Does your child understand what doubling means? The relationship between doubling and halving quantities? That doubling means x2 and halving means /2? How can you guide your child to understanding these relationships? Doubling and halving numbers is one of the foundations of number sense. There is a pattern to doubling numbers. Once your child knows doubles, he or she can add using the strategy "doubles plus 1" (e.g. 6+7) and "doubles plus 2" (e.g. 6+8). Knowing twice a number helps with story problems that use such vocabulary. It also is a great step to learning 4 times tables because you double your double. Finding half of a number shows ones ability to deconstruct a number and understand that it is made up of parts. Solidifying the concept that halving is the same as dividing by 2 is a worthy mathematical task to help young children understand early on. Read on for how you can set up these tasks for your child.
Begin with 0 objects. Then 1, 2, 3 objects (like buttons or coins) and so forth going up sequentially, suggesting your child find a method of keeping track of each number and its results when doubled.
Next, to guide your child to an understanding that double means twice as much, 2 times, or 2 groups of, show photographs of real objects (books, buttons, glasses, blocks, etc.) with an amount next to it that is twice as much. Better yet, engage your child in a game using real objects such as books. She or he must always make double your stack.
Finally, present numerical doubles problems such as 6+6=? and provide your child with a variety of manipulatives to choose from to build a picture of the problem using small chestnuts for example, or legos. Enough practice will help your child develop insight into the problem and to think up more efficient strategies to solve the problem more quickly. Eventually this will result in knowing ones doubles.
The process is engaging and your child is actually “doing” the math in order to know the math as opposed to listening to information about the math in order to know the math. By showing real photographs, brain connections with the surrounding world are created and reinforced with every new photo. Your child is beginning to build the framework, strategies and habits of mind for successfully solving important problems that will undoubtedly arise in his or her future. You are asking your child directly to take responsibility for doing this math and at the same time setting them up for success by providing the environment for success (providing a variety of manipulatives and other math tools as well as a patient and encouraging tone of voice and manner).
Halving can be shown next by going backwards. Count out objects to represent your number, then divide them into 2 equal groups by placing the objects into 2 different circles. I wouldn't recommend introducing odd numbers to halve at this early stage unless your child has specifically asked. (If you decide to work on this, I recommend emphasizing that because one is left over after dividing the rest into equal groups that your original number cannot be halved exactly or divided by 2 and that by having one left over, it means your number must be an odd number). Show the doubling/halving relationship through using the same photographed objects and working backwards as I mentioned earlier. Finally, you will want to introduce problems such as 12/2 as a division problem, half of 8, 8/2 as a fraction which is also a division problem. Include the same environment and encourage the same use of manipulatives as you did with doubling.
Understanding and practicing this forwards and backwards type of relationship with doubles and halves demonstrates how numbers change in predictable patterns when you apply specific rules to them. Furthermore, being able to choose an approach to a problem from the most promising direction is the best definition of fluency I can think of.