Do you know how to find out how many cookies are left on the plate after you eat some? That is subtraction! In this chapter you will learn what subtraction means, how to write it with the minus sign, and how addition can help you find the answer. All the numbers stay within 10.
1. Subtraction means taking from
Sometimes you start with a group of things and then take some away. When this happens, the group gets smaller. Subtracting tells you how many are left.
To subtract means to take away. We start with a number, take some away, and find how many are left.
Look at the picture. There are 7 counters. We cross out 3 of them. The crossed-out counters are gone. Count the counters that are not crossed out: there are 4.
We say: seven minus three equals four. We write \( 7 - 3 = 4 \).
2. Subtraction also means taking apart
There is a second way to think about subtraction. Imagine a whole group that is split into two smaller groups. If you know the whole and one part, you can find the other part.
The whole is 9. One part is 4. The other part is 5. We can write \( 9 - 4 = 5 \). The whole is always the biggest number, and it goes first in a subtraction sentence.
A shelf has 6 toy trucks. A child takes 2 trucks. How many trucks are on the shelf now?
We start with 6 and take away 2. We count what is left: 4 trucks. We write \( 6 - 2 = 4 \).
3. The minus sign and subtraction sentences
The minus sign looks like a short, flat line: \( - \). It tells us to take away. The equal sign \( = \) tells us that both sides have the same value.
A subtraction sentence has three numbers: the number we start with, the number we take away, and the number that is left.
\[ 8 - 5 = 3 \]
Read it as “eight minus five equals three.” You can also say “eight take away five is three.” The first number is the whole, the second is what we take away, and the last is the difference, which is what is left.
The order matters! With subtraction you start with the bigger number. \( 5 - 8 \) is not the same as \( 8 - 5 \). At this grade, we always take a smaller number from a bigger number, or from the same number.
Two special facts are worth remembering. When you take away nothing, nothing changes: \( 6 - 0 = 6 \). When you take away everything, nothing is left: \( 6 - 6 = 0 \).
4. Subtracting with objects and drawings
You can always use objects or a quick drawing to find an answer. Counters, blocks, fingers and little pictures all work.
- Draw the starting number of dots or circles.
- Cross out the number you take away.
- Count the dots that are not crossed out.
- Write the subtraction sentence and the answer.
There are 9 apples in a basket. A farmer picks up 4 of them. How many apples are still in the basket?
Draw 9 circles, cross out 4, and count the circles that are not crossed out. There are 5. We write \( 9 - 4 = 5 \). There are 5 apples left in the basket.
5. Counting back on a number line
A number line helps you subtract too. Put your finger on the number you start with. Then hop back one step for each number you take away. The number where you land is the answer.
We start at 8 and hop back 3 times: 7, then 6, then 5. We land on 5. So \( 8 - 3 = 5 \).
On my planet we say: “Hop back, never forward!” When you subtract, your finger always moves toward zero.
6. Addition and subtraction are partners
Addition and subtraction are opposites. If you add a number and then subtract it, you get back to where you started. This is a powerful trick: you can use an addition fact to solve a subtraction problem.
To find \( 10 - 7 \), ask yourself: “What do I add to 7 to make 10?” The answer is 3, because \( 7 + 3 = 10 \). So \( 10 - 7 = 3 \).
If \( 7 + 3 = 10 \), then \( 10 - 7 = 3 \) and \( 10 - 3 = 7 \). Every addition fact gives you subtraction facts.
7. Fact families
Three numbers that belong together make a fact family. The two smaller numbers are the parts, and the biggest number is the whole. With 3, 7 and 10, we can write four facts.
| Addition facts | Subtraction facts |
|---|---|
| \( 3 + 7 = 10 \) | \( 10 - 3 = 7 \) |
| \( 7 + 3 = 10 \) | \( 10 - 7 = 3 \) |
All four facts use only the numbers 3, 7 and 10. When the two parts are the same number, the family is smaller. For example, 4, 4 and 8 give \( 4 + 4 = 8 \) and \( 8 - 4 = 4 \).
Write the fact family for 2, 6 and 8.
The whole is 8, the parts are 2 and 6. The facts are \( 2 + 6 = 8 \), \( 6 + 2 = 8 \), \( 8 - 2 = 6 \) and \( 8 - 6 = 2 \).
8. Finding the missing number
Sometimes a number is hidden. We can use a box or a question mark for it. Look at this diagram: the whole is 8, one part is 5, and the other part is missing.
To find the missing part, subtract the part you know from the whole: \( 8 - 5 = 3 \). You can also ask “5 plus what makes 8?” The answer is 3 again.
Solve \( 9 - \square = 4 \).
Ask: “9 take away what number leaves 4?” We know \( 4 + 5 = 9 \), so the missing number is 5. Check: \( 9 - 5 = 4 \). It works!
When the first number is hidden, as in \( \square - 3 = 6 \), think of putting the 3 back: \( 6 + 3 = 9 \). The hidden number is 9.
Key takeaways
- To subtract means to take away or to take apart. The answer shows what is left.
- The minus sign \( - \) tells us to take away. We write sentences like \( 8 - 5 = 3 \).
- The whole goes first. \( 6 - 0 = 6 \) and \( 6 - 6 = 0 \).
- You can draw, cross out and count, or hop back on a number line.
- Addition and subtraction are partners: \( 7 + 3 = 10 \) gives \( 10 - 7 = 3 \).
- A fact family uses three numbers to make four facts.
- To find a missing number, think of the addition that goes with it.
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