Maybe you aren't satisfied with your computational skills. If you want to improve them, check the quality of your simple mental computations first. I keep in view simple mental addition and subtraction within the limits of 20, simple mental multiplication and division within the limits of 100. Everyone knows these operations must be carried out correctly and quickly. But how can we measure the correctness and quickness of their execution? For this purpose you can use simple tables which may be named stochastic.
You can draw such tables yourself, but do not waste time. Take the tables free at my site Prevention of Failure in School Math. There are two possibilities to get them: a Word file (TablesWord) and a computer program (PrintTables). The program allows to print both blank tables and checklists for them (the same tables but with the answers). The checklists will help you to find your errors. Furthermore you need a stopwatch to measure a running time.
Each table contains 64 uniform elementary operations on one of the arithmetical rules – addition, subtraction, multiplication or division. I name these tables stochastic because the sequences of addends, subtrahends etc. were chosen by chance. The accidental selection of required numbers simulates spontaneous appearance of corresponding operations in ordinary computations.
As soon as you get the tables, you can begin to examine the quality of your skills. Take one of the tables, switch on your stopwatch, fill in the table, switch off the stopwatch and write down the running time. Then print the corresponding checklist, check your answers and write down number of your errors. Now you can find whether your skills are sufficient to master more complicated computations or not. If you are more than 12 years old, the criteria are next.
Your skills are first-rate if there are no errors and the running time is:
on addition – not more than 2 minutes 25 seconds;
on subtraction – not more than 2 minutes 30 seconds;
on multiplication – not more than 2 minutes 20 seconds;
on division – not more than 2 minutes 10 seconds.
Your skills are good if there are no errors and the running time is:
on addition – not more than 3 minutes 55 seconds;
on subtraction – not more than 4 minutes 00 seconds;
on multiplication – not more than 3 minutes 35 seconds;
on division – not more than 2 minutes 50 seconds.
Your skills are satisfactory if there is not more than 1 error and the running time is:
on addition – not more than 4 minutes 50 seconds;
on subtraction – not more than 5 minutes 00 seconds;
on multiplication – not more than 4 minutes 20 seconds;
on division – not more than 3 minutes 35 seconds.
Your skills are unstable (and hardly sufficient to master more complicated computations) if there are not more than 2 errors and the running time is:
on addition – not more than 6 minutes 55 seconds;
on subtraction – not more than 7 minutes 15 seconds;
on multiplication – not more than 5 minutes 55 seconds;
on division – not more than 5 minutes 10 seconds.
Your skills are bad in all other cases - you have made more than 2 errors OR the running time overcomes the values for the unstable skills.
If you show bad results, you have no chances to master more complicated computations. If your results are unstable, you will have considerable difficulties. Maybe you have them already. But do not lose hope. You can easily improve the situation.
Take the tables again (there are 20 versions). Fill in the tables, measure the running time, check the answers. Soon you will feel your skills become better. Do not stop the work at the satisfactory level and even at the good level. You can perform better! The first-rate skills - this is your goal. You can win and get a very useful prize - the possibility to master well more complicated computations.
For children who are 12 years old or younger I'll list the criteria for the first-rate skills only. More detailed figures you will receive with the tables. Of course the first-rate skills exclude mistakes. So you need only the values of running time.
8 years old: addition – 5 minutes; subtraction – 5 minutes 5 seconds; multiplication – 4 minutes 35 seconds; division – 3 minutes 55 seconds.
9 years old: addition – 4 minutes 40 seconds; subtraction – 4 minutes 45 seconds; multiplication – 4 minutes 15 seconds; division – 3 minutes 35 seconds.
10 years old: addition – 3 minutes 40 seconds; subtraction – 3 minutes 45 seconds; multiplication – 3 minutes 15 seconds; division – 2 minutes 35 seconds.
11 years old: addition – 3 minutes 20 seconds; subtraction – 3 minutes 25 seconds; multiplication – 2 minutes 55 seconds; division – 2 minutes 20 seconds.
12 years old: addition – 2 minutes 40 seconds; subtraction – 2 minutes 45 seconds; multiplication – 2 minutes 30 seconds; division – 2 minutes 15 seconds.
the-first-step-towards-good.
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