Here's the first assignment for my H.E.R.O.E.S! Miss Saarinen will introduce the assignment during class on Thursday, November 12th. You will receive a copy of this post along with a rubric of how you will be graded.
Often times in math, once you've solved the problem and have an answer, you move on without giving an explanation as to why your answer makes sense. Sometimes we get too caught up in just the numerical answer that we are looking for.
It's not very easy to show your work on the computer screen. So, when you are assigned a problem on the blog you'll have to be able to communicate your answer in words. You should include the math language and skills that we've been learning and practicing in class recently. As always see if you can make connections to other situations where the same math could be used.
Choose one of the following problems to solve and write an explanation for. This assignment is due no later than Tuesday, November 17th!
Problem 1
You count from 1 to 100 and you clap while saying the multiples of the number 3 and the numbers that are not multiples of three but have 3 as the last digit. How many times will you clap your hands?
OR
Problem 2
A doorman works according to the following schedule: he worlds for 4 consecutive days and has the fifth day off. Last Sunday he had the day off, and on Monday he started work according to his schedule. After how many days, including that Monday, will he have a day off on Sunday again?
Assignment - In your comment remember to include the following:
* your name (first name and last initial)
* your class
* the answer to the problem you solved.
* an explanation that includes the strategy you used to solve.
* is there another way to solve the problem?
* would you be willing to use the same strategy if the numbers were much larger?
* any additional thoughts you have about the problem(s)
Remember when you "publish the comment" it will not appear on the blog until Miss Saarinen has a chance to read it and approve it.
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37 comments:
Multiples Of Three: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99.
# Ending in Three: 3, 13, 23, 33, 43, 53, 63, 73, 83, 93
Work: 33+10=43 numbers.
Total: 43 numbers.
I listed the multiples of three until it went to the closest it could get to 100 and I listed the numbers ending in three until it got closest to 100. Then I counted how many multiples of three. After, I counted the numbers ending in three and added the numbers together and got 43 numbers for my answer.
-Sareena P ;)
Pentagon math.
Kimberly Conlon
Triangle Math
I chose problem number 2. The answer to my problem is 35 days.
The strategy that I used to solve this problem was creating a list. I made a list that said
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
then I went down five times and marked the days I got with numbers until I reached Sunday again.
I figured out that there is another way to solve the problem. If you multiply 7 (the number of times that it took me to get to Sunday which is also how many days are in a week) by five (the number of days until his day off) then you get 35, which is the answer that I got.
No I do not think that I would use the same strategy with larger numbers because it would probably be very tedious a might take a while.
Sincerely,
Kim Conlon
Karen Demedeiros
Cicle Math
You would clap 46 Times because thats how many multiples 3 has
Nicole Cloutier Triangle Math
ANSWER=43
i have a 100 chart
i then circle all the numbers that are divisible by 3 or all the third numbers
i then circle all the numbers that end in the number 3
i then count the numbers that are circled and get my answer.
I did Problem 2. My answer-In 20 days including that monday, the doorman will have a day off on a sunday. To find the answer I made a table on microsoft word and filled in the days of the week. I highlighted every 5 days until I highlighted a sunday. There are other ways to solve this problem. I would use the same strategy if the numbers were larger.
- Jayde D., Triangle Math
Nicholas Kirby 9-14-09
Square Math Blog Assignment 1
Problem 1
You count from 1 to 100 and you clap while saying the multiples of the number 3 and the numbers that are not multiples of three but have 3 as the last digit. How many times will you clap your hands?
Solution
[12]= multiples and last digit
Multiples of 3 (1-100); 3,6,9,12,15,18,21,24,27,30,[33],36,39,42,45,48,51,54,57,60,[63],66,69,72,75,78,81,84,87,90,[93] 96,99
Last digits; 13,23,[33],43,53,[63],73,83,[93]
Number of claps (multiples): 33
Number of claps (last digit): 6
Number of total claps: 39
To solve this problem I took a piece of paper and wrote down all of the multiples of 3. Then I wrote down all of the numbers that have two digits and the last digit is 3. Then I went back trough both and found all the numbers in common and circled them so I knew I only had to count that number once. After that I counted all of the numbers in the multiples of 3 and got 33. And then I counted all of the last digit numbers accept for the ones I had circled earlier and got 6. Finally I added the two numbers together and got 39 claps total.
I do not think that there is another way to solve the problem, but if there is I thought that you would have to find the LCM and GCF of 3.
I would not be willing to use the same strategy if the numbers were larger because if the numbers were 1-1,000 it would be a lot of work and a ton of thinking to come up with all the multiples of 3 all the way too one thousand.
Sam K.
Triangle
You would clap your hands 39 times.
I figured this out by first finding all of the multiples of 3 between 3 and 100. their are 33 of these. Then, I went through all of the numbers that are not multiples of 3 and picked out the numbers that ended in 3. there were 6 of these. Finally, I added them together to get 39.
I would use this same technique even if the numbers were larger. It is pretty effective.
Nicole Cloutier Triangle Math 11/15
Problem #2
For this problem I got a 100 Chart and started circling all the numbers that were divisible by 3.
Then I counted all the numbers that the last digit ended in,that were not already circled.
I clapped my hands 39 times because 33+6=39.
this is Jeff A answer
triangle math
you would clap your hand 39 times
first i figured out how many multiples of 3 were in 1-100 there were 33, then i wrote out all the numbers that had 3 as the second digit. There were 9 numbers that had a second digit of three but 33 63 and 93 were already multiples of three so 33 plus 6 equals 39
I don think there was any other way to solve the problem
Yes, but it would take longer to solve it
would you clap your hands twice at the numbers 33 63 and 93 since they are multiples of 3 and end in 3?
Noah Alves Pentagon math
Assignment
3*33=99
10*3=30
99+30=129
To solve this problem i wrote down on a paper all of the multiple from 1 to 100 the multiple of 3 and the multiplyed that number by 3 then wrote down all of the numbers that end in 3 and then multiplyed that number by 3 and finally added the two numbers together. There is probably another way to solve this problem but i like to keep things simple. I would probably use a different strategy if the numbers were larger because i like to keep things simple and if i do it like thst then it wont be at all simple.
Shawn F
Pentagon
Problem 2:35 days till the next day off on sunday.
The stratigy I used was a t-chart, then I added all the days and got 35.
There is an other way to solve this problem by listing the days and circle the 5th day.
I will use the stratigy I used for bigger numbers.
I do not have additional thouts.
Elizabeth Costa
Pentagon Math
I solved problem 2
The answer to it is 7 more weeks untill he haS another Sunday off.I sloved it by making a list of the days he would get off untill he got another Sunday off which would be 7 weeks after he had the first Sunday off.I would not be willing to do this problem but with bigger number because then I would have to find a different stradegy to solve my problem. I aslo do not think there is another way that I feel confortable that would help me solve the problem.
Tanor Costa
Pentagon
the answer is twenty I think
I got this answer by multipling the four and 5 together.
The only other way I could think of was by using a chart.
I would use the same method if the #'s were bigger.
What happened to the sixth and seventh day of the week?
Kyle S. 11/16/09
Square Math Blog Assignment
Problem #1
Answer: 38 Times
I found this by listing all of the multiples of 3 up until 99 and then once I checked I had all listed all the numbers that ended in three that I didn't have down already and got 38.
There are other ways to do this but I think this is the easiest.
I would use the same strategy even the numbers where much larger.
I thought this was a fun problem and we played a game like this in Numeracy once during testing because we didn't have enough time before, and with many peoples its quite hard!
pentagon math
let n=number of days till he gets mber of days he works till he gets a day off work.
let 5=number off days
let n=35days
5*7= number of days till he gets sunday off again.
the number off days till he gets sunday off again is 35.
I started off by counting how many days till he gets off sunday again.
then I had to find the number by multiplying 5 by a number to get 35.
This is Ben G
Pentagon
Problem 1
I solved my problem by saying how many times does 3 go into 100. I got 33. Then I found out that 6 numbers ending in 3 that are not multiples of 3 are between 1and 100. Then I added 33 + 6 and got 39.
There is another way to solve this problem. Instead of clapping you could multiply 3* d to find the answer like this:
3*d
Let d= 30
3*30 is 90
You aren’t close enough. You just keep going till you found the number.
No. I would have to clap a lot. I’d rather use the other way.
I thought this problem was a little easy.
Abbi Walsh square math
math problem 1
I found out that the Answer to problem 1 is 38 I figured this out by writting down the numbers 1-100 then circleing the numbers that are a factor of 3 then going back and circleing the numbers that ended in 3. After that I counted up all of the numbers I circled and I got 38 so that Is the answer and the method I used... I could have used a different method which would be claping out saying the numbers 1-100 and claping out the factors and numbers that end with 3 but I felt that I would lose track that way because I'm not the best at mental math but other people who are good at that could do that.
There are 33 multiples of 3 between 1 and 100. I know this because 100/3=33.3. Out of 100, there are ten numbers that end in 3. Only 6 of them are not multiples of three. So there would be a total of 39 claps.
Signed,
Jacob Johnson
Oh, and I decided to do problem #1. Sorry.
Cassidy LaBombard
Square Math
Answer- 39 claps.
To solve the problem I counted by threes and then added up all of the numbers until they got too 100.
I thought this was the easiest way too solve the problem because its alot faster and works better in my head.
Lexie B.
Pentagon math.
Answer; 39 claps.
Explanation; 1-100,
3,6,9,12,13,15,18,21,23,24,27,30,33,36,39,42,43,45,48,51,53,54,57,60,63,66,69,72,73,75,78,81,83,84,87,90,93,96,99. To figure out the answer to this problem I counted by three's and then went back and added all the numbers that ended in three's except the ones I already had.
There is most likely another way to solve his problem but this is the way I solved it.
I think this is the easiest way to solve this problem and I think this is the strategy I would use if the numbers were bigger also.
nick n
pentagon math
the answer to problem number 1 is 40 claps
to answer this question I counted from one to one hundred and when it was a multiple of three or ended in a three I put donw a tally on a piece of paper when I was dont I counted the tallys and got 40 claps
Victoria R
Pentagon Math
The answer to problem 1 is 3 times you would clap your hands. i think this because i pick a random number like 33 and I separated the number by clapping and i clapped twice. and to check my work i chose another number 43 and got the same exact thing. clapped 3 times. i don't think there is another way to solve this problem. Yes I would use the same stratrgy for a much larger number.
Blog assighment #1
Hailey Drobish.
Pentagon.
Problem #1
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 19 20
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
the numbers below are the numbers when you would clap.
3 6 9 12 13 15 23 26 29 30 33 36 39 42 43 45 51 54 57 60 63 66 69 72 73 75 78 81 84 87 90 93 96 99
what i did is went threw the list and found all the divisable numbers of three. then i went back threw and added the numbers that ended in three. that would mean that since there are 34 numbers you would clap 34 times.
Makayla D
circle
you would clap 10 times.
you would clap 10 times because there is 10 numbers that have 3 as the last number.
for my stragy i clapped 1-100 and wrote the number with 3 as a last number.
another way to solve this problem is by counting by 3.
Hayley Dias November 16,2009
Square Math
Problem 1: The answer is 32 claps.
Explanation: Beacuse i wrote on a piece of paper 1-100 and then circled the multiplys of 3 and i got 32 claps through the multiples of 3.
Another Stragady: There is another way that u can solve this problem by thinking of odd number and circleing the multiples of 3.
Yes I would be able to do the same two stragady's for larger numbers.
My thought's about this problem was that it was very easy.
Rebecca C. Triangle Math
Problem 1
Let c=number of claps
1c=total claps
c=49
I will clap 49 times
First I figured out how many times i will clap. I listed the numbers 1-100 and circled all the multiples of three and all numbers ending in three. Then I put the variable in the equation and solved for c.
victoria Nunez
Circle math
Blog assignment #1
problem #1
If you clap on the multiples of three and the numbers with 3 as the last digit from one to onehundred you would clap 38 times. I got my answer by writing out the numbers 1-100 and circled the multiples of three and the numbers with the last digit being 3 and I circled 38 numbers all together.
Chance Gunther
let 1 = days working
let 2 = day off
11112111121111211112111121111211112
after 35days the man will have a day off on a sunday.
Problem 1
Madeline Lessing
Triangle Math
Work:
Multiples:3,6,9,12,15,18,21,24,27,30,33,36,3942,45,48,51,54,57,60,63,66,69,72,75
78,81,84,87,90,93,96,99
#s ending in 3:
13,23,33,43,53,63,73,83,93
Answer:You will clap your hands 42 times.
NatashaP--Pentagon--#1(Blog Assignment)
I Will Clap 39 Times.
I Figured Out This Problem By Listing The Number From 1-100. When I Was Done Listing All The Numbers I Counted 1-2-3 1-2-3 1-2-3. When I Was Finished With That I Looked At The Remaining Numbers And Circled The Ones With 3 As The Last Digit. When That Was Complete I Checked My Work.
There Is Another Way To Figure Out This Problem. Another Way To Figure This Problem Out Is To Actually Clap 100 Times And Write Down A Tally Ever Time You Come To A Number That Is Either A Multiple Of 3 Or has 3 As The Last Digit.
I Would Not Use This Same Strategy If The Numbers Were Larger Because It Would Take Too Long.
kaylee swanson
pentagon math
-problem 1 answer: 33
-explanation: I divided 3 into 100 and got 33(repeated number)
-another way to solve this would be to actually count until 100, by 3 to be surer of the answer.
-if the number were larger, it would probably be easier because 3 can’t go into 100 evenly.
-this problem, made more sense to me than problem 2, because it was easier to visualize how to come up with the answer.
Lauren James
Square Math
Problem 2
the answer is that every 34 days the doorman gets sunday off.
I first solved the problem by setting up a chart and counting how many days until he got sunday off again.
Yes, there is another way because when i finished the problem i realized that it runs in a thirty five day cycle which means that thiry five is a multiple of seven (days of the week) and five. (work cycle)
No, because it would take to much time so i would use the second strategy also because it would be easier.
No i did not have any thoughts because to me the problem was very staight forward.
Natalie B
Triangle
48 numbers
Listed the numbers 1-100 and then circled and colored multiples and ones with 3 in them.
There is probaly a mathamatical way to solve this problem
If the numbers where larger i probaly not want to use the same strategy I did.
I didnt really know how to solve this problem without actually doing it and I always lots track so I then decided to just write it out to help me keep track.
becca mallon-circle math
the answer to problem 1-you have to clap 38 times
jacob lavoie circle: according to the problem the door man has to work 4 days then as a day off. i looked at a calendar and counted every 4 days that he worked and the 5th day off until i got to the next sunday. my answer for problem 2 is 34 days until the door man has the next sunday off.
Kyle O
pentagon
Problem 2: The answer I got is 35.
I got my answer by multiplying and making a chart. I would use this strategy for bigger numbers.
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