Your alarm bells should be going off if you notice your child solely using the traditional algorithm (ie process) below for addition:
Teachers have moved away from this method nowadays, and this is because they understand that children reap much greater benefits from learning to partition numbers to calculate. Simply put, this means breaking bits off one number and adding them to the other, or vice versa. There are many wonderful and varied strategies that teach and reinforce this idea.
Below is an example of a strategy called Bridging, which uses tens grids. Bridging to 10 is a great way to teach partitioning skills while adding 9 to any single digit number. Kids love this strategy!
In this example (9 + 5), we are in fact partitioning the 5 into 4 + 1, and then moving the 1 over to join the 9 and fill up the ten grid on the left-hand side. 9 + 5 has now been rearranged to become 10 + 4. Why? Because 10 plus anything is very easy to add, so it makes sense to rearrange the numbers. This sort of flexibility in mathematical thinking is based on true understanding of number and is something to encourage.
If you want to teach bridging to your child, print some grids (under the free downloads menu), find counters or any small objects and demonstrate how to solve 9 + 5. Explain that you put 9 counters on one grid for the first number, and 5 on the other grid for the second number. Now tell your child that you’re going to bridge to ten, and move one counter across to fill up the ten. Point out that you can now see the answer …10 + 4. Explain that bridging to 10 is a good idea because adding a number to 10 is much easier than adding a number to 9.
Now give your child some grids and counters, and some problems, eg 9 + 4, 9 + 7, 9 + 6.
Bridging to 10 can easily be extended to bridging to 20, 30 or higher when children fully understand it. and can rewrite addition problems such as 9 + 4 as 10 + 3. Bridging to 20 involves adding a single digit number to 19, eg 19 + 6, 19 + 8. Bridging to 30 involves adding a single digit to 29, eg 29 + 3, 29 + 7.