Course Details

Mathematics Grade 1-7

Bestseller ★ 5.0/5 340+ enrolled

Why Choose Online Mathematics Grade 1-7 Classes?

Board-aligned tutors - we match the tutor to your child's curriculum (US Common Core, Ontario, Australian, CBSE, ICSE, IGCSE, Cambridge or Singapore MOE).

Live, interactive 1:1 or small-group classes - the tutor sees your child's work in real time.

Customised practice worksheets - graded, reviewed and explained class by class.

Weekly homework support - assignments and concept revision before the next class.

Periodic class tests aligned to the board's exam pattern.

Detailed progress reports for parents every month.

Flexible scheduling - pick time slots that fit school and after-school activities.

Free demo class so you can meet the tutor before you commit.

Globally available - USA, UK, Canada, Australia, Singapore, UAE, GCC and India.

Recorded sessions provided for missed classes (group format) - no concept is left behind.

Overview

Mathematics Grade 1-7 is WinQuest Online's live, 1:1 or small-group K-7 math programme. Each class is fully aligned to the student's school board - whether that is the US Common Core, Canada (Ontario), Australia v9.0, CBSE (NCERT), ICSE (CISCE), Cambridge Primary, IGCSE 0580 or Singapore MOE. Tutors follow the official scope and sequence, support the school textbook, and add custom practice worksheets, periodic class tests and progress reports for parents.

What You'll Learn

Live interactive sessions
1st one-on-one session
Comprehensive curriculum
No long-term commitment
Personalized learning plan

Grade 1

Age 6+ 60 hrs

Counting & Cardinality

Count to 120 starting from any number - children build fluency counting forward and backward to 120, starting from any chosen number. This includes counting by ones, twos, fives and tens, building a flexible sense of how numbers are ordered.
Read and write numbers up to 120 - reading numerals aloud and writing them accurately, connecting the spoken word to the symbol. Children write the count of a quantity of objects up to 120.
Compare two-digit numbers using >, =, < - using the inequality and equality symbols to compare two two-digit numbers. Children learn to read "37 > 26" as "thirty-seven is greater than twenty-six".

Operations & Algebraic Thinking

Addition and subtraction within 20 - mastery of addition and subtraction facts to 20 using strategies like counting on, making tens, decomposing numbers and using known facts. Speed and accuracy are built progressively.
Properties of operations (commutative, associative) - children learn through hands-on activities that 3 + 4 = 4 + 3 (commutative) and that (2 + 3) + 4 = 2 + (3 + 4) (associative). They use these properties to simplify computation.
Word problems with unknowns in all positions - solving addition and subtraction word problems where the unknown can be in any position (e.g., "5 + ? = 12" or "? + 3 = 8"). Children draw pictures and write equations.

Number & Operations in Base Ten

Place value - tens and ones - understanding that two-digit numbers are made of a number of tens and a number of ones (e.g., 47 = 4 tens + 7 ones). Children use base-ten blocks to model.
Adding within 100 using place-value strategies - using place value, properties of operations and the relationship between addition and subtraction to add a two-digit and a one-digit number within 100.
Subtracting multiples of 10 - subtracting multiples of 10 from two-digit numbers (e.g., 70 - 20 = 50). Children use mental strategies based on place value.

Measurement & Data

Order objects by length; measure with non-standard units - comparing the lengths of objects, ordering them from shortest to longest, and measuring with paper clips, blocks or footprints.
Tell time to the hour and half-hour - reading analog and digital clocks to identify the time to the hour ("3 o'clock") and the half-hour ("half past 3" or "3:30"). Linking time to daily routines.
Organise and interpret data with up to 3 categories - sorting objects and people into up to 3 categories (e.g., favourite fruit), creating a simple data display, and answering questions about the data.

Geometry

Distinguish defining vs non-defining attributes of shapes - children identify the attributes that define a shape (e.g., a square has 4 equal sides and 4 right angles) versus those that don't (size, colour).
Compose 2-D shapes; build composite figures - putting together rectangles, triangles, half-circles and quarter-circles to build new composite shapes. Using pattern blocks and tangrams.
Partition circles and rectangles into halves and quarters - dividing whole shapes into two equal shares (halves) or four equal shares (quarters) and describing each share using the language of fractions informally.

Number Sense and Numeration

Read, represent, compare and order whole numbers to 50 - children read, write and order whole numbers from 0 to 50 using multiple representations (numerals, words, ten frames, base-ten blocks).
Demonstrate understanding of magnitude by counting forward and backward - counting in 1s, 2s, 5s and 10s, both forward and backward, starting from any number up to 50. Building number-line fluency.
Compose and decompose numbers in many ways - showing that 7 can be made as 4+3, 5+2, 6+1 etc., or as 5 ones + 2 ones. Composing builds flexibility for later mental math.

Operations

Add and subtract whole numbers up to 20 - using mental and written strategies including counting on, making 10s, decomposing, doubles and near-doubles. Fluency builds with weekly practice.
Use the relationship between addition and subtraction - children see that 4 + 3 = 7 means 7 - 3 = 4 and 7 - 4 = 3. Fact families are introduced and practised regularly.
Solve problems using objects, drawings and equations - children represent word problems using counters, drawings and equations with an unknown symbol, then explain their reasoning.

Algebra & Patterning (with coding)

Identify, extend and create repeating patterns - patterns of shape, colour, number or sound (e.g., ABAB, ABCABC). Children extend a given pattern and create their own with rules.
Use symbols to represent unknown quantities - children write and solve equations like 5 + ? = 8, using counters and number lines to find the unknown.
Introduce coding concepts - sequencing of events - simple instructional sequences (move forward, turn right) using unplugged coding activities. Children code a partner around a grid.

Measurement

Compare and measure length, mass, capacity using non-standard units - measuring with paper clips, hand spans, cups; comparing two objects directly and indirectly.
Read time to the hour and half-hour - reading analog and digital clocks, linking the time to daily routines (breakfast, school, lunch, dinner, bed).
Identify days of the week, months of the year - sequencing the days and months in order and using a calendar to find dates.

Geometry & Spatial Sense

2-D shapes - sort and classify - sorting circles, triangles, squares, rectangles, hexagons by attributes (number of sides, number of corners, equal vs unequal sides).
3-D solids - identify cube, sphere, cylinder, cone - identifying each by their faces, edges and vertices. Linking to real-world objects (ball, can, ice-cream cone).
Describe location and movement using positional language - "above", "below", "beside", "in front of", "behind", "between"; following and giving directional instructions.

Data & Probability

Collect, organise and read primary data - children pose a question (e.g., "What is your favourite season?"), collect responses, and organise them in a tally chart.
Create concrete and pictograph displays - representing data using concrete graphs (objects on a grid) and pictographs (pictures representing each unit of data).
Describe events as likely or unlikely - identifying everyday events that are certain, likely, unlikely or impossible. Building early probability intuition.

Number

Recognise, model and order numbers to at least 120 - children read, write, order and model numbers up to 120 using a wide range of materials (ten frames, MAB blocks, number lines).
Partition collections; addition and subtraction within 20 - splitting collections into smaller parts and recombining (3 + 4 = 7); subtracting by taking away or finding the difference.
Skip counting in 2s, 5s and 10s - counting forward and backward in jumps of 2, 5 and 10. Connecting to early multiplication and patterns on the number line.

Algebra

Continue and create growing and shrinking patterns - children identify the rule of a growing or shrinking pattern (e.g., 2, 4, 6, 8 - "add 2 each time"), continue it and create their own.
Use equality and inequality (=, not equal) with simple equations - understanding that 3 + 4 = 7 means "the same as" and that 3 + 4 not equal 6. Children write equations.
Connect counting sequences to repeating patterns - children connect the skip-counting sequence (2, 4, 6, 8, ...) to the repeating pattern of "+2". Early algebraic thinking.

Measurement

Use uniform informal units to measure length, capacity and mass - comparing and measuring with paper clips, cups, blocks. Children record measurements and explain.
Tell time on analog clocks to the half-hour - reading analog clocks at the hour and half-hour, and writing the time in both ways.
Name the seasons and months of the year - sequencing the seasons (summer, autumn, winter, spring) and the months of the year using a calendar.

Space (Geometry)

Make, compare and describe 2-D shapes and 3-D objects - children identify, name, draw and build 2-D shapes (circle, triangle, square, rectangle) and 3-D objects (cube, sphere, cylinder, cone, prism).
Give and follow directions using everyday positional language - "in front of", "behind", "beside", "between"; children give and follow directions in space.
Describe transformations - slide, flip, turn - children manipulate shapes by sliding (translation), flipping (reflection) and turning (rotation) and notice what changes and what stays the same.

Statistics

Pose simple questions; collect data - children pose a question of interest (e.g., "What sport do you play?"), gather responses from the class, and record findings.
Represent data with one-to-one displays - data is shown using one symbol per data point (e.g., one block per response). Children build and read these displays.
Interpret data displays - most, least, same - reading a data display to find the category with the most, the least, and any categories with the same count.

Shapes & Space

Solids around us; identify cube, ball, cone, cylinder - children identify 3-D shapes in their environment (a ball, a tin, an ice-cream cone, a die) and group them by shape.
Inside, outside, on; above, below, near, far - children use positional vocabulary to describe where objects are in relation to other objects (the cat is on the mat, the book is inside the bag).
2-D shapes - rectangle, square, triangle, circle - identifying, drawing and naming each shape; tracing and colouring; building pictures using these shapes.

Numbers 1 to 9

Counting, reading and writing numerals 1-9 - children master the count from 1 to 9, recognise the numeral, write it correctly, and link a numeral to a quantity of objects.
Comparison - more, less, equal - comparing two groups of objects and naming which has more, fewer, or the same number. Comparing using number names.
Number names and the zero concept - learning the names "one" to "nine" and introducing "zero" as the count of an empty group.

Addition & Subtraction

Addition and subtraction up to 20 - children add and subtract using objects, pictures and number lines, mastering facts within 20 step by step.
Adding zero; subtracting zero - understanding that 0 + n = n and n - 0 = n. Building the identity property of zero through examples.
Story problems using pictures - children solve simple word problems posed with pictures (e.g., "There are 4 apples and 3 more come. How many in all?").

Numbers 10 to 99

Tens and ones; place value introduction - understanding that 25 means 2 tens and 5 ones; using base-ten blocks or bundles of straws to model.
Compare and order numbers up to 99 - placing numbers in order from smallest to largest; using "greater than", "less than" and "equal to".
Number names of tens - learning the words "ten", "twenty", "thirty", ..., "ninety" and how to construct two-digit number names ("twenty-five" = 25).

Measurement

Long / short, tall / short, heavy / light - comparing objects and using the words long, short, tall, heavy, light, etc. Direct comparison and informal units.
Time - morning, afternoon, evening, night - sequencing the parts of the day, linking to daily routines (breakfast, school, lunch, dinner, bed).
Days of the week and months - learning the seven days of the week and twelve months of the year; using a calendar.

Money & Patterns

Recognise coins and currency notes - identifying Indian coins (1, 2, 5, 10 rupees) and currency notes (10, 20, 50, 100, 200, 500 rupees) by colour, size and value.
Identify, extend and create patterns - patterns of shape, colour, number; extending a given pattern and creating a new one.
Data - simple sorting and grouping - sorting objects into categories (e.g., red vs blue, big vs small) and counting how many in each group.

Number Concept

Counting forward and backward up to 100 - children count from 1 to 100 forward, then from 100 back to 1 backward. They count from any starting number.
Reading, writing and ordering numbers 1-100 - reading number names aloud, writing the numerals accurately and ordering numbers from smallest to largest.
Place value - tens and ones - showing that 47 means 4 tens + 7 ones, using base-ten blocks to model two-digit numbers.

Operations

Addition and subtraction without regrouping (up to 20) - adding and subtracting using ten frames, number lines and the standard column algorithm for two-digit numbers (no carrying or borrowing).
Vertical and horizontal forms - children practise writing additions and subtractions in both horizontal (4 + 3 = 7) and vertical (column) forms.
Word problems involving daily life - solving one-step word problems set in real-life contexts (shopping, sharing, eating, counting toys).

Geometry

Identify lines - straight and curved - children identify and draw straight lines, curved lines, and notice the difference in real-world examples.
Recognise solids and plane shapes around us - identifying 3-D solids (cube, sphere, cylinder, cone) and 2-D plane shapes (square, rectangle, triangle, circle) in their environment.
Open and closed figures - distinguishing open from closed figures by tracing the boundary with a finger; closed shapes form a complete loop.

Measurement

Comparison of length, weight, capacity - comparing two objects directly (which is taller, heavier, holds more) and ordering several objects.
Time - read the clock to the hour - reading an analog clock at the hour and writing the time as "3 o'clock" or "3:00".
Calendar - days, weeks, months - learning the seven days, four weeks in a month, twelve months in a year. Reading dates from a calendar.

Money

Recognise Indian coins and notes - identifying Indian coins (1, 2, 5, 10 rupees) and notes (10, 20, 50, 100, 200, 500 rupees) by appearance and value.
Counting money - simple combinations - making a given total using various coin combinations (e.g., 12 rupees = 5 + 5 + 2 or 10 + 2).
Buying and selling at a shop - role-play of a shopkeeper and customer, practising counting money, giving change, and adding up totals.

Patterns & Data

Identify and continue patterns - finding the rule of a pattern (ABAB, AABB, 1, 2, 3, 4 ...) and continuing it for several more terms.
Collect and represent simple data - gathering data on a topic (e.g., favourite colour) by surveying the class and presenting it.
Group and compare objects - sorting objects into groups based on one attribute (size, colour, shape) and comparing the count in each.

Number

Recognise and use numbers to 100 - children read, write, order and use numbers up to 100; representing them with concrete materials, pictures and digits.
Count on and back in 1s, 2s, 5s and 10s - counting forward and backward in different step sizes, starting from various numbers. Builds number-line fluency.
Place value - tens and ones - understanding that 38 has 3 tens and 8 ones; using base-ten blocks and place-value cards to model.

Calculation

Add and subtract numbers within 20 - mastery of addition and subtraction facts within 20, using a wide range of strategies including counting on, making 10 and number bonds.
Use the +, − and = signs to record calculations - children record their thinking using mathematical symbols: 7 + 5 = 12, 9 - 3 = 6.
Recall pairs of numbers that total 10 - quick recall of number pairs that make 10 (1+9, 2+8, 3+7, 4+6, 5+5). These are the building blocks for later mental math.

Geometry & Measure

Name and describe 2-D and 3-D shapes - identifying, naming and describing 2-D shapes (circle, triangle, square, rectangle, hexagon) and 3-D shapes (cube, cuboid, cylinder, sphere, cone, pyramid).
Compare lengths, masses and capacities - direct comparison of two objects (which is longer, heavier, holds more) and ordering several objects.
Tell the time to the hour and half-hour - reading analog clocks and writing the time at the hour ("3 o'clock") and the half-hour ("half past 3").

Statistics & Probability

Sort objects into sets using one criterion - sorting a collection of objects by one attribute (colour, shape, size) and counting how many are in each set.
Use Venn / Carroll diagrams to sort - introducing simple Venn diagrams (overlapping circles) and Carroll diagrams (yes-no grid) to sort objects.
Discuss and use words like "more likely" / "less likely" - identifying everyday events as more likely or less likely, building early probability intuition.

Thinking & Working Mathematically

Specialising - try examples - children test a general statement (e.g., "all triangles have 3 sides") by trying examples and seeing whether each works.
Generalising - notice patterns - children look at multiple examples and notice the pattern or rule that connects them. Then they generalise.
Conjecturing - make predictions - children make a mathematical prediction based on a pattern (e.g., "the next number will be 12 because we are adding 2 each time").

Whole Numbers

Numbers up to 100 - counting and reading - children count, read and write numbers from 1 to 100 using a variety of representations (ten frames, number lines, base-ten blocks).
Place value - tens and ones - understanding that the digits in a two-digit number stand for tens and ones (47 = 4 tens + 7 ones).
Comparing, ordering, number patterns - comparing two numbers using >, =, <; ordering several numbers; identifying number patterns (e.g., 5, 10, 15, 20, ...).

Addition & Subtraction

Mental and written addition / subtraction within 20 - children use various strategies (number bonds, counting on, doubles) to add and subtract within 20.
Use of number bonds and part-whole model - the Singapore signature: any number can be decomposed into parts. 7 = 5 + 2 or 7 = 3 + 4. Part-whole models are drawn.
Solving 1-step word problems - solving simple problems where one operation gives the answer, using the bar model to represent the unknown.

Multiplication & Division (Introduction)

Multiplication as repeated addition - understanding that 3 x 4 means 3 groups of 4 or 4 + 4 + 4. Children use arrays and equal groups.
Division as sharing and grouping - dividing a quantity into equal shares (sharing) or making groups of a given size (grouping).
Practical examples with concrete materials - children use counters, blocks and real objects to explore multiplication and division through hands-on activity.

Length, Mass and Time

Comparing and measuring length / mass in non-standard units - comparing the length and mass of objects using paper clips, blocks and other classroom objects.
Reading time on an analog clock to the half hour - reading analog clocks and identifying the time at the hour and half-hour.
Using a calendar - reading a monthly calendar to find dates, days of the week and special events. Sequencing months of the year.

Money

Counting amount of money in cents (up to $1) and dollars - identifying Singapore coins (5c, 10c, 20c, 50c, $1) and notes ($2, $5, $10). Counting totals.
Simple shopping situations - role-play of buying small items; identifying the cost and what change is due.
Adding and subtracting money - finding totals of small purchases and the change due. Practical money sense for everyday life.

Picture Graphs

Reading and interpreting picture graphs - reading data displayed as a picture graph; answering questions about the data (which has the most, the least, the total).
Comparing data - comparing the counts in two or more categories on a picture graph.
Constructing simple picture graphs - children gather data from a small survey and build a picture graph to display the results.

Note

Cambridge IGCSE (0580 Maths) is taken in Years 10-11 / Grades 9-10. For Grade 1 the Cambridge Primary Stage 1 framework above is followed.
IGCSE-track international schools follow Cambridge Primary at this stage, with each Primary stage building the foundational thinking that the IGCSE syllabus depends on.
WinQuest maps every Cambridge Primary skill onto the later IGCSE assessment objectives so the long-term progression feels seamless and unforced.

Grade 2

Age 7+ 60 hrs

Operations & Algebraic Thinking

Addition and subtraction within 100 to solve word problems - children apply addition and subtraction within 100 to one-step and two-step word problems involving situations of adding to, taking from, putting together, taking apart and comparing.
Fluently add and subtract within 20 from memory - mastery of the basic addition and subtraction facts to 20, recalled quickly and accurately. Children use strategies (doubles, near-doubles, make ten, count on / back).
Foundations for multiplication - equal groups and arrays - children work with equal groups of objects and rectangular arrays as foundations for multiplication. They count by 2s and 5s on a 100 chart and find sums.

Number & Operations in Base Ten

Place value - hundreds, tens, ones up to 1000 - understanding that the three digits of a three-digit number represent hundreds, tens and ones. Children read, write and represent numbers in many ways.
Add and subtract within 1000 using strategies - children use strategies based on place value, properties of operations and the relationship between addition and subtraction to add and subtract within 1000.
Skip-count by 5s, 10s and 100s - children skip-count forward and backward by 5s, 10s and 100s within 1000, building number-line fluency and patterns for multiplication.

Measurement & Data

Measure length using rulers, yardsticks, meter sticks - children measure length using standard tools, choosing the appropriate unit (inches, feet, yards; centimetres, metres). They estimate then measure.
Tell and write time to the nearest 5 minutes - reading analog clocks (with the minute hand at any 5-minute mark) and writing the time using a.m. and p.m. notation.
Work with $ and cents; bar graphs and pictographs - children identify coins (penny, nickel, dime, quarter), solve money word problems involving $ and cents, and read and create bar graphs and pictographs.

Geometry

Recognise and draw shapes with specified attributes - children identify and draw shapes given specified attributes (a triangle with a right angle; a pentagon with a given number of sides).
Partition rectangles into rows and columns of squares - dividing rectangles into rows and columns of same-size squares and counting them. Foundations for area.
Halves, thirds and fourths of shapes - dividing shapes into 2, 3 or 4 equal shares; describing the shares with the words "halves", "thirds" or "fourths".

Number Sense

Whole numbers up to 200; place value to hundreds - children read, write, represent and compare whole numbers to 200 using multiple representations (numerals, words, base-ten blocks).
Fractions - halves, fourths, eighths - children represent simple fractions of a whole using diagrams and concrete materials.
Compose and decompose numbers - children build numbers in many ways (e.g., 67 = 60 + 7 = 50 + 17 = 6 tens + 7 ones). Flexibility supports mental math.

Operations

Add and subtract within 100 using a variety of strategies - children apply mental, written and algorithmic strategies to add and subtract within 100, with and without regrouping.
Multiplication and division using equal groups - introduction to multiplication and division using equal groups, arrays and skip counting.
Estimation strategies - children estimate sums and differences using benchmarks (nearest 10) before computing, and check whether the answer is reasonable.

Algebra (and Coding)

Patterns - extend and create growing patterns - children identify the rule of a growing pattern (e.g., +3 each time), continue it and create their own.
Equality of expressions using objects and equations - balancing equations like 4 + 3 = ? + 2; building understanding of "=" as a balance.
Introduction to coding - simple sequences - children write a simple sequence of instructions for a partner or virtual character to follow. Foundations of computational thinking.

Measurement

Linear measurement using cm and m - measuring lengths in centimetres and metres using rulers and tape measures. Estimating before measuring.
Time - read analog and digital clocks to the minute - reading both formats, understanding the relationship between them, calculating short durations.
Money - count and add Canadian coins and bills - identifying and counting Canadian coins (5c, 10c, 25c, $1 loonie, $2 toonie) and bills ($5, $10, $20).

Geometry & Spatial Sense

Sort 2-D shapes using their attributes - sorting shapes by number of sides, number of vertices, symmetry and size; making generalisations.
3-D solids - faces, edges, vertices - identifying the faces, edges and vertices of cubes, rectangular prisms, cylinders, cones and pyramids.
Symmetry - lines of symmetry in 2-D shapes - identifying lines of symmetry; sorting shapes by the number of lines of symmetry they have.

Data & Probability

Collect, organise and display data in concrete graphs - posing a question, gathering data, organising it in a tally chart, and displaying it in a concrete graph.
Read and interpret pictographs - reading pictographs where each symbol represents one or more data points; answering questions about the data.
Describe probability - certain, possible, impossible - sorting everyday events into "certain", "likely", "unlikely", "impossible".

Number

Recognise, represent and order numbers to at least 1000 - children read, write, order and represent numbers to at least 1000 using multiple representations.
Investigate division as the inverse of multiplication - children explore the inverse relationship through equal groups and arrays.
Recall addition / subtraction facts to 20 - mastery of basic facts to 20 through repeated practice and strategy use.

Algebra

Continue and describe growing and shrinking patterns - identifying and describing the rule of a growing or shrinking pattern; continuing it.
Use the equals sign to mean balance - understanding "=" as "the same as", not just "the answer is". Balancing equations like 4 + 3 = 5 + 2.
Investigate number sentences - exploring the structure of number sentences (what is on each side) and what makes them true or false.

Measurement

Compare and order objects using formal units (cm, kg) - using standard units to measure and compare length and mass.
Tell time to the quarter-hour - reading analog clocks at quarter-hour intervals (quarter past, half past, quarter to).
Identify the duration of events - children estimate and measure the duration of short and long events (a class, a school day, a season).

Space (Geometry)

Describe and draw 2-D shapes; recognise transformations - drawing and describing 2-D shapes; recognising transformations (slide, flip, turn).
Identify cones, cubes, cylinders, spheres and prisms - identifying and describing common 3-D objects; naming their faces, edges and vertices.
Interpret simple grid maps - reading simple grid maps to find locations using coordinates (e.g., A3, B4).

Statistics

Pose questions; collect, classify and organise data - children pose a question and gather data from peers; classify and organise it.
Create displays of data using lists, tables, picture graphs - representing collected data using multiple display types.
Compare results - comparing data displays to identify which category is most, least, or shared.

Probability

Identify outcomes of familiar everyday chance events - listing the possible outcomes of simple events (e.g., flipping a coin).
Use language - likely, unlikely, certain, impossible - using probability language to describe events.

What is Long, What is Round

Long and round shapes around us - identifying long and round shapes in everyday objects; sorting and grouping them by shape.
Solid shapes - sphere, cylinder, cube, cuboid - identifying these basic 3-D shapes by their properties and finding examples around them.
Comparing and grouping shapes - comparing two solid shapes by their properties and grouping similar shapes together.

Counting in Groups

Grouping in tens and hundreds - children understand that ten ones make one ten and ten tens make one hundred. They group objects accordingly.
Counting in 2s, 5s and 10s - skip counting forward and backward in jumps of 2, 5 and 10 within 200.
Reading and writing 3-digit numbers up to 199 - reading, writing and ordering numbers from 100 to 199; understanding place value.

Addition & Subtraction

Add and subtract 2-digit numbers (with and without regrouping) - children add and subtract two-digit numbers, with and without carrying / borrowing.
Word problems - solving one-step and two-step word problems set in real-life contexts (shopping, counting toys).
Vertical and horizontal sums - writing additions and subtractions in both horizontal (4 + 3 = 7) and vertical (column) forms.

Multiplication (Introduction)

Multiplication as repeated addition - understanding 3 x 4 as 4 + 4 + 4 or as 3 groups of 4. Children use objects and pictures.
Multiplication tables of 2, 3, 5 and 10 - learning and memorising the multiplication tables of 2, 3, 5 and 10 through skip counting and chanting.
Word problems involving multiplication - solving simple multiplication word problems.

Measurement

Length - non-standard and standard units (cm) - measuring length using paper clips, fingers (non-standard) and rulers in cm (standard).
Weight - heavier / lighter; standard units (kg) - comparing weights of objects directly (which is heavier) and using a balance with kg as the standard unit.
Capacity - litres - estimating and measuring how much liquid a container holds, using litres as the standard unit.

Money, Time & Data

Indian currency - notes and coins; adding amounts - identifying Indian currency, counting amounts, adding and subtracting small amounts.
Reading the clock to the hour and half hour - reading analog clocks and writing the time at the hour and half hour.
Pictographs and tally marks - reading and creating pictographs (one symbol per data point) and tally marks.

Number System

1 to 1000 - reading, writing, place value - children read, write and order three-digit numbers; understanding hundreds, tens, ones.
Ordering and comparing 3-digit numbers - placing numbers in order from smallest to largest using "greater than", "less than", "equal to".
Roman numerals up to X - introduction to Roman numerals I to X; reading clocks and chapter numbers.

Four Operations

Addition and subtraction with regrouping - children add and subtract two- and three-digit numbers with carrying and borrowing.
Introduction to multiplication and division - introducing multiplication as repeated addition and division as sharing equally.
Tables of 2 to 10 - memorising the multiplication tables of 2 to 10 through skip counting, chanting and practice.

Geometry

Plane shapes and solid shapes - identifying 2-D plane shapes and 3-D solid shapes and listing their properties.
Lines - straight, curved, intersecting - identifying types of lines, drawing them and naming intersections.
Symmetry - introduction - identifying symmetric shapes and drawing the line of symmetry. Children try with paper-folding.

Measurement

Length - m, cm; weight - kg, g; capacity - L, mL - introducing standard units for length, weight and capacity.
Standard units of measurement - understanding why standard units matter (everyone agrees on the size).
Practical exercises - hands-on measuring of classroom objects; estimating before measuring and checking.

Time & Money

Reading time to the quarter hour - reading analog clocks at quarter-hour intervals.
Days, weeks and months on the calendar - identifying days, weeks and months on a calendar; reading dates.
Indian currency - rupees and paise - identifying notes and coins, counting amounts, and making transactions in role-play.

Patterns & Data

Identifying number and shape patterns - finding the rule of a pattern and continuing it.
Tally charts and pictographs - representing data using tally marks and pictographs.
Bar graphs - introduction - introducing bar graphs as a way to display data visually.

Number

Recognise, read, write and order numbers to 100 - children consolidate two-digit number sense, including reading number words.
Estimate quantities; check by counting - estimating "about how many" objects in a collection, then counting to check.
Recognise and use 2-digit place value - representing two-digit numbers using base-ten materials and digits.

Calculation

Add and subtract 1- and 2-digit numbers within 100 - applying a range of mental and written methods to add and subtract within 100.
Recall doubles to 10 + 10; halves of even numbers to 20 - quick recall of doubles and halves; foundations for multiplication and division.
Multiplication as repeated addition - 2x, 5x, 10x tables - learning the 2x, 5x and 10x tables through skip counting and repeated addition.

Geometry & Measure

Identify quadrilaterals, pentagons and hexagons - naming and identifying polygons by their number of sides.
3-D shapes - faces, edges, vertices - children describe 3-D shapes (cube, cuboid, pyramid, prism, cylinder, cone, sphere) by their faces, edges and vertices.
Read time to the nearest 5 minutes - reading analog clocks where the minute hand is at any 5-minute interval.

Statistics & Probability

Read and interpret block graphs and pictograms - reading and answering questions about block graphs (bar graphs with no gaps) and pictograms.
Sort objects using two criteria (Venn / Carroll) - using two-circle Venn diagrams and Carroll diagrams to sort by two attributes.
Discuss likelihood of events - using "more likely", "less likely", "certain", "impossible".

Thinking & Working Mathematically

Characterising - state properties - children describe a shape, number or pattern by its properties (a triangle has 3 sides).
Classifying - sort by properties - sorting objects, numbers or shapes by one or more properties and explaining the rule.
Improving - refine answers - reviewing and improving a first attempt at a math problem to make it clearer or more accurate.

Whole Numbers

Numbers up to 1000 - place value - reading, writing, comparing and ordering numbers up to 1000 using place-value charts and base-ten materials.
Comparing, ordering and rounding to nearest 10 - rounding two- and three-digit numbers to the nearest 10; comparing and ordering.
Number patterns - identifying and extending number patterns (e.g., 5, 10, 15, 20).

Addition & Subtraction

Within 1000 using mental and written methods - children use mental strategies and the column algorithm to add and subtract within 1000.
Solving 2-step word problems - solving two-step problems where two operations are needed; using the bar model to represent.
Bar model for additive structures - the Singapore bar model for "part-part-whole" and "compare" situations.

Multiplication & Division

Multiplication tables of 2, 3, 4, 5 and 10 - memorising the multiplication tables through skip counting and practice.
Division as sharing equally and grouping - children explore division as sharing and grouping.
Solving simple word problems - one-step multiplication and division word problems.

Fractions

Fractions as part of a whole - representing fractions of a whole using diagrams.
Half, quarter, eighth, etc. (unit fractions) - identifying and writing unit fractions of shapes and sets.
Comparing simple fractions - comparing two fractions with the same denominator or the same numerator.

Measurement

Length, mass, volume - standard units (m, cm; kg, g; L) - measuring with standard units and choosing the appropriate unit.
Time - hours, half hours, quarter hours - reading clocks at the hour, half-hour and quarter-hour intervals.
Money - $ and cents; making change - identifying coins and notes; making change from purchases.

Picture Graphs

Reading and constructing picture graphs with scales - reading picture graphs where each symbol represents 2, 5 or 10 units.
Solving problems using graph data - answering questions and solving problems using the graph data.

Note

Cambridge IGCSE 0580 Maths is taken in Years 10-11. For Grade 2 the Cambridge Primary Stage 2 framework above is followed.
IGCSE-track schools follow Cambridge Primary at this stage, building the foundational skills the IGCSE syllabus depends on.
WinQuest scaffolds Grade 2 students towards the IGCSE assessment objectives that will arrive later.

Grade 3

Age 8+ 60 hrs

Operations & Algebraic Thinking

Multiplication and division within 100; commutative / distributive properties - children master multiplication and division facts within 100. They apply the commutative (4x6 = 6x4) and distributive (4x(5+2) = 4x5 + 4x2) properties to simplify calculation.
Solve two-step word problems using the four operations - children solve word problems involving any of the four operations across two steps. They write equations using a letter for the unknown and check that the answer is reasonable.
Identify and explain arithmetic patterns - children look at addition and multiplication tables to spot patterns (e.g., all even × any = even). They explain the pattern using properties of operations.

Number & Operations in Base Ten

Round whole numbers to the nearest 10 or 100 - using place value to round any three-digit number to the nearest 10 or 100. Children locate the number on a number line to visualise rounding.
Add and subtract within 1000 with fluency - using standard algorithms and mental strategies to add and subtract within 1000 with carrying, borrowing and place-value reasoning.
Multiply 1-digit whole numbers by multiples of 10 - multiplying a one-digit number by a multiple of 10 (e.g., 6 × 40 = 240). Builds foundations for multi-digit multiplication later.

Number & Operations - Fractions

Understand a fraction as a number on the number line - children represent fractions on a number line, marking the position of 1/4, 2/4, 3/4 and 4/4 between 0 and 1.
Equivalent fractions; compare fractions with same numerator or denominator - identifying that 1/2 = 2/4 = 3/6 using diagrams. Comparing fractions like 3/8 and 5/8 (same denominator) or 2/3 and 2/5 (same numerator).
Whole numbers as fractions - understanding that whole numbers can be written as fractions (e.g., 3 = 3/1 = 6/2). Foundation for later operations on fractions.

Measurement & Data

Tell time to the minute; solve elapsed-time problems - reading analog clocks to the minute and calculating elapsed time using number lines (e.g., from 2:15 to 3:50 = 1 hour 35 minutes).
Liquid volumes and masses - g, kg, L - measuring liquid volume in litres (L) and mass in grams (g) and kilograms (kg). Solving one-step word problems involving these units.
Picture and bar graphs; line plots with halves and quarters - reading and creating picture graphs and bar graphs (scaled). Drawing line plots where the measurement is to the nearest half or quarter unit.

Geometry

Categorise quadrilaterals; recognise rhombuses, rectangles, squares - identifying that rhombuses, rectangles and squares are all quadrilaterals and exploring the relationships between them.
Partition shapes into parts with equal areas - dividing a shape into a given number of parts with equal area, even when the parts are different shapes.
Express the area as a unit fraction of the whole - each equal part is a unit fraction of the whole (1/4 of the rectangle, 1/6 of the hexagon). Foundation for area.

Number Sense

Whole numbers up to 1000; place value - children read, write, compare and represent whole numbers up to 1000 using multiple representations (numerals, words, base-ten blocks, number lines).
Fractions - halves, thirds, fourths, fifths, sixths, eighths, tenths - representing simple fractions of a whole and of a set; comparing fractions with the same denominator.
Decimals - tenths - introduction to decimal numbers (0.1, 0.2 ... 0.9) and their relationship to fractions (1/10 = 0.1).

Operations

Multiplication and division facts up to 7 x 7 - building fluency through skip counting, arrays and the inverse relationship between multiplication and division.
Multi-digit addition and subtraction within 1000 - using the standard column algorithm with regrouping, and mental strategies for round numbers.
Properties of multiplication and division - children apply commutative, associative and distributive properties to make calculations easier.

Algebra & Coding

Patterns - children extend and create growing patterns (e.g., 2, 4, 6, 8) and shrinking patterns (50, 45, 40), describing the rule in words.
Solve simple equations using objects, drawings and equations with one variable (e.g., 5 + ? = 12). Models include ten frames and balance scales.
Coding (Ontario's new strand) - children write and execute simple code with conditions (if / then) using ScratchJr or block-based coding platforms.

Measurement

Length - mm, cm, m, km - estimating and measuring using rulers and metre sticks; converting between units (10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km).
Area and perimeter of regular shapes - counting unit squares for area; adding side lengths for perimeter; investigating shapes with the same area but different perimeter.
Mass (g, kg) and capacity (L, mL) - using a balance and measuring jugs; estimating before measuring; solving one-step word problems.

Geometry & Spatial Sense

Polygons - regular and irregular; quadrilaterals - children identify, name and describe quadrilaterals (square, rectangle, rhombus, parallelogram, trapezoid).
Geometric transformations - translations (slides), reflections (flips) and rotations (turns) of 2-D shapes on a grid.
Locate points using grid coordinates (Quadrant I) - children plot and identify ordered pairs and apply this to map reading.

Data & Probability

Construct and read pictographs and bar graphs with appropriate scales; identifying the mode of a small data set.
Mode of a data set - the value that occurs most often; comparing mode to range (highest minus lowest).
Probability of simple events as a fraction (e.g., the probability of rolling a 6 is 1/6); listing possible outcomes of an experiment.

Number

Apply place-value to partition, rearrange and regroup numbers to 10 000 in multiple ways (e.g., 5,347 = 5 thousands + 3 hundreds + 4 tens + 7 ones, or = 53 hundreds + 47 ones).
Multiplication and division facts (3, 4, 5, 8 timetables) using strategies such as doubling, skip counting and the inverse relationship.
Recognise unit fractions (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10) and represent them using diagrams, number lines and concrete materials.

Algebra

Investigate the conditions that make equations true or false (e.g., is 4 + 3 = 5 + 2 true?) - building early equation understanding.
Use number patterns to make predictions - extending patterns and predicting the 10th or 20th term.
Identify, generalise and extend patterns - children describe patterns using words like "add 3 each time" or "double the previous".

Measurement

Use formal units to measure length (cm, m), mass (g, kg) and capacity (mL, L). Choosing the most appropriate unit for each measurement task.
Investigate the area of regular shapes using square units - counting unit squares on rectangles and other simple shapes.
Tell time to the minute on analog and digital clocks; calculating elapsed time using number lines.

Space

Identify symmetry in 2-D shapes - lines of symmetry; folding to check; identifying shapes with one, two or more lines of symmetry.
Make and connect 3-D objects (cubes, rectangular prisms, pyramids, cylinders, cones) to their nets - the flat shape that folds into the 3-D object.
Read grid coordinates and simple maps - locating positions using alphanumeric grid references (e.g., A3, B5).

Statistics

Collect and organise discrete numerical and categorical data using surveys, tally charts and frequency tables.
Create and interpret data displays - dot plots, column graphs, pictographs (with appropriate scales).
Compare data sets to make conclusions; identify the most / least common value.

Probability

Conduct chance experiments (e.g., rolling a die, spinning a spinner) and predict outcomes before testing.
Use fractions to describe likelihood - 1/2 for equally likely outcomes, 1/4 for less likely, etc.

Numbers up to 9999

Reading, writing and ordering 4-digit numbers - place value of thousands, hundreds, tens, ones; expanded form (e.g., 4527 = 4000 + 500 + 20 + 7).
Place value and expanded form - children write any 4-digit number in expanded form and convert back; compare two 4-digit numbers using <, =, >.
Roman numerals up to XX (1-20) - learning Roman numerals I, V, X and the rules for combining (e.g., IV = 4, IX = 9, XIV = 14, XIX = 19).

Addition & Subtraction

Addition and subtraction of 4-digit numbers with regrouping (carrying and borrowing) using the standard column algorithm.
Story problems - one-step and two-step word problems set in real-life Indian contexts (shopping in rupees, distance in km, students in a school).
Estimation by rounding to the nearest 10, 100 or 1000 before computing - checking whether the actual answer is reasonable.

Multiplication & Division

Multiplication tables of 2 to 12 - memorising and applying through skip counting and word problems.
Multiplication by 1- and 2-digit numbers using the standard algorithm; long division by 1-digit numbers (with and without remainder).
Word problems on multiplication and division set in real-life situations - sharing sweets equally, distributing rupees among children.

Fractions

Like fractions (same denominator) - identifying, reading, writing and comparing like fractions like 2/7 and 5/7.
Addition and subtraction of like fractions (e.g., 2/5 + 1/5 = 3/5).
Half, quarter, three-quarter representation - linking to everyday situations like cutting a chapati, a chocolate bar.

Geometry & Measurement

Lines, angles, plane shapes and their properties - straight lines, curves; types of angles (acute, right, obtuse, straight); polygons and circles.
Perimeter and area of rectangles and squares (informal) - counting unit squares for area; adding side lengths for perimeter.
Length, weight and capacity in standard units (cm, m; g, kg; mL, L) - using rulers, balances and measuring jugs.

Money, Time, Data

Money - rupees and paise; addition, subtraction and simple multiplication in money problems.
Time - reading the clock to 5-minute intervals; converting between hours and minutes; reading a calendar.
Data handling - bar graphs and tally charts; reading and creating them from a small data set.

Number System

Numbers up to 9999 - place value, reading, writing and ordering 4-digit numbers; expanded form.
Roman numerals up to XX (1-20) - reading the rules (I, V, X) and writing time on clocks in Roman numerals.
Rounding off and estimation to the nearest 10, 100 or 1000 - children apply this to check the reasonableness of their answers.

Four Operations

Addition and subtraction with regrouping up to 4 digits using the standard algorithm and mental math strategies.
Multiplication by 2-digit numbers using the standard algorithm; introduction to long multiplication.
Division by 1-digit number with remainders; understanding the division algorithm (dividend / divisor = quotient + remainder).

Fractions

Concept of fractions - representing parts of a whole using diagrams; equivalent fractions (1/2 = 2/4 = 3/6).
Like (same denominator) and unlike (different denominator) fractions - identifying and comparing.
Operations on like fractions - addition and subtraction; word problems involving fractions of a whole (e.g., 1/4 of 20 rupees).

Geometry

Line, line segment, ray and angle - distinguishing each by its properties; symbols and notation.
Plane shapes - properties of triangles, quadrilaterals (square, rectangle, rhombus, parallelogram), circle.
Solids - faces, edges, vertices of cubes, cuboids, cylinders, cones, spheres and pyramids.

Measurement

Length, weight, capacity - converting between standard units (mm-cm-m-km; g-kg; mL-L).
Perimeter of rectangle and square (using formulas P = 2 x (l+b) and P = 4 x s).
Word problems on measurement set in everyday contexts.

Money, Time & Data

Money - addition, subtraction, multiplication of currency in rupees and paise; making change.
Time - clock and calendar problems; reading 24-hour clock; converting between 12-hour and 24-hour formats.
Bar graphs and pictographs - reading and creating from a small data set with appropriate scales.

Number

Read, write and order 4-digit numbers; place value - identifying the value of each digit; comparing using <, =, >.
Recognise multiples of 2, 5 and 10 - children identify multiples up to 10 x 10; introduction to factors.
Fractions - halves, quarters, thirds, fifths, tenths - representing using diagrams, number lines and number sentences.

Calculation

Add and subtract using mental and written methods - column addition / subtraction with regrouping; mental strategies like compensation and partitioning.
Multiplication tables - 2x, 3x, 4x, 5x, 6x, 9x, 10x - mastery through skip counting, arrays and chants.
Division as inverse of multiplication - children use known multiplication facts to solve division problems.

Geometry & Measure

Right angles, horizontal, vertical, perpendicular, parallel lines - identifying these in shapes and the environment.
Measure length, mass and capacity using standard units (cm, m; g, kg; mL, L) - choosing the appropriate tool and unit.
Read clocks to the nearest minute on analog and digital; calculate elapsed time.

Statistics & Probability

Collect, organise and present data in tally charts, frequency tables, bar charts with appropriate scales.
Use Carroll and Venn diagrams to sort by 1 or 2 attributes.
Discuss the likelihood of familiar events using words like "certain", "likely", "unlikely", "impossible".

Thinking & Working Mathematically

Specialising - trying specific examples to test a general statement.
Generalising - noticing patterns and making a rule.
Conjecturing - making predictions based on a pattern; critiquing by explaining why something works.

Whole Numbers

Numbers up to 10 000 - place value, reading, writing, comparing and ordering using <, =, >.
Rounding to nearest 10 / 100 - on a number line; using rounded numbers to estimate sums and differences.
Number patterns - identifying the rule of arithmetic sequences and extending them.

Four Operations

Addition and subtraction within 10 000 using mental, written and algorithmic methods.
Multiplication tables 6, 7, 8, 9 (up to 10 x 10) - mastery through varied practice and games.
Bar model for multiplicative structures - the Singapore signature method for representing groups in word problems.

Fractions

Equivalent fractions - children use diagrams and number lines to identify equivalent fractions (e.g., 1/2 = 2/4 = 3/6).
Comparing and ordering fractions - same numerator (e.g., 2/3 vs 2/5) and same denominator (e.g., 3/8 vs 5/8).
Addition and subtraction of like fractions; word problems involving fractions of a whole.

Length, Mass, Volume

Conversion between units (m to cm; kg to g; L to mL) using place-value reasoning.
Solving word problems involving measurement - 1- and 2-step problems set in real-life contexts.
Estimating and measuring - building intuition for sensible answers before computing.

Money

Adding and subtracting money in decimal notation - aligning the decimal point in column work.
Solving real-life money problems - shopping, change, simple budgeting.
Multi-step word problems involving money and the four operations.

Geometry & Statistics

Angles - right angles, perpendicular and parallel lines; identifying these in 2-D shapes.
Area and perimeter - introduction to counting square units and adding side lengths.
Bar graphs - reading and constructing with appropriate scales and axis labels.

Note

Cambridge IGCSE 0580 Maths is sat in Years 10-11. For Grade 3 the Cambridge Primary Stage 3 framework above is followed.
IGCSE-track international schools use Cambridge Primary at this stage, with each Stage building the foundations that the IGCSE syllabus depends on.
WinQuest scaffolds Cambridge Primary skills onto the later IGCSE assessment objectives so the long-term progression feels seamless.

Grade 4

Age 9+ 60 hrs

Operations & Algebraic Thinking

Multiplicative comparison and multi-step word problems - children solve problems by using the four operations (e.g., "Mary has 4 times as many apples as John") and represent these with equations using a letter for the unknown.
Factors, multiples, prime / composite numbers - finding all factor pairs of a whole number 1-100; recognising prime numbers (only 1 and itself as factors) and composite numbers.
Generate and analyse patterns - children build a number / shape pattern from a given rule and identify features of the pattern that are not explicit in the rule.

Number & Operations in Base Ten

Multi-digit whole numbers up to 1 million - place value of millions, hundred-thousands, ten-thousands, thousands; comparing and rounding multi-digit numbers.
Multi-digit multiplication using the standard algorithm; long division (up to 4-digit dividend by 1-digit divisor) with remainder.
Place-value understanding and rounding - rounding to any place; understanding that the value of each digit is 10 times what it would be in the place to its right.

Number & Operations - Fractions

Equivalent fractions and comparing fractions with different denominators using benchmark fractions (1/2) and common denominators.
Add and subtract fractions and mixed numbers with like denominators (e.g., 1 1/4 + 2 3/4 = 4) using visual models and equations.
Multiply a fraction by a whole number (e.g., 3 x 1/4 = 3/4); introduction to decimals to hundredths and their relationship to fractions (e.g., 0.62 = 62/100).

Measurement & Data

Convert larger units to smaller units within a measurement system (e.g., 2 km = 2,000 m; 1 hour = 60 minutes; 1 kg = 1,000 g).
Area and perimeter of rectangles using the formulas A = l x w and P = 2(l + w); applying these to real-world problems.
Line plots displaying measurements in fractions (1/2, 1/4, 1/8); angle measurement in degrees using a protractor; classifying angles as acute, right, obtuse, straight.

Geometry

Draw and identify lines (line, line segment, ray) and angles (right, acute, obtuse); classify two-dimensional shapes by the presence or absence of parallel / perpendicular lines or angles of a specified size.
Lines of symmetry in 2-D figures - identifying shapes with one or more lines of symmetry; folding to check.

Number Sense

Whole numbers up to 10 000 and decimals to tenths - reading, writing, comparing and ordering using multiple representations.
Fractions - equivalent fractions, comparing fractions, mixed numbers and improper fractions, converting between them.
Composing and decomposing numbers in multiple ways using place value (e.g., 3,847 = 3 thousands + 8 hundreds + 4 tens + 7 ones, or 38 hundreds + 47 ones).

Operations

Multi-digit addition and subtraction using the standard algorithm and mental math strategies (compensation, partitioning, friendly numbers).
Multiplication and division by 1-digit numbers using the standard algorithm; estimation before computing.
Multiplication facts to 10 x 10 - mastery through games, chants and timed practice.

Algebra & Coding

Patterns - linear growing patterns (e.g., 3, 7, 11, 15 - rule "+4") and shrinking patterns (e.g., 50, 45, 40, 35 - rule "-5").
Solve equations involving one variable using objects, drawings or the inverse operation (e.g., x + 7 = 15 so x = 8).
Coding (Ontario's new strand) - decomposition (breaking a problem into smaller parts), conditional statements (if / then) using ScratchJr or Code.org.

Measurement

Length, area, perimeter - converting between mm, cm, m and km; calculating perimeter and area of rectangles using formulas.
Area of rectangles, parallelograms, triangles (introduction) - using the appropriate formula for each shape.
Time - reading 24-hour clock (e.g., 17:30 = 5:30 pm); calculating elapsed time using number lines.

Geometry & Spatial Sense

Classify polygons (including quadrilaterals - parallelogram, rhombus, trapezoid, kite) by their properties (sides, angles, symmetry).
Identify lines of symmetry; geometric transformations (translations, reflections, rotations) on a grid.
Use coordinates on the Cartesian plane (Quadrant I only) - locating and plotting ordered pairs.

Data & Probability

Bar graphs, pictographs, line plots, stem-and-leaf plots - reading and constructing each.
Mean (average), median (middle value), mode (most common) of a data set; identifying which measure is most useful for given data.
Theoretical probability (e.g., 1 in 6 for rolling a 6) vs experimental probability (results from actually doing the experiment).

Number

Recognise, represent and compare numbers up to 10 000 using place value; partitioning numbers in multiple ways.
Multiplication facts to 10 x 10 and the related division facts - mastery through games, arrays and the inverse relationship.
Decimals - tenths and hundredths represented on a number line and in fraction form (e.g., 0.7 = 7/10; 0.43 = 43/100).

Algebra

Find unknown values in numerical equations (e.g., 4 + ? = 11) using the inverse operation or trial and error.
Patterns - children extend and create patterns with shapes (geometric) and numbers, describing the rule in words and symbols.
Use the inverse relationship between addition and subtraction, and between multiplication and division, to check answers.

Measurement

Choose appropriate units and tools to measure - rulers for short lengths, tape measures for longer, scales for mass, jugs for capacity.
Compare areas of regular and irregular shapes by counting squares or partitioning into known shapes.
Compare 12- and 24-hour time; convert between the two systems and read both on analog and digital clocks.

Space

Compare 2-D shapes (polygons) and 3-D objects (prisms, pyramids, cylinders, cones, spheres); recognise their nets.
Locate positions using directional language (forward, backward, left, right, clockwise, anticlockwise) and a key on a map.
Symmetry - rotation, reflection, translation; identifying symmetry in everyday objects and patterns.

Statistics

Construct and interpret column graphs and dot plots with appropriate scales for the data being represented.
Identify mode of a categorical data set; recognise when mode is more useful than mean.
Make predictions from data - using a graph to forecast what might happen next.

Probability

Identify everyday events involving chance (weather, dice, coin flip) and predict the likelihood of each outcome.
Order outcomes from least to most likely using the language "impossible", "unlikely", "even chance", "likely", "certain".

Large Numbers

Numbers up to lakhs and ten lakhs (1 lakh = 100,000; 10 lakh = 1 million) using Indian place value (ones, tens, hundreds, thousands, lakhs).
Indian and International place value systems - learning to switch between them (e.g., 12,34,567 in Indian = 1,234,567 in International).
Comparison, ordering and rounding off to nearest 10, 100, 1000 or 10,000 before computing estimates.

Operations on Large Numbers

Addition and subtraction of large numbers (up to 6 digits) using the standard column algorithm with regrouping.
Multiplication by 2- and 3-digit numbers using the standard algorithm; long division by 1- and 2-digit divisors.
BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction) - introduction to the order of operations.

Multiples & Factors

Factors and multiples of numbers - factor pairs, multiples in sequence; tests of divisibility for 2, 3, 5, 9, 10.
Prime, composite, even, odd numbers - identifying each by their factor properties.
HCF (Highest Common Factor) and LCM (Lowest Common Multiple) - introduction by listing method.

Fractions & Decimals

Like and unlike fractions; equivalent fractions; converting unlike to like fractions using LCM of denominators.
Addition and subtraction of like and unlike fractions; mixed numbers.
Decimals - tenths and hundredths; addition, subtraction, comparison and conversion between fractions and decimals.

Geometry & Measurement

Lines, angles (acute, obtuse, right, straight), triangles (scalene, isosceles, equilateral), quadrilaterals (square, rectangle, parallelogram, rhombus), circles.
Perimeter and area of squares and rectangles using formulas; word problems involving perimeter and area.
Length (mm-cm-m-km), weight (g-kg), capacity (mL-L), time (sec-min-hr) and their conversions.

Data & Money

Money - addition, subtraction, multiplication and division of money in rupees and paise; budgeting word problems.
Time - 24-hour clock; conversion between 12-hour and 24-hour formats; reading railway / airline timetables.
Bar graphs - reading and drawing with appropriate scales and axis labels.

Number System

Indian and International numeration systems - the Indian system uses lakh and crore; the International uses million and billion.
Place value, comparison and ordering of large numbers up to crores.
Roman numerals up to L (50) - rules I, V, X, L; combining them (e.g., XLIX = 49, XLVI = 46).

Four Operations

Multi-digit addition, subtraction, multiplication and division using the standard algorithms.
Properties of operations and BODMAS rule (order of operations).
Word problems involving the four operations set in real-life Indian contexts.

Factors, Multiples & Fractions

Factors, multiples, prime and composite numbers; tests of divisibility (2, 3, 5, 9, 10).
HCF and LCM by listing method; using them in word problems (e.g., finding the largest tile that fits a floor).
Fractions - addition, subtraction, multiplication of fractions; mixed and improper fractions.

Decimals

Decimal place value up to thousandths; reading and writing decimal numbers.
Addition and subtraction of decimals using column alignment of the decimal point.
Conversion between fractions and decimals (e.g., 3/4 = 0.75; 1/8 = 0.125).

Geometry

Lines, angles - acute, obtuse, right, straight, reflex; measuring angles using a protractor.
Triangles (scalene, isosceles, equilateral), quadrilaterals (square, rectangle, rhombus, parallelogram, trapezium), circles - their properties.
Symmetry - rotational and reflective; identifying symmetry in shapes and patterns.

Measurement & Data

Perimeter and area of squares, rectangles, triangles using standard units.
Conversions of units (length, weight, capacity, time) - applying in word problems.
Bar graphs and pictographs with appropriate scales; reading and constructing.

Number

Read, write and order 5-digit numbers; introduction to negative numbers (e.g., temperatures below zero, bank balances).
Multiples and factors; common multiples (LCM) and common factors (HCF) by listing.
Fractions, decimals, percentages - introduction; the equivalence between 1/2, 0.5 and 50 percent.

Calculation

Add and subtract decimals to two decimal places; multi-digit multiplication using the standard algorithm.
Multiplication facts to 12 x 12 - mastery through varied practice and applied problems.
Mental strategies for division - using known multiplication facts and partitioning.

Geometry & Measure

Lines and angles - identifying and measuring with a protractor (acute, right, obtuse, reflex).
Perimeter and area of rectangles and compound shapes (rectilinear figures made of rectangles).
Time on a 12- and 24-hour clock; calculating elapsed time using number lines.

Statistics & Probability

Collect, organise and present data using frequency tables and dot plots with appropriate scales.
Find the mode of a data set; comparing mode with mean and median.
Use the language of probability (impossible, unlikely, even chance, likely, certain).

Thinking & Working Mathematically

Identifying and characterising - describing the properties of numbers, shapes or patterns.
Predicting and convincing - making and justifying a mathematical prediction.
Improving and connecting - refining a first attempt at a problem and linking it to previous learning.

Whole Numbers

Numbers up to 100 000 - place value, reading, writing, comparing and ordering.
Multiplication and division by 1- and 2-digit numbers using the standard algorithm.
Order of operations without brackets (multiplication and division before addition and subtraction).

Fractions

Mixed numbers and improper fractions - converting between the two forms.
Addition and subtraction of mixed numbers using common denominators.
Word problems involving mixed numbers (e.g., 2 1/4 cakes shared among 3 children).

Decimals

Decimals up to 3 decimal places - reading, writing, comparing and ordering.
Rounding decimals to the nearest whole number, tenth, hundredth.
Four operations on decimals - addition, subtraction, multiplication by 1-digit, division by 1-digit.

Geometry

Perpendicular and parallel lines - identifying and drawing using a set square.
Squares and rectangles - area and perimeter using formulas; word problems.
Symmetry in 2-D figures - identifying lines of symmetry and drawing them.

Measurement

Conversions involving decimals (e.g., 1.5 km = 1500 m; 2.5 kg = 2500 g).
Time - duration on a 12- or 24-hour clock; reading timetables.
Composite figures - calculating area and perimeter of L-shapes and other rectilinear shapes.

Statistics & Tables

Tables - reading and constructing with appropriate row and column headers.
Bar graphs - reading and constructing with different scales (1 unit = 5 / 10 / 20).
Average (mean) - introduction; finding the average of a small set of values.

Note

Cambridge IGCSE 0580 Maths is sat in Years 10-11. For Grade 4 the Cambridge Primary Stage 4 framework above is followed.
IGCSE-track international schools use Cambridge Primary at this stage, with each Stage building the foundations that the IGCSE syllabus depends on.
WinQuest scaffolds Cambridge Primary skills onto the later IGCSE assessment objectives so the long-term progression feels seamless.

Grade 5

Age 10+ 60 hrs

Operations & Algebraic Thinking

Write and interpret numerical expressions and apply the order of operations (PEMDAS - Parentheses, Exponents, Multiplication / Division, Addition / Subtraction) including grouping symbols.
Analyse patterns and relationships using two rules - children form ordered pairs from corresponding terms of two patterns and graph them on a coordinate plane.
Coordinate pairs on the first quadrant - graphing real-world and mathematical problems involving ordered pairs.

Number & Operations in Base Ten

Place value to thousandths and powers of 10 - children use exponents to denote powers of 10 (e.g., 10^3 = 1,000) and explain patterns when multiplying or dividing by powers of 10.
Multi-digit multiplication using the standard algorithm (4-digit by 2-digit) and division (4-digit by 2-digit divisor) with remainders.
Add, subtract, multiply and divide decimals to hundredths using strategies based on place value, properties of operations and the relationship between operations.

Number & Operations - Fractions

Add and subtract fractions with unlike denominators by finding a common denominator; including mixed numbers.
Multiply a fraction by a fraction using visual models (area models) and understand that the product can be less than either factor.
Divide unit fractions by whole numbers (e.g., 1/4 / 5 = 1/20) and whole numbers by unit fractions (e.g., 6 / 1/4 = 24).

Measurement & Data

Convert measurement units (mm-cm-m-km; g-kg-tonne; mL-L) using place-value reasoning and multiplication / division.
Volume of right rectangular prisms using V = l x w x h and V = base area x height; understanding that volume is measured in cubic units.
Line plots displaying measurements in fractions of a unit (1/2, 1/4, 1/8); using data to solve real-world problems.

Geometry

Graph points on the coordinate plane (Quadrant I only) - using the convention that the first number is x (horizontal) and the second is y (vertical).
Classify two-dimensional figures based on properties (parallel / perpendicular sides, equal-length sides, equal angles).
Hierarchy of shapes - children understand that attributes belonging to a category of shapes also belong to all subcategories (e.g., all rectangles are parallelograms).

Number Sense

Whole numbers and decimals to thousandths - reading, writing, comparing and ordering using multiple representations.
Equivalent fractions; converting between fractions, decimals and percentages (e.g., 3/4 = 0.75 = 75 percent).
Ratios and percentages - introduction; using ratios to compare quantities and percentages to express parts of 100.

Operations

Four operations on whole numbers and decimals - using standard algorithms with regrouping; mental math strategies.
Multiplication and division by 1- and 2-digit numbers using standard algorithm; estimation before computing.
BEDMAS (Brackets, Exponents, Division, Multiplication, Addition, Subtraction) - applying the order of operations correctly.

Algebra & Coding

Patterns - linear (constant change, e.g., +3 each step) and non-linear (changing rate of change) growing and shrinking patterns.
Solve simple equations with one variable using inverse operations (e.g., x + 8 = 15 means x = 7).
Coding (Ontario's new strand) - debugging and modifying code; predicting output before running.

Measurement

Area of triangles (A = 1/2 x b x h), parallelograms (A = b x h), trapezoids (A = 1/2 x (a + b) x h) using the appropriate formula.
Volume of rectangular prisms using V = l x w x h; understanding cubic centimetre (cm^3) and cubic metre (m^3).
Time - elapsed time problems with start and end times across hours and days; converting between time units.

Geometry & Spatial Sense

Polygons - regular (all sides equal) vs irregular; congruent shapes (same size and shape) vs similar shapes.
Transformations on the Cartesian plane - translations, reflections, rotations of polygons on a coordinate grid.
2-D and 3-D figures - properties; classifying solids by faces, edges, vertices and the shape of their bases.

Data & Probability

Stem-and-leaf plots, line graphs, double-bar graphs - reading and constructing each type.
Mean (average), median (middle), mode (most common) and range (max minus min) of a small data set.
Theoretical probability of two independent events (e.g., flipping two coins) using fractions and lists.

Number

Compare and order decimal numbers to thousandths using place value; including on a number line.
Identify and describe factors and multiples; common factors and multiples between two numbers.
Compare fractions with related denominators (e.g., 2/5 and 3/10) by finding a common denominator.

Algebra

Identify patterns in number and shape; describe their rules using words and symbols.
Solve simple equations using inverse operations - children apply this systematically to find an unknown.
Recognise functional relationships (e.g., y = 2x + 1) and represent them in tables, graphs and rules.

Measurement

Choose appropriate metric units (mm, cm, m, km; g, kg; mL, L) to measure given everyday objects and quantities.
Calculate perimeter and area of rectangles using formulas; deriving the area formula for the triangle as half the area of a rectangle.
Compare 12- and 24-hour time systems; convert between them; read both digital and analog clocks.

Space

Connect 3-D objects (cubes, rectangular prisms, pyramids, cylinders, cones) with their nets - the flat shape that folds into the object.
Describe translations, reflections and rotations of 2-D shapes; predict the result of a transformation.
Locate position using grid references on maps; describing routes using compass directions.

Statistics

Pose investigative questions; collect data from surveys or experiments; organise in frequency tables.
Construct and interpret data displays - dot plots, line graphs, column graphs - with appropriate scales.
Calculate the mean (average) of a small data set; identify mean as one measure of "typical" value.

Probability

List outcomes of chance experiments using systematic methods (lists, tables, tree diagrams).
Assign probabilities as fractions or decimals based on the number of favourable outcomes.

Large Numbers & Operations

Numbers up to crores (1 crore = 10 million) using Indian place value (ones, tens, hundreds, thousands, lakhs, crores) and International (millions, billions).
Operations on large numbers - addition, subtraction, multiplication, division; estimation before computing.
BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction) - applying in multi-step calculations.

Factors & Multiples

HCF (Highest Common Factor) by prime factorisation, division and listing methods.
LCM (Lowest Common Multiple) by prime factorisation, division and listing methods.
Tests of divisibility for 2, 3, 4, 5, 6, 8, 9, 10, 11; applying HCF and LCM in word problems.

Fractions & Decimals

Operations on fractions including multiplication of a fraction by a fraction and division of fractions.
Decimals up to thousandths - place value, comparing, ordering; addition, subtraction, multiplication, division.
Conversion between fractions, decimals and percentages; word problems involving discounts and tax.

Geometry

Angles - types (acute, right, obtuse, straight, reflex) and construction using protractor and ruler.
Triangles, quadrilaterals, circles - properties (sides, angles, vertices, diagonals).
Symmetry - lines of symmetry; rotational symmetry; identifying in real-life objects.

Measurement

Perimeter and area of squares, rectangles, triangles using formulas.
Volume of cuboids - introduction using V = l x b x h with cubic centimetres and cubic metres.
Conversion of units of length, weight, capacity, time - applying in real-life word problems.

Data Handling

Pictographs and bar graphs - reading and constructing with appropriate scales.
Pie charts - introduction; reading and interpreting given pie charts.
Average (mean) - introduction; finding mean of a small data set.

Number System

Place value up to crores (Indian) and millions (International); rounding and estimation.
Operations on whole numbers and decimals - applying standard algorithms.
Roman numerals - extending beyond 50 to 100 (C); rules for combining I, V, X, L, C.

Factors, Multiples, Fractions

Prime factorisation; HCF and LCM by prime factorisation, division and listing methods.
Operations on fractions - addition, subtraction, multiplication, division.
Word problems on fractions - applying in real-life contexts (cutting cakes, sharing, distance).

Decimals & Percentages

Decimal place value up to thousandths; conversion between fractions, decimals, percentages.
Operations on decimals - addition, subtraction, multiplication by whole numbers and decimals.
Percentage - introduction; finding percentage of a quantity (e.g., 25 percent of 80).

Geometry

Angles - measurement and construction using protractor; types of angles.
Triangles - types by sides (scalene, isosceles, equilateral) and angles (acute, right, obtuse); angle sum property (sum of angles = 180 degrees).
Circles - parts (centre, radius, diameter, chord, arc, sector, segment) and properties.

Measurement

Perimeter and area of plane figures; volume of cuboid using V = l x b x h.
Time and money - applications including profit and loss simple problems.
Speed - introduction using the relationship speed = distance / time.

Data Handling

Bar graphs, pictographs - reading and constructing.
Mean of ungrouped data - finding the average of a small data set.
Pie charts - reading and interpreting given pie charts.

Number

Read, write, compare and order numbers up to 1 million; place value of millions.
Multiples, factors, common multiples (LCM) and common factors (HCF) by listing and prime factorisation.
Equivalent fractions, decimals and percentages - converting between the three forms.

Calculation

Add and subtract decimals to two decimal places using column alignment of the decimal point.
Multiply and divide whole numbers and decimals by 10, 100, 1000 using place-value reasoning.
Long multiplication (3-digit by 2-digit) and short division (4-digit by 1-digit) using the standard algorithm.

Geometry & Measure

Identify types of triangles (scalene, isosceles, equilateral) and quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium, kite); lines of symmetry in each.
Area of compound shapes (rectilinear figures); volume of cubes (V = s^3) and cuboids (V = l x w x h).
Convert between units of length (mm, cm, m, km), mass (g, kg, tonne), capacity (mL, L).

Statistics & Probability

Construct and interpret line graphs (e.g., temperature over a day) and dual bar charts (comparing two sets).
Find and interpret mode (most common) and median (middle value when ordered).
Predict outcomes of simple experiments using fractions or percentages.

Thinking & Working Mathematically

Conjecturing (making a mathematical prediction) and convincing (justifying it with reasoning or example).
Specialising (testing a general statement with specific cases) and generalising (forming a rule from cases).
Critiquing solutions - evaluating someone else's method and identifying any errors.

Whole Numbers

Numbers up to 10 million - place value, reading, writing, comparing, ordering.
Order of operations involving brackets - applying BODMAS / PEMDAS rule.
Multiplication and division by 10s, 100s, 1000s using place-value reasoning.

Fractions

Division of a proper fraction by a whole number (e.g., 1/2 / 3 = 1/6).
Conversion between mixed numbers and improper fractions; addition and subtraction of fractions with related denominators.
Word problems involving fractions of a whole or set; using bar models to represent.

Decimals & Percentages

Multiplication and division of decimals - including by powers of 10.
Conversion between fractions, decimals and percentages.
Percentages - finding part of a whole (e.g., 30 percent of 50 = 15) and applying in real-life contexts.

Ratio

Ratio as a comparison of two quantities (e.g., 3:5 means for every 3 of A there are 5 of B).
Equivalent ratios; simplifying ratios to lowest terms.
Solving simple ratio problems using bar models - the Singapore signature method.

Geometry & Measurement

Angles - properties of triangles (angle sum = 180 degrees) and quadrilaterals (angle sum = 360 degrees).
Area of triangles using A = 1/2 x b x h.
Volume of a cube (V = s^3) and cuboid (V = l x b x h).

Data Handling

Average (mean) of a set of data - finding average and using it in word problems.
Pie charts - reading and interpreting; using fractions and percentages.
Word problems on average - finding total from average or finding missing value.

Note

Cambridge IGCSE 0580 Maths is sat in Years 10-11. For Grade 5 the Cambridge Primary Stage 5 framework above is followed.
IGCSE-track international schools use Cambridge Primary at this stage. Stages 1-6 build the foundations for Lower Secondary Stages 7-9 and then IGCSE Year 10-11.
WinQuest scaffolds Cambridge Primary skills onto the later IGCSE assessment objectives.

Grade 6

Age 11+ 60 hrs

Ratios & Proportional Relationships

Ratio language - children understand that "the ratio of wings to beaks is 2 to 1" describes a relationship; rate as a per-unit comparison.
Use tables, tape diagrams, double number lines and equations to reason about ratios and rates.
Solve real-world rate and percent problems - including unit pricing, constant speed, and percent of a quantity.

The Number System

Divide fractions by fractions (e.g., 2/3 / 1/4 = 8/3) using visual models and the standard algorithm.
Add, subtract, multiply and divide multi-digit decimals using the standard algorithm; find GCF and LCM of two whole numbers.
Rational numbers - introduce negative numbers on the number line; understand absolute value; identify opposites.

Expressions & Equations

Write, read and evaluate algebraic expressions using variables; apply properties (commutative, associative, distributive) to generate equivalent expressions.
Solve one-variable equations and inequalities using inverse operations; graph solutions on a number line.
Represent and analyse quantitative relationships between dependent and independent variables using tables and graphs.

Geometry

Area of triangles (A = 1/2 x b x h) and special quadrilaterals (parallelogram, trapezoid, rhombus, kite) by decomposing and rearranging.
Volume of right rectangular prisms with fractional edge lengths using V = l x w x h or V = base area x height.
Draw polygons on the coordinate plane using ordered pairs; find surface area of 3-D figures using nets.

Statistics & Probability

Recognise statistical questions as those that anticipate variability; describe distributions by their shape (skewed, symmetric).
Measures of centre (mean, median, mode) and variability (range, interquartile range, mean absolute deviation).
Display data with dot plots, histograms and box plots; choose the most appropriate display for given data.

Number Sense

Whole numbers, decimals, fractions, percents and integers - reading, writing, comparing, ordering on a number line.
Convert between fractions, decimals and percents (e.g., 3/8 = 0.375 = 37.5 percent).
Apply ratio and rate concepts (e.g., 2:3 ratio, 60 km/h rate) in real-world problems.

Operations

Order of operations with decimals and fractions (BEDMAS) - applying brackets, exponents, division / multiplication, addition / subtraction.
Multi-step problems with fractions and decimals - including percent of a quantity in money contexts.
Mental math strategies for percent - 10 percent, 50 percent, 25 percent quick calculations.

Algebra & Coding

Patterns - linear growing patterns; expressing the rule as an algebraic expression (e.g., 3n + 1).
Solve simple equations using inverse operations (one-step and two-step equations).
Coding (Ontario's new strand) - efficient algorithms; comparing two algorithms for the same problem.

Measurement

Area of trapezoids (A = 1/2 x (a + b) x h), parallelograms (A = b x h) and triangles (A = 1/2 x b x h).
Surface area of prisms by adding the areas of the faces (rectangles + 2 triangles for triangular prism).
Volume of prisms (V = base area x height) for triangular, rectangular and other prisms.

Geometry & Spatial Sense

Properties of polygons; congruent (same size and shape) and similar (same shape, different size) figures.
Construct angle bisectors and perpendicular bisectors using compass and ruler.
Cartesian coordinates - all 4 quadrants; plotting and identifying ordered pairs in each quadrant.

Data & Probability

Histograms (continuous data), line graphs (change over time), scatter plots (two-variable data).
Mean, median, mode, range; identifying outliers and their effect on each measure.
Theoretical probability (calculated) vs experimental probability (observed); the law of large numbers.

Number

Identify, describe and use rational numbers (positive and negative fractions and decimals).
Locate decimal numbers on a number line, including between consecutive whole numbers.
Multiply and divide decimals using the standard algorithm and place-value reasoning.

Algebra

Generate, describe and recognise number patterns including those with negative numbers.
Use algebraic conventions and notation (e.g., 3a means 3 x a; ab means a x b).
Solve simple linear equations using inverse operations and the balance method.

Measurement

Calculate perimeter and area of plane shapes (rectangles, triangles, parallelograms, trapezoids).
Connect volume and capacity (1 cm^3 = 1 mL; 1 m^3 = 1000 L).
Use formulas for area (rectangle, triangle, parallelogram) and volume (rectangular prism).

Space

Construct 2-D shapes and 3-D objects from given properties; draw nets of common solids.
Identify and describe transformations (translation, reflection, rotation, dilation) of 2-D shapes.
Coordinate plane in all four quadrants; plotting points and recognising patterns.

Statistics

Compare data sets using mean, median, mode and range; identifying which measure best describes the data.
Interpret data displays with continuous data (histograms, line graphs).
Plan a statistical investigation - formulate question, collect data, analyse, present and interpret.

Probability

Describe probabilities of events as fractions, decimals or percentages between 0 and 1.
Conduct probability experiments and compare predicted vs actual outcomes; explain the difference using the law of large numbers.

Knowing Our Numbers & Whole Numbers

Large numbers - Indian system (lakh, crore) and International system (million, billion); switching between them.
Estimation and rounding to nearest 10, 100, 1000, 10000; Roman numerals up to L (50) and C (100).
Properties of whole numbers - closure, commutative, associative and distributive properties.

Integers & Fractions

Integers - representation on number line, addition and subtraction; using "+" and "-" signs.
Fractions - all four operations on fractions and mixed numbers; word problems.
Decimals - addition, subtraction, multiplication, division; conversions between fractions and decimals.

Algebra

Variables, constants and algebraic expressions - introducing letters to represent unknowns.
Equations - introduction; solving simple equations using inverse operations.
Use of algebra in patterns - generalising patterns using algebraic expressions.

Geometry

Basic geometric ideas - points, lines, line segments, rays, angles, polygons.
Properties of triangles and quadrilaterals - angle sum, sides, vertices.
Circles - centre, radius, diameter, chord, arc; basic constructions using compass and ruler.

Mensuration

Perimeter and area of squares, rectangles, triangles using formulas.
Conversions of units of measurement (length, weight, capacity, time).
Word problems on area and perimeter in real-life contexts.

Data Handling, Ratio, Symmetry

Pictographs, bar graphs, double bar graphs - reading and constructing.
Ratio and proportion - introduction; equivalent ratios; unitary method.
Symmetry - line symmetry and rotational symmetry; identifying axes of symmetry.

Number System

Indian and international numeration; reading, writing, comparing numbers up to crores / billions.
Operations on whole numbers, integers, decimals; properties of operations.
Squares (of numbers up to 30), cubes (up to 20), square roots by prime factorisation.

Fractions, Ratio, Percentage

All four operations on fractions; word problems involving fractions in real-life contexts.
Ratio and proportion - simplification, equivalent ratios, unitary method.
Percentage - conversion between percentages, fractions, decimals; applications in profit / loss / discount.

Algebra

Algebraic expressions and equations - terms, coefficients, variables, constants.
Solving simple linear equations using inverse operations.
Word problems leading to equations - translating English statements into algebraic equations.

Geometry

Lines, angles, triangles, quadrilaterals - basic properties.
Properties of triangles - angle sum property (180 degrees); exterior angle property.
Construction of angles, triangles using ruler and compass; basic geometric constructions.

Mensuration

Perimeter and area of rectangle, square, triangle using formulas.
Volume and surface area of cuboid (V = l x b x h; SA = 2(lb + bh + hl)).
Conversion of units in length, area, volume; word problems.

Statistics & Symmetry

Pictographs and bar graphs - reading and constructing with appropriate scales.
Mean of ungrouped data; finding average of a small data set.
Symmetry - reflection symmetry (lines of symmetry) and rotational symmetry.

Number

Negative numbers in real-life contexts (temperatures, bank balances); plotting integers on a number line.
Square numbers (1, 4, 9, 16, 25, ...) and cube numbers (1, 8, 27, 64, ...); recognising patterns.
Decimals, percentages, fractions equivalences (e.g., 3/4 = 0.75 = 75 percent).

Calculation

Multi-step problems involving the four operations on whole numbers, fractions and decimals.
Order of operations including brackets (BIDMAS / PEMDAS).
Multiplication and division of decimals by whole numbers and by other decimals.

Geometry & Measure

Properties of triangles (scalene, isosceles, equilateral) and quadrilaterals (parallelogram, rhombus, kite, trapezium).
Area of triangles (1/2 x b x h) and parallelograms (b x h).
Volume of cuboids using V = l x w x h.

Statistics & Probability

Construct and interpret pie charts using fractions and percentages.
Find mean, median, mode and range; choosing the appropriate measure for given data.
Compare experimental and theoretical probabilities; explain the convergence as trials increase.

Algebra (introductory)

Use letters to represent unknowns - introducing algebraic notation.
Form and solve simple equations using inverse operations.
Sequence rules in words and symbols (e.g., "add 4 each time" or T(n) = 4n + 1).

Fractions & Ratio

Four operations on fractions including mixed numbers.
Ratio - equivalent ratios, simplifying ratios, comparing 3 quantities (a : b : c).
Word problems involving ratio and fractions; using bar models.

Percentage

Percentage of a quantity (e.g., 30 percent of 80 = 24).
Increase / decrease by a percentage (e.g., increase 60 by 25 percent = 75).
Real-life percentage word problems - discount, GST, profit, loss.

Geometry

Angles in a triangle (sum = 180), on a straight line (sum = 180), around a point (sum = 360).
Properties of triangles (equilateral, isosceles, scalene) and quadrilaterals.
Net of solids (cube, cuboid, prism, pyramid); identifying the solid from the net.

Measurement

Speed = distance / time; average speed; converting between km/h and m/s.
Volume of cubes (s^3) and cuboids (l x b x h).
Area of triangles, parallelograms, trapeziums; area of composite figures.

Algebra (introductory)

Using letters to represent numbers; conventions like 3a, a + b.
Algebraic expressions - formulating and evaluating by substitution.
Solving simple linear equations using inverse operations and the balance method.

Data Analysis

Pie charts - drawing using angles proportional to fractions / percentages.
Average problems - finding total from average, finding missing value.
Distance / time / speed problems - using the formula triangle.

Note

Cambridge IGCSE 0580 Maths is sat in Years 10-11. For Grade 6 the Cambridge Primary Stage 6 framework above is followed (this is the last Primary stage before Lower Secondary Stages 7-9).
IGCSE-track international schools use Cambridge Primary at this stage. Stage 6 builds the foundations of fractions, algebra and proportional reasoning that the IGCSE depends on.
WinQuest scaffolds Cambridge Primary skills onto the later IGCSE assessment objectives.

Grade 7

Age 12+ 60 hrs

Ratios & Proportional Relationships

Compute unit rates with fractions (e.g., a person walks 1/2 mile in 1/4 hour = 2 miles per hour).
Recognise and represent proportional relationships between quantities using tables, equations and graphs (straight line through origin).
Use proportional relationships to solve multi-step ratio and percent problems including simple interest, tax, markups, markdowns, gratuities, commissions, percent error.

The Number System

Apply and extend previous understanding of operations with rational numbers (all four operations on positive and negative fractions and decimals).
Add, subtract, multiply and divide positive and negative integers and fractions using the properties of operations.
Convert rational numbers to decimals - distinguishing between terminating (e.g., 1/4 = 0.25) and repeating decimals (e.g., 1/3 = 0.333...).

Expressions & Equations

Use properties of operations to add, subtract, factor and expand linear expressions with rational coefficients (e.g., 3x + 4 = 4 + 3x; 2(x + 3) = 2x + 6).
Solve multi-step real-life problems with rational numbers, judging whether answers are reasonable.
Solve word problems leading to two-step equations (px + q = r) and inequalities (px + q > r); graph solutions on a number line.

Geometry

Scale drawings and computations with actual lengths and areas; reproducing a scale drawing at a different scale.
Construct triangles given three measurements (SSS, SAS, ASA); recognise when these uniquely determine a triangle.
Area (including circles using A = pi r^2), surface area and volume of 2-D and 3-D figures (prisms, pyramids, cylinders).

Statistics & Probability

Random sampling to make inferences about populations; understanding that random samples produce representative results.
Compare two populations using measures of centre (mean, median) and spread (range, IQR, mean absolute deviation).
Develop, use and compare probability models including uniform and non-uniform; use simulation to estimate probabilities.

Number Sense

Integers and rational numbers; operations on all (addition, subtraction, multiplication, division of positive and negative rationals).
Ratio, rate and proportion - solving real-world problems including conversions and currency exchange.
Powers and exponents - introduction; using a^n notation for whole-number exponents.

Operations

Four operations with integers and fractions using standard algorithms and mental strategies.
Order of operations with rational numbers (BEDMAS); applying brackets, exponents, division / multiplication, addition / subtraction.
Estimation and mental math - rounding before computing; checking the reasonableness of answers.

Algebra & Coding

Solve linear equations with one variable (one-step, two-step, multi-step) using the balance method and inverse operations.
Algebraic expressions - simplification (combining like terms) and expansion (using distributive property).
Coding (Ontario's new strand) - using nested events (events within events); reading and writing more complex code.

Measurement

Area of circles using A = pi r^2; circumference using C = 2 pi r or C = pi d.
Surface area and volume of cylinders using SA = 2 pi r h + 2 pi r^2 and V = pi r^2 h.
Conversion between metric units of length, area, volume, mass and capacity.

Geometry & Spatial Sense

Geometric properties of polygons (interior and exterior angles) and circles (chord, tangent, secant).
Congruence (same size and shape) and similarity (same shape, different size); using ratios of corresponding sides.
Transformations on coordinate plane (4 quadrants) - translations, reflections, rotations, dilations.

Data & Probability

Histograms (continuous data), scatter plots (two-variable data), box-and-whisker plots (5-number summary).
Measures of central tendency (mean, median, mode) and spread (range, IQR); identifying outliers.
Probability - independent events (one doesn't affect the other) and dependent events; multiplication rule for P(A and B).

Number

Solve problems involving the four operations with integers, decimals and fractions; including with negative numbers.
Compare, order and operate with rational numbers; place them on a number line.
Investigate index notation (3^2 = 9; 4^3 = 64) and represent whole numbers as products of prime factors (e.g., 60 = 2^2 x 3 x 5).

Algebra

Substitute pronumerals (variables) to evaluate algebraic expressions (e.g., if x = 3, then 2x + 5 = 11).
Simplify algebraic expressions involving the four operations - combining like terms and using distributive law.
Solve simple linear equations using the balance method and inverse operations.

Measurement

Establish formulas for area of rectangles, triangles, parallelograms by decomposing and rearranging.
Calculate volumes of rectangular prisms using V = l x b x h.
Investigate the relationship between features of circles (circumference / diameter = pi).

Space

Geometric reasoning with parallel lines cut by a transversal - corresponding, alternate, co-interior angles.
Investigate combinations of transformations of shapes - composite transformations.
Locate features on maps using coordinates and grid references.

Statistics

Calculate mean, median, mode and range of a data set; choose the most appropriate measure.
Construct stem-and-leaf plots and dot plots; using them to compare two data sets.
Describe and interpret data displays; identify misleading representations.

Probability

Identify complementary events (A and not-A); use P(A) + P(not-A) = 1.
Determine probabilities for chance events using fractions and decimals.
Construct sample spaces for single-step experiments using lists, tables, tree diagrams.

Integers, Fractions & Decimals

Operations on integers (including negative numbers); using number line to add and subtract integers.
Properties of operations - commutative, associative, distributive on rationals.
Word problems involving integers, fractions and decimals in real-life situations (temperature, banking, sports).

Exponents & Algebra

Exponents and powers - laws of exponents (a^m x a^n = a^(m+n); (a^m)^n = a^(mn)).
Algebraic expressions - terms, coefficients, like and unlike terms; addition and subtraction.
Simple equations - solving using inverse operations and the balance method; word problems leading to equations.

Lines, Angles & Triangles

Lines and angles - related angles (complementary, supplementary, vertically opposite, linear pair); angles formed by parallel lines and transversal.
Triangles - properties; congruence criteria (SSS, SAS, ASA, AAS, RHS).
Pythagoras theorem - introduction; statement and verification.

Comparing Quantities

Ratio and proportion - direct method, unitary method.
Percentage - converting between fractions, decimals, percentages; finding percent of a quantity.
Profit and loss; simple interest using I = (P x R x T) / 100.

Mensuration

Perimeter and area of triangles (Heron's formula introduction) and parallelograms.
Circles - circumference (C = 2 pi r) and area (A = pi r^2).
Surface area and volume of cuboid; word problems.

Symmetry & Data

Lines of symmetry and rotational symmetry; identifying in shapes and patterns.
Data handling - mean, median, mode of ungrouped data.
Bar graphs and pie charts; constructing pie charts using fractions and percentages.

Number System

Integers - operations and properties; using number line.
Rational numbers - representation on number line, operations.
Decimal numbers - operations, rounding to specified place value.

Algebra

Exponents - laws and applications; expressing large numbers in scientific notation.
Algebraic expressions - addition, subtraction, multiplication (monomial x polynomial).
Linear equations in one variable - solving and word problems.

Geometry

Pair of lines and transversal; angle properties (corresponding, alternate, co-interior).
Triangles - construction (SSS, SAS, ASA), congruence properties.
Quadrilaterals and circles - properties and relationships.

Comparing Quantities

Ratio, proportion and percentage - applications in everyday life.
Profit, loss, discount, simple interest.
Direct variation (y = kx) and inverse variation (xy = k).

Mensuration

Perimeter and area of plane figures (triangles, quadrilaterals, parallelograms, trapeziums, circles).
Volume and surface area of cuboid and cube.
Word problems involving mensuration in real-life contexts.

Data Handling

Mean, median, mode of ungrouped data.
Bar graphs and pie charts - reading and constructing.
Probability - simple events using fractions.

Number

Integers, decimals, fractions and percentages - operations and conversions between them.
Powers and roots; squares and cubes; square roots of perfect squares.
Estimation and rounding to specified decimal places or significant figures.

Algebra

Use letters to represent numbers; simplifying algebraic expressions by combining like terms.
Construct and solve linear equations including those with brackets and variables on both sides.
Sequences - generate from a rule and describe the rule in words and symbols (e.g., n-th term).

Geometry & Measure

Angles - types (acute, right, obtuse, straight, reflex) and angle properties of parallel lines and triangles.
Construction of triangles using ruler and compass given specified information.
Area and perimeter of compound shapes; volume of cuboids using V = l x w x h.

Statistics

Calculate mean, median, mode and range; choose appropriate measure for given data.
Construct and interpret bar charts, pie charts, frequency diagrams.
Plan a statistical investigation - question, collect, analyse, present, interpret.

Probability

Use words (impossible, unlikely, even chance, likely, certain) and numbers (0 to 1) to describe probability.
List outcomes of single events systematically.
Compare experimental (from trials) and theoretical (calculated) probability.

Numbers & Algebra

Integers, fractions, decimals, percentages and their interconversions.
Real numbers and number line; rational and irrational numbers introduction.
Algebraic expressions - simplification using like terms and distributive law.

Equations & Inequalities

Linear equations in one variable - solving using inverse operations.
Linear inequalities in one variable - solving and representing on a number line.
Word problems leading to equations and inequalities.

Ratio, Rate, Proportion

Ratio - simplification, equivalent ratios, dividing a quantity in a given ratio.
Rate - speed (constant and average), unit conversions (km/h to m/s).
Direct proportion problems using the unitary method.

Angles & Geometry

Angles formed by parallel lines and transversal - corresponding, alternate, co-interior.
Triangles (equilateral, isosceles, scalene; acute, right, obtuse) and special quadrilaterals - properties.
Polygons - sum of interior angles ((n-2) x 180) and sum of exterior angles (360).

Mensuration

Perimeter and area of plane figures (triangles, quadrilaterals, circles).
Volume and surface area of prisms (rectangular, triangular).
Circles - circumference (C = 2 pi r) and area (A = pi r^2).

Statistics

Data handling - bar charts, dot diagrams, pie charts; choosing appropriate display.
Mean, median, mode of ungrouped data; understanding when each is most appropriate.
Reading and interpreting statistical diagrams from newspapers and reports.

Note

Cambridge IGCSE 0580 Maths is sat in Years 10-11. For Grade 7 the Cambridge Lower Secondary Stage 7 framework above is followed.
Cambridge Lower Secondary (Stages 7-9) is the bridge from Cambridge Primary to IGCSE. Stage 7 introduces algebra, linear equations and proportional reasoning that the IGCSE builds on.
See Mathematics Grade 9-10 for the full IGCSE 0580 syllabus.

Requirements

A laptop or desktop with stable internet
Pencil, eraser, ruler, notebook for working out solved problems
School textbook and notebook (any board) - tutor will adapt to it
For higher grades: a basic calculator

Reviews

5.0 / 5 ★ · 340+ students enrolled

Parents consistently rate our mentors for personalised attention, clear concepts and steady progress. Book a free demo to experience a class first-hand.

Frequently Asked Questions

How do I get started?

Click the Book a Demo button on this page and fill in your child's grade and school board (CBSE / ICSE / IGCSE / Cambridge / US Common Core / Singapore MOE etc.). We will schedule a free trial session with a matching tutor. For details, contact our coordinator on WhatsApp at +91 93308 11581 or email contact@winquestonline.com.

Will the tutor follow my child's school board?

Yes. Every WinQuest tutor is mapped to specific curricula. Before the first class we ask which board your child follows; the tutor uses that board's scope and sequence, supports the school textbook chapter by chapter, and adds worksheets in the board's exam style. We currently support US Common Core, Ontario, Australian v9.0, CBSE (NCERT), ICSE (CISCE), IGCSE 0580 / 0500 / 0610 / 0620 / 0625, Cambridge Primary / Lower Secondary, and Singapore MOE.

How does payment work?

We require monthly advance payments for the number of classes scheduled in that calendar month. We accept Zelle, PayPal, UPI (for India), Stripe and major credit / debit cards. You can select your preferred payment method during the initial enrolment.

What if my child misses a class?

For 1:1 sessions we reschedule a make-up at a mutually convenient time at no extra cost (with at least 24 hours notice). For group classes we share a timed recording of the session on parent request, so your child can catch up before the next class.

How long is each class?

Each class session is 60 minutes long for academic subjects. Frequency is typically twice a week for K-7 grades and 2-3 times a week for high school, based on the board exam timeline and parent preference.

How is progress measured?

Tutors give written feedback on every homework assignment, run a short formative quiz every 4-6 classes, and a longer chapter test at the end of each topic. Parents receive a monthly progress report covering concept mastery, homework completion and test scores.

What is the class size?

For 1:1 sessions the class is just your child and the tutor. For group classes we cap each batch at 6-8 students so every learner gets individual attention and can ask questions in real time.

Are the tutors qualified?

All our tutors are highly qualified subject-matter experts with proven track records - many hold Master's degrees in their subject and several years of school-curriculum teaching experience. Each tutor is interviewed by our academic head before joining and is mapped to specific boards and grades.

What if my child needs to pause for a school break or exam?

Just let us know in advance. There are no contracts - you can pause for a school holiday or final-exam stretch and resume when the student is ready, with no penalty.

What are the requirements?

A laptop or desktop with a stable internet connection is required. Pencil, eraser, ruler and a notebook for working out solved problems. For higher grades a basic calculator. The tutor will list any board-specific requirements (textbook, geometry box, etc.) before the first class.