To help understand the patterns between pictures showing various box units, start by making a table of values listing the picture number of one column and the number of units on the other column. Next, identify what is decreasing and by how many units in each picture and write an equation in words describing the pattern of the pictures. Lastly, replace the words with corresponding variables to complete the equation.
This problem is a little bit challenging because, when you're looking at these number of boxes, you can see it's decreasing. I started out with 16 boxes then I come down to only 12 and then 8 and then 4. It's a little bit different from some of the problems you might have seen, because these numbers are decreasing instead of increasing; the pictures are getting smaller.
What I want to do is look for some kind of patterns, see if I can see anything that I can recognize as a mathematical pattern that I'm familiar with. Like for example in order to help me organize this I'm going to make a table. Where I have picture number and then number of boxes. That's going to help me look for patterns like my picture numbers are 0 1 2 3 and 4. Then if you count up how many boxes there are, 16 then we have 12 then we have 8 and then a 4. This fourth picture has 0 boxes. It's kind of weird we'll deal with it when we get to it.
So that's just another way of representing the same information, and I need to find an equation that describes this. I'm going to start by writing an equation in words. I'll go and change it into mathematical symbols in a second. Number of boxes is going to be equal to something.
Well, one thing I notice, is that I'm starting with 16. My 0 group started with 16. From then it's decreasing. I'm going to say 16 take away something, I don't know what's going to go there yet.
Then let's look at how much it's going down by. Each time I'm subtracting 4 boxes. Like I used to have 4 rows of 4 or 4 columns of 4 now I only have 3 columns of 4. That's the one that got taken away. Here again I'm taking away a column of 4 boxes from the previous picture. What's happening is I'm subtracting 4 every time. You can see it here. Take away 4, take away 4 and on and on.
The way this pattern will be written will be, take away 4 times the picture number. That's how we write it in words or if I wanted to use mathematical symbols, I would use 16 take away 4x. That rule or that equation describes how many boxes there are in each picture number.
Again, this one's kind of weird because, instead of getting bigger, the pictures are getting smaller, but you can still use your pattern techniques. Look for where you're starting from and then look at how much you're changing by. We started with 16 and then we're decreasing by 4 each time.
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