How Many

What is Counting and Number Sense?

Counting is saying numbers in order to find out how many objects are there. Number sense means understanding numbers — knowing how to count, read, write, compare and use numbers in simple ways.

Key ideas a Class 1 child should learn:

• One-to-one correspondence: Point to one object and say one number word for it (one object = one count).
• Stable order: Number words must be said in the same order every time (1, 2, 3, ...).
• Cardinality: The last number said is the total number of objects.
• Order does not matter: Objects can be counted in any order; the total stays the same.
• Compare quantities: Use words and symbols like more, less, equal; symbols >, <, =.
• Simple addition and subtraction: Putting groups together (addition) or taking away (subtraction) using counting.

How to teach or do counting:

1. Start with small groups of real objects (toys, pencils, fruits). Point and count each one.
2. Use a number line from 0 to 10. Move a finger or marker right when you add, left when you subtract.
3. Make simple stories: "You have 2 apples, I give 1 more — how many now?" Count together.
4. Use fingers, tallies (groups of 5), and pictures to show numbers visually.

Why this matters: Good counting and early number sense help children solve problems, do basic addition and subtraction, and understand everyday situations like sharing, grouping and comparing.

What are numerals?
Numerals are the written symbols we use to show numbers. In Class 1 we learn the ten basic numerals (also called digits): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Each numeral stands for a number of objects. For example, the numeral 4 stands for four objects.

Reading and writing numerals
We read numerals by saying the number name (e.g., '5' is read as "five"). We write numerals to show how many things there are: if there are three pencils, we write the numeral 3.

Using numerals to count and compare
Numerals help us count objects in a group and compare groups. We can say which group has more, fewer, or the same number of items by looking at their numerals. We also learn the order of numbers (number sequence) — e.g., 0, 1, 2, 3, 4, 5...

Successor and predecessor (simple rules)
For any number n (from 0 upwards): the successor (next number) is n + 1 and the predecessor (previous number) is n - 1 (only when n > 0). These are simple ways to move forward and backward in the number sequence.

Why numerals matter in daily life
Numerals are everywhere: on houses, clocks, price tags, bus numbers and school roll numbers. Learning numerals helps children recognise and use numbers in real situations.

What are Number Names?

Number names are the words we use to read and write numbers. For example, 3 is read and written as "three" and 10 as "ten". Learning number names helps children tell how many things there are, read numbers in books, and write numbers correctly.

How to form number names (simple rules for Class 1)

• Digits 0–9 each have one-word names: 0 = zero, 1 = one, 2 = two, …, 9 = nine.
• Numbers 10–19 have special names: 10 = ten, 11 = eleven, 12 = twelve, 13 = thirteen, 14 = fourteen, 15 = fifteen, 16 = sixteen, 17 = seventeen, 18 = eighteen, 19 = nineteen.
• Tens (20, 30, 40, ...) have their own names: 20 = twenty, 30 = thirty, 40 = forty, 50 = fifty, etc.
• Two-digit numbers (21–99) are spoken as the tens name followed by the units name: e.g., 24 = "twenty four", 57 = "fifty seven". If the unit is 0, say only the tens name (30 = "thirty").

Why it matters

Knowing number names links counting with reading and writing. It helps children understand questions like “How many?” and communicate quantities clearly.

Zero means none or nothing. When there are no objects to count, we say the number is zero and write it as 0. For example, if a plate has no apples, the number of apples = 0.

Empty set is a group (collection) that has no items. An empty set and the number zero both show 'nothing' in counting. We can show an empty set by empty curly braces { } or by the symbol ∅.

In everyday counting we use zero to say there are no items. In set language we say the set has no elements and call it an empty set.

How to show it: draw an empty container (box, plate, basket) and write 0 under it. Or write the set as { } or ∅.

Comparing quantities means finding out which group has more, which has less, or whether two groups have the same amount. In Class 1 we do this by counting, matching (pairing), or using number signs: > (greater than), < (less than) and = (equal to).

• Count and compare: Count the items in each group and see which number is bigger.
• Matching / Pairing: Match one item from the first group with one from the second. If some items are left unmatched in one group, that group has more.
• Using signs: Use >, < or = to write the result after comparing numbers.
• Use pictures or number line: Draw simple pictures, bars or use a number line to show which quantity is bigger or if they are equal.

Learning goal: children should be able to count small groups (usually up to 20), decide which group is more/less/equal and write the correct sign or word (more, less, same).

Simple combining and separating introduce young learners to addition and subtraction using everyday objects. Combining means putting two groups together and finding how many there are in all (this is the start of addition). Separating means taking some away from a group and finding how many are left (this is the start of subtraction).

Use concrete objects (toys, pencils, buttons) and pictures. Show two small groups, ask the child to count each group, then count all objects together to find the total. For separating, start with a group, remove some objects physically and count what remains.

Steps to teach combining (addition):

• Make two small groups (for example 2 red blocks and 3 blue blocks).
• Ask: "How many red? How many blue?" Count each group aloud.
• Put the groups together and count all objects: "1, 2, 3, 4, 5". Say the number sentence: 2 + 3 = 5.

Steps to teach separating (subtraction):

• Start with a group (for example 5 apples).
• Physically take away some (take away 2 apples).
• Count the remaining apples: "1, 2, 3". Say the number sentence: 5 - 2 = 3.

Use simple language: combine = join, separate = take away. Encourage children to use fingers, draw pictures, and use a number line to make counting easier. Reinforce by asking questions like "How many more?" or "How many are left?"

What this topic teaches: Children learn to count real objects and pictures to answer the question “How many?” They use one-to-one matching (touching each item while counting), group counting, and simple addition or subtraction with objects. The goal is to develop accurate counting and the ability to write the matching numeral.

Step-by-step method:

1. Gather objects or pictures (toys, pencils, buttons, drawn stars, etc.).
2. Line them up or place them clearly so none are hidden.
3. Point to or touch each object one by one and say the number name aloud (one, two, three...). This is called one-to-one correspondence.
4. Stop at the last object. The last number said is the total — write that numeral beside the objects or picture.
5. Check by recounting or grouping (for example, make two groups of three and then count total as 3 + 3 = 6).

Teaching tips:

• Use bright, familiar objects and vary activities (count steps, snacks, fingers, pictures in a book).
• Encourage children to point or place a mark under each item as they count to avoid missing or double-counting items.
• Ask questions like: “How many apples are there?” “How many more to make 5?” to build number sense.
• Use repeated short activities rather than long sessions to keep attention strong.

Common mistakes and how to help:

• Children skip or double-count items — teach them to move an object or place a counter under it as they count.
• Items hidden or overlapped — spread items out in a single row so each is visible.
• Confusing number words and numerals — always pair saying the number with writing the numeral.

Learning outcomes: After practice, children will be able to count objects and pictures up to small numbers (usually 1–20), write matching numerals, and solve simple addition or subtraction problems using objects.

What it means: Representation of numbers means showing a number in different ways so children understand what the number stands for. In Class 1 this is done using objects, pictures, numerals and number names.

Main ways to represent numbers:

• Concrete: Using real objects (fruits, pencils, coins) so children count and see quantity.
• Pictorial: Drawing dots, pictures or using picture-cards to show how many.
• Abstract: Writing the numeral (for example 7) and the number word (for example 'seven').

How to teach step by step:

1. Make a small group of objects. Ask the child to count them one by one.
2. Ask the child to say the number name and then write the numeral.
3. Show the same number with a picture (dots or objects drawn) and with a ten-frame or tally marks.
4. Introduce simple place value: group ten objects together and show that, for example, 12 = 1 ten and 2 ones.

Important ideas for Class 1:

• Zero means none (0 shows no object).
• Count forwards and backwards to learn next (n + 1) and previous (n − 1).
• Use matching: each object matches one count (one-to-one correspondence).
• Use number lines to find 'before', 'after' and to practise counting in order.

In Class 1, 'Exercise Practice and Word Problems' helps children use counting, simple addition and subtraction to solve everyday problems. The aim is to read a short story, find the numbers, decide what to do (add or take away), draw or use objects, write a number sentence and get the answer.

Steps to solve a word problem:

1. Read the problem slowly and understand the scene (who and what).
2. Underline or note the numbers and key words (e.g. 'altogether', 'left', 'more', 'gave').
3. Decide the operation: 'altogether' or 'more' → add; 'left', 'gave away', or 'fewer' → subtract.
4. Use counters, drawings or a number line to model the problem.
5. Write the number sentence (for example 3 + 2 = 5 or 7 - 4 = 3) and check by counting back or reversing the operation.

Helpful tips for young learners:

• Use real objects (blocks, buttons, fruit) to act out the problem.
• Draw pictures or simple boxes to show groups.
• Use a number line to make jumps when adding or subtracting.
• Check answers by doing the opposite operation (addition checks subtraction and vice versa).