Subtraction Within 20

One way to subtract is to count back: start with the first number, then count backward.
Solve: \(13 - 5 = ?\)

• Step 1: Start with the first number. Keep the number 13 in your head and say it out loud: “Thirteen.”
• Step 2: Get your fingers ready. The second number, 5, tells you how many steps to count back. Hold up 5 fingers to keep track of your steps.
• Step 3: Count back from 13. Now, put down one finger for each number you say as you count backward: “Twelve, eleven, ten, nine, eight.”
  • Say “Twelve” \(\rightarrow\) Put down 1st finger.
  • Say “Eleven” \(\rightarrow\) Put down 2nd finger.
  • Say “Ten” \(\rightarrow\) Put down 3rd finger.
  • Say “Nine” \(\rightarrow\) Put down 4th finger.
  • Say “Eight” \(\rightarrow\) Put down 5th finger.

The last number you said is the answer. \(13 - 5 = 8\)

We can also use a number line to subtract: subtracting means taking steps backward on the line.
Solve: \(7 - 3\)

1. Start at the first number. Find the number 7 on the number line. This is your starting point.
2. Jump backward. The second number, 3, tells you how many jumps to make. Since we are subtracting, we move to the left, where the numbers get smaller. Make 3 jumps backward.
3. Find your landing spot. The number you land on is the answer.

After 3 jumps backward, you land on 4. So, \(7 - 3 = 4\).

With the “subtract to make 10” strategy, we break the subtraction into two smaller, easier steps: first, we jump back to 10, and then we subtract the rest.
Solve: \(13 - 5\)

1. Start at the first number, which is 13.
2. Jump back to 10. How many steps do we take to get from 13 to 10? We take 3 steps back.
3. Figure out the rest. We needed to subtract a total of 5. We already subtracted 3. How many more do we need to subtract? We can break 5 into 3 and 2 (\(5 = 3 + 2\)). So, we still need to subtract 2 more.
4. Take the final jump. From 10, jump back 2 more steps. You land on 8.

\(-\) \(=\) \(-\) \(-\)
\(\quad\)
\(\textcolor{white}{-}\) \(=\) \(-\)
\(\quad\)
\(\textcolor{white}{-}\) \(=\)
By breaking 5 into 3 and 2, we can solve the problem easily:$$\begin{aligned}[t]13 - 5 &= 13 - 3 - 2 && \text{(break \(5\) into \(3+2\))}\\ &= 10 - 2 && \text{(\(13-3=10\))}\\ &= 8\end{aligned}$$ So, \(13 - 5 = 8\).

$$\textcolor{colordef}{\text{part 1}} + \textcolor{colorprop}{\text{part 2}}=\textcolor{olive}{\text{total}}$$ $$\textcolor{olive}{\text{total}} -\textcolor{colordef}{\text{part 1}} = \textcolor{colorprop}{\text{part 2}} \quad\quad \textcolor{olive}{\text{total}} -\textcolor{colorprop}{\text{part 2}} =\textcolor{colordef}{\text{part 1}} $$

Because addition and subtraction are linked, you can solve a subtraction problem by thinking of it as a “missing part” addition problem.
To solve \(\textcolor{olive}{13} - \textcolor{colordef}{9}\), ask yourself: “What do I add to 9 to make 13?”

1. Start at \(\textcolor{colordef}{9}\).
2. Count up until you reach \(\textcolor{olive}{13}\): “10, 11, 12, 13.”
3. You counted \(\textcolor{colorprop}{4}\) numbers: \(10\), \(11\), \(12\), \(13\).

Therefore, \(\textcolor{olive}{13} - \textcolor{colordef}{9} = \textcolor{colorprop}{4}\), because \(\textcolor{colordef}{9} + \textcolor{colorprop}{4} = \textcolor{olive}{13}\).

These are the four steps already known (search, try, check, say), made more precise by the model: searching becomes understanding the story; trying becomes drawing a model and choosing the operation; checking and saying are in the last step: we calculate, make sure the answer makes sense, then give it.

1. Understand the Story: Read the problem to identify the parts and the whole.
2. Draw a Model: Use a part-whole bar model to organize the information.
3. Choose the Operation: If the whole is unknown, you add the parts. If a part is unknown, you subtract the known part from the whole.
4. Solve and Check: Calculate the answer and make sure it makes sense in the context of the story.