Lesson 1: Review of Addition

New Concept

Addition is the combining of two groups into one group.

What’s next

Next, you'll apply this concept by writing number sentences, exploring addition's properties, and solving for missing numbers in various problems.

Property

Addition is the combining of two groups into one group. The numbers that are added are called addends, and the answer is called the sum.

Examples

• If you have 4 dots and add 5 more dots, you get a total of 9: $4 + 5 = 9$.
• Combining three groups is easy too: 5 trees, 3 trees, and 4 trees make $5 + 3 + 4 = 12$ trees.
• When D'Anya ran 5 laps and then 8 more, she ran a total of $5 + 8 = 13$ laps.

Explanation

Think of addition as dumping two handfuls of marbles into one big bucket! The separate handfuls are the addends, and the total number of marbles you have in the bucket is the sum. It’s all about combining amounts to find out how much you have all together, which is a neat trick.

Property

When we add two numbers, either number may be first. The order of the addends does not change the sum. For any numbers $a$ and $b$, $a + b = b + a$.

Examples

• Adding five and six gives the same result as adding six and five: $5 + 6 = 11$ and $6 + 5 = 11$.
• You can even shuffle three numbers: $1 + 2 + 3 = 6$ is the same as $3 + 2 + 1 = 6$.
• For this picture of dots, you can write two number sentences: $4 + 5 = 9$ and $5 + 4 = 9$.

Explanation

This property is like making a sandwich! It does not matter if you put the cheese on first or the ham on first; the final sandwich still tastes the same. In addition, changing the order of the numbers you are adding together will not change the final answer, which is super helpful for checking your work.

Property

When we add zero to a number, the number is not changed. The sum is identical to the starting number. For any number $a$, $a + 0 = a$.

Examples

• If you have 9 cookies and someone gives you 0 more, you still have 9 cookies: $9 + 0 = 9$.
• The order doesn't matter either, thanks to the commutative property: $0 + 7 = 7$.
• In the equation $q + 8 = 8$, the only number that works for $q$ is 0.

Explanation

Zero is like a magic mirror in the world of addition. Any number that adds with zero just sees itself perfectly reflected back! Adding zero doesn't change a number’s identity at all. This lazy number is a secret hero for making some math problems way easier by keeping things simple for us to calculate.