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Addition Strategies

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Before I show examples of the different addition strategies I am listing some tasks that it would be useful if children aged 5-7 were familiar with in order to achieve their maximum potential.

They will need to:-

  • Be able to count confidently in 1's 2's 5's and 10's to at least 100 and back and from a given number..
  • Know what 10's and units are.
  • Know their number stories to 10 and doubles to at least 20 (click text to go to number bonds and doubles).
  • Be able to partition 2 digit numbers into 10's and units i.e. - 27 is 20 add 7, 48 is 40 add 8.
  • Know the meaning of highest, largest, greatest, lowest, smallest, before, after and between.

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It is important to remember that we teach many different methods in order that a child can decide which method works best for them. If it gives you the right answer, it is the best method for you!!!

Mental Calculations

The main rule for mental addition is to always start with the largest number. The way it is taught is to tell the children to put the biggest number in their head and then count on i.e. 4+7 they would start with 7 and count on 4. Its not obligatory to start with the largest number but it is far easier and leaves less room for counting errors or losing count when counting on.

"T.U.B."method

"T.U.B." stands for Tens, Units, Both. This is a good strategy for adding two 2 digit numbers and uses partitioning (splitting numbers into tens and units). Here is an example 25 + 13 =38

Step 1. Partition the numbers                                     ( 20 + 5 )  ( 10 + 3 )

Step 2. Add up the tens (put "T" at side)                       T      20 + 10 = 30

Step 3. Add up the units (put "U" at side)                       U        5 + 3 =    8

Step 4. Add "T" and "U" answers together (put "B" for both)   B    30 + 8 = 38

Step 5. Remember to put the answer at the end of the original sum

Empty Number Line Method

Example 1 - adding on a number below 10

23 + 4 =27

Step 1.Draw a horizontal line with a ruler.
Step 2.Put a circle at the left hand end like this.                            

Empty number line
Step 3. Put 23 in the circle (represents putting the largest number in your head as in mental calculation).Number line

 

Step 4. Draw 4 small jumps from the top of the 'head' and write the next number where each jump touches the line.completed sum number  line

Step 5.Remember to write the answer (27) by the original sum.

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37 + 21 = 58
Steps 1 & 2 are the same as for the first example.
Step 3. Partition 21 into 20 and 1 (2 tens and 1 unit).
Step 4. Draw to large jumps representing the two 10's and write the numbers underneath as before.number line 10's numbers
Step 5. Draw 1 small unit jump and write the number underneath as before remembering that this is only a count of 1 and not 10.

number line 10's and units

 

Step 6.Remember to put the answer (58) by the original sum.

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100 square method

It is hoped that after learning this method children will be able to visualize the 100 square in their mind and use it both in addition and subtraction. It is an excellent aid to counting in tens because the children can see that the next tens number they need lies under the number they are on. Similarly if they are counting back, the next number they need lies above the one they are on e.g. count on from 12 in tens, the number under 12 is 22 then 32 etc. So they can therefore just follow down the column (or up if subtracting) and eventually they will not need to use the 100 square, they will see it in their mind. 

Example of addition using 100 square.           
25 + 12 =37                                                     Click here for printable 100 square

Step 1. Partition the 12 into 10 and 2, then locate 25 on the 100 square (shown yellow).

Step2. Add on the 10 (obtained when 12 was partitioned) by going down 1 square to 35 (shown red)

Step 3. Count on the 2 units (obtained when 12 was partitioned) by going along 2 squares (shown blue). Answer 37

Step 4. Remember to write the answer by the original sum.

To add larger 2 digit numbers follow the same method, just move down the required number of tens i.e. for 37, move down 3 tens and across 7 units.

100 square

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