Count Objects Up To 20 — CCSS.K.CC.5 - Kindergarten Math

SECTION 1

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!

Long Ago • Tally Marks

People scratched lines on bones and rocks to keep track of things. Each line stood for one object.

Ancient Times • Number Words

People started using words like "one, two, three" to say how many things they had.

Hundreds of Years Ago • Written Numbers

People began writing numbers like 1, 2, 3, all the way up to 20 and beyond!

Today • Counting Everywhere

We count every day — at the store, at school, and at home. Counting helps us understand the world!

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!

SECTION 2

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

When you count, touch or point to each object one time. Say one number for each thing. Don't skip any, and don't count one twice!

Keep the Order

Always say the numbers in the right order: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

The Last Number Tells "How Many"

When you finish counting, the last number you say tells you the total. This is called the cardinal number.

It Doesn't Matter Where You Start

You can start counting from any object. No matter where you begin, the total stays the same!

Count Out a Number

If someone says "Give me 7 blocks," you can count out exactly 7 from a bigger group. Stop when you reach the number!

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KEY IDEA

Think of counting like giving each object a name tag with a number on it. The first thing gets the tag "1," the next gets "2," and so on. The last name tag you give out tells you how many things there are in all!

SECTION 3

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!

Each star has a number below it. We start at 1 on the left and count to 12 on the right. The last number, 12, tells us there are 12 stars in all.

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!

SECTION 4

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!

The top part shows 15 apples in 3 rows of 5. Count across each row: Row 1 is 1–5, Row 2 is 6–10, Row 3 is 11–15. The bottom shows 8 dots in a circle. Pick a starting dot and count around!

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!

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Helpful Tip

When counting in a circle, try placing a small mark (like a penny or a sticker) next to your starting object. That way you know when to stop!

SECTION 5

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.

The 8 hearts are spread all around. We counted each one carefully: top to bottom, left to right. We could also cross each heart out after counting it. The answer is 8 hearts.

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!

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Remember!

For scattered objects, we practice with up to 10 things. For lines, arrays, and circles, we can count up to 20 things!

SECTION 6

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.

Example 1: How many crayons are in this row?

1
Step 1 — Look at the objects

You see crayons in a line. Point to the first crayon on the left.
2
Step 2 — Touch and count each one

Touch each crayon as you say: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. Make sure you say one number per crayon!
3
Step 3 — Say the last number

The last number you said is 14. That is the total!

There are 14 crayons.

Example 2: Count out 9 blocks from a pile of 20 blocks

1
Step 1 — Know the number you need

Someone says: "Please give me 9 blocks." You need to count out exactly 9 from the big pile.
2
Step 2 — Pick up one at a time and count

Pick up one block and say "1." Pick up another and say "2." Keep going: 3, 4, 5, 6, 7, 8, 9.
3
Step 3 — Stop at 9!

When you say "9," stop! Do not pick up any more blocks. You are done!

You counted out exactly 9 blocks. 🎉

SECTION 7

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

Types of object arrangements from easiest to hardest

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KEY IDEA

Imagine you have 10 toys. Whether you put them in a line, a grid, a circle, or scatter them on the floor, there are still 10 toys! The number doesn't change. Only how carefully you need to count changes.

SECTION 8

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

Counting now vs. what comes next

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.

SECTION 9

Practice Problems

Try these problems! Think carefully and take your time.

Question 1: CONCEPTUAL

You count a group of stickers: 1, 2, 3, 4, 5, 6, 7. The last number you said was 7. How many stickers are there?

Show answer

There are 7 stickers. When you count, the last number you say tells you the total. You said 7 last, so there are 7 stickers. This is called the cardinal number — it tells you how many in all.

Question 2: BASIC COUNTING

Count the dots in this line: ● ● ● ● ● ● ● ● ● ● ● ● (twelve dots). How many dots are there?

Show answer

There are 12 dots. Point to each dot and count: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. The last number you say is 12, so there are 12 dots. Counting in a line is the easiest because you can start at one end and go straight to the other end.

Question 3: INTERMEDIATE

There are buttons in an array: 4 rows with 4 buttons in each row. How many buttons are there in all? Count to find out.

Show answer

There are 16 buttons. Count across Row 1: 1, 2, 3, 4. Then Row 2: 5, 6, 7, 8. Then Row 3: 9, 10, 11, 12. Then Row 4: 13, 14, 15, 16. You counted all 4 rows and the last number was 16. So there are 16 buttons in the array.

Question 4: APPLIED

Your teacher says: "Please get me 13 crayons from the box." The box has 20 crayons. How do you count out exactly 13?

Show answer

You pick up one crayon at a time from the box and count: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. When you say "13," you stop. Do not pick up any more! You now have exactly 13 crayons. There will be 7 crayons left in the box, but you don't need to count those — you just needed to count out 13.

Question 5: CRITICAL THINKING

Sam counted 8 scattered leaves. Then he rearranged them into a straight line and counted again. He got 8 again. Why did he get the same number both times? Would the answer change if he put them in a circle?

Show answer

Sam got 8 both times because the number of leaves did not change. Moving objects around does not add or take away any objects. Whether the leaves are scattered, in a line, or in a circle, there are still 8 leaves. The arrangement only changes how you count — not how many there are. If he put them in a circle, he would still count 8!

SUMMARY

What We Learned

Summary

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!