2 step estimation example

We are told a teacher bought 12 sheets of stickers to use on the homework of her students. Each sheet had 48 stickers. At the end of the year, the teacher had 123 stickers remaining. Which is the best estimate for the number of stickers the teacher used?

So like always, pause this video and see if you can have a go at this before we work on this together.

All right, now let's work on this together. The first thing to appreciate is we just have to figure out an estimate; we don't have to figure out the exact number of the stickers that were used. Let's see if we can do that.

So let's see. We have 12 sheets of stickers, and each sheet had 48 stickers; 48 stickers per sheet. So how many stickers did the teacher start off with? Well, there were 12 sheets times the number of stickers per sheet, so times 48. This is going to be the number that they started off with.

Now, if we want to figure out the number that are used, we just have to figure out, okay, from the number that was started, how many are left over? And then that's how many were used. So how many were left? Well, 123 were remaining at the end of the year, so that's this number right over here.

If we calculate that first, the number to start, we subtract out the number that are remaining; then that will be equal to the number of stickers that the teacher used. Now, once again, we don't have to figure out exactly; we just have to estimate.

I'm just going to try to figure out friendlier numbers to work with. So instead of 12, let's imagine—actually, I'll stick with 12. 12 I can work with. But let's say that this is going to be approximately equal to—so in parentheses, instead of 48, I'll say it's roughly 50. So this is going to be approximately 12 times 50.

Instead of 123, I'll say that's roughly a friendlier number; it might be 120 or it might be a hundred. Let's just do 120. So minus 120. We could have done a hundred, and so we could figure out what this is in our heads or with a little bit of paper.

12 times 5 is 60, so 12 times 50 is 600. And then 600, if we had 100 here, 600 minus 100 would be 500, or 600 minus 120 is 480.

So what we want to do is look at the choice and see which of these choices is closest to roughly 500 or roughly 480. And so let's see, out of all of these, actually they have exactly 480, which is so they estimated exactly the way we happen to estimate.

Now, not every person is going to do that. We could have chosen, instead of 123 becoming 120 in our estimate, we could have put 100 there, and then we would have gotten 500. But even if 500 was our estimate, 480 still would have been the closest to that estimate.