"USE YOUR BRAIN, NOT YOUR CALCULATOR."

MENTAL MATH

The ability to do math in your head is a skill that I don't believe we spend enough time on with students. If you think about it, when presented with a mathematical situation, most people would first try to do it in their head. For example, if a recipe serves 12 people and calls for 3/4 cups of flour, how much flour would you need if you wanted to serve 24 people? If an answer can't be found mentally, a person would likely try a calculator next. If a calculator weren't available, pencil and paper would be the next option. In this day and age, I believe kids (and adults) use calculators "reflexively". That means they use it before thinking whether or not the question could be answered more quickly just using their brain. I found over the space of a few months of working on Mental Math in class, I can get most kids to not use the calculator reflexively (at least in my room). This must be constantly reinforced in the regular classroom activity also. My constant refrain was "Use your brain, not your calculator."

When you begin doing Mental Math, many kids will want to use paper and pencil methods in their head. This must be discouraged or you won't get anywhere. For example, let's add 66+48. You DON'T want them adding 6+8, getting 14, putting down the 4 (in their mind), carrying the 1. Then they add 6+4, get 10 add the 1, get 11, put it next to the 4 (in their mind) and end up with 114. That is very inefficient for mental math. They could, however, add 70+50, getting 120 and then subtract 4 and subtract 2 (or just subtract 4+2), getting 114. Or they could add 60+40, getting 100 and then add 6+8, getting 14 and then adding 100+14. Or take 4 off of the 48, leaving 44 and add that to 66, getting 70, and then adding 40 and then 4 (or adding 44 all at once). Early in their mental math experiences let them come up with their own strategies, but also show them some efficient strategies that you know they can use in other situations.

The Mental Math questions I will eventually show (I used with 8th graders) are based on the work of Larry Leutzinger of Area Education Agency 7 in Cedar Falls, Iowa. I modified some of the questions and then added some of my own. He advocated using 5 questions a day. For me it is easier to do 8 questions every 2 to 3 days. Each teacher has to find what works best for him or her. I feel it is invaluable for middle school students to be forced to "use you brain, not your calculator." You then should see less "reflexive" use of the calculator.

My classroom procedure for this was the following: Students get out their Mental Math answer sheet, and stand up next to their desk. I give the question orally and then repeat it once. They think about while they are standing, then sit down to write their answer (all they can write is an answer), then stand back up. The standing and sitting is helpful for several reasons. First they get to move around a little. Second, you can observe who comes up with an answer quickly and who takes a while. Third, when everybody is back up, I can go on to the next question. Sometimes a question is difficult and I will give them a little longer. In some cases I will feel they have had enough time and I will move on to the next question even if some have not written an answer. I normally do not grade their performance on mental math. I do all of the questions this way. Then we go over each question in class. I have already prepared a transparency showing what I think is(are) the best way(s) to do the question and then see if they have any unique alternative methods. I usually ask for a show of hands as to who got each question right. Then at the end I might ask who got 8 out of 8,7 out of 8, and so on. The whole purpose is for students to develop the ability to think and reason mathematically and to be confident in using their brain to do math mentally. One other positive benefit to doing mental math this way is that it will increase the listening skills of the students since they do not see the questions, they hear them.

It is necessary to do Mental Math on a regular basis or you will lose whatever gains you have made. It takes awhile for students to gain confidence in their ability to do math in their head. Sometimes the reason that they are not successful is that the methods they are using are inefficient for mental work. You must show them a variety of ways to do math mentally, which will give them tools they can use, but it also builds their desire to think more creatively on their own. I have also seen the “spillover” of their increased confidence into the other areas of their math class. Of course if they aren't taught methods that will work, then the opposite consequences take place.

Here are some examples of Mental Math questions. In upcoming posts I will supply more questions.

MENTAL MATH QUESTIONS

Mental Math #1
1.58+16
2.How many inches are in 6 feet?
3.What is 50% of 54?
4.Mary has five times as much money as Bob. If Bob has 40 cents, how much does Mary have?
5.Five and one-third yards is how many feet?
6.A class has 24 students. Three-fourths of the class were participating in athletics. How many students in that class are participating in athletics?

Mental Math #2
7.Estimate the product of 196 and 52.
8.48+62
9.62 times .5
10.What is 3/8 of 40?
11.What is 2/3 of 21?
12.If a quart of milk costs 75 cents, what would be the cost of a gallon of milk?
13.20 feet is how many yards?
14.A trip takes two hours and forty minutes. If you need to be at your destination by 4:15 pm, you need to leave no later than what time?

Mental Math #3
15.27/2
16..939 (100)
17.66+48
18.Six and one-half minus two and one-fourth
19.If a dozen oranges cost $1.80, what would be the cost of six oranges?
20.165cm is equal to how many meters?
21.What is 75% of 32?
22.You make a purchase for $1. 72. If you pay with a $5 bill, how much change should you get back?

Mental Math #4
23.If a pound of candy costs $2.80, what would 4 oz. of that candy cost?
24.What is 10 squared divided by 5?
25.How many eights of an inch are in four inches?
26.You make a purchase for $5.73. You pay with a $10 bill. How much money should you get back?
27.Joe has three fourths as much money as Alice. If Alice has $30, how much does Joe have?
28.How many tenths in ten and one-half?
29.Two thirds minus one half.
30.The average classroom at SLMS has 22 students. If there are 20 classrooms in the school, how many students are in the school?

Mental Math #5
31.What is the reciprocal of 3?
32.A shirt costs $9.35 to make. How much would it cost to make 10 000 of those shirts?
33.How many inches are in 8 feet?
34.Write a quick estimate of the product of 55 and 47.
35. A special breakfast meal at McDonalds costs $2.50? What would five of those meals cost?
36. Three fourths plus one third.
37. A sweater normally costs $60 but is on sale for 20% off. What is the sale price?
38. What number is halfway between 16 and 30?