Knowing basic math facts by heart is one aspect of mental math. The other aspect is providing exercises that challenge your student to come up with the correct answer on his own or via recommended calculation strategies. For example, a possible strategy used by your fifth-grade boy to solve 36 + 38 = 74 might be the following: he might add 30 + 30 = 60, and then simply add 14, since he already knows that 6 + 8 = 14. It is essential that your student be able to deduce and memorize basic facts.
Narrow down the calculations by beginning with pairs of numbers that total 10, for example, 6 + 4, 7 + 3, 8 + 2, 5 + 5, and 9 + 1. The goal is for your student to recall these immediately. Gradually continue to work on doubles of single integers, such as 3 + 3, 5 + 5, and 7 + 7. Use models or images to help the boy visualize the calculations, if necessary. It is recommended to limit the calculations to only numbers from 0 to 10 before proceeding. Once these are mastered, you can gradually present more complex calculations. These include working with multiples of 10 or introducing subtraction while limiting facts to numbers under 20. For example, your fifth-grade boy will know by heart that 8 + 7 = 15, 15 - 7 = 8, and 15 - 8 = 7.
Rounding up, rounding down, partitioning and identifying tens and doubles are just a few of the strategies that can help your student get better at mental math. Partitioning is explained as follows: adding 145 + 233 can be calculated by adding the hundreds first (100 + 200 = 300), adding the tens (40 + 30 = 70), adding the single integers (5 + 3 = 8) and finally adding all three results (300 + 70 + 8 = 378). Teach your student to identify near doubles, such as 17, which is near the double of 9 + 9 = 18. Also, teach your student to identify numbers that are near multiples of ten, such as 39, which can be rounded up to 40. These strategies make calculations much easier.
Teach your student to use previous knowledge of easy calculations to solve complex operations. For example, use the knowledge of 15 + 15 = 30 to solve 154 + 157 = 311, or 150 + 150, which can be treated as 15 + 15 with a zero added. Bridging through multiples of 10 is another way your student can learn to do quick mental calculations. For example, 57 + 8 can be seen as 57 + 3 to reach 60. Simply add the remaining 5 + 60 = 65.
Choosing appropriate strategies will depend on the level at which your student is currently working. Encourage him to participate. Ask him about the thinking process that led him to a certain result, for example, "How did you come up with that result?" and "Did you solve that by partitioning?"