Addition & subtraction
The idea
Putting amounts together and taking them apart are the two most useful moves in arithmetic. Addition joins groups: 36 buttons plus 27 buttons makes one bigger collection. Subtraction works the other way: it can take some away, or it can measure the gap between two amounts, like how many more stickers your friend has than you. You already know counting and place value, and both moves lean on them hard.
The best mental habit is to work with tens and ones instead of single counts. To add 36 + 27, add 20 first to get 56, then 7 more to get 63 — friendly chunks instead of 27 tiny hops. The two operations also undo each other, which gives you a free checking tool: if 45 + 18 = 63, then 63 − 18 must be 45.
One trap to avoid: when subtracting, some people line up the digits and always take the smaller digit from the bigger one, whichever row it is in. That fails in a problem like 63 − 18, because the 3 ones are fewer than the 8 you must remove. The fix is regrouping: break one ten into ten ones, so the 63 becomes 5 tens and 13 ones, and then the subtraction works honestly.
Worked example
A jar holds 36 buttons. You drop in 27 more, and later you take out 18 buttons for a craft project. How many buttons are in the jar now?
- First join the two groups. Split 27 into friendly parts: 36 + 20 = 56, then 56 + 7 = 63. The jar holds 63 buttons after you drop yours in.
- Now remove 18. Take the tens away first: 63 − 10 = 53. Then take the ones: 53 − 8 = 45.
- Notice the ones place in 63 − 18: you cannot take 8 ones from 3 ones, so one ten must be broken into ten ones. That is exactly why the always-take-small-from-big shortcut gives wrong answers.
- Check by adding back: 45 + 18 = 63, which matches the jar before the craft. Since addition undoes subtraction, the answer holds.
Answer. There are 45 buttons left in the jar.
Check your understanding
- How does breaking a number into tens and ones make adding in your head easier?
- Why can you check a subtraction problem with addition, and how would you show this to a friend?
- What does subtraction mean besides taking away — how can it compare two amounts?
- Where does the extra ten come from when the ones add up past 9, like in 36 + 27?