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Key Point: Place value formula: N = 100×H + 10×T + 1×O (where H, T, O are digits 0–9)
What are numbers up to 999?
Numbers up to 999 are all whole numbers from 0 to 999. Each number can be shown using three place-value positions: hundreds, tens and ones (units).
Place value
Every digit in a three-digit number has a value depending on its place:
Example: In 347, the 3 is in hundreds place (3×100 = 300), 4 is in tens place (4×10 = 40), 7 is in ones place (7×1 = 7). So 347 = 300 + 40 + 7.
Writing numbers
Numbers can be written in different ways:
Comparing and ordering
To compare two numbers up to 999, compare hundreds first, then tens, then ones. The number with the larger digit in the first place where they differ is greater. To order, list numbers from smallest to largest (ascending) or largest to smallest (descending).
Successor and predecessor
The successor of a number is the number that comes next (add 1). The predecessor is the number that comes before (subtract 1). Example: successor of 149 is 150, predecessor of 200 is 199.
Even and odd numbers
If the ones digit is 0, 2, 4, 6 or 8 the number is even. If the ones digit is 1, 3, 5, 7 or 9 the number is odd. Example: 268 is even, 173 is odd.
Grouping and base-10 blocks
We can represent numbers with blocks: 1 hundred-block = 100 small cubes, 1 ten-rod = 10 cubes, single cubes = ones. Group tens into hundreds when there are ten tens.
Number line
Plotting numbers on a number line helps to understand size, distance between numbers, successor/predecessor and simple addition/subtraction by moving right/left.
Key Point: Place value of a digit = digit × (value of its place).
Face value of a digit is the value of the digit itself as it is written. For example, in 458, the face value of 5 is 5.
Place value of a digit depends on the position (place) of the digit in the number. Each place has a value: Ones = 1, Tens = 10, Hundreds = 100, and so on. To get the place value, multiply the digit by the value of its place.
Examples with a three-digit number 345:
Observe:
Special note about zero: If a digit is 0, its face value is 0 and its place value is also 0. Example: in 507, the tens digit is 0, so it contributes 0 × 10 = 0.
How to find place value quickly:
Key Point: General (place-value form): If a number has digits d_n d_{n-1} ... d_2 d_1 d_0, then Standard form = d_n d_{n-1} ... d_0 and Expanded form = d_n × 10^n + d_{n-1} × 10^{n-1} + ... + d_1 × 10^1 + d_0 × 10^0.
Standard form is the normal way we write a number using digits (for example, 3 7 4 is written as 374). Expanded form shows a number as the sum of each digit multiplied by its place value (for example, 374 = 300 + 70 + 4). Expanded form helps children see the value of each digit in a number.
How to convert:
Why it matters: Expanded form builds place-value understanding, makes addition and subtraction easier (you can add or subtract each place separately), and helps with mental math.
Key Point: If number A has more digits than number B, then A > B (for positive whole numbers).
What is comparing numbers?
Comparing numbers means finding out which of two or more numbers is greater, smaller or whether they are equal. We use the signs > (greater than), < (less than) and = (equal to).
Simple rules to compare numbers (step-by-step):
Tips for young learners:
Real-life examples:
Practice idea: Give pairs of numbers, ask the child to place them on a number line or draw counters, then write the correct sign (>, <, =).
Key Point: If comparing two numbers: compare highest place value first (hundreds → tens → units). The number with larger digit in the first differing place is greater.
What is Ordering Numbers?
Ordering numbers means arranging numbers from smallest to greatest (ascending order) or from greatest to smallest (descending order). For Class 3 students, this uses place value (units, tens, hundreds) and number lines to compare and sort numbers.
Key ideas and steps
Tips for young learners
Key Point: Successor of n = n + 1
Before, After and Between are basic ideas about ordering whole numbers. They help us know which number comes just before (predecessor), which comes just after (successor), and which numbers lie between two given numbers.
Successor (After): The number that comes immediately after a given number. To get the successor of any number, add 1.
Predecessor (Before): The number that comes immediately before a given number. To get the predecessor of any number, subtract 1.
Numbers Between: The whole numbers that come after the smaller number and before the larger number when you count by 1s. When two numbers are consecutive (difference 1), there are no numbers between them.
How to find them (steps):
Tips: Use a number line or a hundreds-chart to see the order of numbers. For a calendar (days), the day after 14th is the 15th (successor); the day before 1st of a month is the last day of the previous month (special case of predecessor).
Key Point: Even numbers: last digit is 0, 2, 4, 6, or 8.
Even numbers are whole numbers that can be divided into two equal groups with nothing left over. Examples: 0, 2, 4, 6, 8, 10, ...
Odd numbers are whole numbers that cannot be divided into two equal groups; one will be left over. Examples: 1, 3, 5, 7, 9, 11, ...
Two quick ways to tell:
Remember: 0 is an even number. Even and odd are opposites — every whole number is either even or odd.
Key Point: Common difference (d) = term(n) − term(n−1) (use to see how the sequence changes)
What is a number pattern or sequence?
A number pattern (or sequence) is a list of numbers arranged in an order that follows a rule. Children in Class 3 learn to look for the rule, continue the pattern and find missing numbers.
Types of patterns you meet in Class 3:
How to find the rule:
Using a number line and objects: A number line helps you jump forward or backward by the rule (for example, jump 2 steps when counting by 2s). Use beads, blocks or stamps to make patterns visible and easy to continue.
What we practise: finding the next two numbers, filling in the missing numbers, writing the rule in words ("add 2"), and creating our own patterns.
Key Point: Addition rule: a + b → start at a, move b steps to the right, result = final position.
What is a number line?
A number line is a straight line with numbers placed at equal spaces. It helps us count, add, subtract and compare numbers. Usually 0 is shown, numbers to the right are greater, and numbers to the left are smaller.
How to draw a number line
How to use a number line
Tips for Class 3 students
Key Point: Greatest number rule: arrange digits in descending order (largest to smallest) and place them left to right.
What the topic teaches: This topic shows how to arrange a given set of digits to make the largest (greatest) or the smallest (least) whole number possible. Children use the idea of place value (hundreds, tens, ones, etc.) to decide which digit goes in which place.
Basic idea: For any set of digits, the digit in the highest place (leftmost) contributes most to the number. So to make the greatest number, put the largest digit in the highest place, then the next largest, and so on. To make the smallest number, put the smallest digit in the highest place, then the next smallest, etc. One important rule: when making the smallest number, you cannot put 0 in the highest place (leftmost). If 0 is one of the digits, place the smallest nonzero digit first, then the zeros, then the rest in ascending order.
Step-by-step method:
Why it works: Each place (units, tens, hundreds, thousands) is worth 10 times the place to its right. Putting a larger digit in a higher place increases the total value much more than changing a lower place does. That is why ordering by size with attention to the leftmost place gives the greatest or smallest value.
Key Point: General form: write number + suffix (st, nd, rd, th). Example: n → nth.
What are ordinal numbers?
Ordinal numbers tell the position or order of things in a list: 1st, 2nd, 3rd, 4th, and so on. They answer the question "Which one?" (for example, "Which student finished first?"). This is different from cardinal numbers, which tell how many.
How to form ordinal numbers
Using ordinal numbers
We use ordinals when describing rank, order in a line, floors in a building, dates in a month (1st, 2nd, 3rd), and steps in a process.
Words and symbols
You can write ordinals as words (first, second, third, fourth) or as numbers with suffixes (1st, 2nd, 3rd, 4th). The general form is "n-th" when speaking generally (for example, "the nth student").
Key Point: Place-value expansion: 347 = 3×100 + 4×10 + 7×1
What is mental math? Mental math means doing calculations in your head without using pen and paper or a calculator. It helps children become faster and more confident with numbers.
Why practise mental math? It improves number sense, memory, concentration and problem-solving. CBSE Class 3 topics that use mental math include place value, addition, subtraction, multiplication tables, simple division, pattern recognition and estimation.
Simple techniques and tips
Practice approach