Addition as Joining and Putting Together - First Grade Mathematics

Addition is one of the most exciting and natural things you can do with numbers. Whenever you take two separate groups of items and bring them together into one big group, you are adding! Think about building a train: you have three red cars on one track and two blue cars on another track. When you couple them together, you create a brand-new, longer train of five cars. In this chapter, you will discover the core meaning of addition as joining and putting together, learn how to see parts inside a whole, and model addition with your hands.

The Action of Joining

Addition always starts with two or more smaller groups called parts, and combines them into one total amount called the whole.

The Action of Joining:
Group 1 (Red Balls):      (O)  (O)  (O)          -> Part 1 = 3
                                 +
Group 2 (Blue Balls):          (O)  (O)          -> Part 2 = 2
------------------------------------------------------------------
Joined Together (All):    (O)  (O)  (O)  (O)  (O) -> Whole  = 5

Active Joining vs. Static Combining

There are two ways addition happens in real life: Active Joining: You already have 3 toys, and a friend walks over and gives you 2 more. Items are actively moving into the group. Static Combining: You look at a fruit bowl that has 3 green apples and 2 red apples sitting side by side. Even though no apples are moving, you put the two colors together in your mind to find the total number of apples.

The Word "Sum" and "Total"

The answer you get when you add two or more numbers together is called the sum or the total. When you join 3 and 2, the sum is 5.

Modeling Addition with Concrete Tools

You can act out addition stories using everyday tools to see the math in action.

Connecting Cube Trains:
[Train A: 4 green cubes]  +  [Train B: 3 yellow cubes]
        |                           |
   [#|#|#|#]             +       [#|#|#]
                \             /
                 v           v
           Snap them together!
                 v           v
           [#|#|#|#|#|#|#]
      Total Train: 7 cubes long!

Using Two Colors to Keep Parts Visible

When you snap cubes together, use two different colors. This allows your eyes to see the two separate parts (4 green and 3 yellow) even after they are connected into one whole train of 7.

Practice Exercises

Exercise 1: You have 3 toy airplanes on a runway. 3 more airplanes land on the runway. What action did you take, and how many airplanes are on the runway now?

Exercise 2: In a garden, there are 4 yellow butterflies and 5 orange butterflies resting on flowers. What are the two parts, and what is the whole sum of butterflies?

Exercise 3: Explain the difference between an active joining story and a static combining story in your own words.

Exercise 4: Draw or describe how you would use counters of two different colors to show the addition problem 2 joined with 6.

Solutions and Explanations

Solution to Exercise 1: The action is joining (addition). You had a part of 3 airplanes and joined 3 more airplanes to it. In all, there are 6 airplanes on the runway (3 + 3 = 6).

Solution to Exercise 2: The two parts are 4 yellow butterflies and 5 orange butterflies. The whole sum is 9 butterflies in total, because joining 4 and 5 makes 9 (4 + 5 = 9).

Solution to Exercise 3: In an active joining story, new items physically arrive and are added to an existing group (like 2 more ducks swimming over to join 3 ducks). In a static combining story, two groups are already sitting together and you combine them in your mind (like counting how many red crayons and blue crayons are already in a box).

Solution to Exercise 4: Place 2 red counters in a row on the left, and place 6 yellow counters in a row right next to them on the right. Slide them together so they form one single line of counters, and count the total to find 8 counters in all.