Lesson 1: Introduction to Addition

What is addition?

Addition is a way to put things together. When you add two amounts, you're counting them together, as one larger amount. Addition happens all the time in real life.

  • For instance, if this rabbit has babies ...

  • For instance, if this rabbit has babies ... she's adding to her family.

  • We can count the number of rabbits to find out how many there are.

  • We can count the number of rabbits to find out how many there are.

  • We can count the number of rabbits to find out how many there are.

  • We can count the number of rabbits to find out how many there are.

  • The total is 4. If you have 1 mother rabbit and 3 babies, you have 4 rabbits total.

What if there were four more rabbits?

As you can see, if you have 4 rabbits and add 4 more, you'll have 8 rabbits in total. You could write it like this:

4 + 4 = 8

4 + 4 = 8 is a mathematical equation. You could read it like this: Four plus four equals eight. A mathematical equation is basically a math sentence. It uses numbers and symbols instead of words. When we write out equations with addition, we use two symbols: + and =.

The plus sign (+) means two things are being added together. This is why we put it between the rabbits—we had 4 rabbits and added 4 more.

The other symbol in our equation is the equals sign (=). When you see the equals sign in an equation, it means two are more things are equal, or equivalent. Things that are equivalent don't always look or seem exactly alike, but they mean the same thing.

For instance, when you see someone you know, there's a few things you might say:

Hi = Hello = Hey

These words aren't exactly alike, but they mean the same thing. They're all ways to greet someone.

In math, the equals sign shows that two numbers or expressions mean the same thing, even though they might look different. Remember our rabbits? Because there were 8 rabbits total, we wrote 8 to the right of the equals sign.

8 = 8

See how each side means 8? There are 8 rabbits on the left, and the number 8 on the right. Both sides are equal.

Try This!

Fill in the blanks to complete the equations.

two rabbits and three rabbits

one rabbit and five rabbits

four rabbits and two rabbits

Writing Expressions

On the last page, we looked at some mathematical expressions. Expressions are useful, since they can help you keep track of the amounts you're adding.

Any addition problem can be turned into a written expression. For instance, say that you planned to have three friends come over for dinner. At the last minute, you invite two more. To get the total number of friends who are coming to your house, you might write an expression like this:

3 + 2

The expression is just another way of describing the situation: three friends plus two more are coming over for dinner.

Try This!

Write these situations as mathematical expressions. Don't solve the problems yet — simply set them up.

You ate three pieces of pizza for lunch. At dinner, you ate two more:

You already waited five minutes to see the doctor. The nurse tells you to wait five more minutes:

Your coat has four buttons on the right side and three buttons on the left side:

Solving Problems

Now that you know how to write addition problems, let's solve some. When you're just getting started, you might find it easier to use counting to solve problems.

Try This!

For instance, can you use counting to write and solve this problem?

With that problem, you were able to count the objects you were adding. In real life, some people like to count with their fingers. Other people use small objects, like buttons or pennies. Others might make small marks on a piece of paper. When you're learning to add, it's OK to count! The more you practice, the easier it will get to add without counting.

Ways to Count

Let's look at two ways to solve addition problems with counting. First, we'll count with objects.

  • To count with objects, use the objects to show each number in the expression. Let’s try it with this expression, 2 + 3.

  • The first number is 2, so we'll need 2 objects.

  • The first number is 2, so we'll need 2 objects.

  • The first number is 2, so we'll need 2 objects.

  • The next number is 3. We'll grab 3 more objects.

  • The next number is 3. We'll grab 3 more objects.

  • The next number is 3. We'll grab 3 more objects.

  • Now we can finish our equation. All we have to do is count!

  • Now we can finish our equation. All we have to do is count!

  • Now we can finish our equation. All we have to do is count!

  • Now we can finish our equation. All we have to do is count!

  • Now we can finish our equation. All we have to do is count!

  • There are five objects total, so our answer is 5

  • To finish, we'll write 5 to the right of the equals sign.

slideshow1 Another way to solve addition problems is to use a number line.

  • Counting with a number line only takes a few steps.

  • To use a number line, you count by moving right one number at a time.

  • To use a number line, you count by moving right one number at a time.

  • To use a number line, you count by moving right one number at a time.

  • Let’s practice adding with a number line. We'll try this problem, 5 + 2.

  • We need to start counting from the first number in our expression.

  • Here, that number is 5.

  • So, we start counting at the 5 mark on the number line.

  • Next, we’ll count right from the second number in our expression.

  • We’ll move right 2 times.

  • We’ll move right 2 times.

  • We’ll move right 2 times.

  • We landed on 7. This means that 5 + 2 is 7.

  • We'll write 7 to the right of the equals sign. Our equation is complete!

Practice!

Practice adding these problems. There are 5 sets of problems, with 3 problems in each set.

Set 1

6 + 1 =
2 + 0 =
5 + 3 =

Set 2

4 + 5 =
3 + 1 =
2 + 2 =

Set 3

1 + 8 =
0 + 3 =
7 + 6 =

Set 4

4 + 8 =
9 + 1 =
7 + 5 =

Set 5

5 + 5 =
3 + 2 =
6 + 8 =

Assessment

Want even more practice? Try out a short assessment to test your skills by clicking the link below:

Start Assessment

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