POTW #29 is below: Some patterning and number sense connections on this one!
Thursday, April 7, 2016
POTW #29 - Necklace Patterns
POTW #28 ignited some debate in class as to how to most effectively
answer it (and actually, whether it could be answered at all). Please
see two possible ways to solve this surprisingly challenging question.
The first solution deals more with factors/multiples and number sense
in general. The second solution uses algebra.
POTW #29 is below: Some patterning and number sense connections on this one!
POTW #29 is below: Some patterning and number sense connections on this one!
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My work was done hard copy. This is the answer I obtained:
ReplyDeleteIn the first 160 beads, 50 of them will be blue, assuming the pattern continues.
Here's How I solved it:
ReplyDeleteI noticed that for every time a new group of beads were added the total amount of beads would be a multiple of 3 (3, 6, 18, and then 30 after the 4th group of beads are added) in in every new amount ⅓ of the beads are blue, so if we continue the pattern ( 3, 6, 18, 30, 45, 63, 84, 108, 135, 165) you see that we end up not being able to finish the set by 160 and still need to put 5 ,more beads on, at this point the set is 10 beads or each question and since blue beads go last, that means the last 5 beads are blue so only 5 blue beads are added on the necklace compared to the 10 red and 10 green added on, at this point 1, 2, 3, 4, 5, 6, 7, 8, 9, 5 blue beads were added from first making the necklace, meaning by the 160 beads 50 are blue
My work is on hard copy but I did obtain an answer of 50 blue beads in the first 160 beads.
ReplyDeleteI did mine as hard copy.
ReplyDeleteI did mine hard copy.
ReplyDelete50 beads in 160. To do this, i added 3 beads to per rotation to 6 to 9 and so forth, until i go above the 160 beads. then i reverse the step, go to the previous sum which is 135 beads, and decide it by 3, that leaves me with 45 beads sharp. At that time it was 9 beads of each color per rotation. that means the next one is 10 beads per rotation. so then take 135 away from 160. 160 - 135 = 25. since blue is the last color rotated and there is 10 colors rotated, i take 20 beads ( i.e. beads before blue that are rotated through) and that leaves me with 5 blue beads. I add that to the full rotation total of 45 and that hives me the 50 beads per rotation in a total of 160 beads with the pattern given.
ReplyDeleteMy answer is 50 beads are blue out of the first 160, hard copy.
ReplyDeleteMy work was dome hardcopy.
ReplyDeleteForgot to post online yesterday :(
ReplyDeleteI completed it hardcopy and got the answer of 50 blue beads in first 160.