\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)

Subtraction Within 20

Definitions


Have you ever given away some of your toys or candies to a friend? When you do that, you're subtracting! Let’s see: if you have 13 cubes, and you give 5 cubes to your friend, how many cubes do you have left?
\(-\) \(=\)

Now you have 8 cubes left! In math, we write it like this: $$13-5=8$$
\(-\) \(=\)


Definition Subtraction
Subtraction means taking something away. When we subtract, we find out how many are left.
  • The \(-\) symbol means "subtract."
  • The \(=\) symbol shows that the two sides are the same.
We can represent subtraction as:
  • Numbers: $$13 - 5 = 8$$
  • Cubes:
    \(-\) \(=\)
  • Fingers:
    \(-\) \(=\)
  • Words:
    thirteen minus five equals eight
  • Part whole model:

Number Line Method

Method Subtracting using the Number Line
We want to find \(13 - 5\).
  • Place a marker on 13.
  • Move 5 steps backward.
So, \(13 - 5 = 8\).

Making 10 Method

Method Subtracting with the Making 10 Method
To subtract \(13 - 5\), we can break down the subtraction into two steps by first making 10.
    1. Start with 13: We have 13 as our starting number.
    2. Make 10: Ask yourself, How many do we need to reach 10? Since we’re subtracting, we need to remove 3 first to reach 10. Now, we’re left with \(13 - 3 = 10\).
    3. Finish the Subtraction: We still need to subtract 2 more from 10, which gives us \(10 - 2 = 8\).
  • \(-\) \(=\) \(-\) \(-\)

    \(\textcolor{white}{-}\) \(=\) \(-\)

    \(\textcolor{white}{-}\) \(=\)
  • \(\begin{aligned}[t]13 - 5&=13 - 3 - 2\\&=10 - 2\\&=8\\\end{aligned}\)
So, \(13 - 5 = 8\).

Addition and Subtraction Link


Imagine you have 2 red apples, and your friend gives you 3 blue apples.
  1. How many fruits do you have now?
  2. If you eat the 3 blues apples, how many are left?
  3. Can you see the connection between the two questions?

  1. Now you have 5 apples in total.$$\textcolor{colordef}{2} + \textcolor{colorprop}{3} = \textcolor{olive}{5}$$
  2. If you take away the 3 blues apples, you’ll be left with 2 red apples.$$\textcolor{olive}{5} -\textcolor{colorprop}{3} =\textcolor{colordef}{2}$$
  3. See how addition and subtraction are linked? Adding 3 to 2 gives 5, and removing 3 from 5 brings us back to 2. $$\textcolor{colordef}{2}+\textcolor{colorprop}{3}=\textcolor{olive}{5}\text{ and }\textcolor{olive}{5} -\textcolor{colorprop}{3} =\textcolor{colordef}{2}$$


Proposition Addition and Subtraction Link
Addition and Subtraction are opposites:Adding and subtracting are opposites:$$\begin{aligned}\textcolor{colordef}{\text{part 1}} + \textcolor{colorprop}{\text{part 2}}&=\textcolor{olive}{\text{total}}\\ \textcolor{olive}{\text{total}} -\textcolor{colordef}{\text{part 1}} &= \textcolor{colorprop}{\text{part 2}}\\ \textcolor{olive}{\text{total}} -\textcolor{colorprop}{\text{part 2}} &=\textcolor{colordef}{\text{part 1}} \\ \end{aligned}$$
Example
Calculate: \(\textcolor{olive}{19} - \textcolor{colordef}{18}\)

  • Because \(\textcolor{colordef}{18}+\textcolor{colorprop}{1}=\textcolor{olive}{19}\), \(\textcolor{olive}{19} - \textcolor{colordef}{18}=\textcolor{colorprop}{1}\)

Method Counting On
For \(\textcolor{olive}{13} - \textcolor{colordef}{9}\):
  1. Start with \(\textcolor{colordef}{9}\).
  2. Count forward 10, 11, 12, \(\textcolor{olive}{13}\). We added \(\textcolor{colorprop}{4}\) numbers to reach \(\textcolor{olive}{13}\).
So, \(\textcolor{olive}{13} - \textcolor{colordef}{9} = \textcolor{colorprop}{4}\) because \(\textcolor{colordef}{9}+\textcolor{colorprop}{4}=\textcolor{olive}{13}\).

Problem-Solving Methods

In math, we often need to find answers to problems that involve either adding or subtracting. Here’s how we can solve these problems step-by-step.
Method Steps to Solve Word Problems
  1. Understand the Problem: Read the problem carefully. Look for keywords like "altogether" for addition or "left" for subtraction.
  2. Decide on the Operation: Determine whether you need to add or subtract to solve the problem.
  3. Set Up the Equation: Write the equation that matches the problem. If you are finding the total, use addition. If you are finding what is left, use subtraction.
  4. Solve and Check: Solve the equation. After you find the answer, check if it makes sense with the problem.
Example
You have 5 candies, and your friend gives you 3 more. How many candies do you have now?

  • Start with the \(\textcolor{colordef}{5}\) candies you have, and add the \(\textcolor{colorprop}{3}\) candies your friend gave you.
  • \(\textcolor{colordef}{5}+\textcolor{colorprop}{3}=\textcolor{olive}{8}\)
  • So, you have \(\textcolor{olive}{8}\) candies in total.