# Math patterns example 2 | Applying mathematical reasoning | Pre-Algebra | Khan Academy

I want to make little townhouse

shapes with toothpicks. So this would be

my first townhouse. I’ve used 3 toothpicks

so far– 4, 5, and 6. So that is my first townhouse. Now, let me make a little table

here keeping track of things. So I’ll do that in white. So here’s my table to

keep track of things. So this is the number of houses,

and then this is the toothpicks that I’m using to

make that house. So this first house here,

took me 6 toothpicks– 1, 2, 3, 4, 5, 6. Now let’s make our second house. And these are going

to be townhouses. They’re going to

share common walls. So I’m going to

add 1, 2, 3, 4, 5 toothpicks for my second house. Now, why did I only

have to add 5 and not 6? Well, they shared

a common wall here so I didn’t have to add

another toothpick here for this left-hand side wall. So starting with

the first house, I really just had

to add 5 toothpicks. I had to add 5 toothpicks to get

to now 11 total toothpicks if I want two houses. I think you see the trend here. What about 3 of these? Well, this is going

to be another 5– 1, 2, 3, 4, 5 toothpicks. So we’re going to add

5 again and get to 16. Let’s do 4 just

for good measure. So the fourth one, we’re

going to add another 5– 1, 2, 3, 4, 5. So the fourth one, we’re going

to add another 5 gets us to 21. Now, I want to think about,

can we, using this pattern, figure out how many

toothpicks it would take for us to, say, make

50 of these townhouses or even 500 of these townhouses,

or even 5,000 of them? Now we just have to

look at this pattern here and see can we come up

with an equation for each of these actual values? So, for example,

we see a pattern that– well, we

already recognize that we started

with 6, and we’re adding 5 every time

we add a house. So when you add the second

house, you add 5 once. The third house, you start

with 6, and you add 5 twice. The fourth house, you start with

6 and you add 5 three times. So let’s actually

write that down. So 21 is equal to– you start

with 6, you start with this 6 here, and then you add 5

three times, plus 5 times 3. When you had the 3 houses,

once again, you started with 6 and you added 5 two times. Let me do that same color. And you added 5 two times. Plus 5 times 2. When you had 2 houses,

you started with 6 again. This is equal to 6 and you

added 5 once, so plus 5 times 1. And then when you had

1 house– and it’ll fit the same pattern–

you started with 6, and how many times

did you add 5? Well, you didn’t add 5. You could say that you

added 5 zero times. So you might see a

little pattern here. However many houses you needed,

you take one less than that and multiply it by

5, add that to 6, and you get the

number of toothpicks. And actually, let

me rewrite this. So I could rewrite this as

6 plus 5 times 4 minus 1. I could write this as 6

plus 5 times 3 minus 1. You could write this as

6 plus 5 times 2 minus 1. You could rewrite this as

6 plus 5 times 1 minus 1. And maybe that makes a

pattern a little bit clearer. This 4 is right over here. This 3 is right over here. This 2 is right over here. And then this 1 is

right over here. So now, I think we

are ready to think about what would happen if

we wanted to make 50 houses. So let’s try to do that. Let me do that in orange. This right over here

is our 50th house. So this is the shared

left wall it has. This is the 50th

house right over here. So how many total

toothpicks for 50 houses? So if we have 50

houses, well, we can use the pattern

that we came up with. It’s going to be equal

to, starting with our 6, the first house requires 6. And then we’re going to add

5 for each incremental house, so plus 5 for each

incremental house. And how many incremental

houses are there going to be? Well, there are going to be

50 minus 1 incremental houses. Why minus 1? Well, you already built

one of them with the 6. Then for every extra

one– so there’s going to be 49 extra

houses– you’re going to add 5

toothpicks apiece. So this is going to be

equal to 6 plus 5 times 49. And that is 245. So 6 plus 245 is

equal to 251 sticks. And what’s really neat

about this pattern we just came up with is you

could use it to figure out how many sticks you

would need for a million of these little

toothpick townhouses.

whoa! it felt like being newton when I wrote the equation at the beginning of the video.

i Think Ur Wrong Because 6+5=11×49=539

plz answer me and check it i am right that ur wrong because i have a test in 2 days an i wanna learn

Thanks

It's wrong!

use Latis to do multiplication plz u do everything WRONG

This is what I do when I'm too lazy to study and I'm addicted to my phone ðŸ˜‚

thanks

Sir .. can u solve my problem.. 100-100/100-100 what is answer

lol

can i ask for the formula that u used to solve that 50 houses?

Thanks I have learn it!! im just a grade 5 student

eh i do my sequence differently well what would I write is: start at 6 and add 5 each time (doesn't have to be add it can be any operation and how many operation for example multiply 5 and add 1 each time) thats what my teacher taught me.

can you make a video with more complicated patterns