In keeping with the theme of mental math, I would like to propose that students in grades 2+ be challenged with learning to add and subtract any two digit numbers. This can easily be supported by using the 100 chart until the number relationships become second nature to the students. After that students can either just do the mental calculations, or they can close their eyes, “see” the 100 chart in their minds, and calculate from the visual image they produce.
It is easiest to begin by adding/subtracting 1 and 10 from a given number. If students have done the 100 chart tic-tac-toe, this will be an extension of that. From there it is easy to move on to adding/subtracting more than one (2 to 9) and multiples of 10.
The answer to 38 + 10 is 48, which is immediately below 48. The answer to 38 + 20 is 58, found two rows below 38, which is the same as adding 10 twice. The answer to 38 – 1 is 37, found to the immediate left of 38 on the 100 chart. The answer to 38 – 5, 33, is found five spaces to the left of 38.
When it comes to adding and subtracting other two-digit numbers, the above procedures can be combined. To add 54 + 23 a student can move down two rows (adding 20) and then move right three squares (adding 3) to end up at 77.
Strategies can be developed for adding or subtracting numbers that would “wrap around” ends of the 100 chart. When adding 54 + 29 rather than move down two rows and try to count 9 to the right (which moves down to the next row) students can devise strategies that make use of “nice” or “friendly” numbers. In the above example it is much easier to add 30 to 54 and then subtract one for a total addition of the required 29.
My personal belief is that every student above grade 2 and every adult should be able to add and subtract two-digit numbers mentally with ease. If the skill is not there, it is only because it has not been developed and practiced.
Spending a few minutes every math class on mental math helps develop life-long skills. Most of us, as adults, do much more mental math and estimation than we do with paper and pencil for exact amounts. We figure time, mileage, money, etc. daily in our heads.
Help your students develop their mental math skills by planning these kinds of practice sessions into your lessons.