📐

Grade 6 Mathematics

Build your mathematical reasoning and problem-solving skills.

Unit Outline

Number August – October 2025

Number Sense — Place Value, Operations & Integers

We are building fluency with whole numbers, negative numbers, and the order of operations — the foundation for all future mathematics.

Key Concept: Form

Related Concepts: Representation, Simplification

Global Context: Identities and Relationships

"The form in which we represent numbers determines how we understand and work with them."

Your Learning Journey

Place Value Read, write, and compare numbers up to millions

Rounding & Estimation Round numbers and estimate calculations

BIDMAS Apply the correct order of operations

Negative Numbers Add, subtract, and compare integers on a number line

Factors, Multiples & Primes Find HCF, LCM, and identify prime numbers

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 Place Value & Number Systems ⬇ Download 2 Rounding & Estimation ⬇ Download 3 Order of Operations (BIDMAS) ⬇ Download 4 Negative Numbers ⬇ Download 5 Factors, Multiples & Primes ⬇ Download 6 📚 Full Revision (all topics) ⬇ Download

Worksheets

📖 Revision Booklet ⬇ Download 📝 Place Value ⬇ Download 📝 Rounding & Estimation ⬇ Download 📝 BIDMAS ⬇ Download 📝 Negative Numbers ⬇ Download 📝 Factors & Multiples ⬇ Download 💻 Full Revision Worksheet (Fillable) ⬇ Download 🤖 Upload Completed Worksheet → Get Instant Feedback 🤖 Open

Review Games

🔢 Number Sense Review

15 questions · Multiple choice · Shuffled each time

↗ New Tab

Join Dots — Number Sense

15 questions · Multiple choice · Shuffled each time

↗ New Tab

Videos

🎬🎬 How Big Is a Googol? (TED-Ed)↗ 🎬🎬 Why Do We Use BIDMAS? (Numberphile)↗ 🎬🎬 A Brief History of Negative Numbers (TED-Ed)↗ 🎬🎬 The Sieve of Eratosthenes (TED-Ed)↗

Key Vocabulary

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

Place Value & Operations

🔢 Place Value 位值

The value of a digit based on its position in a number. e.g. the 5 in 3,500 represents 500.

🔵 Integer 整数

Any whole number — positive, negative, or zero. e.g. −3, 0, 7.

📋 BIDMAS 运算顺序

Brackets, Indices, Division, Multiplication, Addition, Subtraction — the order of operations.

📈 Index / Power 指数/幂

A small number written above and to the right showing how many times to multiply. e.g. 2³ = 2×2×2 = 8.

🎯 Estimate 估算

An approximate answer found by rounding numbers before calculating.

🔗 Factor 因数

A number that divides exactly into another number. e.g. factors of 12 are 1, 2, 3, 4, 6, 12.

✖️ Multiple 倍数

The result of multiplying a number by an integer. e.g. multiples of 3 are 3, 6, 9, 12...

⭐ Prime Number 质数

A number with exactly 2 factors: 1 and itself. e.g. 2, 3, 5, 7, 11, 13.

🔝 HCF 最大公因数

Highest Common Factor — the largest number that divides exactly into two or more numbers.

🔄 LCM 最小公倍数

Lowest Common Multiple — the smallest number that is a multiple of two or more numbers.

➖ Negative Number 负数

A number less than zero, written with a minus sign. e.g. −5, −12.

📏 Absolute Value 绝对值

The distance a number is from zero on the number line, ignoring the sign. |−7| = 7.

🚀 Extension Activities

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

🎯

Number Systems Around the World

Research Project

Research how ancient Chinese (rod numerals), Korean (Hangul numerals), and Roman number systems worked. Can you do basic addition in each system? Create a poster comparing them to our modern system.

🛒

Nanjing Market Challenge

Real-World Maths

You have ¥200 to buy ingredients for dinner for 4 people at a Nanjing market. Plan a meal, estimate costs, and calculate change. Include multiplication and division in your working. Present your menu and budget.

🧮

The 24 Game

Number Puzzle

Using exactly 4 numbers and any operations (+, −, ×, ÷), make the answer 24. Start with easy sets (1, 2, 3, 4) then try harder ones (3, 3, 8, 8). Create 5 of your own puzzles for classmates to solve.

Explore

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

🧮

BIDMAS Step Calculator

Mr Zocchi

Enter any expression and see BIDMAS applied step by step.

📏

Number Line Explorer

MathsBot

Explore positive and negative integers. Practise adding and subtracting by moving along the number line.

↗ Open Tool

🎮

Factor Game

NCTM Illuminations

Play the Factor Game against the computer. Choose numbers strategically based on their factors.

↗ Open Tool

🔢

Desmos Scientific Calculator

Desmos

Use this calculator for order of operations practice. Check your BIDMAS working.

↗ Open Tool

Self-Quiz

Click a question to reveal the answer.

What is the value of the 4 in 45,209?

40,000 — the 4 is in the ten-thousands place.

Round 3,847 to the nearest hundred.

3,800 — the tens digit is 4 (less than 5), so round down.

Calculate: 6 + 2 × 5

16 — multiplication before addition: 2 × 5 = 10, then 6 + 10 = 16.

Calculate: (8 − 3)² + 1

26 — brackets first: 5, then index: 25, then add 1 = 26.

What is −4 + 9?

5 — start at −4, move 9 to the right = 5.

What is −6 − (−2)?

−4 — subtracting a negative is adding: −6 + 2 = −4.

List all factors of 24.

1, 2, 3, 4, 6, 8, 12, 24.

Is 51 prime? Explain.

No — 51 = 3 × 17, so it has more than 2 factors.

Find the HCF of 18 and 24.

6 — factors of 18: 1,2,3,6,9,18. Factors of 24: 1,2,3,4,6,8,12,24. Largest common: 6.

Find the LCM of 6 and 8.

24 — multiples of 6: 6,12,18,24. Multiples of 8: 8,16,24. Smallest common: 24.

What is 5³?

125 — that's 5 × 5 × 5.

Estimate 48 × 21 by rounding both numbers.

≈ 50 × 20 = 1,000.

Order from smallest: 3, −1, 0, −5, 2

−5, −1, 0, 2, 3.

A lift starts at floor 3, goes down 7 floors. What floor?

Floor −4 (3 − 7 = −4, four floors below ground).

Common mistake: '6 + 2 × 3 = 24.' Explain the error.

The student added first (6+2=8) then multiplied (8×3=24). BIDMAS says multiply first: 2×3=6, then 6+6=12.

Why is zero neither positive nor negative?

Zero is the boundary between positive and negative numbers. It has no direction — it's not above or below zero, it IS zero.

Give a real-life example where negative numbers are useful.

Temperature (−5°C), bank overdraft (−$50), below sea level (−200m), lifts going underground (floor −2).

Maths Toolkit

Useful tools and references for your mathematical work.

🔢 Desmos Scientific Calculator Open Tool ↗ ✖️ Multiplication Table Open Tool ↗

Unit Outline

Number October – December 2025

Fractions, Decimals & Percentages

We are learning to work fluently with fractions, decimals, and percentages — converting between forms and applying the four operations.

Key Concept: Relationships

Related Concepts: Equivalence, Representation

Global Context: Identities and Relationships

"Understanding the relationships between fractions, decimals, and percentages allows us to represent and compare quantities in different ways."

Your Learning Journey

Understanding Fractions Identify, compare, and simplify fractions

Adding & Subtracting Add and subtract fractions with different denominators

Multiplying & Dividing Multiply and divide fractions using Keep-Change-Flip

Decimals Convert between fractions, decimals, and percentages

Percentage Problems Find percentages of amounts and apply to 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 Understanding Fractions ⬇ Download 2 Equivalent Fractions & Simplifying ⬇ Download 3 Adding & Subtracting Fractions ⬇ Download 4 Multiplying & Dividing Fractions ⬇ Download 5 Decimals & Percentages ⬇ Download 6 📚 Full Revision (all topics) ⬇ Download

Worksheets

📖 Revision Booklet ⬇ Download 📝 Understanding Fractions ⬇ Download 📝 Equivalent Fractions ⬇ Download 📝 Adding & Subtracting Fractions ⬇ Download 📝 Multiplying & Dividing Fractions ⬇ Download 📝 Decimals & Percentages ⬇ Download 💻 Full Revision Worksheet (Fillable) ⬇ Download 🤖 Upload Completed Worksheet → Get Instant Feedback 🤖 Open

Review Games

🍕 Fractions & Decimals Review

15 questions · Multiple choice · Shuffled each time

↗ New Tab

Join Dots — Fractions & Decimals

15 questions · Multiple choice · Shuffled each time

↗ New Tab

Videos

🎬🎬 How to Order Fractions (TED-Ed)↗ 🎬🎬 Percentages Explained (TED-Ed)↗ 🎬🎬 The Magic of Decimals (Numberphile)↗ 🎬🎬 Fractions Are About Comparing (TED-Ed)↗ 🎬🎬 Fractions, Decimals and Percentages (Math Antics)↗

Key Vocabulary

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

Fractions

🍕 Fraction 分数

A number representing part of a whole, written as numerator/denominator. e.g. 3/4.

⬆️ Numerator 分子

The top number in a fraction — how many parts you have.

⬇️ Denominator 分母

The bottom number in a fraction — how many equal parts the whole is divided into.

🟰 Equivalent Fractions 等值分数

Fractions that look different but have the same value. e.g. 1/2 = 2/4 = 3/6.

✂️ Simplify 化简

Divide numerator and denominator by their HCF to make the fraction as simple as possible.

📈 Improper Fraction 假分数

A fraction where the numerator is larger than the denominator. e.g. 7/4.

🔀 Mixed Number 带分数

A whole number and a fraction combined. e.g. 1¾.

🔗 LCD 最小公分母

Lowest Common Denominator — the smallest denominator shared by two fractions. Needed for adding/subtracting.

🔄 Reciprocal 倒数

A fraction flipped upside down. The reciprocal of 3/4 is 4/3. Used in division (Keep-Change-Flip).

Decimals & Percentages

🔹 Decimal 小数

A number using a decimal point to show values less than one. e.g. 0.75 = three quarters.

💯 Percentage 百分比

A number out of 100. 'Per cent' means 'out of 100'. e.g. 75% = 75/100 = 0.75.

🔄 Convert 转换

Change from one form to another: fraction ↔ decimal ↔ percentage.

🚀 Extension Activities

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

🍕

Fraction Feast

Real-World Investigation

Visit a restaurant menu (real or online) from Nanjing, Seoul, or Berlin. If you split dishes equally between different group sizes, what fraction does each person get? Calculate for groups of 2, 3, 4, and 6.

📊

Percentage Detective

Data Collection

Walk around NIS or a shopping area. Find 10 real-world uses of percentages (discounts, battery levels, test scores, weather forecasts). Photograph each one and explain what the percentage means in context.

🎲

FDP Card Game

Game Design

Design a card matching game where players match equivalent fractions, decimals, and percentages (e.g. 1/4 = 0.25 = 25%). Make at least 20 sets. Test it with a partner.

Explore

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

🍕

Fraction Visualizer

Mr Zocchi

See fractions on a fraction wall. Add, subtract, multiply, divide with visual feedback.

🧱

Fraction Wall

MathsBot

Explore equivalent fractions visually. See how 1/2 = 2/4 = 3/6 by comparing the bars.

↗ Open Tool

🍕

Fractions Intro

PhET Simulation

Build fractions using shapes and number lines. See how fractions relate to division.

🔢

Desmos Scientific Calculator

Desmos

Use for converting between fractions, decimals, and percentages.

↗ Open Tool

Self-Quiz

Click a question to reveal the answer.

Simplify 12/18.

2/3 — divide both by HCF (6): 12÷6=2, 18÷6=3.

Convert 3/4 to a decimal.

0.75 — divide 3 by 4.

Convert 0.4 to a fraction in simplest form.

2/5 — 0.4 = 4/10 = 2/5.

Convert 60% to a fraction.

3/5 — 60/100 = 3/5.

Calculate: 2/5 + 1/3

11/15 — LCD is 15: 6/15 + 5/15 = 11/15.

Calculate: 7/8 − 1/4

5/8 — convert 1/4 to 2/8: 7/8 − 2/8 = 5/8.

Calculate: 3/4 × 2/5

6/20 = 3/10 — multiply across then simplify.

Calculate: 2/3 ÷ 4/5

10/12 = 5/6 — Keep-Change-Flip: 2/3 × 5/4 = 10/12 = 5/6.

What is 1/3 of 45?

15 — 'of' means multiply: 45 ÷ 3 = 15.

Convert 2¾ to an improper fraction.

11/4 — 2 × 4 = 8, then 8 + 3 = 11. So 11/4.

Which is larger: 3/7 or 5/12?

3/7 — convert to same denominator (84): 36/84 vs 35/84.

What is 15% of 80?

12 — 10% is 8, 5% is 4, so 15% = 8 + 4 = 12.

A shirt costs $40. It's 25% off. What is the sale price?

$30 — discount = 25% of 40 = $10. Sale price = 40 − 10 = $30.

Explain the 'Keep-Change-Flip' rule.

To divide fractions: Keep the first fraction, Change ÷ to ×, Flip the second fraction. Then multiply across.

Common mistake: '1/3 + 1/4 = 2/7.' Explain the error.

You CANNOT add numerators and denominators separately. You need a common denominator first: 4/12 + 3/12 = 7/12.

Explain why dividing by a fraction makes a number bigger.

'How many halves fit in 3?' → 6. Dividing by 1/2 is the same as multiplying by 2. The smaller the fraction you divide by, the bigger the answer.

A pizza has 8 slices. You eat 3/8. Your friend eats 25% of the pizza. Who ate more?

You: 3/8 = 0.375 = 37.5%. Friend: 25%. You ate more.

Maths Toolkit

Useful tools and references for your mathematical work.

🔢 Desmos Scientific Calculator Open Tool ↗ 🧱 Fraction Wall Open Tool ↗

Unit Outline

Measurement & Geometry March – April 2026

Geometry — Volume & Capacity

We are learning to calculate perimeter, area, surface area, and volume, and to convert between volume and capacity.

Key Concept: Relationships

Related Concepts: Equivalence, Measurement

Global Context: Scientific and Technical Innovation

"Understanding the relationships between dimensions helps us measure and compare the space around us."

Your Learning Journey

Perimeter Calculate the perimeter of 2D shapes including circles

Area Find the area of triangles, rectangles, and circles

Surface Area Calculate the surface area of prisms by unfolding nets

Volume Calculate the volume of prisms and cylinders

Capacity Convert between cm³, mL, and litres using the golden rule

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 Perimeter ⬇ Download 2 Area ⬇ Download 3 Surface Area ⬇ Download 4 Volume ⬇ Download 5 Capacity ⬇ Download 6 📚 Full Revision (all topics) ⬇ Download

Worksheets

📖 Revision Booklet ⬇ Download 📝 Perimeter ⬇ Download 📝 Area ⬇ Download 📝 Surface Area ⬇ Download 📝 Volume ⬇ Download 📝 Capacity ⬇ Download 💻 Full Revision Worksheet (Fillable) ⬇ Download 🤖 Upload Completed Worksheet → 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

🎬🎬 How to Find the Area of a Circle (TED-Ed)↗ 🎬🎬 How One Equation Changed the World — Pi (TED-Ed)↗ 🎬🎬 Area and Perimeter (Math Antics)↗ 🎬🎬 Volume of Prisms (Math Antics)↗

Key Vocabulary

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

Perimeter & Area

🔲 Perimeter 周长

The total distance around the outside of a 2D shape. Measured in cm, m.

⬛ Area 面积

The amount of space inside a 2D shape. Measured in squared units (cm², m²).

⭕ Circumference 圆的周长

The perimeter of a circle. C = 2πr or C = πd.

🥧 Pi (π) 圆周率

The ratio of a circle's circumference to its diameter. Approximately 3.14159.

📐 Perpendicular Height 垂直高度

The vertical distance at 90° from the base. Must use this (not the slant) in area formulas.

3D Shapes & Volume

📦 Surface Area 表面积

The total area of all faces of a 3D shape. Imagine unfolding it into a flat net.

🧊 Volume 体积

The amount of space inside a 3D shape. Measured in cubed units (cm³, m³).

💧 Capacity 容量

How much liquid a container can hold. 1 cm³ = 1 mL (the golden rule).

🔷 Prism 棱柱体

A 3D shape with the same cross-section along its entire length. Volume = area of cross-section × length.

📋 Net 展开图

A flat pattern that folds up to make a 3D shape. Used to calculate surface area.

🚀 Extension Activities

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

🏠

Dream Bedroom Designer

Design Challenge

Design your dream bedroom on graph paper. It must fit inside a 5m × 4m room. Calculate the perimeter, area of the floor, and volume of the room. Include furniture with real measurements. Calculate how much paint you need for the walls.

🏛️

Famous Buildings Measurement Challenge

Research & Calculation

Research the dimensions of 3 famous buildings: Nanjing's Zifeng Tower, Seoul's Lotte World Tower, and Berlin's TV Tower. Calculate the volume of each (approximate as rectangular prisms). Which has the greatest volume? Create a comparison infographic.

🎁

Gift Wrapping Olympics

Practical Challenge

Bring 3 different-shaped boxes to class. Measure each one, calculate the exact surface area, then cut wrapping paper to those exact dimensions. Who can wrap their boxes with the least wasted paper?

🏊

Pool Capacity Investigation

Real-World Maths

The NIS pool is 25m × 16m × 1.6m deep. Calculate: How long would it take to fill using a garden hose (15 L/min)? How many students could swim at once if each needs 5m² of space? How much would it cost to heat at ¥0.05 per litre per degree?

Explore

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

⬜

Area Builder

PhET Simulation

Build shapes on a grid and discover the relationship between dimensions and area.

📦

GeoGebra 3D Calculator

GeoGebra

Build 3D shapes and rotate them. Visualise how surface area wraps around a shape and how volume fills the inside.

↗ Open Tool

🔄

Unit Rates

PhET Simulation

Practice converting between units — a key skill when converting between volume (cm³) and capacity (mL, L).

🔢

Desmos Scientific Calculator

Desmos

Use this calculator for area and volume calculations involving π.

↗ Open Tool

Self-Quiz

Click a question to reveal the answer.

What is perimeter?

The total distance around the outside of a 2D shape.

What is the formula for the circumference of a circle?

C = 2πr or C = πd.

What is the formula for the area of a triangle?

A = ½ × base × perpendicular height.

Why must you use the PERPENDICULAR height, not the slant side?

The perpendicular height is the true vertical distance from base to top (at 90°). The slant side is longer and gives the wrong answer.

What is surface area?

The total area of ALL the faces of a 3D shape. Imagine unfolding it into a flat net.

What is the formula for the surface area of a rectangular prism?

SA = 2(lw + lh + wh).

What is volume?

The amount of space inside a 3D shape. Measured in cubed units (cm³, m³).

What is the formula for the volume of a triangular prism?

V = area of triangle × length = (½ × b × h) × l.

What is the golden rule for capacity?

1 cm³ = 1 mL (exactly).

Convert 1 m³ to litres.

1 m³ = 1,000 L.

A fish tank is 50cm × 30cm × 40cm. How many litres does it hold?

V = 60,000 cm³ = 60,000 mL = 60 L.

A cube has side length 6 cm. Find its volume and surface area.

Volume = 6³ = 216 cm³. Surface area = 6 × 6² = 216 cm².

What is the area of a circle with radius 5 cm?

A = πr² = π × 25 ≈ 78.5 cm².

What is a prism?

A 3D shape with the same cross-section along its entire length — like slicing bread, every slice is the same.

Common mistake: using the slant height instead of perpendicular height. Why does this give the wrong answer?

The slant height is longer than the perpendicular height. Using it overestimates the area because the formula assumes a 90° angle at the base.

A swimming pool is 25m × 10m × 2m. How many litres of water does it hold?

V = 25 × 10 × 2 = 500 m³. 1 m³ = 1000 L. So 500 × 1000 = 500,000 L.

Two shapes have the same area. Must they have the same perimeter? Explain.

No. A 4×4 square (area 16, perimeter 16) and a 2×8 rectangle (area 16, perimeter 20) have the same area but different perimeters.

Maths Toolkit

Useful tools and references for your mathematical work.

🔢 Desmos Scientific Calculator Open Tool ↗ 📐 GeoGebra 3D Open Tool ↗

Unit Outline

Algebra April – June 2026

Algebra — Expressions, Equations & Sequences

We are learning to write algebraic expressions, substitute values, solve one-step and two-step equations, and explore number patterns.

Key Concept: Logic

Related Concepts: Equivalence, Generalisation

Global Context: Identities and Relationships

"Logic helps us generalise relationships and solve problems using algebraic representations."

Your Learning Journey

Expressions Write and simplify algebraic expressions

Substitution Replace variables with numbers to evaluate expressions

One-Step Equations Solve equations using inverse operations

Two-Step Equations Solve equations that need two steps to isolate x

Sequences Find patterns and write rules for number sequences

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 Writing Algebraic Expressions ⬇ Download 2 Substitution ⬇ Download 3 Solving One-Step Equations ⬇ Download 4 Solving Two-Step Equations ⬇ Download 5 Number Sequences & Patterns ⬇ Download 6 📚 Full Revision (all topics) ⬇ Download

Worksheets

📖 Revision Booklet ⬇ Download 📝 Algebraic Expressions ⬇ Download 📝 Substitution ⬇ Download 📝 One-Step Equations ⬇ Download 📝 Two-Step Equations ⬇ Download 📝 Sequences & Patterns ⬇ Download 💻 Full Revision Worksheet (Fillable) ⬇ Download 🤖 Upload Completed Worksheet → 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

🎬🎬 Why Do We Use Variables? (TED-Ed)↗ 🎬🎬 Patterns in Nature — Fibonacci (TED-Ed)↗ 🎬🎬 How to Solve an Equation (Math Antics)↗ 🎬🎬 What Is Algebra? (Math Antics)↗

Key Vocabulary

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

Expressions & Equations

❓ Variable 变量

A letter that represents an unknown number. e.g. x, n, y.

📝 Expression 代数式

A combination of numbers, variables, and operations. e.g. 3x + 5. No equals sign.

⚖️ Equation 方程

A mathematical statement with an equals sign. e.g. 2x + 3 = 11.

🔢 Coefficient 系数

The number in front of a variable. In 5x, the coefficient is 5.

🔒 Constant 常数

A number on its own (not multiplied by a variable). In 3x + 7, the constant is 7.

🔄 Substitute 代入

Replace a variable with a number to evaluate an expression. If x=3, then 2x+1 = 7.

↩️ Inverse Operation 逆运算

The opposite operation used to solve equations. + ↔ −, × ↔ ÷.

🤝 Like Terms 同类项

Terms with the same variable raised to the same power. 3x and 5x are like terms. 3x and 3y are not.

Sequences

📊 Sequence 数列

An ordered list of numbers that follow a pattern or rule.

1️⃣ Term 项

Each number in a sequence. The 1st term, 2nd term, etc.

➕ Common Difference 公差

The fixed amount added or subtracted each time in a linear sequence.

🔮 nth Term 第n项

A formula to find any term in a sequence without listing them all. e.g. T(n) = 3n + 1.

🚀 Extension Activities

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

🔮

Pattern Hunters

Investigation

Find 3 number patterns in the real world around Nanjing (floor tiles, building windows, stair steps). Photograph each one, write the sequence, find the nth term rule, and predict the 100th term.

🎮

Code Your Own Function Machine

Coding Challenge

Use Scratch (scratch.mit.edu) to build an interactive function machine. The user enters a number, the machine applies a rule, and shows the output. Can you make it show the rule as an equation?

↗ Open Resource

💰

Taxi Fare Comparison

Real-World Algebra

Research taxi fare formulas for Nanjing, Seoul, and Berlin. Write each as an algebraic expression. Create a graph comparing the cost for journeys from 1 km to 20 km. Which city is cheapest for a 5 km ride? A 15 km ride?

Explore

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

⚖️

Equation Solver

Mr Zocchi

Enter any equation and see it solved step by step with checking.

🔢

Sequence Finder

Mr Zocchi

Enter a sequence and discover the nth term rule instantly.

🟦

Algebra Tiles

MathsBot

Use virtual algebra tiles to model and solve equations visually.

↗ Open Tool

⚙️

Function Machine

MathsBot

Explore input-output relationships. What rule turns the input into the output?

↗ Open Tool

📈

Desmos Graphing Calculator

Desmos

Type in equations and see them as graphs. Try y = 2x + 1 and watch the line appear.

↗ Open Tool

⚖️

Equation Balance Scale

Mr Zocchi

Solve equations step by step with a visual balance. See how each operation keeps both sides equal.

Self-Quiz

Click a question to reveal the answer.

What does 4n mean?

4 × n — a number next to a letter means multiply.

Write an expression for: five more than a number x.

x + 5.

If x = 6, what is 3x − 4?

14 — substitute: 3(6) − 4 = 18 − 4 = 14.

Simplify: 7a + 2a

9a — add the coefficients of like terms.

Simplify: 3x + 5 + 2x − 1

5x + 4 — combine like terms: 3x+2x = 5x, 5−1 = 4.

Solve: x + 12 = 20

x = 8 — subtract 12 from both sides.

Solve: 5x = 35

x = 7 — divide both sides by 5.

Solve: x/4 = 9

x = 36 — multiply both sides by 4.

Solve: 3x + 2 = 17

x = 5 — step 1: 3x = 15, step 2: x = 5.

Solve: 2x − 7 = 11

x = 9 — step 1: 2x = 18, step 2: x = 9.

What is the next term: 5, 9, 13, 17, ___?

21 — the common difference is +4: 17 + 4 = 21.

Find the rule for: 4, 7, 10, 13, 16...

T(n) = 3n + 1 — starts at 4, goes up by 3 each time.

What is the difference between an expression and an equation?

An expression has no equals sign (e.g. 3x + 2). An equation has one (e.g. 3x + 2 = 11).

What is an inverse operation? Give an example.

The opposite operation. Addition ↔ Subtraction, Multiplication ↔ Division. Used to isolate the variable.

Common mistake: '2x + 3x = 5x².' Explain the error.

Adding like terms keeps the same power: 2x + 3x = 5x (not 5x²). You only get x² when you MULTIPLY: x × x = x².

Explain in words what the equation 3x + 5 = 20 means.

'I think of a number, multiply it by 3, add 5, and get 20. What was my number?' Answer: x = 5.

Why do we use inverse operations to solve equations?

We need to 'undo' what's been done to x. If x was multiplied by 3, we divide by 3. If 5 was added, we subtract 5. Always doing the same to both sides keeps the equation balanced.

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, Averages & Chance

We are learning to collect, organise, and interpret data using averages and graphs, and to calculate and compare probabilities.

Key Concept: Relationships

Related Concepts: Representation, Justification

Global Context: Globalisation and Sustainability

"Understanding relationships in data helps us make informed decisions about the world around us."

Your Learning Journey

Collecting Data Design surveys and organise data in frequency tables

Averages Calculate mean, median, mode, and range

Charts & Graphs Choose and draw appropriate graphs for different data types

Introduction to Probability Calculate theoretical probability as a fraction

Experimental Probability Compare experimental results to theoretical predictions

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 Collecting & Organising Data ⬇ Download 2 Mean, Median, Mode, Range ⬇ Download 3 Charts & Graphs ⬇ Download 4 Introduction to Probability ⬇ Download 5 Experimental vs Theoretical Probability ⬇ Download 6 📚 Full Revision (all topics) ⬇ Download

Worksheets

📖 Revision Booklet ⬇ Download 📝 Collecting & Organising Data ⬇ Download 📝 Mean, Median, Mode, Range ⬇ Download 📝 Charts & Graphs ⬇ Download 📝 Introduction to Probability ⬇ Download 📝 Experimental Probability ⬇ Download 💻 Full Revision Worksheet (Fillable) ⬇ Download 🤖 Upload Completed Worksheet → 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

🎬🎬 What Is Probability? (TED-Ed)↗ 🎬🎬 How Statistics Can Be Misleading (TED-Ed)↗ 🎬🎬 The Best Way to Win a Game of Chance (TED-Ed)↗ 🎬🎬 Averages Explained (Math Antics)↗

Key Vocabulary

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

Data & Averages

📋 Data 数据

Information collected through observation, measurement, or survey.

🏷️ Qualitative Data 定性数据

Non-numerical data describing qualities or categories. e.g. favourite colour, type of pet.

🔢 Quantitative Data 定量数据

Numerical data that can be measured or counted. e.g. height, test score.

➗ Mean 平均数

Add all values and divide by the count. The 'average' most people think of.

🎯 Median 中位数

The middle value when data is arranged in order. Not affected by outliers.

🏆 Mode 众数

The most frequently occurring value. A dataset can have no mode, one mode, or multiple modes.

↔️ Range 范围/极差

The difference between the highest and lowest values. Shows how spread out the data is.

⚠️ Outlier 离群值

A value that is much higher or lower than the rest of the data. Affects the mean but not the median.

Probability

🎲 Probability 概率

How likely an event is to happen. Written as a fraction, decimal, or percentage between 0 and 1.

🎯 Outcome 结果

A possible result of an experiment. e.g. rolling a 4 on a die.

📊 Sample Space 样本空间

The set of all possible outcomes. For a coin: {Heads, Tails}.

📐 Theoretical Probability 理论概率

Probability calculated using logic: P = favourable outcomes ÷ total outcomes.

🧪 Experimental Probability 实验概率

Probability found by actually doing an experiment: P = successes ÷ total trials.

🚀 Extension Activities

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

📈

NIS Data Journalist

Data Collection & Analysis

Conduct a survey of at least 30 NIS students on a topic you choose (favourite food, hours of sleep, screen time). Collect data, calculate mean/median/mode, create appropriate charts, and write a short 'news article' presenting your findings.

🎲

Is This Game Fair?

Probability Investigation

Design a simple game using dice or coins. Play it 50 times and record results. Calculate the theoretical probability vs. experimental probability. Is the game fair? If not, how would you change it?

🏅

Olympic Medal Predictor

Data Analysis

Research medal counts from the last 3 Olympics for China, South Korea, and Germany. Identify trends. Use your data to predict how many medals each country will win at the next Olympics. Explain your reasoning with graphs.

Explore

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

🎲

Probability Simulator

MathsBot

Roll dice hundreds of times and see how experimental probability approaches theoretical probability.

↗ Open Tool

📊

Create a Graph

NCES

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

↗ Open Tool

🔢

Desmos Scientific Calculator

Desmos

Use for calculating averages and probabilities.

↗ Open Tool

🎲

Probability Lab

Mr Zocchi

Roll dice and flip coins. Compare experimental vs theoretical probability. Watch the Law of Large Numbers in action.

Self-Quiz

Click a question to reveal the answer.

What is the mean of: 3, 5, 7, 9, 11?

7 — sum is 35, divide by 5 = 7.

What is the median of: 12, 3, 8, 15, 6?

8 — ordered: 3, 6, 8, 12, 15. Middle value is 8.

What is the mode of: 4, 7, 2, 7, 9, 3, 7?

7 — it appears most often (3 times).

What is the range of: 20, 5, 14, 8, 31?

26 — highest (31) minus lowest (5) = 26.

Why is the median sometimes better than the mean?

The median isn't affected by outliers. A very high or low value pulls the mean but not the median.

What type of graph shows change over time?

A line graph — the x-axis is time, points are connected to show the trend.

A fair die is rolled. What is P(3)?

1/6 — one favourable outcome out of 6 equally likely outcomes.

A spinner has 3 red, 2 blue, 5 green sections. What is P(blue)?

2/10 = 1/5 — there are 2 blue out of 10 total sections.

What does P = 1 mean?

The event is certain to happen. Probability ranges from 0 (impossible) to 1 (certain).

You flip a coin 100 times and get 47 tails. What is the experimental P(tails)?

47/100 = 0.47 — experimental probability = successes ÷ total trials.

Is rolling a 7 on a standard die possible?

No — a standard die has faces 1–6. P(7) = 0 (impossible).

What is the difference between discrete and continuous data?

Discrete = counted in whole numbers (e.g. number of siblings). Continuous = measured on a scale (e.g. height, time).

A class survey shows 12 out of 30 students prefer football. What percentage?

40% — 12/30 = 0.4 = 40%.

What does a tally chart help you do?

Organise raw data by counting frequencies. Each group of 5 uses a gate (||||̸) for easy counting.

A student says 'the average test score was 72%.' Which average might be misleading here?

If they used the MEAN, a few very low or very high scores could pull it up or down. The MEDIAN would give a better picture of a 'typical' student's score.

You flip a coin 10 times and get 7 heads. Does this mean the coin is unfair?

Not necessarily. With only 10 flips, variation is normal. With more flips (100, 1000), the experimental probability should get closer to 0.5 if the coin is fair.

Explain why P(event) + P(not event) = 1.

Something either happens or it doesn't — those are the only two possibilities, and they cover everything. So their probabilities must add to 1 (certainty).

Maths Toolkit

Useful tools and references for your mathematical work.

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