In the first article I talked about how important it is to master mental mathematics so that this can help you through both school and in life situations.

In this article I help you to take the first step of mental mathematical knowledge, which is to memorize the addition of single-digit numbers – being the numbers 0-9. When two of these single-digit numbers are added the value is a number in the range 0-18.

The message from the first article was that the calculator should not be the first point of help when you are confronted with a problem, and should only be used when it is necessary.

Whereas adding two single-digit numbers may seem trivial for you, it has been my experience with learners of all grades that even these basic facts are not fully memorized, and they sometimes take the learners are few seconds to think, and sometimes a few tries before they get the right answer. Based on this I start your journey into mental mathematics with this simplest of the simplest situations.

When you are adding numbers, of any size, you will break down the problem of adding larger numbers into the smaller problem of adding individual digits, and to the basic memorized facts of single-digit addition. To become proficient in more complex problems, you must be able to very quickly add single-digit numbers quickly.

The general problem of single-digit addition is

where and are digits from the range 0-9, being 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Let us categorize into three groups:

- firstly, those which add to a number which is less than 10 – such as
- secondly, those which add up exactly to 10 – such as
- thirdly, those which are larger than 10 – such as

The second of these three groups is important in another context, finding which numbers can add up to a specific number, which in this case is 10, but we would equally choose any other number, such as 7 or 12. This is called “*number bonds*” and will be addressed in a later article.

In the CAPS curriculum. you must add numbers up to 10 in Grade 1, and the adding up to 20 by Grade 2, and these must be memorized. It is not acceptable for learners in the senior grade to not have learned these simple addition facts, since they waste a lot of time in performing calculations which they should have memorized and are also likely to get these wrong. These simple additions are fundamental to all of arithmetic, and occur in all calculations involving numbers throughout all of mathematics.

I want you to download the document in the link below; print it out; and keep this handy at all times until this is mastered.

Mental Arithmetic – Adding Digits

When you are ready, download the following exercises, and work through each of these until you can meet the time limits I have set for these based on your grade. Once you are finished, check the answers and correct errors immediately and then redo the correct answer a number of times to ensure that you have memorized this properly, since it is quite easy to remember the incorrect answer and to keep making the same mistake over and over again.

I am providing four worksheets, each with 10 questions. and these should be addressed in sequence. For Grades 1-3 these are not expected to be done fast, but rather carefully. From Grades 4 these must be part of your memorized facts and from Grades 7 you must be able to recall these facts in 15 seconds or less for all 10 – as fast as you can write you should be putting down the correct answer.

Email me if you have any suggestions and hints and also to tell me about your experiences with these worksheets.