Hands-on math!

Mental Math

Mental math is a key feature of our lessons. It is a key recommendation of the National Council of Teachers of Mathematics. This is the ability of the students to solve math problems in their heads without using pencil and paper. We begin most lessons with 5 mental math questions. The kids take out a blank sheet of paper, number 1 through 5 and then the coach calls out the problems verbally, giving the students time to do the calculation in their heads and write down the answer. This has to be done very carefully so as to not frustrate the students with problems over their heads or insufficient time to do the calculations. Here are some tips on giving your students mental math:
  1. At the beginning of the school year give the students easy problems. Problems that only involve the multiplication table, addition, subtraction and maybe division. Problems like these:
    • "What is 4 times 3 minus 1?"
    • "Multiply 5 times 4 and then divide by 2"
    • "What is the sum of the first 4 numbers?"
    • "Start with 16, double it and then subtract 10"
    • "Take a half of 18 and then subtract 5"
  2. Do not let the students use their fingers to count!
  3. At least in the beginning, make sure each student has written down an answer before going on to the next question. If you are unsure that each student has done the calculation, say "Everybody ready?" before going on to the next problem. (Hint: If their eyes are on the ceiling, then they are not done!)
  4. This is sorta obvious, but NO CALCULATORS!
  5. Most mental math questions involve 2 or more calculations, like all 5 of the above examples. When starting to give students mental math at the beginning of the school year, pause after the first calculation to let them do that one before continuing with the second part. For example, in the first example above, say "What is 4 times 3 ... (pause) ... minus 1?" When students become more proficient at mental math you can eliminate this help.
  6. For each lesson, try to use concepts learned in the previous lessons. For example in the first year for lesson 7 (fraction multiplication and mixed numbers), give a few mental math questions about areas of triangles (the subject of lesson 6). For example, "What is the area of a triangle whose base is 8 inches and whose height is 4 inches?"
  7. An entire set of mental math questions about operations with zeroes is always a good idea. For example:
    • "What is 5 times 100?"
    • "What is 8 times a thousand?"
    • "What is 800 divided by 10?"
    • "What is 80 times 40?"
    • "What is 200 times 20?"
We encourage you to make up your own mental math questions based on the progress of your students. Most lessons have 5 mental math questions, but these are only suggestions (both the questions and the number of questions). Give them mental math questions that exercise concepts of previous lessons, particularly the parts of previous lessons that homework has shown that they struggled with. If some of the students had trouble with the area of triangles (in first year lesson 6), for example, then in weeks after lesson 6 throw in a triangle area question here and there. If some students are having trouble with parts of the multiplication table (for example 8 X 7 or 9 X 6) throw those multiplications into their mental math.

Mental math can be a powerful tool in your students' hands if used properly.