Additive and multiplicative relationships

We are told that Miguel and a group of friends play soccer during recess each day. More students join them to play. The table below shows the relationship between the number of students joining Miguel and his friends and the total number of students playing soccer.

So let's see. On Monday, seven students joined, and then there are 14 students playing soccer. Six on Tuesday, six students joined, 13 students playing soccer.

All right, I think I get what's happening. What type of relationship exists between the number of students joining and the total number of students playing soccer? And if we look at the choices, it looks like they're trying to figure out whether it's a multiplicative relationship or an additive relationship. A multiplicative relationship means one variable will always be the same number times the other variable. In an additive relationship, it'll always be the same difference. Or if you start with one variable, you could always add the same amount to get to the other variable.

So pause this video and think about is this a multiplicative relationship? I always have trouble saying multiplicative. Is it multiplicative or is it additive, and why? Well, let's see. If we first think this might be multiplicative, then we go, we could say 7 * 2 is 14, but then 6 * 2 would be 12, which isn't what we see here. So it definitely doesn't look multiplicative.

Let's see if it's additive. 7 + 7 + 7 would be 14. 6 + 7 is 13. 11 + 7 is 18. 4 + 7 is 11. So it looks like additive, where you start with a number of students joining, and you can add seven every time to get the total number of students playing.

So it is an additive relationship. We can rule out these first two choices. The relationship is additive because the pattern is to add seven to the number of students joining in order to get the total number of students playing. Yep, I think that's right. The relationship is additive because the number of students joining is less than the total number of students playing soccer.

No, just that alone wouldn't make it additive. It has to be the same difference; you can start with one variable and add the same amount. Let's do another example here.

So they tell us each day a baker makes multiple batches of cookies. We see the relationship on different days between the number of batches made and total number of cookies, and they're essentially asking us the same thing. So pause this video and think about this. Is this multiplicative or is it additive?

Well, let's see. Let's try multiplicative. Five; to get from 5 to 30, you can multiply by 6. 8 * 6 is 48. 9 * 6 is 54. 12 * 6 is 72. So it's pretty clear that it is multiplicative. You could try to add the same amount to these, but you're not. If you say 5 + 25 is 30, but 8 + 25 is not 48, so it's definitely, definitely multiplicative.

So it's multiplicative because the pattern is to multiply the number of batches by six in order to get the total number of cookies. Yep, that looks right. This B isn't right because you're not multiplying by eight. If you multiplied by eight, you would go from five to 40. So we are done.