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### Course: 5th grade > Unit 13

Lesson 2: Number patterns- 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
- Algebraic thinking: FAQ

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# Graphing sequence relationships

Explore the concept of numerical patterns. Understand how to generate two sequences using given rules, identify relationships between corresponding terms, form ordered pairs from these terms, and graph these pairs on a coordinate plane. Created by Sal Khan.

## Want to join the conversation?

- Is there a way to describe both sequences simultaneously in a single expression?(12 votes)
- Not really, because you need an equation to describe how x gives you y. To do this you need an equation. 5x by itself would be considered an expression. But that is not enough info to give you the sequence for getting y. You need the "equation" 5x=y to describe the sequences for x and y to plot them. Hope this helps. :)(28 votes)

- Can anybody tell me why x and y are traditional letters?(13 votes)
- because coordinate planes is normally used to represent data but when someone is using it with no data the axes are
**unknown**so people use letters to represent the unknown so the axis x is unknown or not assigned and axis y is unknown or not assigned. so people use letters as a placeholder. I wish I helped(16 votes)

- Can someone help me? I can't figure out the following challenge Visualizing and interpreting relationships between patterns. If you see this please answer! Thanks for your time(6 votes)
- Think of the plot area as two number lines. The first number in an ordered pair goes to the right and the second number in an ordered pair goes number goes up. (Right UP!). Easy enough to plot on the graph. That's the easy part. The part you might be having problems with is finding out the relationship between the numbers.

Example

Sequence X: Start at the number 5 and the rule is add one. So sequence X would read 5, 6, 7, 8, 9 and so on.

Sequence Y: Start at the number 10 and the rule is add two. So the sequence Y would read 10, 12, 14, 16, 18 and so on.

Your ordered pairs would be (5,10) (6,12) (7,14) (8,16) (9,18)

Do you notice a pattern? 5x2=? 6x2=?

Could you say that the numbers on the Y axis are two times as large? I hope this helps some.(8 votes)

- what is a constant number? Please reply, I have a test tomorrow...(4 votes)
- A fixed value.

In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

Example: in "x + 5 = 9", 5 and 9 are constants

If it is not a constant it is called a variable.

I think.(7 votes)

- Why X and Y and not any other letters?(6 votes)
- x and y are the traditional letters so when your starting out you can use whatever you want but later on, always use them because they can mean different things in algebra.(1 vote)

- Can someone help me? I can't figure out the following challenge Visualizing and interpreting relationships between patterns. If you see this please answer! Thanks for your time(2 votes)
- Its really easy. All you do is enter in the box the data for the x and y axis

Example: y start 4, add 3

x start 1, add 2(3 votes)

- balls balls balls balls balls balls balls balls(2 votes)
- balls balls balls balls(2 votes)

- what are inputs and outputs?(2 votes)
- An input is a number, any number. Let's say that you have this big fancy machine. If you put a number in it, a different number comes out. That is the output. But there's always a rule. A rule is a statement. For example, add 5, subtract 9, etc. Let's say you have the number 3. You put the 3 through the machine. The rule is times 5. The output is 15.

Hope this helps!(1 vote)

- why does X go first? and how does this apply in real life?(0 votes)
- Hi, the way I usually explain this to my students by comparing it to the rules of the road. Why does everybody drive on the left in the UK (or the right in the US)? Because if everybody drove where they wanted it would be chaos. So I tell my students that mathematicians decided to always write X first. This way, if you had to whatsapp coordinates to someone in Fiji he or she will know what you meant and if they sent you coordinates you would be able to plot them the way the your Fijian friend meant. So it's basically convention so that we can communicate clearly, no matter where we're from.

How does this apply to real life? Oh, some of the most beautiful maths in the world is based on this. This is one of the first skills that you learn that eventually becomes calculus and calculus is the maths that people used to put a man on the moon and describe the motion of stars*. You are literally on the path to learning rocket science. Isn't that amazing? *(I'm over-simplifying but I think you get the idea).(10 votes)

## Video transcript

Voiceover: You are given
the following starting numbers and rules for
two sequences of numbers. The first sequence, Sequence x, starting number should be one, and then the rule is add one. Sequence y, starting
number should be five, and then the rule should be add five. Fill in the table with the
first three terms of x and y. Then plot the ordered pairs (x,y) on the graph below. So let's see, Sequence x. They say, the starting number, the starting number should be one. So the starting number is one, and then the rule, to
get to the next number, you just add one. So, one plus one is two. Two plus one is three. Fairly straight forward. Now, let's look at Sequence y. They're saying the starting
number should be five. Starting number five,
and then the rule is, to get the next term, we just add five. So, five plus five is ten, ten plus five is fifteen. Now they want us to plot these things. Let's see, we plot them as ordered pairs, so we're going to have the point (1,5). When x is one, y is five. We see that there, x is one, y is five. When x is two, y is ten. When x is two, y is ten, and then when x is three, y is fifteen. When x is three, y is fifteen, and wee see that. For every one we move to the right, for every one we increase
in the horizontal direction, every one we increase in
x, we increase five for y. We increase one for x,
we increase five for y. So now we just have one
last thing to answer. The terms in Sequence y are blank, times the terms in Sequence x. So you immediately see, this term, five, is five times one. Ten is five times two. Fifteen is five times
three, and it makes sense. You started five times higher, and here you added one
each time, and we see that visually right over here, we add one each time, while here we add five times as much each time. We add five each time. The terms in Sequence y are five
times the terms in Sequence x. We got it right.