First Grade Mastery Review - Second Grade Mathematics

Before embarking on the new concepts of second grade, taking time to revisit and celebrate what you learned in first grade gives you a solid foundation for everything ahead. In first grade, you explored numbers up to 120, learned how to compose and decompose numbers within 20, mastered the basic addition and subtraction fact families, and discovered that two-digit numbers are built from groups of tens and remaining ones. This review chapter walks you through each of these critical cornerstones in thorough detail, ensuring your mathematical muscles are warmed up and ready for higher-level problem solving.

Counting and Number Sequences up to 120

A crucial milestone of first grade was counting beyond 100 all the way to 120. Counting past 100 follows the exact same repeating pattern as counting from 1 to 20, but with a hundred in front.

Past 100 Sequence:
101, 102, 103, 104, 105, 106, 107, 108, 109, 110,
111, 112, 113, 114, 115, 116, 117, 118, 119, 120

The Crossing-the-Decade Landmark

When counting forward, the most common place where learners pause is crossing from a nine to the next ten. For example, after 109 comes 110. After 119 comes 120. Recognizing that 9 ones turn into a fresh ten allows you to count forward and backward smoothly.

Reading and Writing Numbers

Every number between 1 and 120 can be written with digits or words. For example, 115 is read as one hundred fifteen, not one hundred and fifteen. Writing numbers clearly with proper digit spacing ensures your work remains readable.

Place Value: Understanding Tens and Ones

Every two-digit number is made of two place values: the tens place on the left and the ones place on the right.

Number: 64
Tens Column: 6 rods  = 60
Ones Column: 4 cubes =  4
Total Value: 60 + 4  = 64

+-------------------+-------------------+
|     Tens (10s)    |     Ones (1s)     |
+-------------------+-------------------+
|         6         |         4         |
|   (Value = 60)    |    (Value = 4)    |
+-------------------+-------------------+

The Value of a Digit Depends on Its Position

The digit 4 by itself means four single items. But when the digit 4 is in the tens place, as in the number 42, it represents 4 groups of ten, or 40 items. Understanding that position determines value is the foundation of our entire decimal numbering system.

Expanded Form of 2-Digit Numbers

Expanded form breaks a number apart to reveal the true value of each digit added together. The number 78 in expanded form is written as 70 + 8. The number 91 is written as 90 + 1.

Addition and Subtraction within 20

In first grade, you moved away from counting on your fingers one by one toward using smart mental math strategies within 20.

Strategy 1: Doubles Facts
6 + 6 = 12
7 + 7 = 14
8 + 8 = 16

Strategy 2: Near-Doubles (Doubles Plus One)
7 + 8 = (7 + 7) + 1 = 14 + 1 = 15

Strategy 3: Make-a-Ten
8 + 5 = 8 + (2 + 3) = (8 + 2) + 3 = 10 + 3 = 13

The Doubles and Doubles-Plus-One Strategy

Knowing your doubles facts by heart unlocks many nearby facts. If you know that 6 + 6 = 12, then 6 + 7 must be just 1 more, which is 13. If you have 6 + 5, it is 1 less than 12, which is 11.

The Make-a-Ten Strategy

Ten is the friendliest number in math. When adding 9 + 6, you take 1 from the 6 and give it to the 9 to make a full 10. That leaves 5 ones. Adding 10 + 5 instantly gives you 15.

Fact Families and the Inverse Relationship

Addition and subtraction are inverse operations, meaning they undo each other. A fact family is a group of related mathematical equations that use the exact same three numbers.

Fact Family for 4, 9, and 13:

Part 1: 4
Part 2: 9
Whole:  13

Addition Equations:
4 + 9 = 13
9 + 4 = 13

Subtraction Equations:
13 - 9 = 4
13 - 4 = 9

Commutative Property of Addition

The commutative property states that the order of the addends does not change the sum. Whether you start with 4 apples and add 9 apples, or start with 9 apples and add 4 apples, you still have 13 apples in all.

Subtraction as Finding an Unknown Addend

When you see the subtraction problem 13 - 9 = ?, you can think of it as an addition question: What number plus 9 makes 13? Since you already know that 9 + 4 = 13, you know immediately that 13 - 9 = 4.

Basic Comparison and Measurement Concepts

First grade introduced comparing two quantities to determine which is greater, which is lesser, or whether they are equal.

Comparison Symbols:
> means "is greater than"   (Example: 45 > 32)
< means "is less than"      (Example: 19 < 28)
= means "is equal to"       (Example: 50 = 50)

Remembering Comparison Symbols

Think of the comparison symbol as an open mouth that always wants to eat the larger quantity. If the open mouth faces left ( > ), the larger number comes first. If the point touches the left number ( < ), the smaller number comes first.

Ordering Numbers

When putting three or more numbers in order from least to greatest, you first look at the tens digit. For the numbers 38, 72, and 19, the tens digits are 3, 7, and 1. Since 1 ten is the smallest, 19 comes first. Next is 38, and the greatest is 72.

Practice Exercises

Exercise 1: Write the number that comes directly after 109, and explain what happens to the place value digits when you count to that number.

Exercise 2: Write the number 85 in expanded form, and state how many tens and how many ones are inside it.

Exercise 3: Write the complete fact family of four equations using the numbers 7, 8, and 15.

Exercise 4: Use the make-a-ten mental strategy to solve 9 + 7. Explain each step of your thinking in words.

Solutions and Explanations

Solution to Exercise 1: The number that comes directly after 109 is 110. In the number 109, there are 1 hundred, 0 tens, and 9 ones. When you add 1 more to 9 ones, it creates a complete group of ten. The ones digit resets to 0, and the tens digit increases from 0 to 1, producing 110.

Solution to Exercise 2: The number 85 in expanded form is written as 80 + 5. It contains 8 tens (which have a total value of 80) and 5 ones (which have a total value of 5).

Solution to Exercise 3: The complete fact family consists of two addition equations and two subtraction equations: 7 + 8 = 15, 8 + 7 = 15, 15 - 8 = 7, and 15 - 7 = 8.

Solution to Exercise 4: To solve 9 + 7 using the make-a-ten strategy, look at the number 9 and determine how many it needs to make 10. The number 9 needs 1 more. Decompose 7 into 1 and 6. Give the 1 to 9 to form 10. Then add the remaining 6 to 10: 10 + 6 = 16. Therefore, 9 + 7 = 16.