This is the first lesson with the two classes who offer this course. I have planned to do some calculator activities with the teachers and get them to reflect on the roles of the calculator in the primary mathematics classroom. The students were asked to find a pair of two-digit numbers such that AB x CD = BA x DC. As expected, solutions such as 11 x 33 and 12 x 21 came quickly. Later, solutions using three or four distict digits such as 24 x 84 and 63 x 12 were given. One class gave nine different solutions while the other gave eight. As usual the students observed relationship between the product of the tens digits and the product of the ones digit (such as 2 x 8 and 4 x 4 in 24 x 84 and 6 x 1 and 3 x 2 in 63 x 12). In 93 x 26, students observed the relationship between the ratio 9/6 and 3/2. It is good that some students could say that these two are essentially the same. It shows that they were making linkages. It was particularly satisfying when one student gave an incorrect answer 41 x 22 (which I wrote down without judgement) and another group of students using that as a basis to obtain a correct answer 42 x 12. I was thrilled when another student came up with a novel observation that in 24 x 84, doubling the 24 gives 48 and reversing the 48 gives 84 - which is the larger number. Similarly with 42 x 12, doubling 12 gives 24, reversing the digits in 24 gives 48 - and, hey, that's the larger number. I was so excited by this that I forgot to tell the class that this is a rare observation. It could well be the first time I hear it although I have done this lesson countless number of time.
At the end of the lesson, I was wondering if my students could see the role of the calculator in this activity. And how the role of the calculator in this activity is different from its role in the other activities that we did that day and in subsequent lessons.
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