Understanding numbers

Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.

Student lesson

Words to know

1. Discover: how many do you see?

Aminata has a basket. She picks 3 mangoes from the tree: 🥭🥭🥭. Her friend Sorie has an empty basket. He has no mangoes yet.

Look at your own hand. How many fingers do you see on one hand? How many eyes do you have? How many noses?

We use numbers to answer the question “how many?”. Numbers help us every day. We see them at the shop, on the clock, on the road and at school.

Think and talk: How many mangoes does Aminata have? How many does Sorie have? Where have you seen numbers today?

2. Learn it step by step

Idea 1: A number tells how many

When we want to know how many, we count. Here is how to count:

1. Point to the first thing and say “one”.
2. Point to the next thing and say the next number.
3. Touch each thing one time only. Do not skip any. Do not count any twice.
4. The last number you say tells how many.

Try it: Count the fingers on one hand. Is the last number you say 5? Then you have 5 fingers on that hand.

The counting rules

1. Say the numbers in the same order every time: 1, 2, 3, 4, 5.
2. Give each thing one number, and give each number to one thing.
3. The last number you say tells how many.
4. You can start with any thing. The answer is the same if you count each thing once.
5. You can count anything: apples, claps, steps or sounds.

Idea 2: Numerals and number words

We can write a number in two ways. The mark 3 is a numeral. The word three is a number word. They both mean the same number.

Write each numeral big and neat, and start at the top. Say the number each time you write it. Practise first in sand, with chalk, or by drawing in the air with your finger, and then use a pencil.

Idea 3: Zero means none

Sometimes there is nothing to count. Aminata gives all her mangoes away. Now her basket has zero mangoes. We write 0. Zero is a real number. It does not mean “no number”. It means none.

Idea 4: Numbers do different jobs

The same kind of mark can do different jobs. Always ask: what is this number telling me?

Idea 5: Moving things does not change how many

Aminata has 4 mangoes in a line: 🥭🥭🥭🥭. She puts them in a ring. Are there still 4? Yes. Count again to check. The number stays the same when you move things, spread them out or push them close together. It changes only if some are added or taken away.

Idea 6: See small groups at once

You do not always need to count. Look at these dot patterns. With practice, your eyes can see 1, 2, 3, 4 or 5 dots at once. This is like the dots on a dice.

Try it: Ask a friend to show you a few seeds for two seconds, then cover them. Say how many you saw. Then uncover them and count to check.

3. Worked examples

Example 1 (I show you): count the stars

How many stars? ⭐⭐⭐⭐

1. Touch the first star. Say “one”.
2. Touch the second star. Say “two”.
3. Touch the third star. Say “three”.
4. Touch the fourth star. Say “four”. There are no more stars.
5. The last number is four. There are 4 stars.

Example 2 (We do it together): choose the numeral

Which numeral goes with these mangoes? 🥭🥭🥭🥭🥭

1. Count together, touching each mango once: 1, 2, 3, 4, 5.
2. The last number is five.
3. The numeral for five is 5.

Example 3 (You try): what job is the number doing?

For each, say: how many, order, label or measure? (a) the 7 on a house, (b) 3 pencils, (c) Sorie came 2nd in the race.

Did you know?

The numbers we write today, 0 1 2 3 4 5 6 7 8 9, are used by people all over the world. A child in Freetown, a child in London and a child in Tokyo can all read them. That is why learning numbers helps you everywhere.

Why this matters

You need numbers to buy things and to know the time. You need them to find a bus and to share fairly. All other mathematics starts with numbers.

4. Explore: number hunt and counting game

Number hunt. You need paper and a pencil. Look around your room or classroom for numbers.

1. Find three numbers (on a clock, a book, a calendar, a coin, a sign or a box).
2. Write each number on your paper.
3. For each one, say: does it tell how many, the order, or is it a label?
4. Show your list to a partner and explain one of your numbers.

Count and clap. Ask a friend to clap some times, from 1 to 5. Listen and count the claps. Say the number, then write the numeral. Swap places and play again.

5. Practise

Say it in a sentence

Use these sentence starters when you talk about numbers. Say them out loud.

• “There are ___ mangoes. The last number I said is ___.”
• “This number is a ___ (how many, order or label) because ___.”
• “Zero means ___.”

Guided practice (try, then open the answer)

Independent practice

Level 1: Start

1. What does a number tell us?
2. Count the fish and write the numeral: 🐟🐟🐟
3. Draw 4 circles. Write the numeral.
4. Write the numeral for the word two.
5. Write the number word for 1.
6. Which number means there is none?

Level 2: Grow

1. Count the birds and write both the numeral and the number word: 🐦🐦🐦🐦🐦
2. Draw 5 flowers. Write the numeral.
3. Is the 12 on a football shirt telling how many players?
4. Which group has 3? Group A: 🍌🍌. Group B: 🍌🍌🍌. Group C: 🍌🍌🍌🍌.
5. Write one place where you saw a number today.

Level 3: Stretch

1. Give one example of a number that tells how many, one that tells the order and one that is a label.
2. A basket has 0 eggs. Is it empty? Explain with words.
3. Your friend says, “The 3 on my door means there are 3 doors.” What do you tell your friend?
4. Make up your own question about counting and ask a partner to answer it.

All the answers are in the answer key below. Try first, then check.

6. Apply: everyday mathematics

At the market. You have 2 bananas and your friend has none. How many bananas does your friend have? How can you show it with a number?

In the queue. Four children stand in a line. Say who is first and who is last by number.

At home. You count the cups on the shelf and say “1, 2, 3, 4, 5”. How many cups are there?

7. Common mistakes

8. Lesson summary and revision card

9. Check and master

Answer all 14 questions. You will see feedback after each one.

Show my result

10. Key takeaways

• A number tells how many.
• Count by touching each thing once. The last number said tells how many.
• We write numbers as numerals (3) and as number words (three).
• Zero means none.
• Numbers can tell how many, tell the order, name something or measure.

11. Next lesson

Lesson 2: Counting objects from 0 to 10. You will count more objects, one by one, and say how many there are.

Exam practice

These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.

1. Circle the number that tells how many apples: 🍎🍎🍎   2   3   4 [1 mark]
2. Write the numeral for the word five. [1 mark]
3. Write the number word for the numeral 2. [1 mark]
4. A cup has no water in it. Write the number that tells how much water. [1 mark]
5. Count the stars: ⭐⭐⭐⭐. Write the numeral and the number word. [2 marks]
6. Tick the number that is a label: (a) the 4 on a bus (b) four mangoes. [1 mark]
7. Draw 3 circles. Write the numeral under them. [2 marks]
8. Sorie, Aminata and Fatmata stand in a line. Sorie is at the front. Who is 1st? [1 mark]
9. What does zero mean? Give one example. [2 marks]
10. Look at these: the 7 on a house, 3 apples, 2nd in a race. Write “how many”, “label” or “order” for each. [3 marks]
11. Four stones are in a line. A child moves them into a circle. How many stones are there now? Say how you know. [2 marks]

Total: 17 marks.

Printable worksheet

1. Circle the group that shows 4: 🍎🍎🍎 or 🍎🍎🍎🍎
2. Draw 2 circles and write the numeral.
3. Write the number that means none.
4. Write one place where you see a number.
5. Say whether it tells how many or is a label: the number 12 on a football shirt.
6. Count and write the numeral: 🐟🐟🐟🐟🐟
7. Write the number word for 4.
8. Write the numeral for the word three.
9. Draw 0 stars. What do you draw?
10. Who is 2nd: Sorie (1st), Aminata (2nd), Fatmata (3rd)?
11. True or false: Zero means none.
12. Write your own sentence that uses a number.

Homework

At home, find three numbers. Write them down and draw where you found each one. For each, tell a family member whether it tells how many, the order, or a label. Then count five things in your home and write the numeral and the number word for how many. If you cannot find printed numbers, count three groups of things and write each number.

Answer key and marking scheme

Worksheet answers: 1 the second group (4 apples); 2 two circles and 2; 3 zero (0); 4 any sensible place; 5 it is a label, a name for the player; 6 5; 7 four; 8 3; 9 nothing, because 0 means none; 10 Aminata; 11 true; 12 any sentence that uses a number correctly.

Independent practice answers: Level 1: 1 how many; 2 3; 3 four circles and 4; 4 2; 5 one; 6 zero (0). Level 2: 1 5 and five; 2 five flowers and 5; 3 no, it is a label; 4 Group B; 5 any sensible place. Level 3: 1 for example 3 mangoes (how many), 2nd place (order), house 7 (label); 2 yes, it is empty because there are none; 3 the 3 is a label for the door and does not tell how many doors; 4 any sensible question.

Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 C, 7 A, 8 B, 9 C, 10 A, 11 B, 12 C, Challenge 1 A, Challenge 2 B.

Mastery and remediation

Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.

If a learner struggles

1. Find the misconception: Learners may think every number tells how many, or that zero is not a number. Show house numbers and bus numbers as labels, and an empty basket for zero.
2. Explain another way: use real objects first, then pictures, then the numeral.
3. Show a simpler example: Count 1 to 3 real objects together and write the number each time.
4. Guided practice: work through one example together and let the learner try the next one.
5. Reassess: use the quiz again, the worksheet or the exam practice.
6. Move on when the learner shows Silver-level evidence independently.

For parents and guardians

Your child is learning that numbers tell how many, that we count by touching each thing once, and that zero means none. You do not need to be good at mathematics to help.

• Count with your child every day: steps, spoons, fruit, shoes. Touch each thing once.
• Ask “how do you know?” after each answer, and listen.
• Go on a number hunt at home: on the clock, the phone, the cooker, a coin.
• Praise effort, not only right answers. Mistakes are how we learn.
• If your child is stuck, go back to real objects such as stones or seeds before using pictures or writing.
• Ten to fifteen minutes of practice a day is better than one long session.

Teacher package