Time and Time Again Help Yourself

During teaching Robert to substitute  digital times with equivalent verbal phrases, I noticed that he  had difficulties finding  the number of minutes missing to the full hour.  He did not have difficulties with easy times: 10;55, 10:50, 10:45. But to replace 10:47 with an expression, “13 minutes before 11 o’clock”, he had to first find the difference 60-47. Finding the difference is not the problem for Robert.  Problem was that he did not know he had to find it in the first place.   Every time he encountered similar time, he was startled as he kept forgetting what to do.

So I kept reminding him, “Find the difference 60-47”. Then I switched to telling Robert, “Find the missing minutes.” Finely, my direction was, “Help yourself”.

I often use the phrase, “Help Yourself” as the last, the least (?) invasive but the most general prompt, hoping that by the time I use it, Robert would establish a  strong connection between this phrase and the step he needs to take.

I realized, however, that if Robert was able to calculate the difference 60-47  in his mind then the whole problem would become straightforward. As long as Robert doesn’t immediately see that 47 minutes are 13 minutes away from the full hour, he is  distracted  and not often sure what to do next.

Before zeroing on mental computation I  checked what Robert could and couldn’t do,  I noticed some strange results.  For instance, Robert didn’t have any problems subtracting one digit number from two digits one: 56-8, 22-5, and so on except finding those differences which seemed the easiest for me: 30-7, 100-5.

I also observed that when Robert  wrote the subtraction 60-47 vertically and I didn’t let him write anything else: no regrouping, no crossing, and no “borrowing” but asked him to LOOK at the numbers, IMAGINE what he should do, and, TELL me the answer, he could do that.

But when the subtraction was written horizontally, the same directions did not bring any results.

Yet, the problem with vertical subtraction was that without seeing the numbers Robert was unable to calculate their difference and there was no next step that would lead to solving problems mentally.  So I decided to apply the same method  I used a year ago with subtracting from 100. (As a preparation for counting the  change from a dollar.)

To transfer Robert’s ability from subtracting on paper to mental calculation I followed those steps:

I presented a model, 100-47=100-40-7.

Robert first mentally subtracted 100-40 and wrote the answer, 60, above the  minus sign. Then he mentally subtracted  7 from 60 and wrote =53 at the end of the expression.In the following problems he wrote the model himself.

During the next step, Robert still wrote, “100-40-7 but he was not allowed to write 60  above the first difference but he had to keep it in his mind and use it for the  second operation.

During the third step, Robert was not allowed to write 100-40-7  but he had to say, “Hundred take away forty is sixty.  Sixty take away 7 is fifty-three.”and write =53 at the end of the problem.

Now, I replaced 100 with 60, and Robert practiced finding the differences: 60-47, 60-32, 60-59 with the help of the expressions: 60-40-7, 60-30-2, 60-50-9 either written or said aloud.

Robert easily mastered the first and the second step but we are still working on the third.  It might be that Robert’s difficulties with saying long sequences of words affect his thinking performance. I will try to reduce the number of words. Maybe that will help.

Despite the fact that Robert still has some difficulties with mental computation, after a page of subtractions from 60 , we return to the page with digital times.  When Robert stumbles, I just tell him, “Help Yourself.” and he does.