Counting Objects (0 to 10) - First Grade Mathematics
Counting is one of the most powerful skills you will ever learn because it allows you to answer the question: "How many are there?" Whether you are counting how many crayons are in a box, how many ducks are swimming in a pond, or how many steps lead up to your bedroom, counting gives you an exact number. In this chapter, you will master counting collections of items from zero all the way to ten, learn how to keep track of items so you never recount the same thing twice, and discover why zero is such a special number.
The Counting Sequence from 0 to 10
When we count, we use a specific order of number words that never changes. Each number word represents a quantity that is exactly one more than the number before it.
The Number Staircase from 0 to 10:
10 | [#][#][#][#][#][#][#][#][#][#]
9 | [#][#][#][#][#][#][#][#][#]
8 | [#][#][#][#][#][#][#][#]
7 | [#][#][#][#][#][#][#]
6 | [#][#][#][#][#][#]
5 | [#][#][#][#][#]
4 | [#][#][#][#]
3 | [#][#][#]
2 | [#][#]
1 | [#]
0 | (empty space)
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Understanding Zero
Zero represents an empty set or nothing to count. If there are three birds on a branch and all three fly away, there are 0 birds left on the branch. Zero is the starting point of our counting numbers.
Step-by-Step Counting Order
The counting sequence is: zero, one, two, three, four, five, six, seven, eight, nine, ten. When you move forward along this staircase, each step goes up by exactly one item. Two is one more than one, three is one more than two, and this pattern continues all the way to ten.
Keeping Track of Counted Objects
When items are scattered across a table or drawn all over a page, it is easy to get mixed up. Skilled mathematicians use special strategies to keep track of what they have already counted.
Scattered Objects vs. Organized Line:
Scattered: Organized in a Line:
* *
* * ---> * * * * *
* 1 2 3 4 5
(Easy to lose track) (Point from left to right)
The Move-and-Count Strategy
If you are holding real objects like buttons or coins, place them in a pile on your left. As you say each number out loud, slide one object over to your right. When the pile on your left is empty, the last number you said is your total.
The Mark-and-Count Strategy
When counting pictures printed in a book, you cannot move them with your fingers. Instead, use a pencil to draw a small light slash through each picture as you count it. This mark shows your eyes: "I already counted this one!"
The Cardinal Principle: The Last Number Tells How Many
When counting a group of objects, the final number word you say is not just the name of the last item; it represents the total count of the entire collection.
Counting 4 Apples:
(Apple) (Apple) (Apple) (Apple)
"one" "two" "three" "four"
^
|
Total quantity for ALL of them = 4!
Order Does Not Change the Total
You can count a row of five blocks starting from the left, or you can count them starting from the right. You can even count the middle block first. As long as you count every block once and only once, the total will always be five. The order of counting never changes the quantity.
Practice Exercises
Exercise 1: Say the counting sequence out loud from 0 to 10. Which number comes immediately after 6, and which number comes immediately before 9?
Exercise 2: Look at this group of pennies: (o) (o) (o) (o) (o) (o) (o). Count the pennies carefully and state the total number.
Exercise 3: If you have a bowl with 4 grapes and you eat all 4 of them, how many grapes remain in the bowl? What numeral describes this amount?
Exercise 4: Imagine a table with 8 building blocks scattered everywhere. Describe two different strategies you can use to make sure you count all 8 blocks without missing any or counting any block twice.
Solutions and Explanations
Solution to Exercise 1: The counting sequence from 0 to 10 is: zero, one, two, three, four, five, six, seven, eight, nine, ten. The number that comes immediately after 6 is 7. The number that comes immediately before 9 is 8.
Solution to Exercise 2: Counting the pennies one by one gives one, two, three, four, five, six, seven. There are 7 pennies in all.
Solution to Exercise 3: When all 4 grapes are eaten, there are no grapes left in the bowl. The quantity is zero, and the numeral written for this is 0.
Solution to Exercise 4: One strategy is the move-and-count method: move each block one at a time from one side of the table to the other as you count it. Another strategy is to line up the blocks in a straight row before counting, pointing to each block from left to right so your eyes can follow an orderly path.