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### Course: 6th grade foundations (Eureka Math/EngageNY) > Unit 4

Lesson 4: Topic E & F: Foundations- Graphing patterns on coordinate plane
- Interpreting patterns on coordinate plane
- Interpreting relationships in ordered pairs
- Graphing sequence relationships
- Tables from rules that relate 2 variables
- Rules that relate 2 variables
- Identify points on a line
- Graphs of rules that relate 2 variables
- Relationships between 2 patterns

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# Interpreting relationships in ordered pairs

Explore the concept of numerical patterns, focusing on how to generate, identify, and graph these patterns on a coordinate plane. Understand the relationships between corresponding terms in two different patterns and how these relationships can be represented as ordered pairs. Created by Sal Khan.

## Want to join the conversation?

- What is a constant?(11 votes)
- A constant is a specific number. In the expression 2x+6, the 6 is a constant. It will not change. The 2 is the coefficient of the variable X. Since the value of X can change, the value of 2X will also change accordingly. This is why we don't typically call the 2 a constant.

Hope this helps.(25 votes)

- Whats a constant number?(9 votes)
- Its a number that constantly stays the same.(10 votes)

- Why is pattern A the horizontal axis while pattern B is your vertical axis. Pretty sure somebody already asked this but I forget so...(11 votes)
- It is because thats the way its graphed.(4 votes)

- I have a question. If you have numbers 0, 3,and 9 and need y for each greater by 0.75, how do you solve?(2 votes)
- 0.75 is the fraction equivalent of 3/4.

If you add 3/4 to 0, it becomes 3/4, and its decimal equivalent remains 0.75

If you add 3/4 to 3, it becomes 3 3/4, or 15/4. Its decimal equivalent is 3.75

If you add 3/4 to 9, it becomes 9 3/4, or 39/4. Its decimal equivalent is 9.75

I hope that this was helpful! :)(11 votes)

- ' 'I get it, Its just that some of the problems are just very confusing.. I don't know why..' '(6 votes)
- Why do we need the axes for the example?(5 votes)
- Does anyone know this. It is
**very confusing**(3 votes)- Dude you arn't even
**Listening**(4 votes)

- How can I report a problem with this video? the name of this video is mistyped, it says "
*Number patterns:: interpreting and graphing relationships*" there should only be one of these ( : ), not two...(2 votes)- It's not really a mistype. So you don't have to worry about it, There is nothing wrong with the video it self, so you can't report a problem with a video with no errors.(5 votes)

- Describe similarities and differences between between pairs of graphs and scenarios?(3 votes)
- In pattern A, why do we have to multiply by a constant number in order to get the next term, why can't we add a number?(2 votes)
- You could add, but the number you would add is not constant, because you would have to add 1 to get from 1 to 2, add 2 to get from 2 to 4, add 4 to get from 4 to 8, add 8 to get from 8 to 16, add 16 to get from 16 to 32, add 32 to get from 32 to 64, and so on.

By the way, pattern A is an example of a geometric sequence, because it involves multiplying by a constant number. In contrast, sequences that involve adding a constant number are called arithmetic sequences.

Have a blessed, wonderful day!(2 votes)

## Video transcript

Below are ordered pairs
that represent the first six terms of two given patterns. The first value in each pair
is a term from pattern A. And the second value is a term
from pattern B. In the answer box, there are different
statements about the two patterns. Choose all correct statements. So let's think about
what's going on here. They said the first
term is pattern A. So the first term in each of
these coordinates is pattern A, or in each pair is
pattern A. So pattern A goes from 1, to 2, to
4, to 8, to 16, to 32. So it looks like
pattern A, to go from the first term
to the second term, we multiplied by 2. And then to go from the
second to the third term, we also multiplied by 2. And we just keep
multiplying by 2. And we just keep doing that. 8 times 2 is 16. 16 times 2 is 32. Now let's think about what's
going on with pattern B. So pattern B is the second
number in each of these pairs. And it's just always 3. So there's a couple of ways
you can think about it. You could just say,
pattern B's always 3. You could say pattern
B starts at 3, and we're just
adding 0 every time. Or you could say that
pattern B starts at 3, and we are multiplying
by 1 every time. Either of those
would give you just 3 showing up over and over again. So now that we've
looked at these pairs, we show the corresponding terms
for pattern A and pattern B, let's look at the choices here
and see which of these apply. In pattern A, you can get
from any term to the next by multiplying by
a constant number. Well, that looks right. We go from the first
term to the second term by multiplying by 2. Then we multiply by 2 again
to get to the third term. Then we keep multiplying by 2. So that constant number
that we're multiplying by to get to the next term is 2. So this looks right. The next pair should
be 52 comma 3. So let's think about this. If we keep doubling
for pattern A-- so this is going to be times 2. 32 times 2 is 64. And then if we'd say that this
is 1 times the previous term, we're just going
to get a 3 again. So it should be 64 comma
3 should be the next one. They say the next pair
should be 52 comma 3. So that's not right. If we graph the
pairs, the points will be on the same line. So let's think about
that a little bit. Let's think about that. So this is my vertical axis. This is my horizontal axis. On the horizontal axis,
I will graph pattern A. And on my vertical axis, I will
graph pattern B. And let's see. Pattern A goes all
the way up to 32. So I'm going to
try my best here. So let's say that this is 32. Then half of that
is going to be 16. Half of that is going to be 8. Half of that is going to be 4. Half of that is going to be 2. And half of that
is going to be 1. So these are all the points on
pattern A. But for any of them, the corresponding term
on pattern B is 3. So we have, when pattern A
is 1, pattern B is 3-- 1,3. When pattern A is
2, pattern B is 3. When pattern A is
4, pattern B is 3. When pattern A is
8, pattern B is 3. When pattern A is 16, pattern--
this is like a tongue-- when pattern A is 16, pattern B is 3. When pattern A is
32, pattern B is 3. And you see, they
all sit on a line. They all sit on this horizontal
line, or at least the way that we've drawn it. They all sit on this
line that you probably can't see in yellow. So let me do it
in this red color. They all sit on this
line right over here. So this looks right. If we graph the
pairs, the points will be on the same line. So I'll go with that one. In pattern B, you can get
from any term to the next by multiplying by
a constant number. Well, yeah, even though
every term is the same term, but you can get from a 3 to a
3 by always multiplying by 1. 1 is a constant number. So we're just multiplying
every term by 1. So that also seems to be right. So all of these are right,
except the second one. The next pair isn't 52 comma 3. It's going to be 64 comma 3.