant of Proportionality 比例常数

The fixed multiplier k in y = kx. Found by dividing y by x.

1️⃣ Unitary Method 归一法

Find the value of ONE unit first, then multiply. e.g. 5 costs $15 → 1 costs $3 → 8 costs $24.

📏 Scale 比例尺

The ratio between a drawing/model and real life. e.g. 1:50000 means 1 cm = 500 m.

🔍 Scale Factor 比例因子

The multiplier used to enlarge or reduce. Scale factor 3 means every length × 3.

⏱️ Rate 速率

A ratio comparing two quantities with different units. e.g. 60 km/h, $5/kg.

🛒 Best Buy 最优购买

Finding which option gives the most for the least money by comparing unit prices.

🚀 Extension Activities

Go beyond the textbook. Choose an activity that interests you and challenge yourself.

🍜

Recipe Scaler

Real-World Maths

Find a recipe for a Korean, Chinese, or German dish that serves 4 people. Use ratio to scale it up for 30 people (a class party). Calculate exact ingredient quantities. What challenges arise when scaling recipes?

🗼

Scale Model Challenge

Design & Calculation

Choose a famous building (Zifeng Tower, N Seoul Tower, Brandenburg Gate). Calculate a scale that would make a model fit on your desk. Build the model to that exact scale. Show all ratio calculations.

🗺️

Map Scale Navigator

Practical Maths

Using a map of Nanjing with a given scale, plan a walking tour of 5 landmarks. Calculate the real distance between each stop and total distance. How long would the tour take at 5 km/h walking speed?

Explore

Interactive simulations and tools. Use these to deepen your understanding.

🍕

Fraction & Ratio Visualizer

Mr Zocchi

Visualize ratios as fractions with instant operations.

⚖️

Proportion Playground

PhET Simulation

Explore proportional relationships visually. Change one quantity and watch the other scale.

🛒

Unit Rates

PhET Simulation

Compare prices at a market. Find the best buy using unit rates.

🔢

Desmos Scientific Calculator

Desmos

Use for ratio and proportion calculations.

↗ Open Tool

📊

Ratio Splitter

Mr Zocchi

Visualise sharing in a ratio with a bar model. Try splitting won, yuan, euros, or recipe ingredients.

Self-Quiz

Click a question to reveal the answer.

Simplify the ratio 20:12.

5:3 — divide both by HCF (4).

Share £45 in the ratio 2:7.

Total parts = 9. One part = £5. So £10 and £35.

5 books cost $30. How much do 8 books cost?

$48 — unit cost = $6, then 8 × $6 = $48.

y is directly proportional to x. When x=4, y=20. Find k.

k = y/x = 20/4 = 5. So y = 5x.

Using y = 5x, find y when x = 9.

y = 5 × 9 = 45.

A map scale is 1:25000. 6 cm on the map = ? metres in reality.

6 × 25000 = 150,000 cm = 1,500 m = 1.5 km.

Convert the ratio 7:3 to the form 1:n.

Divide both by 7: 1 : 3/7 = 1 : 0.43 (2 d.p.).

Increase 60 by 20%.

20% of 60 = 12. So 60 + 12 = 72.

Decrease 150 by 30%.

30% of 150 = 45. So 150 − 45 = 105.

A car uses 5L per 80km. How much fuel for 200km?

200 ÷ 80 = 2.5. So 5 × 2.5 = 12.5 litres.

Common mistake: 'Ratio 4:5 means 4/5 of the total.' Explain the error.

4:5 has 9 total parts. The first share is 4/9, NOT 4/5. The denominator is the total parts, not the second number.

Speed = distance ÷ time. A train covers 420km in 3.5 hours. Find the speed.

420 ÷ 3.5 = 120 km/h.

Explain the unitary method with an example.

Find the cost of 1 item first. e.g. 6 pens = $18 → 1 pen = $3 → 10 pens = $30.

Why must you multiply BOTH parts of a ratio by the same number to keep it equivalent?

Multiplying both parts preserves the relationship. Changing only one side makes it a different comparison.

Maths Toolkit

Useful tools and references for your mathematical work.

🔢 Desmos Scientific Calculator Open Tool ↗ ⚖️ Unit Rate Calculator Open Tool ↗

Unit Outline

Number October – December 2025

Number Systems — Integers, Powers & Standard Form

We are developing fluency with integer operations, powers and roots, prime factorisation, HCF/LCM, and standard form for very large and small numbers.

Key Concept: Form

Related Concepts: Representation, Simplification

Global Context: Scientific and Technical Innovation

"The form in which we represent numbers determines how efficiently we can work with them."

Your Learning Journey

Integer Operations Multiply and divide with negative numbers confidently

Powers & Roots Calculate squares, cubes, and their roots

Index Laws Apply the laws for multiplying and dividing powers

Prime Factorisation Express any number as a product of primes using factor trees

Standard Form Convert between ordinary numbers and standard form

Assessment Criteria

All MYP Mathematics assessments are marked against four criteria (A–D), each scored 1–8. Here is what each level looks like.

Knowing and Understanding

Select and apply mathematical techniques to solve problems.

1–2

Attempts to use mathematical knowledge but with frequent errors.

3–4

Applies mathematical knowledge to solve routine problems. Some errors in complex situations.

5–6

Selects and applies appropriate mathematical knowledge to solve problems accurately.

7–8

Selects and applies mathematical knowledge with precision in both familiar and unfamiliar situations.

Investigating Patterns

Select and apply mathematical problem-solving techniques, describe patterns, and make generalisations.

1–2

Identifies simple patterns when given guidance.

3–4

Applies problem-solving techniques, describes patterns, and attempts a general rule.

5–6

Applies techniques to find patterns, describes and verifies general rules.

7–8

Discovers complex patterns, proves general rules, and justifies conclusions with mathematical reasoning.

Communicating

Use correct mathematical language, notation, diagrams, and conventions.

1–2

Shows some working. Uses basic mathematical language.

3–4

Shows working with some organisation. Uses some mathematical notation correctly.

5–6

Shows clear, well-organised working. Uses correct notation and diagrams consistently.

7–8

Communicates mathematical thinking with precision, clarity, and sophisticated use of notation.

Applying Mathematics in Real Life

Transfer mathematical knowledge to real-life situations and discuss the degree of accuracy.

1–2

Identifies a real-life context but struggles to apply mathematics to it.

3–4

Applies mathematics to a real-life situation and discusses the result.

5–6

Models a real-life situation mathematically, discusses accuracy, and draws conclusions.

7–8

Creates sophisticated mathematical models for real-life problems, critically evaluates accuracy and limitations.

Lesson Slides

1 Integer Operations ⬇ Download 2 Powers & Roots ⬇ Download 3 Prime Factorisation ⬇ Download 4 HCF & LCM ⬇ Download 5 Standard Form ⬇ Download 6 📚 Full Revision (all topics) ⬇ Download

Worksheets

📖 Revision Booklet ⬇ Download 📝 Integer Operations ⬇ Download 📝 Powers & Roots ⬇ Download 📝 Prime Factorisation ⬇ Download 📝 HCF & LCM ⬇ Download 📝 Standard Form ⬇ Download 💻 Full Revision Worksheet (Fillable) ⬇ Download 🤖 Upload → Get Instant Feedback 🤖 Open

Review Games

🔢 Number Systems Review

15 questions · Multiple choice · Shuffled each time

↗ New Tab

Join Dots — Number Systems

15 questions · Multiple choice · Shuffled each time

↗ New Tab

Videos

🎬🎬 Prime Factorisation Explained (Math Antics)↗ 🎬🎬 Standard Form / Scientific Notation (Math Antics)↗ 🎬🎬 The Sieve of Eratosthenes (TED-Ed)↗ 🎬🎬 Powers of 10 — from Atoms to the Universe (Eames)↗

Key Vocabulary

Essential terms for this unit. Use these to build your mathematical vocabulary.

Integers & Powers

🔵 Integer 整数

Any positive or negative whole number, or zero.

📈 Power / Index 幂/指数

The small number showing repeated multiplication. In 5³, the power is 3.

🔢 Base 底数

The number being multiplied. In 5³, the base is 5.

√ Square Root 平方根

The number that multiplied by itself gives the original. √49 = 7.

∛ Cube Root 立方根

The number that multiplied by itself 3 times gives the original. ∛8 = 2.

✖️ Index Law — Multiply 指数乘法法则

Same base: ADD the indices. aᵐ × aⁿ = aᵐ⁺ⁿ.

➗ Index Law — Divide 指数除法法则

Same base: SUBTRACT the indices. aᵐ ÷ aⁿ = aᵐ⁻ⁿ.

0️⃣ Zero Index 零指数

Any non-zero number to the power 0 equals 1. a⁰ = 1.

Factors & Standard Form

🌳 Prime Factorisation 质因数分解

Writing a number as a product of prime factors. 60 = 2² × 3 × 5.

🌲 Factor Tree 因数树

A diagram used to break a number into prime factors by repeated division.

🔝 HCF 最大公因数

Highest Common Factor. From prime factorisations, take the LOWEST power of each shared prime.

🔄 LCM 最小公倍数

Lowest Common Multiple. From prime factorisations, take the HIGHEST power of each prime.

🔬 Standard Form 标准形式/科学记数法

A × 10ⁿ where 1 ≤ A < 10. Used for very large or very small numbers.

🚀 Extension Activities

Go beyond the textbook. Choose an activity that interests you and challenge yourself.

🔐

Prime Number Codebreaker

Puzzle Challenge

Create a secret code where each letter maps to a prime number (A=2, B=3, C=5...). Write a coded message for a classmate to crack. Research why prime numbers are used in real encryption (RSA).

📱

Powers of 2 in Technology

Research

Computer memory uses powers of 2 (1 KB = 2^10 bytes). Research how file sizes work. How many photos (3 MB each) fit on a 64 GB phone? Express all values as powers of 2 where possible.

Explore

Interactive simulations and tools. Use these to deepen your understanding.

🌳

Factor Trees

MathsBot

Build factor trees to find prime factorisations. Then use them for HCF and LCM.

↗ Open Tool

🔢

Desmos Scientific Calculator

Desmos

Practice powers, roots, and standard form calculations.

↗ Open Tool

📏

Number Line Explorer

MathsBot

Visualise integer operations on a number line.

↗ Open Tool

Self-Quiz

Click a question to reveal the answer.

Calculate: (−8) × (−4)

32 — negative × negative = positive.

Calculate: (−15) ÷ 3

−5 — negative ÷ positive = negative.

What is 2⁵?

32 — that's 2×2×2×2×2.

What is √196?

14 — because 14 × 14 = 196.

Simplify: 3⁴ × 3²

3⁶ = 729 — add indices: 4+2=6.

Simplify: 7⁸ ÷ 7⁵

7³ = 343 — subtract indices: 8−5=3.

What is 10⁰?

1 — any non-zero number to the power 0 equals 1.

Express 84 as a product of prime factors.

84 = 2² × 3 × 7.

Find the HCF of 36 and 48.

12 — 36=2²×3², 48=2⁴×3. HCF=2²×3=12 (lowest shared powers).

Find the LCM of 36 and 48.

144 — LCM=2⁴×3²=144 (highest powers).

Write 0.00045 in standard form.

4.5 × 10⁻⁴ — move decimal 4 places right.

Write 6.2 × 10⁵ as an ordinary number.

620,000 — move decimal 5 places right.

Common mistake: '2³ × 2⁴ = 2¹².' Explain the error.

You ADD indices when multiplying same base, not multiply them. 2³ × 2⁴ = 2⁷ = 128.

Common mistake: '√16 + √9 = √25 = 5.' Why is this wrong?

You can't add under separate roots. √16 + √9 = 4 + 3 = 7 (not √25 = 5).

Why is standard form useful?

It makes very large/small numbers readable and comparable. e.g. 0.000000003 m = 3 × 10⁻⁹ m is much clearer.

Maths Toolkit

Useful tools and references for your mathematical work.

🔢 Desmos Scientific Calculator Open Tool ↗ 🌳 Factor Tree Tool Open Tool ↗

Unit Outline

Geometry March – April 2026

Geometry — Angles, Shapes & Transformations

We are learning angle properties, classifying triangles and quadrilaterals, and performing transformations (reflection, rotation, translation).

Key Concept: Form

Related Concepts: Space, Measurement

Global Context: Personal and Cultural Expression

"The form and properties of shapes allow us to describe and transform the space around us."

Your Learning Journey

Basic Angle Facts Use angles on a line, at a point, and vertically opposite

Parallel Line Angles Identify and calculate alternate, corresponding, and co-interior angles

Polygon Angles Find interior and exterior angles of any polygon

Transformations Perform and describe reflections, rotations, and translations

Constructions Construct triangles and bisectors with compass and ruler

Assessment Criteria

All MYP Mathematics assessments are marked against four criteria (A–D), each scored 1–8. Here is what each level looks like.

Knowing and Understanding

Select and apply mathematical techniques to solve problems.

1–2

Attempts to use mathematical knowledge but with frequent errors.

3–4

Applies mathematical knowledge to solve routine problems. Some errors in complex situations.

5–6

Selects and applies appropriate mathematical knowledge to solve problems accurately.

7–8

Selects and applies mathematical knowledge with precision in both familiar and unfamiliar situations.

Investigating Patterns

Select and apply mathematical problem-solving techniques, describe patterns, and make generalisations.

1–2

Identifies simple patterns when given guidance.

3–4

Applies problem-solving techniques, describes patterns, and attempts a general rule.

5–6

Applies techniques to find patterns, describes and verifies general rules.

7–8

Discovers complex patterns, proves general rules, and justifies conclusions with mathematical reasoning.

Communicating

Use correct mathematical language, notation, diagrams, and conventions.

1–2

Shows some working. Uses basic mathematical language.

3–4

Shows working with some organisation. Uses some mathematical notation correctly.

5–6

Shows clear, well-organised working. Uses correct notation and diagrams consistently.

7–8

Communicates mathematical thinking with precision, clarity, and sophisticated use of notation.

Applying Mathematics in Real Life

Transfer mathematical knowledge to real-life situations and discuss the degree of accuracy.

1–2

Identifies a real-life context but struggles to apply mathematics to it.

3–4

Applies mathematics to a real-life situation and discusses the result.

5–6

Models a real-life situation mathematically, discusses accuracy, and draws conclusions.

7–8

Creates sophisticated mathematical models for real-life problems, critically evaluates accuracy and limitations.

Lesson Slides

1 Angle Properties ⬇ Download 2 Triangles & Quadrilaterals ⬇ Download 3 Transformations ⬇ Download 4 Coordinates & Midpoints ⬇ Download 5 Constructions & Loci ⬇ Download 6 📚 Full Revision (all topics) ⬇ Download

Worksheets

📖 Revision Booklet ⬇ Download 📝 Angle Properties ⬇ Download 📝 Triangles & Quadrilaterals ⬇ Download 📝 Transformations ⬇ Download 📝 Coordinates & Midpoints ⬇ Download 📝 Constructions ⬇ Download 💻 Full Revision Worksheet (Fillable) ⬇ Download 🤖 Upload → Get Instant Feedback 🤖 Open

Review Games

📐 Geometry Review

14 questions · Multiple choice · Shuffled each time

↗ New Tab

Join Dots — Geometry

14 questions · Multiple choice · Shuffled each time

↗ New Tab

Videos

🎬🎬 Angles in Parallel Lines (Math Antics)↗ 🎬🎬 Tessellations — How Shapes Tile (TED-Ed)↗ 🎬🎬 The Hidden Beauty of Symmetry (TED-Ed)↗ 🎬🎬 Transformations — Rotations and Reflections (Math Antics)↗

Key Vocabulary

Essential terms for this unit. Use these to build your mathematical vocabulary.

Angles

📐 Acute Angle 锐角

An angle less than 90°.

📐 Obtuse Angle 钝角

An angle between 90° and 180°.

🔄 Reflex Angle 优角

An angle greater than 180° but less than 360°.

✖️ Vertically Opposite 对顶角

Angles formed where two lines cross. They are always equal.

🇿 Alternate Angles 内错角

Z-shaped angles between parallel lines. They are equal.

🇨 Co-interior Angles 同旁内角

C-shaped angles between parallel lines. They add to 180°.

🇫 Corresponding Angles 同位角

F-shaped angles in matching positions at parallel lines. They are equal.

Shapes & Transformations

🔺 Isosceles Triangle 等腰三角形

A triangle with 2 equal sides and 2 equal base angles.

🔺 Equilateral Triangle 等边三角形

A triangle with all 3 sides and all 3 angles equal (each 60°).

➡️ Translation 平移

Sliding a shape without rotating or flipping it. Described by a vector.

🪞 Reflection 反射/对称

Flipping a shape across a mirror line. Each point is the same distance from the line.

🔄 Rotation 旋转

Turning a shape around a fixed point by a given angle and direction.

🟰 Congruent 全等

Exactly the same shape and size — identical when placed on top of each other.

🚀 Extension Activities

Go beyond the textbook. Choose an activity that interests you and challenge yourself.

🕌

Symmetry in Architecture

Photo & Analysis Project

Photograph or find images of 5 buildings from China, Korea, and Germany that show different types of symmetry. Identify reflection lines, rotational symmetry order, and any tessellations. Create an annotated gallery.

🎨

Islamic Geometry Artist

Creative Maths

Islamic geometric patterns use reflection, rotation, and tessellation. Follow a tutorial to create your own pattern using compass and ruler only. Identify all the transformations in your design.

🏙️

Nanjing Coordinate Treasure Hunt

Practical Challenge

Using a coordinate grid overlaid on a map of the NIS campus, create a treasure hunt with 10 clue locations given as coordinates. Include at least 2 clues that require reflecting or translating a point to find the next location.

Explore

Interactive simulations and tools. Use these to deepen your understanding.

📐

GeoGebra Geometry

GeoGebra

Draw shapes, measure angles, and perform transformations interactively.

↗ Open Tool

📏

Angle Tool

MathsBot

Practice measuring and drawing angles with a virtual protractor.

↗ Open Tool

📈

Desmos Graphing Calculator

Desmos

Plot coordinates and explore transformations on a graph.

↗ Open Tool

Self-Quiz

Click a question to reveal the answer.

Angles on a straight line add up to...

180°.

Angles around a point add up to...

360°.

Angles in a triangle add up to...

180°.

Angles in a quadrilateral add up to...

360° — it splits into 2 triangles (2 × 180°).

Two angles are co-interior. One is 125°. Find the other.

55° — co-interior angles add to 180°.

What are alternate angles?

Z-shaped angles between parallel lines — they are equal.

Reflect point (4, −2) in the x-axis.

(4, 2) — the x stays, the y changes sign.

Reflect point (4, −2) in the y-axis.

(−4, −2) — the x changes sign, the y stays.

Rotate (3, 1) by 180° about the origin.

(−3, −1) — both coordinates change sign.

What does 'congruent' mean?

Exactly the same shape and size.

Describe the translation from (2, 5) to (6, 3).

Vector (4, −2) — right 4, down 2.

An isosceles triangle has an angle of 50° at the top. Find the base angles.

Each base angle = (180° − 50°) ÷ 2 = 65°.

What is the interior angle sum of a hexagon (6 sides)?

(6−2) × 180° = 720°.

Common mistake: 'Alternate angles add to 180°.' Why is this wrong?

Alternate angles are EQUAL (not supplementary). It's co-interior angles that add to 180°.

Explain the difference between reflection and rotation.

Reflection flips across a line (creates a mirror image). Rotation turns around a point (orientation preserved).

Maths Toolkit

Useful tools and references for your mathematical work.

📈 Desmos Graphing Calculator Open Tool ↗ 📐 GeoGebra Geometry Open Tool ↗

Unit Outline

Algebra April – June 2026

Algebra — Expressions, Equations, Inequalities & Graphs

We are extending algebraic skills to include expanding brackets, solving multi-step equations and inequalities, finding nth term rules, and plotting linear graphs.

Key Concept: Logic

Related Concepts: Equivalence, Generalisation

Global Context: Identities and Relationships

"Logic allows us to generalise relationships, predict outcomes, and represent them graphically."

Your Learning Journey

Expanding Brackets Multiply out single brackets and simplify

Factorising Take out common factors from expressions

Solving Equations Solve multi-step equations including unknowns on both sides

Sequences & nth Term Find the rule for a linear sequence and use it to predict any term

Linear Graphs Plot y = mx + c and interpret gradient and intercept

Assessment Criteria

All MYP Mathematics assessments are marked against four criteria (A–D), each scored 1–8. Here is what each level looks like.

Knowing and Understanding

Select and apply mathematical techniques to solve problems.

1–2

Attempts to use mathematical knowledge but with frequent errors.

3–4

Applies mathematical knowledge to solve routine problems. Some errors in complex situations.

5–6

Selects and applies appropriate mathematical knowledge to solve problems accurately.

7–8

Selects and applies mathematical knowledge with precision in both familiar and unfamiliar situations.

Investigating Patterns

Select and apply mathematical problem-solving techniques, describe patterns, and make generalisations.

1–2

Identifies simple patterns when given guidance.

3–4

Applies problem-solving techniques, describes patterns, and attempts a general rule.

5–6

Applies techniques to find patterns, describes and verifies general rules.

7–8

Discovers complex patterns, proves general rules, and justifies conclusions with mathematical reasoning.

Communicating

Use correct mathematical language, notation, diagrams, and conventions.

1–2

Shows some working. Uses basic mathematical language.

3–4

Shows working with some organisation. Uses some mathematical notation correctly.

5–6

Shows clear, well-organised working. Uses correct notation and diagrams consistently.

7–8

Communicates mathematical thinking with precision, clarity, and sophisticated use of notation.

Applying Mathematics in Real Life

Transfer mathematical knowledge to real-life situations and discuss the degree of accuracy.

1–2

Identifies a real-life context but struggles to apply mathematics to it.

3–4

Applies mathematics to a real-life situation and discusses the result.

5–6

Models a real-life situation mathematically, discusses accuracy, and draws conclusions.

7–8

Creates sophisticated mathematical models for real-life problems, critically evaluates accuracy and limitations.

Lesson Slides

1 Expanding & Simplifying Expressions ⬇ Download 2 Solving Multi-Step Equations ⬇ Download 3 Inequalities ⬇ Download 4 Sequences & nth Term ⬇ Download 5 Plotting Linear Graphs ⬇ Download 6 📚 Full Revision (all topics) ⬇ Download

Worksheets

📖 Revision Booklet ⬇ Download 📝 Expressions ⬇ Download 📝 Equations ⬇ Download 📝 Inequalities ⬇ Download 📝 Sequences ⬇ Download 📝 Linear Graphs ⬇ Download 💻 Full Revision Worksheet (Fillable) ⬇ Download 🤖 Upload → Get Instant Feedback 🤖 Open

Review Games

🔤 Algebra Review

14 questions · Multiple choice · Shuffled each time

↗ New Tab

Join Dots — Algebra

14 questions · Multiple choice · Shuffled each time

↗ New Tab

Videos

🎬🎬 How Algebra Makes Life Easier (TED-Ed)↗ 🎬🎬 The Fibonacci Sequence — Nature's Code (TED-Ed)↗ 🎬🎬 Solving Equations (Math Antics)↗ 🎬🎬 Plotting Linear Graphs (Math Antics)↗

Key Vocabulary

Essential terms for this unit. Use these to build your mathematical vocabulary.

Expressions & Equations

📝 Expression 代数式

Numbers, variables, and operations combined. No equals sign. e.g. 3x + 5.

⚖️ Equation 方程

A mathematical statement with an equals sign. e.g. 3x + 5 = 20.

📤 Expand 展开

Multiply out brackets. e.g. 3(x + 4) = 3x + 12.

📥 Factorise 因式分解

The reverse of expanding — take out a common factor. e.g. 6x + 12 = 6(x + 2).

↔️ Inequality 不等式

Uses < > ≤ ≥ instead of =. Shows a range of values. e.g. x > 3.

🤝 Like Terms 同类项

Terms with the same variable and power. 5x and 3x are like terms. 5x and 5x² are not.

Sequences & Graphs

📊 Linear Sequence 线性数列

A sequence with a constant difference. e.g. 3, 7, 11, 15 (difference = 4).

🔮 nth Term 第n项

A formula to find any term directly. e.g. T(n) = 4n − 1.

📈 Gradient 斜率

The steepness of a line. m in y = mx + c. Rise ÷ Run.

🎯 y-intercept y轴截距

Where the line crosses the y-axis. c in y = mx + c.

📉 Linear Graph 线性图

A straight-line graph. Every linear equation (y = mx + c) gives a straight line.

📍 Coordinate 坐标

A pair (x, y) showing position on a grid. x = horizontal, y = vertical.

🚀 Extension Activities

Go beyond the textbook. Choose an activity that interests you and challenge yourself.

📱

App Pricing Analyser

Real-World Algebra

Compare subscription pricing for 3 apps (Spotify, Netflix, iQIYI). Write each as an algebraic formula (monthly cost × months + sign-up fee). Graph all three. At what point does the most expensive become the cheapest? Find the intersection.

🌡️

Temperature Converter App

Coding Challenge

Build a temperature converter in Scratch or Python that converts between °C, °F, and Kelvin. Use the substitution formulas. Add a feature that shows the current temperature in Nanjing, Seoul, and Berlin in all three units.

↗ Open Resource

🔢

Fibonacci in Nature

Investigation

The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13...) appears everywhere in nature. Find at least 5 examples in flowers, shells, or pinecones. Photograph them, count the spirals, and verify they match Fibonacci numbers.

Explore

Interactive simulations and tools. Use these to deepen your understanding.

⚖️

Equation Solver

Mr Zocchi

Solve equations with brackets and unknowns on both sides — step by step.

📈

Graph Plotter

Mr Zocchi

Plot y = mx + c lines. Adjust gradient and intercept. Compare multiple lines.

🔢

Sequence Finder

Mr Zocchi

Find the nth term for arithmetic, geometric, and quadratic sequences.

⚖️

Equality Explorer

PhET Simulation

Solve equations visually using a balance. See why the balance method works.

📈

Graphing Lines

PhET Simulation

Plot lines by changing m and c in y = mx + c. See how gradient and intercept affect the line.

📊

Desmos Graphing Calculator

Desmos

Type any equation to see its graph. Try y = 2x + 3, y = −x + 5, etc.

↗ Open Tool

⚖️

Equation Balance Scale

Mr Zocchi

Solve multi-step equations visually. Add, subtract, multiply, or divide both sides and watch the balance respond.

Self-Quiz

Click a question to reveal the answer.

Expand: 4(2x + 3)

8x + 12 — multiply each term inside by 4.

Expand and simplify: 3(x + 5) + 2(x − 1)

3x + 15 + 2x − 2 = 5x + 13.

Factorise: 10x + 15

5(2x + 3) — HCF of 10 and 15 is 5.

Solve: 5x − 3 = 2x + 12

3x = 15, so x = 5. (Collect x terms, then divide.)

Solve: 3(x + 4) = 21

3x + 12 = 21. 3x = 9. x = 3.

Solve the inequality: 2x + 1 > 9

2x > 8, so x > 4. (Same as equations, but keep the inequality sign.)

Find the nth term of: 5, 8, 11, 14, 17...

Common difference = 3. When n=1: 5 = 3(1)+2. So T(n) = 3n + 2.

What is the 20th term of T(n) = 3n + 2?

T(20) = 3(20) + 2 = 62.

In y = mx + c, what does m represent?

The gradient (steepness). Positive = uphill, negative = downhill.

In y = 2x − 3, what is the y-intercept?

−3 — the line crosses the y-axis at (0, −3).

Plot y = x + 1. Give two coordinates.

When x=0: y=1 → (0,1). When x=3: y=4 → (3,4). Join with a straight line.

Common mistake: 'Expand 2(x + 3) = 2x + 3.' Explain the error.

You must multiply BOTH terms: 2 × x = 2x AND 2 × 3 = 6. Answer: 2x + 6.

Common mistake: 'When you divide both sides of an inequality, flip the sign.' Is this always true?

Only when dividing by a NEGATIVE number. Dividing by a positive keeps the sign the same.

Explain the difference between an expression and an equation.

Expression = no equals sign (e.g. 3x + 5). Equation = has equals sign (e.g. 3x + 5 = 20).

A line passes through (0, 4) and has gradient 2. Write its equation.

y = 2x + 4 (gradient m=2, y-intercept c=4).

Maths Toolkit

Useful tools and references for your mathematical work.

📈 Desmos Graphing Calculator Open Tool ↗ 🟦 Algebra Tiles Open Tool ↗

Unit Outline

Statistics & Probability June – July 2026

Probability & Statistics — Data Analysis & Chance

We are learning to collect and analyse data using averages and frequency tables, represent data with statistical diagrams, and calculate probabilities for combined events.

Key Concept: Relationships

Related Concepts: Representation, Justification

Global Context: Globalisation and Sustainability

"Analysing relationships in data allows us to make evidence-based decisions."

Your Learning Journey

Frequency Tables Calculate averages from grouped and ungrouped frequency tables

Statistical Diagrams Draw and interpret pie charts, scatter graphs, and histograms

Probability Theory Calculate probabilities and use P(not A) = 1 − P(A)

Combined Events List outcomes using sample space diagrams and tree diagrams

Correlation Describe relationships between variables using scatter graphs

Assessment Criteria

All MYP Mathematics assessments are marked against four criteria (A–D), each scored 1–8. Here is what each level looks like.

Knowing and Understanding

Select and apply mathematical techniques to solve problems.

1–2

Attempts to use mathematical knowledge but with frequent errors.

3–4

Applies mathematical knowledge to solve routine problems. Some errors in complex situations.

5–6

Selects and applies appropriate mathematical knowledge to solve problems accurately.

7–8

Selects and applies mathematical knowledge with precision in both familiar and unfamiliar situations.

Investigating Patterns

Select and apply mathematical problem-solving techniques, describe patterns, and make generalisations.

1–2

Identifies simple patterns when given guidance.

3–4

Applies problem-solving techniques, describes patterns, and attempts a general rule.

5–6

Applies techniques to find patterns, describes and verifies general rules.

7–8

Discovers complex patterns, proves general rules, and justifies conclusions with mathematical reasoning.

Communicating

Use correct mathematical language, notation, diagrams, and conventions.

1–2

Shows some working. Uses basic mathematical language.

3–4

Shows working with some organisation. Uses some mathematical notation correctly.

5–6

Shows clear, well-organised working. Uses correct notation and diagrams consistently.

7–8

Communicates mathematical thinking with precision, clarity, and sophisticated use of notation.

Applying Mathematics in Real Life

Transfer mathematical knowledge to real-life situations and discuss the degree of accuracy.

1–2

Identifies a real-life context but struggles to apply mathematics to it.

3–4

Applies mathematics to a real-life situation and discusses the result.

5–6

Models a real-life situation mathematically, discusses accuracy, and draws conclusions.

7–8

Creates sophisticated mathematical models for real-life problems, critically evaluates accuracy and limitations.

Lesson Slides

1 Data Collection & Sampling ⬇ Download 2 Averages & Measures of Spread ⬇ Download 3 Statistical Diagrams ⬇ Download 4 Probability — Theory & Experiments ⬇ Download 5 Combined Events & Sample Spaces ⬇ Download 6 📚 Full Revision (all topics) ⬇ Download

Worksheets

📖 Revision Booklet ⬇ Download 📝 Data Collection ⬇ Download 📝 Averages & Spread ⬇ Download 📝 Statistical Diagrams ⬇ Download 📝 Probability ⬇ Download 📝 Combined Events ⬇ Download 💻 Full Revision Worksheet (Fillable) ⬇ Download 🤖 Upload → Get Instant Feedback 🤖 Open

Review Games

📊 Probability & Statistics Review

14 questions · Multiple choice · Shuffled each time

↗ New Tab

Join Dots — Probability & Statistics

14 questions · Multiple choice · Shuffled each time

↗ New Tab

Videos

🎬🎬 How Statistics Can Be Misleading (TED-Ed)↗ 🎬🎬 The Monty Hall Problem (TED-Ed)↗ 🎬🎬 Is Anything Truly Random? (TED-Ed)↗ 🎬🎬 Scatter Plots Explained (Math Antics)↗

Key Vocabulary

Essential terms for this unit. Use these to build your mathematical vocabulary.

Data & Averages

➗ Mean 平均数

Add all values, divide by count. Affected by outliers.

🎯 Median 中位数

The middle value when data is ordered. Not affected by outliers.

🏆 Mode 众数

The most common value. Can have more than one or none.

↔️ Range 极差

Highest − lowest. Measures spread.

📋 Frequency Table 频率表

A table showing how often each value or group of values occurs.

📊 Grouped Data 分组数据

Data collected into intervals (e.g. 0-10, 11-20). Cannot find exact mode or median.

📐 Mean from a Frequency Table 频率表的平均数

Total (value × frequency) ÷ total frequency.

Probability

🎲 Probability 概率

How likely an event is. Between 0 (impossible) and 1 (certain).

📊 Sample Space 样本空间

The set of all possible outcomes. Can be shown in a list, table, or tree diagram.

🔗 Independent Events 独立事件

One event doesn't affect another. P(A and B) = P(A) × P(B).

🚫 Mutually Exclusive 互斥事件

Events that cannot happen at the same time. P(A or B) = P(A) + P(B).

📈 Relative Frequency 相对频率

Experimental probability = number of successes ÷ number of trials.

📉 Correlation 相关性

The relationship between two variables on a scatter graph. Positive, negative, or none.

🚀 Extension Activities

Go beyond the textbook. Choose an activity that interests you and challenge yourself.

🎯

Sports Statistics Analyst

Data Project

Choose a sport popular in all three cultures (e.g. football, basketball, table tennis). Collect data from recent tournaments for Chinese, Korean, and German teams. Calculate averages, create comparison charts, and predict outcomes.

🎰

Design a Fair Carnival Game

Probability Design

Design a carnival game that uses probability. Calculate the theoretical probability of winning. Test it 100 times. Is your game fair? If you charged ¥5 to play and gave ¥15 prizes, would you make or lose money over 100 games?

Explore

Interactive simulations and tools. Use these to deepen your understanding.

🎲

Dice Simulator

MathsBot

Roll hundreds of dice and compare experimental vs theoretical probability.

↗ Open Tool

📊

Create a Graph

NCES

Build bar charts, pie charts, line graphs, and scatter plots from your data.

↗ Open Tool

🔢

Desmos Scientific Calculator

Desmos

Calculate averages, probabilities, and frequency table means.

↗ Open Tool

🎲

Probability Lab

Mr Zocchi

Simulate dice, coins, and two-dice sums. Compare experimental and theoretical probability with up to 1000 trials.

Self-Quiz

Click a question to reveal the answer.

Find the mean from a frequency table: Value 1(×4), 2(×6), 3(×8), 4(×2).

Total = 4+12+24+8 = 48. Count = 20. Mean = 48÷20 = 2.4.

Data set: 3, 5, 5, 7, 9, 12, 45. Which average best represents the data?

Median (7) — the mean (12.3) is pulled up by the outlier 45.

A die is rolled and a coin is flipped. List the sample space.

12 outcomes: 1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T.

P(A) = 0.4, P(B) = 0.3. Events are independent. Find P(A and B).

P(A and B) = 0.4 × 0.3 = 0.12.

P(rain) = 0.6. What is P(no rain)?

P(no rain) = 1 − 0.6 = 0.4.

Are 'rolling a 3' and 'rolling a 5' mutually exclusive?

Yes — you can't roll both on one die at the same time. P(3 or 5) = 1/6 + 1/6 = 2/6 = 1/3.

A scatter graph shows points going down from left to right. What type of correlation?

Negative correlation — as x increases, y decreases.

You flip a coin 200 times and get 112 heads. What is the relative frequency?

112/200 = 0.56 = 56%.

Why does experimental probability get closer to theoretical with more trials?

The Law of Large Numbers — random variation averages out with many trials.

What is the difference between discrete and continuous data?

Discrete = counted (number of pets). Continuous = measured (height, time).

When would you use a pie chart vs a bar chart?

Pie chart: showing proportions of a whole. Bar chart: comparing frequencies across categories.

Common mistake: 'After 3 heads, tails must be next.' Why is this the Gambler's Fallacy?

Each flip is independent. The coin has no memory. P(tails) = 0.5 every single time.

Calculate the range and interquartile range of: 2, 5, 8, 12, 15, 20, 25.

Range = 25−2 = 23. Q1=5, Q3=20. IQR = 20−5 = 15.

Why is the IQR sometimes more useful than the range?

The IQR ignores extreme values/outliers. It shows the spread of the middle 50% of data.

Maths Toolkit

Useful tools and references for your mathematical work.

🔢 Desmos Scientific Calculator Open Tool ↗ 📊 Create a Graph Open Tool ↗