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CCSS.Math:

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.