Addition within 20

1Summary 重點摘要

Teens plus ones: add ones first, carry when over ten.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Make tenWhen two numbers add up to more than 10, first make one of them into a full ten; this is called making ten. Why make a ten? Whole tens are easy to work with, so the hard sum becomes two easy steps. Example: for 8 + 5, adding 2 to 8 makes 10, so split 5 into 2 and 3; first 8 + 2 = 10, then add the remaining 3 to get 13. Take care that the piece split off must exactly complete the bigger number to a ten, or everything after goes wrong; before splitting, think how far the bigger number is from ten.
2. Step 2: Column formIn column form the digits must line up in their places, ones under ones and tens under tens; this is the first requirement of column work. Why line up? Only digits of the same place value may be added directly. Example: for 8 + 5, both 8 and 5 are ones, so write them one under the other; put the + sign on the left of the bottom line, draw a line below, and write the answer under it. The usual error is slanted digits with ones sitting over tens, which ruins the sum, so settle the positions before writing.
3. Step 3: Add the ones firstIn columns we add the ones place first; this order is fixed, and the tens may not go first. Example: the ones 8 + 5 = 13; 13 holds 1 ten and 3 ones, so we write only 3 in the ones place; the other 10 ones are bundled as 1 ten, ready to go to the tens place, and this step is called filling a ten. Take care that only one digit sits in the ones place; writing the whole 13 there counts the ten twice, and the answer breaks at once.
4. Step 4: CarryWhen the ones place fills to 10, one ten is carried to the tens place; this is carrying, the key step in addition within 20. Example: for 8 + 5 we write 3 in the ones place and the carried 1 in the tens place; tens 1 and ones 3 read as 13. Only when the carrying is done is the answer complete. The most common fault is forgetting the carry and writing 3, which is 10 short; after working, check that the tens place holds the carried 1, a habit that prevents every such slip.
5. Step 5: Another onePractise one more with making ten and with columns, and let the two ways check each other. Example: for 9 + 4, add 1 to 9 to make 10 and split 4 into 1 and 3; 10 + 3 = 13. In columns, the ones give 9 + 4 = 13: write 3 and carry 1, and the answer is again 13. When both ways agree, you can be confident. Take care to split the smaller number to complete the bigger one, which costs the least effort; splitting the other way, trying to stretch 9 to complete 4, only makes the work harder.
6. Step 6: Adding without carryingNot every addition needs carrying; if the ones add to less than 10, just write them down, with no carrying at all. Example: for 12 + 4, the ones 2 + 4 = 6, which is less than 10, so we simply write 6 in the ones place; no new ten comes to the tens place, so it stays 1, and the answer is 16. Take care that even without carrying, ones still face ones and tens face tens; putting the 4 under the tens digit gives a wrong answer, so format matters as much as the working.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Carry when the ones pass ten.
• Make ten: 8 + 5 = 8 + 2 + 3 = 13.
• In columns, ones under ones.
• Add the ones first, then the tens.
• Remember to add the carried 1.