Have you learned the addition facts and learned about place value? If so, you are ready to do addition with pencil and paper. Remember that it is very important to write neatly and to line up numbers so that digits with the same place value are directly above or below each other. Neatness helps you avoid careless mistakes.

EXAMPLE 1: Jimmy had 34 cents, and his sister gave him 23 cents more. Then how much did he have? Use pencil and paper.

THINK: Is this a combining problem? Do you need to add or multiply? What is the number question?

COMPUTE: First, write the number question vertically--one number on top of the other. Now, add the numbers in the ones place and then the tens place.

     34 
    +23 
     57

CHALLENGE 1: Vicki had $25 , and she earned $12 more. Now how much money does she have?

CHALLENGE 2: Make these additions with a pencil:

27 + 51 = ? , 44 + 55 = ? , 26 + 62 = ? , 91 + 8 = ?, 73 + 25 = ?

EXAMPLE 2: Timmy found 3 golf balls on Monday, 2 on Tuesday, and 6 on Wednesday. How many balls did he find? Add from the top down.

THINK about the number question and write it vertically. How many addition facts must you remember?

COMPUTE: Try adding the three amounts.

(One way to do it: Start at the top and add 3 plus 2 for the first sum, which is 5. Then you add 5 and 6 for the last sum.

     3
     2
    +6
    11

CHALLENGE 3: Mark spent $4 for a movie ticket, $3 dollars for popcorn, and $2 on a soft drink. How much did he spend?

CHALLENGE 4: Make these additions vertically with a pencil:

4 + 2 + 3 = ? , 3 + 5 + 2 = ? , 3 + 3 + 2 = ? , 2 + 1 + 6 = ?

EXAMPLE 1: Tommy had 79 cents. He gave his sister 20 cents. How much money does Tommy have left?

THINK: Is this a combining or separating problem? This is a take-away type of subtraction problem. What is the number question?

COMPUTE: Write the number question vertically. Then subtract the 0 from 9 and then the 2 tens from 7 tens.

     79 minuend
    -20 subtrahend
     59 remainder

CHALLENGE 1: Marty had $27, and he spent $13. How much did he have left?

EXAMPLE 2: Tommy now has 59 cents and his sister has 20 cents. How much more money does Tommy have compared to his sister?

THINK: Is this a combining or separating problem? This is a separating problem, but you compare amounts rather than take away. You find the difference instead of the remainder. But you separate one amount from another by subtracting just as you did in the take away problem. You just find out how much more one amount is compared to another. Write the number question vertically.
COMPUTE:

     59 minuend
    -20 subtrahend
     39 difference

CHALLENGE 2: A teacher asked her class what flavor of ice cream they wanted for a party. She found that 18 liked chocolate compared to 14 that liked strawberry. How many more kids wanted chocolate compared to those that wanted strawberry?

EXAMPLE 3: Jeff's mother baked 24 cookies. Thirteen had chocolate chips in them. The rest didn't. How many cookies had no chocolate chips in them?

THINK: Is this a combining or separating problem? This is the third kind of subtraction problem. There are two groups. You are given the number in one group and the total number, and you determine how many are in the second group. You could write the number question as an addition number question with a missing addend, 13 + ? = 24, or as a subtraction question, 24 - 13 = ?. Write the subtraction number question vertically.
COMPUTE AND CHECK

CHALLENGE 3: There are 27 children in a third grade class. Fourteen are girls. How many are boys?

CHALLENGE 4: Make these subtractions with a pencil:

45 - 34 = ? , 54 - 32 = ? , 69 - 27 = ? , 75 - 25 = ? , 87 - 80 = ? , 99 - 66 = ?

[You will need 3 dimes and 11 pennies.]

EXAMPLE 1: Jerry has a coin case that has two coin slots. The first slot holds just 9 pennies, and he has 9 pennies in it. The slot on the left holds 9 dimes, and he has 2 dimes in it. Make a column of 9 pennies, and on the left make a column of 2 dimes.

Jerry found 2 pennies that he wants to put in his coin case, but his penny slot is full. His friend has a dime. What can Jerry do with the help of his friend so that he can keep all of his coins in the case?

If you figured out that he could change 10 pennies for 1 dime and put the dime in the dimes slot, you can see what carrying means in addition. He couldn't get 11 pennies in the pennies slot, so he "carried" 1 ten over to the dimes slot. So exchange 10 of your pennies for a dime and put it in the dime column. Now you have 3 dimes in the dimes column and 1 penny in the pennies column. You have added 2 to 29 by carrying, and you now have a total of 31.

Let's show this addition another way. Do you remember how you write numbers the "long way"? Write twenty-nine as a numeral? Now write it the long way: 20 + 9. Add 2 to the nine, and it will look like this: 20 + 11. This won't do because you can't have 11 in the ones place, which will only hold 9. So you carry 1 ten from the 11 over to the tens place by regrouping the 20 + 11 like this: 30 + 1.

 29      20 +  9
+ 2     +      2
         20 + 11  Carry 1 ten over to the 10s.
         30 +  1 or 31

THINK: What is the number question?

COMPUTE: First, see if you can make the addition by writing 24 the "long way" and regrouping.

Second, write the number question vertically and make the addition without carrying.

 24
+ 8
 12
+20 Bring down 20 from the 24.
 32

 1 (1 ten taken from 12 is carried over to the 10s place.)
 24
+ 8 
 32

CHALLENGE 1: Dorothy had 27 cents. She was given another 25 cents. Then how much did she have? Use all three ways that you just learned to make the addition.

CHALLENGE 2: A group of 16 soldiers lined up with 18 other soldiers. How many soldiers were there in all? Use just the shortcut way of carrying to make the addition.

CHALLENGE 3: Make these additions by the shortcut way of carrying with a pencil:

34 + 26 = ? , 45 + 27 = ? , 56 + 37 = ? , 68 + 54 = ?

CHALLENGE 4: Kenny paid $1.85 for ball and $5.25 for a bat. How much did he spend?

CHALLENGE 5: Make these additions with a pencil and paper:

$1.38 + $2.24 = ? , $3.47 + $0.36 = ? , $6.59 + $4.56

CHALLENGE 6: Mr. Brown drove 655 miles on the first day of a family vacation trip. He drove 576 miles the second day. How many miles did he travel in all?

CHALLENGE 7: Make these additions with pencil and paper:

355 + 966 = ? , 456 + 654 = ? , 787 + 878 = ? , 468 + 1,574 = ?

CHALLENGE 8: Mr. Green had $999 in the bank. He put in 1 more dollar. Then how much did he have in the bank? Make the addition with pencil and paper and show that you have mastered carrying.

[You will need 3 dimes and 11 pennies. Go to and print out the subtraction with borrowing models.]

EXAMPLE 1: Do you remember Jerry and his coin case? He now has 3 dimes and 1 penny in his coin case. He needs another penny so that he and his friend can each drop a penny in a wishing well. What can he do to get two pennies and what will he have left in his coin case after they drop the pennies in the well? Put 3 dimes in a column and put 1 penny to the right next to the dimes.

You probably figured out that you can take or borrow 1 of your dimes from your dime column and change it for 10 pennies. You will then have 2 dimes and 11 pennies. You then can take away 2 pennies leaving 2 dimes and 9 pennies or 29 cents.

Here is how this would look writing numerals the "long way" and regrouping:

 31          30 + 1     20 + 11
- 2         -     2    -      2
                        20 +  9 or 29

THINK: What is the number question written vertically?

COMPUTE: Show how you can make the subtraction with dimes and pennies. Ted has 3 dimes + 4 pennies.

One way to do it: You have a column of 3 dimes and a column of 4 pennies. You can borrow 1 dime from your dime column and exchange it for 10 pennies. Then you have 2 dimes and 14 pennies. Next, you take away 6 pennies leaving 2 dimes and 8 pennies or 28 cents.

Now look at subtraction model [a]. You can't take 6 from 4, so you borrow 1 ten from the 3 tens in the tens place. You draw a line through the 3 and write a 2 above it to show that 2 is left in the tens place. Next, write 1 above and a little to the left of the 4 to show that you now have 14 from which to subtract 6 leaving 8. There is nothing to subtract from the 2 in the tens place, so you just bring it down. The remainder is 28 cents.

Using paper and pencil solve Ted's problem by subtracting 6 from 34.

CHECK the answer with addition.

CHALLENGE 1: You have 37 cents. Count out 3 dimes + 7 pennies. You need to pay me 9 cents, but you only have 7 pennies. What must you do? After paying me, how much do you have left? Now make this subtraction with paper and pencil.

CHALLENGE 2: Jimmy has 33 toy soldiers and Tommy has 24. How many more soldiers does Jimmy have compared to Tommy? Make the subtraction with paper and pencil.

CHALLENGE 3: Skip had $56, and he spent $38 for a birthday present. How much did he have left? Use paper and pencil.

CHALLENGE 4: Make these subtractions with a pencil:

20 - 1 = ? , 33 - 6 = ? , 42 - 28 = ? , 50 - 12 = ? , 66 - 39 = ? , 75 - 48 = ?

CHALLENGE 5: Kevin had $1.00 or 100 cents. He spent 10 cents. How much did he have left?

CHALLENGE 6: Tommy took $2.25 from his piggy bank and bought a kite for $1.85. How much did he have left?

CHALLENGE 7: Make these subtractions with a pencil:

135 - 26 = ? , 220 - 111 = ? , 100 - 5 = ? , $2.22 - $0.33 = ?

EXAMPLE 3: Mr. Green had $1,000 in the bank. He took out $1. How much did he have left in the bank? Make the subtraction with a pencil and show that you have mastered borrowing.

THINK: What Is the number question?

COMPUTE: Look at subtraction model [b] and make the calculation.

Summary: You borrow 1 from the thousands place which makes 10 hundreds to put in the hundreds place. You borrow 1 hundred from the 10 hundreds which leaves 9 hundred. The 1 hundred borrowed makes 10 tens in the tens place. You borrow 1 ten from the 10 tens which leaves 9 tens in the tens place. You now have 10 in the ones place from which you subtract 1.

CHECK: We know that 999 plus 1 is 1,000.

CHALLENGE 8: Andre bought a widget for 21 cents and handed the clerk a dollar bill. How much change should he get back?

For further explanation and practice on addition and subtraction go to Addition and to Subtraction