The POTW #5 solution and POTW #6 question (Grade 7 & 8 together again) are below. This week's POTW is great for our next unit in math...Number Sense!
POTW #5 Solution:
To find the mean we first add up all the numbers in the data set:
7cm + 4cm + 5cm + 5cm + 15cm + 14cm + 7cm + 16cm + 2cm + 4cm + 2cm + 9cm + 5cm + 6cm + 4cm + 6cm + 9cm
This gives us 120cm as their total hair lengths. Now we divide it by the 17 numbers in the data set. The mean is 7 cm (rounded). To figure out the mode we just look for the numbers that repeat the most.
Mean: 7
To find the mode you simply look at the number that appears the most in the data:
In our case 7 and 2 both appear twice, more then any other number. So,
Mode: 7 and 2
To find the range we take the largest number in the data set and see the difference between the largest and the smallest number in a data set.
16cm - 2cm
16cm - 2cm
Range: 14cm
After that we have to find the total amount of hair the 5 boys in the neighboring class have. So we find this by taking their mean hair length, 7cm and then add the 2cm that would make the new mean.
7cm + 2cm = 9cm
Now that we know that the new mean is 9cm, we multiply it by the number of boys we have data from. That will give us the total amount of hair when adding the 5 boys from the other class.
After that we have to find the total amount of hair the 5 boys in the neighboring class have. So we find this by taking their mean hair length, 7cm and then add the 2cm that would make the new mean.
7cm + 2cm = 9cm
Now that we know that the new mean is 9cm, we multiply it by the number of boys we have data from. That will give us the total amount of hair when adding the 5 boys from the other class.
9cm x 22 boys = 198cm
Now we have our total. We can subtract the total from ONLY the boys in Jilly & Jolly’s class.
198cm - 120cm = 78cm
Therefore the boys in the other class have a total hair length of 78cm.
+EXTENSION : ANSWER
Now we have our total. We can subtract the total from ONLY the boys in Jilly & Jolly’s class.
198cm - 120cm = 78cm
Therefore the boys in the other class have a total hair length of 78cm.
+EXTENSION : ANSWER
Aleks 7cm
|
Fred 2cm
|
Stanley 5cm
|
Ethan 5cm
|
Maxwell 7cm
|
Nick 9cm
|
Yoav 4cm
|
Alan 9cm
|
Ryan 4cm
|
Can 6cm
|
Cole. S 14cm
|
Mathew 4cm
|
Ivan 5cm
|
Richard 16cm
|
Mateo 6cm
|
Derek 15cm
|
Dhruv 2cm
|
+BONUS QUESTION : ANSWER
Jilly is Michelle
Jolly is Arus
If you responded “Arus and Michelle” instead of “Michelle and Arus” you are
ultimately incorrect.
Thanks for tuning into “how to waste time with Jilly and Jolly” Good day.
SALUTATIONS,
-m / Jilly
Jolly is Arus
If you responded “Arus and Michelle” instead of “Michelle and Arus” you are
ultimately incorrect.
Thanks for tuning into “how to waste time with Jilly and Jolly” Good day.
SALUTATIONS,
-m / Jilly
ADIOS
-a / Jolly
POTW
ReplyDeleteI'll first list the facts and question along with it.
- 100 of each number.
- Largest number possible
1-100
1s=1,10,11,12,13,14,15,16,17,18,19,21,31,41,51,61,81,91,100=20(1s)
2s=2,12,20,21,22,23,24,25,26,27,28,29,32,42,52,62,72,82,92=20(2s)
Every digit will now be 20 of them
3-9=20 each
0 has a different amount
0=10,20,30,40,50,60,70,80,90,100=10(0s)
101-199
Everything is 20 by logic.
2-9=20
0=...
The only thing that matters is however many 1s you can go up to. That is the answer. I should've realized that earlier, but now I know. The reason behind this is because all the digits can take only 40 max up to 199 except for 1. Since 1 is included a lot in the 100s, I'll have to continue to use intervals.
20
100-20=80
80
101to111=15
80-15=65
...
It keeps on going. To save time I just "ctrl f" it.
The largest number is 162.
Grade 8 POTW:
ReplyDeleteFrom what I think it is,the answer should be 171. This is because first, I counted the number of 1's from 1 to 100. This is because that is the first number that will run out, since we get to 100 first before 200, 300 and so on. This way, I can easily find out that the number will not be larger than 200, since the 1s will run out before we can get to 200. After reaching 100, I decided to count some more to try to find a pattern, so I counted to 120, and found that there were only 57 1's left. I found a pattern that every 10 numbers, from 101 to 110, for example, there are 11 1's. So, I will first go to 120 because that was where I was before, divide 57 by 11, which gives me 5 with a remainder of 2. With this five, it means that I can count by 10 five times since there is 121-130, 131-140, 141-150, 151-160, and 161-170.
After counting by 5 tens, I go from 120 to 170. However, I still have 2 1's left! This means that I can go to the next number, 171, since I have plenty of 7's left and 2 1's which is exactly what the number has! Thus, I run out of number 1's so I cannot go to 172, and 171 is the largest number I can count to.
P.S. I actually got 181 at first, because I miscounted and added an extra 10. Then, I used Java to code this problem because I thought it would be fun to figure this out. Fortunately, it took me about 15 minutes and I found out that I was wrong. Thank God!
Also, I was wondering where the grade 7 POTW is?
-Alan
Lol I'm still wrong, better find out where it is, answer is actually 162. -Alan
DeleteGrade 7/8
ReplyDeleteI found that each time you count to 100 every number from 1-9 has 81 left. 0 has 89 left. I kept counting up like this 101112131415161718192021222324252627282930313233343536373839404142434445464748494505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697989910010110210310410510610710810911011111211311411511611711811912012112212312412512612712812913013113213313413513613713813914014114214314414514614714814915015115215315415515615715815916016116216316416516616716816917017117217317417517617717817918018118218318418518618718818919019119219319419519619719819920020120220320420520620720820921021121213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300. I then did ctrl+f to see how many one’s there were after counting up to 300. I found that there were 159 one’s. I then kept removing numbers until I found that there were only 100 one’s when I counted up to 162. At 162 when I did ctrl+f I found that there were 99 1’s. So the largest amount of numbers you can count to without using 100 of the number is 162.
The largest number you can count up to without running out of digits is 162. I got this answer by knowing that the most frequent number I will count is 1. I then listed 1-200 and subtracted numbers until I got 100 ones. I reached 100 ones at 162.
ReplyDeleteso first I know that 0-9 will include (-1) for all numbers. and moving up from 10-19, it will be (-1) for all numbers and (-10) for 1 since you have to use it for the 10. now if this continues, the same pattern will occur so that means when you reach 99, you will have (-10)+(-10) for every number. so now we are at 80 digits for each digit.moving up, it is the same equation expect now for every 10, you have to subtract (-10) from 1 and in the beginning, (-10) for 0. so from 100-109, subtract 1 from every digit except for 1 and 0. (-11) for 1, (-11) for 0. from 110-119, subtract 21 from 1 and 1 for all digits except 1. so clearly now in the 100`s we are going to run out of 1`s first and fast. for 120-129, subtract 11 1`s, 1 for all digits, and 11 2`s. now that I know 1`s are going to run out first, I can now just calculate how many 1`s per 10. so every 10, its (-11) 1`s. at number 129, we are at roughly 37 1`s. that means we can only go to the 160`s. 11x3 = 33. 33 - 37 = 4. so my final answer is 164.
ReplyDeletewhoops my bad, from 1-159 we have use 96 1`s( 20+11+21+44). we can only use 4 more 1`s so 160, 161, 162 will use 4 1`s. therefore the actual answer 162. sorry, I just realized I over complicated the question...
ReplyDeleteoh and another thing, I said 164 because I forgot that 161 had a "1" and I forgot to add the "1" somewhere back from 110 - 159.
ReplyDeleteI got 162 for the POTW, did my work on paper.
ReplyDeleteI knew that I really only had to solve how many times the 1 repeats. This is because when we get into the hundreds, the number one will repeat plenty of times, and we would not be able to even reach 200. So, as many other people did, I typed out the numbers and did ctrl + f (just to save time), and figured out the max number you can create. That number is 162.
ReplyDelete162, hardcopy
ReplyDeleteFirst, I found out what number you get up to using 100 ones. I chose one, because once I get into the hundreds, one would appear the most often
ReplyDelete1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91, 100.
Up to 100, I have used 21 ones.
I continued counting:
101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122 ... 200
Up to 200, I used 119 ones. I added the 2 together and got 140. I took out 40 numbers until I got to 100.
After I deleted all the other numbers, the last number I got was 162.
Grade 8 POTW
ReplyDeleteThe largest number you can count to is 162 (did my work on paper)
Grade 8 POTW:
ReplyDeleteThe largest number you can get to is 162. I did my work in my math notebook.
GRADE 8 POTW:
ReplyDelete162 (count on paper)
The highest possible number is 162
ReplyDelete(Work on Gapps)
162 =)
ReplyDeleteThe highest possible number is 162 as you would run out of 1's after 162
ReplyDeleteOh look! Here's another POTW where I used Ctrl+F to help me answer the question!!!
ReplyDeleteIt seemed logical that the number would be less then 200 because I would use a lot of 1s on the 100s. So I typed out all the numbers from 1-200 and did Ctrl+F to find the max number using 100 ones.
My work was done on a document which I shared with Mr. Milette and Ms. Fairbarn
Oh wow, would you look at that? I got 162!!!!
I know that the number 1 will appear most, because it will appear in every number after we get to 100.
ReplyDeleteCounting would take too long, so I did it the easy way by copy pasting a number chart of 1 - 200 onto Google Docs and using Ctrl F (a very handy tool in this question) to see how many 1's appear. I found that from the numbers 1 - 200, the number 1 appeared a total of 140 times, which is 40 over the limit. I deleted 40 1's, and I got 162.
:P
The highest number is 162. WORK IS IN MATH JOURNAL.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteActually, I'm going to type it online.
ReplyDeleteI was predicting that one will appear most because in a sequence from 1 to 200, one appears the most because in the 1 hundred part, one appears in most digits.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200.
Instead of retyping all the numbers from 1 to 200, I found a online chart from 1 to 200, Pasted it on a document and went ahead and did Ctrl F.
One appeared 40 times.
Since 1 has to appear 100 times instead of 140, I took out 40 numbers that had a 1 in the sequence going down.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
The last number I got was 162.
Grade 7/8 POTW
ReplyDeleteThe question is basically asking to do this:
- Count every number including a one 100 times (count by ones because this is the digit that will pop up the most if we are counting up to 200, which I can assume the final answer will not go past 200)
So doing it the long way, I counted all the numbers including 1 as a digit.
1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, and 162
Up to 162, the number one shows up 100 times.
So, he largest number I can count to is 162
POTW
ReplyDeleteMy method was pretty simple. I only used the 1 digits since they account for the majority of the digits from 1-200. Then, on a piece of paper I wrote down all the numbers from 1-200, and counted how many times the digit one appeared (which I later realized would have been more efficiently completed online, but it's alright). Anyways, after I counted the digit "1" 140 times, I came to my next dilemma. The limit was 100 digits, and I counted 140. So I subtracted 100 from 140 (which equals 40), and removed that many "1" digits which left me with the number 162. Therefore, the largest number you can get is 162!
Grade 8:
ReplyDeleteThe largest number you can get is 162. I did my work on my math notebook
The largest number you can get is 162. I know this because I copied and pasted all the numbers from 1 - 200 and command + f'd the number 1. It appeared 140 times but we had to get it down to 100. That is why I removed as many numbers as I needed to which left me with 162.
ReplyDeleteI made a list of numbers from 1-200 and counted the number of numbers with the digit 1. I got 140. I relized that we could use 100 "ones" to create the biggest number so I just happened to have an ordered list and elimitaded the first 100 1's and ended up at the number 162
ReplyDeleteGrade 7/8 POTW
ReplyDeleteThe largest number you can count to without running out of digits is 162.
I did this work in a random notebook I found, as well as a document where I pasted a bunch of numbers and used the classic Ctrl+F like everyone did to save time.
*I congratulate whoever actually took the time to count how many 1's appeared until there were 100*