These three words are like cousins. They are related and cannot be separated from each other. To understand one, you need to understand the others.

The other night I was tutoring a grade 7 student. They were learning how to find percents involving degrees of angle in a circle. One of the questions was to find the percentage that 288 degrees is of the entire circle (360 degrees).

The student did not know where to start, let alone feel comfortable working with the large numbers. So I suggested simplifying the numbers to help. In almost any given question, you can simplify it to start. There are several way to do this.

Halve both numbers until you get to two familiar numbers.

288/360 becomes 144/180. 144/180 becomes 72/90.

At this point I could continue to halve both numbers and get 36/45. This fraction still would not help me arrive at the percentage without using a calculator. I could though, go from 36/45 to 4/5 by dividing 9 out as a common factor. 4/5 = 8/10 which is 80%.

Another way to approach this would be to halve both numbers until we get to 72/90 and from here, recognize that we could divide out 9 from both to end up with 8/10.

In the end, it is important for students to have the intuition for manipulating numbers. Being able to use multiple strategies other than a calculator is the ultimate goal of number sense. Math should not always be used as a means to an end, but as a vehicle for bigger and better things.

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