Subtraction within 20

1Summary 重點摘要

Teens minus ones: break a ten when ones not enough.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Check the onesTo subtract a one-digit number from a two-digit number, first look at the ones place; this step decides which method to use. Why look at the ones first? Ones can only be taken from ones, and when they fall short, extra help is needed. Example: in 13 - 5, the ones place has only 3, and 3 cannot take away 5, so we may not subtract directly in the ones place and must break one ten open. The usual error is skipping the check and taking the smaller digit from the bigger at once, which is simply wrong; always judge before working.
2. Step 2: Break a tenWhen the ones cannot subtract, split the two-digit number into a full ten and the ones, then subtract with the ten; this is called breaking a ten. Why does it work? A whole ten minus a one-digit number is basic work already learned, so the hard part turns easy at once. Example: split 13 into 10 and 3; subtract with the ten first: 10 - 5 = 5, then add the 3 back, 5 + 3 = 8, so 13 - 5 = 8. Take care that the part broken off is one whole ten, and after subtracting the ones digit must be added back; forgetting that step loses the ones.
3. Step 3: Borrow in columnsIn columns, when the ones cannot subtract, we borrow from the tens place; borrowing and breaking a ten are the same idea written two ways. Example: for 13 - 5, borrow 1 ten as 10 ones, so the ones place becomes 13; 13 - 5 = 8, write 8 in the ones place. The tens place lent out 1 ten and has 0 left, which we need not write, so the answer is 8. The most common fault is borrowing yet forgetting to reduce the tens digit by 1, leaving it unchanged, which makes the answer 10 too big; reduce the tens digit the moment you borrow.
4. Step 4: Count back works tooSubtraction can also be done by counting back, a method that suits smaller subtrahends especially well. Example: for 14 - 6, start at 14 and count back 6 steps: 13, 12, 11, 10, 9, 8; six steps land on 8, so 14 - 6 = 8. Use your fingers to keep track of the steps, folding one down at each step, and check once at the end, then nothing goes wrong. Take care that the number of steps back equals the number subtracted; one step more or less gives a wrong answer, and the folded fingers are the best check.
5. Step 5: Another onePractise one more with breaking the ten; once familiar, the whole process can happen in your head. Example: 15 - 8: split 15 into 10 and 5; first 10 - 8 = 2, then add the ones back, 2 + 5 = 7, so 15 - 8 = 7. Fluency means finishing these two steps in the mind without writing anything. Take care of the order, subtracting with the whole ten first and adding the ones back after; reversed, the working tangles and the result easily goes wrong.
6. Step 6: CheckA subtraction answer can be checked by adding; this is checking, a good habit against mistakes. Why does it work? Subtraction and addition undo each other, so adding the subtracted part back must return the starting number. Example: 15 - 8 = 7; check with 7 + 8 = 15, and adding back gives exactly the starting 15, so the subtraction is right. After every subtraction, it is worth adding back once. Take care that the check adds the subtrahend and the answer; with any other numbers, even a careful check finds nothing.

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Break a ten when ones are not enough.
• 10 - 5 = 5, then add the ones back.
• The tens place drops by 1 after borrowing.
• Count back works: 14 - 6 = 13, 12, 11, 10, 9, 8.
• Check subtraction with addition.