Numbers

What is Counting?
Counting is saying numbers in order to find how many objects are there. We start from a number (usually 1 or 0) and say the next number one by one: 1, 2, 3, 4, ...

Number Sequence
A number sequence is numbers arranged in a particular order. The most common is the natural sequence where each number comes after the previous one by 1 (for example 1, 2, 3, 4...). Sequences can be increasing (forward), decreasing (backward), or skip-counting (by 2s, 5s, 10s).

Key ideas for Class 1

• Forward counting: go up by 1 (1, 2, 3...).
• Backward counting: go down by 1 (10, 9, 8...).
• Before and After: the number before n is n − 1; the number after n is n + 1.
• Between numbers: the number that comes between 4 and 6 is 5.
• Number line: a straight line that shows numbers in order helps children see the sequence visually.

How to teach and practise

• Use objects (toys, pebbles, fruits) and ask children to count them aloud.
• Point to numbers on a number line while counting forward and backward.
• Use everyday routines: steps climbed, pages in a book, plates on a table.
• Introduce simple skip counting using groups (pairs for 2s, fingers for 5s, tens in a full hand of ten).

Why it matters
Counting and understanding number sequences build the foundation for addition, subtraction and place value. Good fluency with sequences helps children solve basic problems and understand patterns.

Zero is a number that means 'nothing' or 'no objects'. We use zero when there are no items to count. It is written as the digit 0.

Key ideas:

• Zero means none: if a basket has 0 apples, there are no apples in it.
• Zero is the starting point on a number line. It comes before 1 and after negative numbers (but in Class 1 we usually use 0 and positive numbers).
• Zero is an even number and it is neither positive nor negative.
• Zero is important as a placeholder in numbers (for example, in 10 the 0 shows there are no ones).
• Adding zero to a number does not change the number. Taking away all of something leaves zero.

Simple classroom language: 'Zero means nothing. If you have zero candies, you have no candies left.'

What are Numerals and Number Names?

A numeral is the symbol we write to show a number (for example, 4, 12). A number name is the word form of that numeral (for example, "four", "twelve"). Class 1 students learn to read, write and match numerals and their number names for small numbers.

How they relate

Each numeral has a corresponding number name. We use objects, pictures and counting to understand the meaning of a numeral and then write its name in words.

Learning steps and tips

• Count real objects (fingers, pencils, fruits) and say the numeral aloud.
• Match the numeral with the correct number name.
• Practice tracing and writing both numerals and number names.
• Use number lines and ten-frames to visualise order and quantity.

Common list (0 to 20)

Activities for practice

• Make cards with numerals on one set and number-name words on another; let children match pairs.
• Use everyday counting: how many apples? write the numeral and the word.
• Trace numerals and words, and colour as a reinforcement activity.

What is Representation of Numbers?

Representation of numbers means showing a number in different ways so children understand what the number stands for. For Class 1, this includes:

• Using numerals (e.g. 7)
• Using number names (e.g. "seven")
• Using pictures or objects (e.g. 7 apples)
• Using tally marks or a number line

Key ideas:

• Digits 0–9 are basic symbols used to make all numbers.
• Two-digit numbers are made from tens and ones. For example, 14 = one ten and four ones.
• Grouping objects (for example, making a bundle of ten sticks and some single sticks) helps children see how numbers are formed.

How to teach and show:

• Count real objects (fingers, blocks, beads) and write the matching numeral and name.
• Use a number line to show position, before/after and how numbers increase by 1.
• Use a ten-frame or bundle-of-ten model to introduce tens and ones visually.

What it means

Numbers come one after another in order. For any number:

• After a number is the next number (one more).
• Before a number is the previous number (one less).
• Between two numbers are the numbers that come after the first and before the second.

How to find them

• To find the after of n: add 1 (n + 1).
• To find the before of n: subtract 1 (n - 1).
• To find numbers between two numbers a and b (with a < b): list numbers greater than a and less than b.

Simple steps for children

1. Use a number line or number cards and find the position of the given number.
2. Move one step right to get the after; move one step left to get the before.
3. To list numbers between, count forward from the first number until you reach the second, but do not include the two end numbers.

Notes

• If we start counting from 1, there is no number before 1 unless we include 0. In many early class activities numbers start from 1, but teachers may introduce 0 later.

What are ordinal numbers? Ordinal numbers tell the position or order of things — who is first, second, third, and so on. They answer the question “Which one?” For example: 1st (first), 2nd (second), 3rd (third).

Difference from cardinal numbers: Cardinal numbers tell how many (1, 2, 3). Ordinal numbers tell the place or rank (1st, 2nd, 3rd).

How to form ordinals: Most numbers get the suffix -th (4 → 4th). Numbers ending in 1, 2, 3 usually use -st, -nd, -rd (1 → 1st, 2 → 2nd, 3 → 3rd), but 11, 12 and 13 are exceptions and take -th (11th, 12th, 13th).

Common words: 1st = first, 2nd = second, 3rd = third, 4th = fourth, 5th = fifth, 6th = sixth, 7th = seventh, 8th = eighth, 9th = ninth, 10th = tenth.

Usage tip: Use the word "the" before an ordinal when pointing to one specific item (the first page, the third child).

Class activity ideas: Line up toys or students and ask "Who is 4th?"; mark dates on a calendar as ordinals (5th, 10th); run a short race and label the winners 1st, 2nd, 3rd.

What is place value? Place value tells us the value of a digit depending on its position in a number. In two-digit numbers we use the tens place and the ones (units) place.

Tens and ones explained:

• Every tens stands for a group of 10 items. The digit in the tens place shows how many groups of ten there are.
• Every one (unit) stands for a single item. The digit in the ones place shows how many single items remain after making groups of ten.

Example: in the number 34, the '3' is in the tens place and means 3 groups of ten (3 × 10 = 30). The '4' is in the ones place and means 4 single ones. So 34 = 3 tens and 4 ones = 3 × 10 + 4.

Expanded form and comparison: We can write any two-digit number in expanded form as (tens × 10) + ones. When comparing two two-digit numbers, first compare the tens digits — the number with more tens is larger. If tens are equal, compare the ones.

How to teach/visualize: Use real objects (sticks of ten and single cubes), a simple 2-column place-value chart labeled 'Tens' and 'Ones', and number lines with jumps of 10. Encourage children to make groups of ten from sets of objects and count remaining ones.

What is a two-digit number? A two-digit number is any whole number from 10 to 99. It has two places: the tens place (left) and the ones place (right). The digit in the tens place tells how many groups of ten there are; the digit in the ones place tells how many single units there are.

Formation (How to make a two-digit number)

• Choose a digit for the tens place (1 to 9). This gives that many groups of ten.
• Choose a digit for the ones place (0 to 9). These are the single units.
• Write them together: tens digit then ones digit. For example, tens = 3 and ones = 4 makes 34 (three tens and four ones).

Decomposition (How to break a two-digit number)

• Split the number into tens and ones. For example, 57 = 5 tens and 7 ones.
• Write the number as the sum of the tens-part and the ones-part: 57 = 50 + 7.
• You can use objects (groups of ten sticks and single counters), a place-value chart, or subtraction by tens (e.g., 57 − 50 = 7) to find the parts.

Concrete tools and methods

• Base-10 blocks: one rod = ten, one small cube = one. Place rods and cubes to form or break numbers.
• Place-value chart: two columns labeled Tens and Ones to show each digit.
• Number line: jump by tens and then by ones to form a number from 0 or to decompose it.

Why it matters

Understanding formation and decomposition helps children read, write, compare numbers, and perform addition and subtraction by tens and ones.

What it means: Comparing numbers means finding which number is smaller, which is larger, or whether they are equal. Ordering numbers means arranging a group of numbers from smallest to largest or from largest to smallest.

Words and symbols: We use the words "greater than", "less than" and "equal to" and the symbols > (greater than), < (less than) and = (equal to). For example, 7 > 5 means 7 is greater than 5, 3 < 4 means 3 is less than 4, and 6 = 6 means both numbers are the same.

Easy ways to compare:

• Count objects: Put the same kinds of objects side by side (e.g., apples). The group with more objects is the greater number.
• Use a number line: Numbers to the right are greater. If a number is to the right of another, it is larger.
• Use pictures: Draw or imagine pictures (stars, blocks). The picture with more items shows the larger number.

Ordering numbers: To put numbers in ascending order means to arrange them from smallest to largest (e.g., 1, 3, 5). To put numbers in descending order means to arrange them from largest to smallest (e.g., 9, 6, 2).

Simple steps to compare two numbers:

1. Count how many items each number represents.
2. If one count is more, that number is greater. Use the symbol > or <.
3. If counts are the same, the numbers are equal and use =.

Why this is useful: Comparing and ordering help in everyday choices — sharing things fairly, knowing who is taller, arranging books from smallest to biggest, and reading numbers correctly.

What is a Number Line?

A number line is a straight horizontal line with numbers placed at equal distances. It helps children see numbers in order, count, compare sizes, and learn simple addition and subtraction. For Class 1 we usually use numbers from 0 or 1 up to 10 or 20.

How to draw a simple number line

• Draw a straight horizontal line.
• Mark equal spaces on the line (these are points where numbers go).
• Write 0 (or 1) at one point and then write 1, 2, 3… in order to the right.
• Put an arrow at the right end to show numbers continue (or stop at a chosen number for practice).

How to use it

• Counting: Move from left to right to count up.
• Compare: A number to the right is greater; a number to the left is smaller.
• Addition: Start at the first number and make jumps to the right for each addend.
• Subtraction: Start at the first number and make jumps to the left to subtract.

Important ideas for Class 1

• Successor (next number) is one step to the right.
• Predecessor (previous number) is one step to the left.
• Use small objects (coins, buttons, stars) on the number line to show steps visually.

What are Even and Odd Numbers?

Numbers tell us how many things there are. An even number is a number that can be grouped into pairs with nothing left over. An odd number cannot be grouped into pairs without one left over.

Simple ideas for Class 1 students:

• Even numbers: 0, 2, 4, 6, 8, ...
• Odd numbers: 1, 3, 5, 7, 9, ...

How to check a number

• Try to make pairs (groups of two). If all objects pair up, the number is even.
• If one object is left without a pair, the number is odd.

Useful tip: Look at the last digit of a whole number. If the last digit is 0, 2, 4, 6 or 8, the number is even. If it is 1, 3, 5, 7 or 9, the number is odd.

Activities to understand:

• Use counters, buttons or pencils and try to make pairs.
• Line up objects and circle them two by two — leftover shows an odd number.
• Use a number line and colour even numbers one colour and odd numbers another colour.

Skip counting means counting forward by the same number each time instead of counting by ones. It helps children see number patterns and prepares them for addition and multiplication. Common skip counts are by 2s, 5s and 10s.

How to do skip counting:

• Pick a starting number (often 0 or 1).
• Pick the step (the number you add each time) — for example 2, 5 or 10.
• Keep adding the step to get the next numbers: start, start + step, start + 2×step, start + 3×step, and so on.

Simple ways to teach and show patterns:

• Number-line hops: draw a number line and make equal jumps for each step (equal-length hops show the pattern visually).
• Grouping objects: place objects in groups of the step size (pairs for 2s, groups of 5 for 5s).
• Number chart highlighting: color every 2nd, 5th or 10th number on a 1–100 chart to make the repeat pattern visible.

Why it matters: skip counting makes adding many equal groups faster, helps with telling time (clock minutes), counting money and begins the idea of multiplication (for example, five 5s = 25).

Reading, Writing and Dictation of Numbers teaches children how to recognise numbers (figures), say their names (words) and write them when they hear them. For Class 1 we usually work with numbers from 0 to 99, focusing on single-digit and two-digit numbers.

Reading: To read a number, look at its digits and say the place values from left to right. For a two-digit number, the left digit is the tens and the right digit is the ones. Example: 42 is read as "forty two" because 4 is in the tens place (4 tens = 40) and 2 is in the ones place.

Writing: Writing has two parts — writing in figures (digits) and writing in words. Teach children to write each digit in the correct box (tens box, ones box). Also practise writing the number name: 17 -> "seventeen"; 50 -> "fifty". Use zero as a placeholder (e.g., 05 is written as 5).

Dictation: Dictation means the teacher says a number name and the child writes it in figures, or the teacher shows/says the figure and the child writes/reads the number name aloud. Example teacher says "thirty three" and the child writes 33. For correct dictation, students must know number names and place values.

Place value idea (simple): Every digit has a place. In a two-digit number: Number = (Tens × 10) + (Ones × 1). Example: 56 = (5 × 10) + (6 × 1) = 50 + 6.

Tips for practice: Use real objects (pencils, apples), number lines, tens-and-ones boxes, an abacus or bead strings, and clear oral dictation exercises. Start with single digits, then teens, then all two-digit numbers. Emphasise clear handwriting and correct spacing for tens and ones.