here’s a fun one
assuming this grid goes on forever this way
where’s 1000? pause here and think about it
now if you need more help
focus on finding patterns
in the classroom
before I ask to find 1,000
I say “tell me three patterns you notice”
and then we can use those patterns to find 1,000
for example
a pattern that we can notice is that we double each time we go down a cell
and we can use this to find 1000
because we can go backwards with this
every time we go up a cell
we’re dividing by 2, so above 1,000 is 500
above that is 250 and above that is 125
and we know to stop there
because we have all of the positive odd numbers in the top row
so we see that 1,000 is in the fourth row
in the column that starts with 125
and another pattern that we can notice
is that this is basically a multiplication table
of the powers of 2 and the positive odd numbers
for example 8×5=40, 4×7=28
so what power of 2 times what positive odd number equals 1,000?
well 8×125
so 1,000 is found in the row that starts with 8
and the column that starts with 125
now here’s one more pattern
some of you may notice that in the first row
I’m jumping by 2 in the second row
I’m jumping by 4 in the third row
I’m jumping by 8 and so forth
and we can use this to find 1,000 by writing an equation
for example if I think that 1,000 is found in the row that starts with 4
I can write it like this if I start at 4
how many times do I need to jump 8 to reach 1,000?
but when we solve for the variable here
we don’t get an integer meaning that it is not in this row
because 1,000 would be in between jumps
now when we write an equation for the road that starts with 8
we get an integer as our answer
if I start at 8, how many times do I need to jump 16 to reach 1,000?
and we see that that is 62 times
so since we’re already at the first column with 8
and we jump 62 times that means 1,000 is found in the 4th row
63rd column
so I got this problem from this book over here
and this is the first mathematical task that I do in my courses
because math is a study of patterns
so I have students practice finding patterns
and we can use those patterns to help us solve problems
like we did in this video
so how did you find 1000?
or what was your favorite way?
please share in the comments