# Strange old multiplication table found in Oklahoma school

Today I read an article about chalk boards from 1917 discovered in an Oklahoma school. One of the chalkboards included the following curious image:

(Oklahoma City Public Schools)

The article states that the picture was used to teach multiplication tables, but I can't figure out how it works. Can someone here explain it?

• It seems to me that the teacher would point to random numbers around the circle and ask the students to perform the multiplication. Commented Jun 6, 2015 at 21:59
• @mixedmath Ahh, that could well be it. Commented Jun 6, 2015 at 22:01
• is this 7 on lower left, between 5 and 9? Commented Jun 7, 2015 at 6:19
• Notice the alternating pattern on the bottom. 2, left to 3, right to 4, left to 5, right to 6, left to 7, right to 8, left to 9. That seems unlikely if it's supposed to be random. Commented Jun 7, 2015 at 22:12
• @JoelReyesNoche When I originally asked the question, I expected it to have more of a mathematical context than historical or educational. Turns out I was wrong, and it falls squarely on the education side of things, but I didn't know that when I asked. Commented Jun 9, 2015 at 5:11

This must be for an in-class multiplication exercise. It has 22 numbers from 2-12 (excluding 10) arranged in semi-random order around the outer rim, and multipliers 2x-8x in a column in the middle.

Note that the numbers on the outer rim don't occur with equal frequency. The frequencies are:

2
3 3 3
4 4
5 5
6 6 6
7 7 7 7
8 8 8
9 9
11
12


I interpret the frequency as indicating importance of practicing the different multiplications. Multiplication by 1 and 10 are too easy to need practice; by 2 is next easiest; then 4,5,9; then 3,6,8; finally 7 is hardest. The largest numbers, 11 and 12, are de-emphasized as less important to learn by rote.

Probably the exercise worked by the teacher selecting a multiplier from the center column (e.g. "3x") and a starting point on the circle (e.g. 8 on top). She would then call on a student who would answer aloud "three times eight is twenty-four!" With a correct answer she would then call on another student to do the next problem: "three times seven is twenty-one!" This would repeat in rapid succession with the teacher picking students in no particular order. When the teacher was satisfied with the performance on "3x" she would pick another multiplier and continue.

The reason to have the numbers in unsorted order around a circle is to facilitate practicing the multiplications in unsorted order. A circle is used so the exercise can continue indefinitely without the teacher having to pause the flow. And the teacher's full attention can be on the students; she doesn't need to look back at the board at all. The students are called in random order so everyone needs to follow along, preparing to answer each question in case they are called upon. Then students see the numbers to multiply, do the problem mentally, and then hear the answer called out in formulaic singsong. This repeats.

The same exercise could work with all students calling out answers in unison. That version emphasizes even more the rote singsong memory, but would allow weaker students to slide through mumbling along with little fear of being called out on it. That might serve as a warmup or conclusion to the individuated version, to bring the class together.