Get ready for 6th grade
- Graphing patterns on coordinate plane
- Interpreting patterns on coordinate plane
- Interpreting relationships in ordered pairs
- Graphing sequence relationships
- Rules that relate 2 variables
- Tables from rules that relate 2 variables
- Graphs of rules that relate 2 variables
- Extend patterns
- Relationships between 2 patterns
Explore the concept of numerical patterns, focusing on how to generate, identify, and graph them on a coordinate plane. Understand the relationship between corresponding terms in two different patterns, and how changes in one pattern affect the other. Created by Sal Khan.
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The following graph represents the first five terms of two given patterns. In the answer box, there are different statements about the two patterns. Choose all correct statements. So here, for each point, this point right over here, this represents its horizontal coordinate is the first term of pattern A, which is 4. And its vertical coordinate is the first term in pattern B, which is 1. And then we could do that for the other points as well. So actually, let's figure out what the values are. So we have pattern A and then we have pattern B. So the first term for pattern A is 4. And when pattern A is 4, the first term for pattern B is 1. The second term for pattern A is 7. And when pattern A is 7, pattern B is also 7. Third term, pattern A is 10, and pattern B is 13. And then the fourth term, pattern A is 13, and pattern B is 19. And then finally, fifth term, pattern A is 16, and pattern B is 25. Now, before even looking at these, let's see what we can think about these patterns here. So it looks like pattern A starts at 4, and it increases by 3 every time. To go from one term to the next, you just have to add 3. Now, what about for pattern B? Well pattern B starts at 1, and every term here it looks like you're adding 6. So when pattern A increases by 3 and we're moving in the horizontal direction based on the fact that pattern A is represented on the horizontal axis, we're going to move up 6 in the vertical axis, and we see that here. Pattern A increases by 3 from one term to the next. And when that increased by 3, pattern B increased by 6 from one term to the next. And we see that it keeps doing that. Now, let's think about what we have over here to see which of these statements actually apply to this. For every term in pattern A, multiply the term by 2 and then subtract 7 to get the corresponding term from pattern B. So let's see if that holds up. So according to this, if this was true, I should be able to take this, multiply it by 2 and subtract 7 and get that. So let's see. Is 1 equal to 2 times 8 minus 7? Sorry, 2 times 4 minus 7. So 2 times this number, 2 times 4 minus 7. Well, 8 minus 7 is equal to 1. Is this right over here equal to 2 times this 7 minus 7? Well, yeah, it's equal to 7. Is 13 equal to 2 times 10 minus 7? Well, yeah, 20 minus 7 is 13. Is 19 equal to 2 times 13 minus 7? 26 minus 7 is 19. Is 25 equal to 2 times 16 minus 7? Well, 32 minus 7 is 25. So this first statement checks out. For the corresponding term, the value of pattern B is two times the value of pattern A minus 7. Now let's look at the second one. The terms of pattern B are always greater than or equal to their corresponding terms from pattern A. Well, no, that's not right. It's true for a couple of scenarios. Here for the third, fourth, and fifth term, or actually for the second, third, fourth, and fifth terms, pattern B is equal to or greater than pattern A. But for the first term, it's not true. Pattern A is greater, so this is not right. To get from each point to the next, you need to move 3 units to the right and 6 units up. Well, that's exactly what we talked about. From one term to the next, pattern A, along our horizontal axis, we increased by 3, while pattern B, which is plotted on our vertical axis, by 6. So you move 3 to the right and 6 up. So that is right. The second terms of both patterns are 7. Well, yeah, we see that right over here. The second terms are 7. We have 7 here, and we have 7 there. And so that is right as well. So the only one that doesn't apply is this second one. This is not right.