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# Math patterns: table

CCSS.Math:

## Video transcript

so let's say I have tables where I can fit one person at either of the short ends of the table so I could fit one person there I could fit one person there you could view this is we're looking down we're looking from above the table here so we could put one person at either of the short ends of the table and then on these longer ends right over here we can fit two people we can fit two people at the longer end so when you have one table so when you have one table you could fit one two three four five six people you could fit six people now let's think about what happens as we add tables end to end to this table right over here so let's imagine now two tables so here we have one table and it's going to touch ends with this table right over here and because it touches ends right over here we're kind of making it one big continuous table you can't fit someone here anymore so now how many people can we fit let's see we can fit one two three four five and then on this table which is identical you could fit six seven eight nine and then you could put one person at the end right over here so when you have two tables you can now fit end to end you can now fit a total of ten people let's keep going and see if we can think of a pattern here so let's put three tables here so one table two tables and three tables so just as before we could put one at each end so that's two people then we have three four five six seven eight nine 10 11 12 13 14 folks 14 folks so what does it look like is happening here well if you just look at the numbers we went from 6 to 10 to 14 it looks like we're adding it looks like we're adding four people every time we actually add a table now does that actually make sense so let's think about this first situation let's imagine these are real people I'll make this person in blue right over here if you were to bring over this new table if you bring over table - so this is table 1 if you bring over table 2 this blue person has to move and so where could they move us say that they always insist on sitting at the end of a table so the blue person moves to the new end of the table the new end of the table they move right over here so how many new people could move to this combined table now that you brought that second table in well the new people the new people I will do in I will do in this purple color the new people are that person let me do it in a more unique color this person this person this person and this person so you were able to add four new people with a new table one way to think about it is a new table is going to have one usable end here that usable end is going to be taken by the person who is already at the usable end of when you had less tables and so you're really able to the real addition is the two sides here so you're adding four people every time you add a table so it makes complete sense so based on this you could think about without even having to draw these diagrams what would happen or how many people you would be able to fit if you had four or five or six or however many tables so you could imagine if you have if you have four tables we just have to add four and you should be able to sit 18 people if you have five tables you should be able to fit 22 people and on and on and on