Why Do We Count?
People have been counting for a very, very long time! Long ago, before people had numbers written down, they needed to know how many things they had. A farmer wanted to know: How many sheep do I have? A family wanted to know: How many apples did we pick? Counting helps us answer the question "how many?" — and that is one of the most important questions in all of math!
Today, you will learn how to count objects up to 20. You will count things in a line, in a rectangle shape, in a circle, and even things that are scattered all around. Let's get started!
The Big Ideas of Counting
Before we start counting, let's learn some important rules. These rules help us count the right way every time!
One-to-One: Touch and Count
Keep the Order
The Last Number Tells "How Many"
It Doesn't Matter Where You Start
Count Out a Number
Counting in a Line
The easiest way to count is when objects are in a straight line. You start at one end and move to the other end. Touch each object and say one number. Let's look at 12 stars in a line!
When objects are in a line, it is easy to see where to start and where to stop. You just go from one end to the other. Try pointing to each star and saying the number out loud!
Counting in Rectangles and Circles
What Is a Rectangular Array?
A rectangular array is when objects are set up in neat rows and columns — like eggs in an egg carton or seats in a classroom. Even though there are many objects, you can still count them one by one.
Here is a tip: count across the top row first. Then move to the next row and keep going. Don't go back to a row you already counted!
Counting in a Circle
When objects are in a circle, there is no clear start or end. Here is what to do: pick one object to be your starting point. You can even put your finger on it! Then count around the circle in one direction. Stop when you get back to the one you started with. Don't count that first one again!
Counting Scattered Objects
Sometimes objects are not in a nice line or neat rows. They might be scattered — spread out all over the place, like toys on the floor! This is the trickiest kind of counting. When objects are scattered, you need to be very careful so you don't skip one or count one twice.
Tips for Counting Scattered Objects
- Move them! If you can, move each object to a new pile as you count it.
- Cross them out. If the objects are on paper, make a small mark on each one after counting.
- Line them up. You can rearrange scattered objects into a line to make counting easier!
- Go slowly. Take your time. It is better to be right than to be fast!
Worked Example: Count and Count Out
Let's do two examples together. First, we will count objects. Then, we will count out a number of objects from a bigger group.
Comparing Different Arrangements
Objects can be arranged in many ways. Some ways make counting easier. Let's compare them!
| Arrangement | What It Looks Like | How Hard? | Tip |
|---|---|---|---|
| Line | Objects in a straight row | Easiest! ⭐ | Start at one end, go to the other |
| Array | Rows and columns, like a grid | Easy ⭐⭐ | Count one row at a time |
| Circle | Objects in a ring shape | Medium ⭐⭐⭐ | Mark your starting point |
| Scattered | Objects all over the place | Hardest ⭐⭐⭐⭐ | Move or cross out each one |
From Counting to Adding
You are learning something really important! Once you can count well, you will be ready for the next big step: addition and subtraction. Adding is just counting more objects, and subtracting is counting how many are left!
| What You Know Now | What You'll Learn Next |
|---|---|
| Count objects up to 20 | Count objects past 20 — up to 100! |
| Count out a number of objects | Add two groups together: 3 + 5 = ? |
| Say "how many" after counting | Compare: Which group has more? Which has fewer? |
| Count scattered objects (up to 10) | Count scattered objects in bigger groups |
Every math skill you learn later builds on counting. Counting is like the foundation of a house — everything else is built on top of it! Keep practicing and you will be ready for all the fun math ahead.
Practice Problems
Try these problems! Think carefully and take your time.
What We Learned
You learned how to count objects up to 20 to answer the question "how many?" You practiced counting things in a line, in a rectangular array (rows and columns), and in a circle. You also learned to count scattered objects up to 10 by crossing them out or moving them. The last number you say tells you how many there are in all.
You also practiced counting out a certain number of objects from a bigger group — you pick up one at a time and stop when you reach the number you need. Remember: touch each object one time, say the numbers in order, and no matter how you arrange objects, the total stays the same. Keep practicing and counting will become easy!