When interpreting graphs representing real life situations, observe how the line of the graph moves along the x- and y-axes. The "steepness" of the graph at various points tells you the rate at which something is occurring. The steeper the graph, the quicker the variable on the y-axis is changing.
One of the neat things about graphs is that you can use them to describe things that you wouldn't think about describing in a Math classroom. Like for example these problems are all about how much popcorn was in a bowl.
So what I want you guys to do is take about like 10 seconds look at this graph and see if you can come up with a story in your head that describes what's going on in this situation.
Okay that wasn't quite 10 seconds but I bet a lot of you have ideas. Here is what I thought of this person made some popcorn and then it was too hot so they had to let it cool for a while the amount stayed constant because they weren't eating anything. It was just sitting in the bowl then they started the movie they were eating they were eating, they were eating and then the movie got really scary so they started eating more slowly and then they didn't finish the popcorn.
At the end they kind of like filled up or maybe the movie got really scary and they just left their bowl kind of like one third of the way full.
Check out this one, this one's a little different. So you might have come up with something different this is what I personally thought. They had some popcorn in the bowl they were walking with it they weren't eating anything. Here you are walking with your popcorn and then dropped it and half the popcorn spilled all over you can see the amount like suddenly drops and then after they dropped it they picked up what was left and then they went and they started eating at a constant pace. They didn't finish the bowl there were some still left at the end.
Try this last one here. So here maybe they didn't let it cool for very long compared to those people they let it cool just like a short amount of time, and then they ate at the same steady constant pace until the bowl was all gone. You'll see here that the popcorn hits like the very bottom. There is no more left.
This might seem like kind of like fun like this isn't really Math, like what are we doing? This actually is Math what I really want your brains to start thinking about is a really important Math concept which is rate of change. How fast does something change, how fast is this guy eating compared to that guy or the first problem we looked at where the person ate pretty fast and when the movie got scary so they slowed down.
That's the kind of thing that shows a lot in Math when you start getting to the idea of slope. But until then just keep in mind that graphs like this can describe things that you wouldn't think to describe in a Math classroom.
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