Math for Parents
Tim Whiteford PhD

Addition and Subtraction concepts and skills.

 Addition and Subtraction algorithms.

Use the term "regroup" instead of "borrow" and "carry". These two latter terms are left over from the equal addition method of doing the subtraction algorithm. We now use the decomposition method.  

In the equal addition method ten ones was added to the top number and one ten was added to the bottom number. A small 1 was put next to the ones in the top number and a small 1 next to the tens in the bottom number accompanied by the language "borrow 1 and pay it back".

Regroup means to change, for example, 14 ones into 1 ten and 4 ones. Or to change 1 ten and 4 ones into 14 ones as needed in some subtraction problems.

The word 'ten' is a noun in the tens place and an adjective when referring to ones.

 The equals sign is a symbol of equality and not an operation sign.

 Some strategies; 

47 + 25 = __         40 + 20 = 60  and 5 + 7 = 12    
                             so   60 + 12 = 72 (60 – 12)  
This can be done vertically too. 

41 – 25 = __          41 – (20 + 5) is (41 – 20) – 5      
                             or       21 – 5 = 16

112  -  89 = __       89 to 90   = 1
                             90 to 100 = 10
                             100 to 112  = 12
                          so 89 to 112 = 23 (1 + 10 + 12)

Traditional strategies can also be used (as long as there is  understanding of the regrouping process).

    46                 58                  834
 + 36               + 72                +487

    82                 67                  824
  - 58              - 49                 -368 

1. Addition and subtraction can be seen as inverse operations (join and separate).  

2. Addition and subtraction algorithms can be developed together.

      7 + 2 = 9                   2 + 7 = 9
      9 – 2 = 7                   9 – 7 = 2

 3. Many problems traditionally seen as subtraction can be solved 
      through addition. This is the missing addend idea.

     “What is 9 minus 2?”  “What do I add to 2 to get 9?”

 4.  Connect algorithm to real world problems.  
      Which operation can be used to solve a particular problem?        
      When this has been decided the problem becomes an arithmetic 
      exercise.

 Problem situations for which addition or subtraction can be used can be classified as change, compare, and part-part-whole problems. The Investigations program suggests that children not be expected to categorize problems in this way but should be exposed to a variety of these types of problems.

 A. Change Problems

           Join Problems  

                   1.  Result unknown.                          
                   2. Change unknown. 
                   3. Initial unknown.

          Separate Problems (not the disappearing concept)

                    1.  Result unknown.
                    2.  Change unknown. 
                    3.  Initial unknown.

B. Compare problems

          1.  Difference unknown. 
          2.  Larger unknown. |
          3.  Smaller unknown.

 C. Part-part-whole.

     1.  Whole unknown. 
     2.  Part unknown.

 Addition Facts

 Strategies

1. One-More-than and Two-More-than   

2. Facts with zero. 

3. Doubles. 

4. Near doubles 

5. Make ten facts.

These five ideas account for 88 of the 100 facts.  The remaining 12 facts are really only 6 because of the turnaround idea.

Avoid reliance on counting.

Subtraction Facts