I hope you are all warm and dry! Last week, we made some interesting discoveries about division. We looked at a series of problems, including the following:
48 divided by 8
24 divided by 4
12 divided by 2
We looked at the problems and drew arrays to represent them. In doing so, we noticed that they all had the same quotient. In looking at the arrays, we realized that the total area was being divided by 2 (the dividend) and so was the number of columns (the divisor), but the number of rows always stayed the same. This helped us develop a conjecture:
If the dividend and divisor are both multiplied or divided by 2, then the quotient remains the same.
The students realized that they could keep going to find other problems with the same quotient. They multiplied both dividend and divisor by 2 to create 96 divided by 16, which would also be 6. They then kept dividing both and found that 6 divided by1 and 3 divided by ½ would also give you a quotient of 6!
We discussed the fact that when we have a difficult problem, we can sometimes make it into an easier problem if we look at the relationships between the numbers in the problem. They were dividing by fractions by using relationships, even though they may not know procedures for division of fractions.
Reminder: Test tomorrow on division. Students worked on a review sheet today and class that they are bringing home with them.