Subtraction as Taking Away - First Grade Mathematics

If addition is the math superpower of putting things together, subtraction is the equally amazing superpower of taking things away! Imagine you have five warm, freshly baked cookies on a plate. If you eat two of those delicious cookies, you have taken them away from the plate. How many cookies are left? Three cookies! In this chapter, you will discover the foundational meaning of subtraction as separation and removal, learn how to model taking away with physical objects, and see what happens to a whole when a part is removed.

The Action of Taking Away

Subtraction always begins with a whole group, removes a part of that group, and leaves behind a smaller part called the remainder or difference.

The Action of Taking Away:
Start with a Whole:      (*)  (*)  (*)  (*)  (*)     -> 5 Cookies
                                  |    |
Take away 2 cookies:             [X]  [X]            -> Take away 2
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Remaining Part:          (*)  (*)  (*)               -> 3 Cookies left!

The Three Roles in Subtraction:

The Whole (Total): The full group you start with before anything is removed (here, 5 cookies). The Part Taken Away: The items that leave, get eaten, roll away, or break (here, 2 cookies). The Part Left Over (Difference): The items that remain behind (here, 3 cookies).

The Group Always Shrinks

When you take items away from a group, the amount left behind is always smaller than the starting whole (unless you take away zero). Subtraction makes quantities decrease.

Modeling Taking Away with Your Hands

There are several ways to physically model the action of taking away.

Modeling Taking Away with Connecting Cubes:
Step 1: Build a train of 6 cubes:       [#|#|#|#|#|#]  (Whole = 6)
Step 2: Snap off 2 cubes:               [#|#|#|#]  +  [#|#] (Snapped away!)
Step 3: Count the remaining cubes:      [#|#|#|#]  -> 4 cubes left!

The Slide-Away Strategy

When using loose counters like pennies or beans, place all 6 on your mat. When the problem says to take away 2, physically slide two counters off the mat and into a cup. Then count the counters still resting on the mat.

Drawing Subtraction Pictures

When solving subtraction problems on paper, draw circles for the whole group. Then draw a clear slash mark / through the items being taken away. Count the circles that do not have a slash through them to find your answer.

Practice Exercises

Exercise 1: You have 7 helium balloons. 3 balloons pop. What action occurred, and how many balloons are left floating?

Exercise 2: There are 8 apples in a fruit bowl. A family eats 5 of the apples. Identify the starting whole, the part taken away, and the part remaining.

Exercise 3: Draw or describe the quick math sketch you would make to solve: "Start with 9 circles, take away 4."

Exercise 4: Explain why the answer to a subtraction problem is usually smaller than the starting number.

Solutions and Explanations

Solution to Exercise 1: The action is subtraction (taking away). You started with a whole of 7 balloons and 3 were removed. There are 4 balloons left floating (7 - 3 = 4).

Solution to Exercise 2: The starting whole is 8 apples. The part taken away is 5 apples (the ones eaten). The part remaining is 3 apples (8 - 5 = 3).

Solution to Exercise 3: Draw a row of 9 circles: o o o o o o o o o. Draw a slash through 4 of the circles: o o o o o / / / /. Count the remaining unslashed circles: there are 5 circles left.

Solution to Exercise 4: The answer to a subtraction problem is usually smaller than the starting number because you are removing items from the group. When items leave a collection, fewer items remain.