Subtraction within 10

1Summary 重點摘要

Subtraction means taking away, count what is left.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Subtracting is taking awaySubtracting means taking some away from the starting amount and seeing how many are left; this is the basic meaning of subtraction. Why learn it? Because in life things are eaten, used up or given away. Example: a plate has 5 apples; take 2 away and 3 are left, so we write 5 - 2 = 3. Take care that after taking away, the number we work out is what remains, not the part removed; the question asks how many are left, and the two must not be mixed up.
2. Step 2: Read the symbolsThe sign for subtraction is -, read as minus, and a full reading includes the symbols. Example: 5 - 2 = 3 reads 'five minus two equals three'. The - sign means take the second number away from the first, and the number gets smaller, just the opposite of addition. The usual error is swapping the two numbers around, treating 5 - 2 as 2 - 5; in subtraction the order must never be swapped, which is different from addition and worth memorising.
3. Step 3: Cross outWhen working it out in your head is hard for the moment, draw a picture to help; this method is called crossing out. First draw every thing as a circle, cross out the part taken away, then count the circles that are not crossed out. Example: for 7 - 3, draw 7 circles, cross out 3 of them, and 4 are left, so 7 - 3 = 4. Drawing is clear to see and best for beginners. Take care that the number crossed out equals the number subtracted; one circle too many or too few makes the answer wrong.
4. Step 4: Count backTo subtract, start from the bigger number and count back step by step; this is called counting back. Why does it work? Taking one thing away moves the count one step back. Example: for 9 - 4, start at 9 and count back 4 steps: 8, 7, 6, 5; stop at 5, so 9 - 4 = 5. The usual mistake is counting back a number of steps different from the number subtracted, one step too many or too few; hold up a finger for each step and fold one down, letting your fingers keep the count.
5. Step 5: Zero factsSubtracting 0 takes nothing away, so what is left is unchanged; subtracting everything leaves nothing at all. Example: 4 - 0 = 4, because nothing is taken; 4 - 4 = 0, because everything is taken. These two special cases must be kept clear: one leaves the number exactly the same, the other turns it into 0, and they are exact opposites. The common error is working out 4 - 0 as 0, or 4 - 4 as 4; both mistakes reverse the rule, so never mix them.
6. Step 6: Addition partnersAddition and subtraction are partners, and each can check the other. Putting together makes more, and taking a part away goes back to the other part. Example: 3 + 4 = 7, so 7 - 4 = 3 and 7 - 3 = 4. With this link, after working out 7 - 3 = 4 you can add 4 + 3 to see whether it returns to 7. Take care that the check must use the very two numbers from the sum; if other digits are used, even a careful check will never find the mistake.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Subtraction = take away, count what is left.
• - is minus; answers get smaller.
• Count back: for 9 - 4 count 8, 7, 6, 5.
• Subtract 0: no change; subtract itself: 0.
• Check with addition: 5 + 3 = 8 checks 8 - 3 = 5.