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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 patterns on coordinate plane

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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- hi, im doing a poll. do you like sal??(51 votes)
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- how does a sponge hold water if its full of holes?🤔

Is a leaf called a leaf cause it leaves the tree?🤔(5 votes)- Great questions!

1. A sponge can hold water despite being full of holes because of the properties of the material it's made of. A sponge is made of a porous material that absorbs water due to capillary action. This means that the tiny holes or pores in the sponge create a network of small tubes that draw in and hold water. When a sponge is squeezed, the water is forced out of the pores, but when it's released, the sponge regains its shape and can hold water again.

2. The word "leaf" actually has its roots in an old English word "leafan" which means "to leaf or to grow leaves". The word "leaf" refers to the flattened structure attached to a tree or plant that is used for photosynthesis and respiration. So, a leaf is called a "leaf" because that's what it is and what it does, not because it "leaves" the tree. However, the word "leave" as in "to leave the tree" does come from a different word, "lafian", which is also an old English word that means "to allow to remain, leave behind".(2 votes)

- 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.(4 votes)
- The correct statements are:

- For every term in pattern A, multiply the term by 2 and then subtract 7 to get the corresponding term from pattern B.

- To get from each point to the next, you need to move 3 units to the right and 6 units up.

- The second terms of both patterns are 7.

The statement "The terms of pattern B are always greater than or equal to their corresponding terms from pattern A" is not correct.(3 votes)

## Video transcript

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.