Kindergarten Readiness Review - First Grade Mathematics

Before stepping into first grade mathematics, it is helpful to look back and celebrate the wonderful math skills you already know. In kindergarten, you learned to count objects by pointing one by one, recognize numbers up to ten, compare whether a group has more or less, and spot common shapes like circles and squares. Reviewing these foundation skills ensures that your math muscles are warmed up and ready for the exciting new topics ahead.

Counting Small Collections with Precision

Counting is the bedrock of all mathematics. When you count, every object gets exactly one number word in order.

Counting Five Stars:
   *       *       *       *       *
  [1]     [2]     [3]     [4]     [5]
 "one"   "two"  "three"  "four"  "five"

The Touch-and-Count Rule

To count accurately without missing any items or counting an item twice, touch each object with your finger as you say its number name out loud. If objects are scattered on a table, move them into a straight line or slide each one over as you count it.

The Cardinality Principle

The last number you say when counting a group tells the total number of objects in that group. If you count five blocks and say "one, two, three, four, five," the number 5 represents the entire collection. You do not need to recount them; five is the quantity.

Recognizing and Writing Numerals 0 to 10

A numeral is a written symbol that stands for a specific quantity.

Numerals and Their Values:
0 : (none)
1 : *
2 : * *
3 : * * *
4 : * * * *
5 : * * * * *
6 : * * * * * *
7 : * * * * * * *
8 : * * * * * * * *
9 : * * * * * * * * *
10: * * * * * * * * * *

Zero Means None

The numeral 0 stands for zero, which means having no objects at all. If a bowl has no apples in it, there are 0 apples in the bowl.

Linking Words, Quantities, and Numerals

Every quantity has three representations: the actual items you can touch, the spoken word you say (like "four"), and the symbol you write (like "4"). Connecting these three forms helps you understand what numbers truly mean.

Comparing Groups: More, Fewer, and Equal

Mathematicians frequently compare two collections to see which group has a larger quantity or if they are the exact same size.

Matching Two Groups:
Group A:  (O)  (O)  (O)  (O)      -> 4 circles
           |    |    |
Group B:  [X]  [X]  [X]           -> 3 squares

One circle is left over!
Group A has MORE than Group B.
Group B has FEWER than Group A.

Matching One-to-One

The clearest way to compare two groups is by pairing them up one-to-one. Line up the items in both groups side by side. If every item in the first group has a partner in the second group and none are left over, the two groups are equal. If one group has items left without partners, that group has more.

Using Comparison Words Correctly

Use the word "more" or "greater" when a collection has a larger amount. Use the word "fewer" or "less" when a collection has a smaller amount. Use "equal" or "the same" when both collections contain the exact same count.

Practice Exercises

Exercise 1: Look at this group of dots: . . . . . . Count them one by one and state the total number. Write down both the number word and the numeral.

Exercise 2: Group X has 5 toy cars. Group Y has 7 toy cars. Which group has more cars, and which group has fewer cars? How do you know?

Exercise 3: If you have a plate with 3 cookies and you eat all 3 cookies, what numeral describes the number of cookies left on the plate?

Exercise 4: Draw or imagine 4 triangles lined up next to 4 circles. Does one shape have more, or are they equal?

Solutions and Explanations

Solution to Exercise 1: Counting the dots one by one gives one, two, three, four, five, six. The total number of dots is six. The numeral is 6, and the number word is six.

Solution to Exercise 2: Group Y has more cars because 7 is a larger quantity than 5. Group X has fewer cars because 5 is a smaller quantity than 7. When counting forward, 7 comes after 5.

Solution to Exercise 3: The numeral that describes the remaining cookies is 0 (zero), because there are no cookies left on the plate.

Solution to Exercise 4: The two groups are equal. When you pair each of the 4 triangles with one of the 4 circles, every single shape has a partner with none left over, meaning both groups have the exact same count of 4.