🌱 Starter Village · Arithmetic
Addition
Add whole numbers fluently, from single-digit facts to multi-digit sums with regrouping. Addition means combining amounts.
In short
- Addition combines amounts, and the order you add in never changes the total.
- Written addition works column by column from the ones, carrying whenever a column reaches 10.
- A carried digit is a real ten or hundred moved into the column where it belongs.
- Estimating first turns a wrong answer into an obviously wrong answer.
What addition means
Addition combines amounts. If you have 24 gold coins and find 18 more, addition tells you how many you hold now.
Two useful facts follow straight from the meaning:
- The order does not matter: 24 + 18 = 18 + 24. This is the commutative property, and it lets you start from whichever number is easier.
- Grouping does not matter either: (7 + 3) + 8 = 7 + (3 + 8). This is the associative property, and it is what makes "look for a friendly pair" legal.
Facts you should know without thinking
Fluency with sums to 20 makes every later topic faster. Two strategies build it:
- Make a ten. For 8 + 5, take 2 from the 5 to fill the 8 up to 10, leaving 3. So 8 + 5 = 10 + 3 = 13.
- Use a double. 7 + 8 is one more than the double 7 + 7 = 14, so it is 15.
These are not tricks to replace understanding. They are the reasoning that eventually becomes instant recall.
Adding bigger numbers: place value and carrying
Written addition works one place-value column at a time, starting at the ones.
If a column adds to 10 or more, only the ones digit of that total stays. The ten that is left over is worth exactly one unit of the next column, so it moves there — that is carrying (also called regrouping).
476 + 258 ----- Ones: 6 + 8 = 14, write 4 and carry 1 ten. Tens: 7 + 5 + 1 = 13, write 3 and carry 1 hundred. Hundreds: 4 + 2 + 1 = 7. Result: 734.
Nothing is invented here: the carried 1 is genuinely one ten or one hundred, moved to the column where it belongs.
Estimate first, compute second
Before adding, round each number and add the rounded values in your head. 476 + 258 is roughly 500 + 260 = 760, so an answer of 734 is believable and an answer of 6,214 clearly is not.
Estimating costs a few seconds and catches the most damaging errors — a misplaced digit or a dropped carry.
Addition in word problems
Words that usually mean addition: *altogether, in total, combined, gained, more than before, sum*.
Do not rely on keywords alone; picture what is happening. Ask: is the amount growing? If yes, you are adding.
A reliable routine:
- Underline each number and write what it counts.
- Write the number sentence before computing anything.
- Answer with a unit, not just a bare number.
Worked examples
Example 1
387 + 465 = ?
- Estimate: about 390 + 470 = 860.
- Ones: 7 + 5 = 12. Write 2, carry 1 ten.
- Tens: 8 + 6 + 1 = 15. Write 5, carry 1 hundred.
- Hundreds: 3 + 4 + 1 = 8.
- 387 + 465 = 852, which is close to the estimate of 860.
Example 2
Mira collects 128 crystals on Monday and 249 on Tuesday, then is given 35 more. How many does she have altogether?
- Three amounts are being combined, so this is addition.
- Number sentence: 128 + 249 + 35.
- Add two at a time: 128 + 249 = 377.
- 377 + 35 = 412.
- Mira has 412 crystals. (Estimate check: 130 + 250 + 35 = 415.)
Practice problems, with solutions
Three problems of increasing difficulty, each with the full working. In the game these are generated fresh every time; these three are fixed so this page always shows the same ones.
Problem 1
Difficulty 1 of 57 + 3 = ?
Answer: 10
- Ones: 7 + 3 = 10 — write 0 and carry 1 ten
- 7 + 3 = 10
Problem 2
Difficulty 3 of 5? + 17 = 91
Answer: 74
- part + part = whole, so whole - known part = missing part.
- 91 - 17 = 74
- Check: 17 + 74 = 91
Problem 3
Difficulty 4 of 579 + 95 + 62 + 25 = ?
Answer: 261
- Start with 79.
- + 95 = 174
- + 62 = 236
- + 25 = 261
Common mistakes
- Forgetting to carry, so each column is written on its own: 47 + 58 becomes 95 instead of 105.
- Misaligning the columns when the numbers have different lengths.
- Adding a carried digit into the wrong column.
- Choosing addition from keywords alone when the situation is really a comparison.
What you should be able to do
- Recall addition facts within 20 automatically.
- Add multi-digit numbers using place value and regrouping.
- Add three or more numbers by looking for friendly pairs that make ten.
- Choose addition to solve "how many altogether" word problems.
Where this fits in the curriculum
Common Core
- 2.OA.B.2
Grade 2 — Fluently add and subtract within 20; know all sums of two one-digit numbers from memory.
- 3.NBT.A.2
Grade 3 — Fluently add and subtract within 1000 using strategies based on place value.
- 4.NBT.B.4
Grade 4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.