Developing an understanding in number

9. Written mathematics

The four major ways of working with numbers are: addition, subtraction, multiplication and division.

Your child needs to understand the meaning, use and connections between additions, multiplication, subtraction and division.

Strategies for solving operations mentally have been discussed for each operation. There is also a suggested method for carrying out the written calculation. The method is called an algorithm (sometimes spelled algorism).

Concrete materials, especially Multibase Arithmetic Blocks (MAB), play a major role in the development of all the algorithms. The ‘hands on’ approach will help your child see and understand the process, making the link between the concrete representation and the written algorithm stronger.

Remember to enable your child to use number sentences and operations efficiently and fl exibly, he/she needs to use a variety of mental, paper and calculator computational strategies for each operation, meeting needed degrees of accuracy and judging the reasonableness of results.

Addition

The following teaching steps illustrate the sequence using MAB.

1. MAB should be used to represent each number (preferably placed on the MAB card).
   
   
2. Next, the ‘ones’ should be pushed together while saying 4 and 3 make 7. The 7 is then written in the ones column.
   
   
3. Next, the ‘tens’ are pushed together to find that 4 tens and 3 tens equal 7 tens. The 7 is written in the tens column. The answer is 77.
   
   

Subtraction

Subtraction is a little more difficult. Questions requiring solution using the subtraction algorithm may be asked in several different ways.

• Take away – How many left?
  
  For example:
  
        I had 14 marbles and gave away 3 of them.
        How many are left?
  
  
• Comparison
  
  For example:
  
        I have 12 marbles and you have 7.
        How many more marbles do I have than you?
  
  
• Complementary addition
  
     For example:
  
        I have 40 marbles but I need 59.
        How many more do I need to buy?

Subtraction is the reverse process of addition. This is a very important concept your child should grasp.

     For example:

     5 + 3 = 8    therefore     8 – 5 = 3

The subtraction algorithm is easily demonstrated using MAB.

     For example:

1.  
   
2. How many ones have to be taken away? (4)
   How many ones are left? (3)
   Write the 3 in the ones column.
   
   
3. How many tens have to be taken away? (3)
   How many tens are left? (5)
   Write the 5 in the ones column.
   
   

Multiplication

In Year 3 multiplication is introduced as repeated addition.

For example:

3 + 3 + 3 + 3 is the same as 4 lots of 3 or 4 x 3.

Initially the vertical setting out of the algorithm is introduced.

         

Through the use of concrete material, an understanding of the relationship between addition and multiplication is developed.

Division

Division is the reverse process of multiplication and is introduced as repeated subtraction.

Dividing is separating a number into several equal groups.
When we divide 6 by 3 we are separating 6 into 3 equal groups of 2.

Or, if we are separating 24 objects into 6 equal groups of four, we would take (or subtract) four objects at a time from the large group and place them in 6 equal groups. In mathematical terms this would be: 24-4-4-4-4-4-4.

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These four related facts are called a fact family.

It is important your child understands the reversibility of mathematical relationships.