Problem 1You count from 1 to 150 and you clap while saying the multiples of the number 6 and the numbers that are not multiples of six but have 6 as the last digit. How many times will you clap your hands?
OR
Problem 2A bus driver works according to the following schedule: he works for 5 consecutive days and has the sixth 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.
52 comments:
Dear Ms. Saarinen,
I did problem number one and did a oraganized list. When i did this list i got 40 claps all together. When i did the organized list i first wrote down all the multiples of six all the way up to 150. After that i wrote down all the multpiles from six to 250 that had the last number six. Then i counted them up all together to get 40 claps. I tried to actually do the claping but i got confused with the claping, number, and keeping track of all the special numbers.
Kaelin C.
Jessica B North
I answered problem one and got thirty five for an answer.I got my answer by using an organized list.I wrote down the numbers one through one hundred fifty. Then I went through the list and counted the numbers that were either a multiple of six or has six has the last digit.Another way to solve this problem is by dividing six by one fifty and then add ten to the result since there are ten other digits that end in six but aren't multiples of six.I would still use the same method for a larger number because it was organized and I got the answer fast.
Noah Hanmer North Math
If you count from 1 to 150 and you clap while saying multiples of 6 and numbers ending in 6 out loud, you will clap 35 times. To solve this problem, I drew a graph with 15 rows and 10 columns to represent the #s 1 through 150. I then filled in all multiples of 6.
To start, there were 25 multiples of 6. These consisted of 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, and 150. I got the first 10 multiples, then I realized you could go down every third row on my chart to find the multiples. This represented adding 30, which was the easiest to do on my chart. Then I just filled in the row with every number ending in 6 that had not already been filled in. There were 10 numbers, and they were 16, 26, 46, 56, 76, 86, 106, 116, 136, and 146. I added these 10 numbers to the multiples of 6 (25+10) to get 35 numbers, or 35 times you will clap.
Another strategy I could use to solve this problem would be to act it out (Strategy 1), or I could also just find the pattern and use it to help fill in the chart (Strategy 6). I would likely use this strategy if the numbers were in the thousands, or even higher.
For problem 2, it asked “If a bus driver works for 5 days and has the 6th day off, and he had this Sunday off, how many days will it be before he has another Sunday off?” It will be 42 days before the driver has another Sunday off. To solve this problem, I drew a calendar page (mainly a regular grid), and I labeled the days of the week. I crossed off the first Sunday, counted 5 days and crossed off the 6th (a Saturday), and I repeated the pattern. (I also saw the pattern as going forward a whole week, then subtracting a day.) When I got to the next Sunday in the pattern, I counted all of the days that had passed. There had been 42.
Other strategies I could have used to solve this problem would be to format the data into a table (Strategy 3), or to guess and check until I found the answer (Strategy 5).I would definitely use the same strategies if the numbers were much higher- even if that meant going through multiple years of time. Overall, I enjoyed these problems. They were very easy. My major complaint may be that they were too easy. I found the answers for both within minutes of looking at the problems. A suggestion for next time would be to make them a little harder.
Elizabeth Hennen~ North Math
1. A. 6 multiples and numbers the last digit 6 come up 35 times from 1 -150.
B. What I did was write out all the numbers between 1 and 150 in a table and circled each one that corresponded with the problem and counted each one after.
C. The other way to solve this is to act it out. Have one person clap each time that is relevant to the situation, and have another record how many times you clapped.
D. I would not be willing to use this number with a much larger number because it would take a rather long time.
E.
2. A. After 42 days the bus driver will have a Sunday off. you7
B. I made a chart that had the days of the week and the number week it was. I wrote down whether he was working or not until I came to a day where he didn’t work on a Sunday. Then I went back and counted how many days it took.
C. The other way to solve this is to draw a picture or make a list.
D. I would not be willing to use this method because it would take rather long.
Elizabeth Hennen~ North Math
1. A. 6 multiples and numbers the last digit 6 come up 35 times from 1 -150.
B. What I did was write out all the numbers between 1 and 150 in a table and circled each one that corresponded with the problem and counted each one after.
C. The other way to solve this is to act it out. Have one person clap each time that is relevant to the situation, and have another record how many times you clapped.
D. I would not be willing to use this number with a much larger number because it would take a rather long time.
E.
2. A. After 42 days the bus driver will have a Sunday off. you7
B. I made a chart that had the days of the week and the number week it was. I wrote down whether he was working or not until I came to a day where he didn’t work on a Sunday. Then I went back and counted how many days it took.
C. The other way to solve this is to draw a picture or make a list.
D. I would not be willing to use this method because it would take rather long.
Jacob.A West
Problem2- Answer is 42 days
What i did was make a table. I wrote down Monday-Sunday and then xed off the days he had of until i got my answer which was 42.
I think that you could solve the problem another way by just counting in your head.
I would use the same strategy if the numbers where larger, because i think that making a table is the most visual way to solve this type of problem.
Alan .A
North math
Problem 1
If you were to count up to 150 while clapping when you say multiples of 6 and numbers that are not multiples of 6 but have 6 as their last digit you would clap a total of 35 times.
I used brainstorming and saw this problem as a division problem. So first I divided 150 by 6 and got 25. This showed there are 25 multiples of 6 that are in 150. Then I counted out all of the numbers that had 6 as the last digit in 150. I got 16, 26, 36, 46, 56, 66, 76, 86, 96, 106, 116, 126, 136 and 146. Next I took out of the 14 numbers that were multiples of 6 and got 10 left over numbers. Finally I added 25 and 10 to get 35 claps.
Yes. Instead of brainstorming someone could make an organized list. They could have just written down all the multiples and counted them. Then do the same for the last steps. The result would be then same if the counted right.
I would be willing to use my strategy if the numbers were much larger. My strategy would work fine.
Problem 2
The bus driver would have to wait 41 days until getting another Sunday off.
I made a chart for this problem. First I made the chart have 7 columns each one had a day of the week. Monday, Tuesday, Wednesday ext. I first started on Monday and wrote a 1. This stands as a day of work and so did numbers 2, 3, 4 and 5. When the driver had a day off I put an off. This went on until I hit a Sunday off. When I got to the Sunday it had taken 41 days.
The only other way I can see to solve this problem is with a list.
I would still use my method although it may take some tine to complete the chart it is very precise unless I count wrong.
I thought these problems were not just work like normal math problems but instead very enjoyable.
Caleb D. West math
Problem 2 12/4/11
The bus driver will have another day off on Sunday after 42 days. I got this answer by first counting out the first six days after the Sunday he had off and I got Saturday as his next day off. Then I counted out six more days starting with Sunday and I got Friday. I thought that I might see a pattern, but I wasn’t sure so I kept going. I got Thursday as the next time the bus driver would have a day off and realized there was a pattern. It was, the days off were going backwards. (Example: From Saturday to Friday to Thursday.) So, I knew it was Wednesday then Tuesday then Monday and finally Sunday. There were seven groups of six days before he was off on Sunday again, so I multiplied seven by six and got 42 days.
Another way to get the answer would be, subtract seven (days in a week) from the number of days he works plus the day off. If it’s a negative number you will subtract that many days from the first day off, if it’s a positive number then you add. If it’s the one I just did then you would do six minus seven which gives you negative one. You get the day before Sunday which is Saturday and so on. Then you will figure out how many groups there are before the next Sunday off. Finally, you would multiply the number of groups by the number of days before the next day off.
I would not be willing to do my first way with bigger numbers, but I would do the other way with any type of numbers big or small.
I liked thinking of other ways to solve the problem. Here is another. If the days worked plus the day off are NOT a multiple of seven, then there will always be seven groups of the days before the next day off. So you can just multiply seven by however many days worked plus the day off in the first group.
Madison C.
South Math
My answer to problem 1 is 37.
I got this answer by dividing 150 by 6 and got 25. Then I went through the non multiples of 6 that end in 6 and got 12 numbers. I added 25 and 12 and got 37.
Another way to solve this problem is counting it out and make hash marks every time you reach a multiple of 6 or a number ending in 6.
I would be willing to use the same strategy if the numbers were much larger.
From Geneva C. in North math. The answer to problem one is 35 claps. The strategy I used was writing down all the multiples of 6 all the way through 150. I totaled them and got 25. Then, on a separate list, I wrote down all the numbers that ended in 6 up to 150. I crossed out the numbers in that list that were also multiples of 6 and ended up with 10 numbers. To get my answer, I added 10 to 25. Another way to solve the problem would be to make a list of all the numbers 1-150. Then circle all the numbers that are either multiples of 6 or end in 6. Then you count all the circled numbers to get the total. I would use the first way if there were a larger amount of numbers because it is quicker and more efficient. The answer to problem 2 is, after 41 days, the bus driver will have the day off on Sunday again. I solved this problem by writing down all the days of the week (S,M,T,W,TH,F,SA,). Then I circled Sunday and counted 5 days. I circled the 6th day and continued until the day I circled was Sunday. Another way to solve the problem would be to multiply the 6 days of the bus drivers work schedule by the 7 days of the week to get 42. Since you don't count the first Sunday, subtract 1 day to get 41. I think of it as finding the lowest common multiple. I would probably use the first way even if the number was a lot bigger. This is because even if you do the math right for the second way, if you don't know what to subtract, the answer will be incorrect. These problems were really easy but coming up with another solution for the 2nd one was interesting.
Patrick M North
For problem number one I got an answer of clapping a total of thirty five times. To solve this problem I made a graph with six columns. Then I counted to one hundred and fifty and circled the multiples of six and the numbers that ended with six. Another way I found of solving this problem was that you could act it out by having a friend count how many times you clapped while you clap. I think that this problem solving method was affective for this problem however if the numbers were larger I think that it would take longer but it will still be affective.
For problem number two I got that after forty two days he would get another Sunday off. I solved this problem by making what looked somewhat like a calendar. Then I marked the Sunday he got off with an x then I counted five days and put another x and when I got to Sunday again I put another x and counted all the days including that Sunday. Another way I found that you could do this problem was to look for the pattern that every five days the day off went backwards for example one week would be Tuesday off the next would be Monday. I think that this problem solving method was good but the pattern method was faster. Overall I thought that this was a good problem.
Boris Apple
North Math
12-5-11
Problem 1.) How Many multiples of six in 150. I got 35 claps. I made a list of 150 and circled all of the multiples of six and numbers ending in six.
2.)How many days until the man has a free day on a Sunday. My answer was 42 days including the Sunday off. I first made a chart of all the days he would work from that first day off forward. I put a W in the box if it was a work day and a X if it was a day off. When the X was on a Sunday that was the next day off.
James A. South Math
I chose option 1. My answer was 35 claps. First, I did a number grid from 1 to 150. Next, I circled the multiples of 6 and the non-multiples that ended with 6. To do that, I circled all the numbers from 1 to 150 that ended with a 6. Then I used my agenda to help me find all the multiples of 6. My agenda only goes as far as the 12's tables. I ended with 12 times 6, which is 78. From there, I counted up 6 every time and circled that number. I did this until I got to 150.
This was hard because the problem had so many parts. If I had to do a problem like this again, I would use the same strategy. If there was a problem like this that was harder and used bigger numbers, I think I could still use the same strategy to get the answer.
I think there is another way to solve this problem. Instead of using a number grid, you could just keep doing 6 plus 6 plus 6 until you got to 150 and write down all the multiples as you count. For the non-multiples, you could start with 6 and add 10 over and over again until you got to 150.
Cassidy A.
West Math
1.You will clap your hands 35 times.
2. The strategy I used was I said the multiples of six and clapped my hands and recorded it by making tallies. Then I said the numbers again except this time I clapped when I said the numbers that end in 6 but were not multiples of 6 and made tallies.
3. Another way to solve this problem is to write out the numbers from 1 to 150 and highlight the multiples of 6 with yellow and then go back through the numbers and highlighted the numbers that were not multiples of 6 but had 6 as the last digit with a different highlighter. Then add up the numbers highlighted.
4. I would not be willing to use the same strategy. I found the second strategy, with the highlighting, easier because I was able to see the number I highlighted.
Cassidy A.
West Math
1.You will clap your hands 35 times.
2. The strategy I used was I said the multiples of six and clapped my hands and recorded it by making tallies. Then I said the numbers again except this time I clapped when I said the numbers that end in 6 but were not multiples of 6 and made tallies.
3. Another way to solve this problem is to write out the numbers from 1 to 150 and highlight the multiples of 6 with yellow and then go back through the numbers and highlighted the numbers that were not multiples of 6 but had 6 as the last digit with a different highlighter. Then add up the numbers highlighted.
4. I would not be willing to use the same strategy. I found the second strategy, with the highlighting, easier because I was able to see the number I highlighted.
Cassidy A.
West Math
1.You will clap your hands 35 times.
2. The strategy I used was I said the multiples of six and clapped my hands and recorded it by making tallies. Then I said the numbers again except this time I clapped when I said the numbers that end in 6 but were not multiples of 6 and made tallies.
3. Another way to solve this problem is to write out the numbers from 1 to 150 and highlight the multiples of 6 with yellow and then go back through the numbers and highlighted the numbers that were not multiples of 6 but had 6 as the last digit with a different highlighter. Then add up the numbers highlighted.
4. I would not be willing to use the same strategy. I found the second strategy, with the highlighting, easier because I was able to see the number I highlighted.
I had made a chart\table showing the days of the week and checking off the numder of days he had worked all the way until the next sunday he had of and i had gotten 26 days untill his next sunday off.
Sincerly,
Zaccary Francis
Passion M East math 12-6-11 Answer;35 claps.What I did was I had a list of multiples of 6 and then I listed ''not'' multiples but have 6 as a last digit.There are many ways to answer the problem but I thought adding was the easiest way to solve the problem,and I also used my head.If the number was larger I wouldn't use the same strategy because it would take too long.In class I,ve been working on problems similar to the blog assignment.
Hi my name is Devon L and I’m in south math. I did problem 1 and the strategy I did to find the answer (which is 35) is I made a list from 1 to 150. Then I circled all of the multiples of 6 and every number that ended in 6. Another way you could solve this problem is you could make a chart from 1 to 150 and color all the multiples and every thing that ends in 6. If the number was much larger then I would still use the same strategy because it was very helpful.
Michaela G. North Math
For Problem 1, I got the answer of 35 times that I would clap my hands. I got this answer by first making a list of all the multiples of 6 until I got close to 150, since it says from 1 to 150. So it looked like this: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 and EST.… until I got to 150 because 6 can go into 150, twenty- five times. After, I listed all the numbers that had 6 in the ones until I got up to 146. When I got all the numbers listed, I count all the numbers and got a total of 25 times I would clap. Another way that I could’ve gone about to find the total would to do 6/150=25 then to find out all the numbers that had 6 in the ones but to leave out the ones that were divisible by 6. Yet another way I could’ve done it was to try to find a pattern and then find the answer that would still be 35 times I would clap. Now, if the numbers would larger I would probably not use the strategy I used first to find out the answer. I say this because it would probably take longer to try to figure out, especially since it’s larger numbers.
For Problem 2, I got the answer of 42 days that a bus driver would have a Sunday off again. I got this answer by making a table and filling it out. To make the table, I wrote the names of the day and repeated it constantly. For example, I did this: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, Monday, Tuesday, and so on. So on the top row of the table, I put the names of the days the same way I did just above. In the second row I made a box right below each day. Then, I used X’s for the days that are marked for every 6 days because in the problem it says the bus driver works 5 consecutive days and on the 6th day he is off. To fin my answer of 42 days, I just counted the number of days that I wrote down and got the answer of 42 days. Another way that I could’ve figured it out was to fin a pattern, which was that first Sat. was marked then Fri. was marked and I continued to go backwards until I got to Sun. to get my answer. After, I counted the number of marks I made, which was 7 marks, and then since the mark was every 6th day, I did 6*7 to get the answer of 42 days, also. Now, if the numbers were larger I would probably not use the strategy I used but probably determine a pattern strategy because the strategy I used was much longer but the pattern one I much shorter.
Keiana Rodrigues
West-math
Problem #2
The bus driver has work 5consecutive days and had the sixth day off. But last Sunday he had the day off and then on Monday he started working doing his regular schedule. The bus driver will have 42 days including that Monday before he has another Sunday off.
To figure this problem out you have to count out 5 days until you get 1 of the 5th days to be on Sunday. So if you were to count out 5 days you would first land on Friday. Then the next 5 days the next 5th day would be on a Wednesday. If you keep doing this, in 42 days and the next few fridays one of them will be on a Sunday so he will have that day off. The strategy I used to figure this problem was I made a picture/ diagram.
I couldn’t find out any other way to solve the problem. You don’t have to make a picture/diagram you could do out the math.
If the numbers were much higher than these I would still use the same strategy. I feel that drawing a picture/diagram is the best way of finding out the answer to this problem.
Kayla Squatrito East Math
The answer to problem two is 35. The strategy I used was making a picture. When I was drawing the picture, I used lines to show the days and used boxes as days off. And in those boxes I put the letter of the day. Once I got to Sunday I counted all the days including the days off an I got 35 days until the bus driver gets another Sunday off. Well for another way to do this is to brainstorm I guess. This is because I don’t know another way to solve this. I think to draw a picture is the easiest way to figure this out. If there was a bigger number I would use the same strategy because I don’t mid drawing out pictures. My thoughts about the problem are that I think it was easy and making pictures is an easier way to find some answers.
Sawyer L
West Math
12/5/11
The problem I did was the first. If you count from 1 to 150 and you clap saying the multiples of 6 and the numbers that aren’t a multiple of 6 but end in 6, you clap your hands 35 times. I know this because when I was doing this I made a table of the numbers 1 to 150 of 6. After I had done this I started to cross out the numbers that were not multiples of 6 and didn’t end in 6. when I had done all of these steps I counted all of the multiples of 6 and the ones that ended in 6 and got 35. There is another way you could have done this problem. Instead of writing all the numbers from 1 to 150 you could have done a chart of multiples of 6 and then added the numbers that end In 6 into that chart and counted them. If the numbers were larger I would not have done the same strategy. I would have done the table of the multiples. I thought this problem was a good problem and I thought about it for a while. However I thought this problem was a little easy. Overall I liked this problem.
so if you claped your hands while counting the multiples of 6 and the numbers that end in 6, you would clap 35 times.
Logan A. North Math
Problem 1: the answer is 35. To get this answer i listed all of the numbers from 1 to 150 and then i counted all of the ones with 6 as the secondary number or that was a multipe of six. There is probably another way to do this problem but i am not aware of this method. No i wouldn't do my method if the numbers were larger.
Problem 2:
The answer i got for this problem was 49 days i got this by seeing if the day that the bus driver got off went forwards every week or backward every week. once i found out tht it went backwards i then counted how many weeks it would take for the day off to go back to sunday i then multiplyed that by 7 to get my answer. I am sure that there is another way to solve this problem. If the numbers were larger i would still do my method
Pearsums A. - North MATH
PROBLEM 1: If i counted from 1 to 150 and clapped every time i said the multiples of six or a number that had 6 as its last digit, i'd clap 35 times.
To get this answer, i wrote the numbers from 1 to 150 and i crossed off every one that either was a multiple of six, or it had six as its last digit. when i looked at all the numbers crossed off, i counted 35. So the answer is thirty five.
Another way to solve this problem would be to actually say the numbers out loud, and clap every time i said a number pertaining to the rules given. Then i could've counted how many times i clapped and that would be my answer.
I would not use my strategy if the numbers were larger. That would mean more numbers to write down at the start, more numbers to cross off, and more crossed off numbers to count. I would not be very willing to do more work with this method if it had larger numbers.
Actually, i thought this problem was quite creative. It was fun to figure out and i liked its creativity and ability for many methods that i can use to solve it. Nice one Ms. Saarinen!!!
PROBLEM 2: If today a bus driver has sunday off, and his schedule is that he works for five consecutive days, and has the sixth day off, he would have to wait 42 days until he had another sunday off.
To figure out this answer, i literally drew a calendar and marked each day as W (for work) or O (for off). Starting as monday as a work day, i kept on doing this until i put an "O" on sunday. Then, i counted all the days up to the sunday. I counted 42.
Another way i could have solved this problem would to multiply six times seven. Six represents the sixth day off and seven represents the number of days in a week. The product of 6 and 7 is 42.
I would be willing to use this strategy if the numbers were larger. Drawing out the calendar isn't too hard, and its a great visual!!!
Yay!!! I liked this problem as well. I think these blogs are fun!!!!
Brittany S. North Math
1. If you were to count from 1 to 150, while you clap when you get to the multiples of 6 and numbers with six as there last digit, you would get 34 claps. I got this as my answer because, on every one of the multiples of 6, I clapped, then recorded it as a tally on a separate sheet of paper. After that step, I clapped on every one that had six as a last digit. I recorded each clap as a tally on a paper also. There were some numbers that fell into the multiples of six category, and the number with the last digit as 6, so I only counted those once. After I was finished clapping, I added all of my tally marks together, and got 34 claps. There is also another way to solve the problem. If you wanted too, you could write all the numbers from 1 to 150 on a piece of paper and circle the ones that are a multiple of 6 or have six as the last digit. And if they fall into both, you only count them once. Then, you could count all the circles. But, this would be a longer process than the first strategy. I would be willing to use the same strategy even if there were larger numbers. This is because; the second strategy would be an even longer process with bigger numbers.
2. After 35 days, the bus driver will be able to get off a Sunday again. To solve this problem, I made a list of all the days of the week and counted off and circled the day he would have off. After many repeats of this process, I finally got to the point where he would have a Sunday off again. There isn’t another strategy to solve this problem because there is only one way you can do it. I would be willing to use the same strategy if there were larger numbers because it is the only strategy. One thought I have about this problem is why his schedule goes on a 6 consecutive day work schedule then the seventh day off. But, this would make him have a day off on the same day every week.
Kalesta B
West
I solved problem 2 the answer I got 35 days. I wrote down very week according to his schedule I got for the 1st week his day off was on a Saturday. The 2nd week his day off was a Friday. The 3rd week his day off was a Thursday. The 4th week his day off was a Wednesday. The 5th week his day off was a Tuesday. The 6th week his day off was a Monday. The last week his day off was finally a Sunday. No I do not know any other way to solve the problem. Yes I would be willing to use this strategy for bigger numbers. My thoughts are that once I got the pattern I knew that all the other problems would be like it. In other words once I got the “flow of things” I knew how to solve the rest of the problems.
James D from South Math here. I have completed problem 2 and i'm going to share my answer and my strategy. in 42 days will the bus driver have a day off on a Sunday. I sort of used the Use or look for a pattern strategy, with a few tweaks. You see... i Wrote down the days and followed the directions by labeling The 5 days the bus driver worked and then marked the 6th as a day off. it took a while but i found the answer. There may be more ways to find the answer but i cannot find another one of the ways because i have a limited amount of time to finish a lot of homework. tally another blog assignment done for James D.
Ben Cloutier
North Math
The answer to the claps problem is 35 claps. I made a list. I wrote 1, 2, etc. all the way to 150. I then circled multiples of 6 and last digits of 6. To answer this, you could act out and physically clap and count the claps. I would use the same strategy because this one was so effective.
The answer to the bus problem is 42 days until a Sunday off. I made a list. I made a calender, basically, andjust filled in spaces with W and O symbolizing work and days off. You also could find a pattern and just continue it. I'd just use the same strategy, though.
Harrison Q.
West Math
The answer to problem two is 41 days (it will be 41 days before the bus driver has another Sunday off).
To solve the problem, I first came up with the variable w=work day, and b=break day. Then I wrote a list starting with Sunday was a B day, Monday was a W day, Tuesday was a W day, etc. It took 41 days for Sunday to be another break day.
When I look at it visually, like a calendar, I can see that there is a diagonal line moving to the left over the course of 6 weeks showing his break days, and then the pattern repeats. I think that there is probably an expression for it but I can't think of it.
I would not want to use my original strategy if the numbers were much larger because it takes too long. I would use my other strategy because it is quicker.
Mark Read west math
Strategy
W=work
O=off day
S m t w th f s s m t w t f s s m t w t f s s m t w t f s s m t w t f s s m t w t f s s m t w t f s s m t w t f s s
The answer is 42 more days and the bus driver will have a day off on another Sunday.
Another way to solve this would have been to multiply 8 weeks times six days 8x6
I would have tried to use the strategy that I used first to try and solve the problem
Alec D. North Math
Problem 1-
You will clap your hands 40 times. I used the use or look for a pattern strategy. You could also use logical reasoning. I wouldn't be willing to use the same strategy if the numbers were larger. This reminds me of the problem solvers we used to do in 5th grade.
Problem 2-
The bus driver will have to wait 41 days until he has another Sunday off. I used the make a table or chart strategy. You could also use the look for a pattern strategy. If the numbers were larger, I wouldn't be willing to use the same strategy.
Blog Assignment
Jackson Kneath
North Math
For problem number one I wrote every number until one hundred fifty. I then went in circling every single factor of six it was very simple without a problem. I then went through my giant list of numbers and found all of numbers that ended with six and circled them as well. I then counted up all of the numbers that where circled which surprisingly took sometime considering I kept either loosing count or I just recounted to come up with the correct answer I finally came out with a total of thirty-five. You would clap your hands thirty five times. Obviously for someone that hasn’t read the problem you would be very confused. The problem was asking how many times you would clap your hands if you counted to one hundred fifty and clapped every time you came across a factor of six or a number ending in six. How many times would you clap? Like I said before I came out with thirty-five claps. I’m sure if I made a table to complete this assignment, I would have no problem getting the same answer because I could have made it just like the way I dealt with the problem. I usually make tables and charts when dealing with problems like this one but I went with just writing it out and it worked out. In conclusion For my answer to problem number one I got thirty five.
For problem number two I wrote the days of the week five times I then went through and circled the day it landed on every five days until it landed on a Sunday. Twenty days later it landed on a Sunday. This time it took me literally three seconds it was very easy and simple. I had no problem what so ever. I pretty much used the same strategy as I used in the first problem. I usually make a table but again I didn’t that is only because it was very simple. At first I really thought this would be a load of painful work but then realized it was quite easy and simple and I’m sincerely obliged to that. In conclusion I got twenty days for my answer.
Noah P, Problem 1- my answer is 27, the way i got my answer is by getting all the multiples of six and then adding up the numbers that end up with 6 and i got 27
Drayton Y. East Math I did problem 1 and the answer was 35 claps.I wrote 1 to 150 and circled the multiples of 6 and numbers that ended with 6.Another way to answer the problem is to make a tally of each multiple and number that ends with six.
Johnny m.1You count from 1 to 150 and you clap while saying the multiples of the number 6 and the numbers that are not multiples of six but have 6 as the last digit. How many times will you clap your hands? 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/ 134 135 136/ 137 138/ 139 140 141 142 143 144/ 145 146/ 147 148 149 150/. explanation- I wrote down 1 to 150 and i put slashes at every multiple of 6 and after every number with sick in it. You will clap 34 times
I choose to do Problem #1 where you had to clap each time there was a multiple of six or a number whose last digit was six. You had to do this all way to one-hundred fifty. To solve this problem I first wrote all the numbers from one to one-hundred-fifty on a piece of white lined paper. After I finished doing this which was very time consuming, I went back and circled all the numbers which were a multiple of six or whose last digit was six. As I was circling the numbers I drew a tally mark a few lines down from my list of multiples for every time I had circled a number. When I had finished circling and reached one hundred fifty, it was time to count my tally marks. I had six groups of five tally marks and four extra ones. Since 6*5 is 30 and there were four extra tally marks I concluded that there were thirty-four tally marks. Now I know that you would have to clap thirty-four times from one to one-hundred fifty. Another way you could solve this problem was to write all the numbers from one to one-hundred-fifty and to actually clap it out when you got to a multiple of six or a number whose last digit was six and then you could keep tally marks on how many claps you did. Personally, if the numbers were much larger I would not want to use the strategy I did, because it would be rather time consuming and it would take me a long time to just to write out the numbers. I thought this problem was rather time consuming but I felt it was the easier of the two problems.
Mollie Rigby-North
1. You will clap your hands 34 times. I made an orgnized list by putting all the multiples of six in one row and all the numbers that end with six in the other row. Then I added the totals of each row together to get my answer. anothr way you could do it is by dividing 150 by 6 and that is how many multiples of six there are. Then you would list the numbers that end with six and add the quotient of the first step with the sum of the second to get your answer. If the numbers were larger I wouldn't use my first strategy, I would use my second option. I don't have any questions about this.
2. After 42 days, the bus driver would have another Sunday off. I solved this by making a chart. on one side it had the days off going from the first Sunday, then to Saturday and so on until I got back to sunday. on the other side I had the days he worked in that week. I added all the days together and got 42. another way to do it is by making a diagram.
I would use my strategy if the numbers were bigger. I wanted to know if we counted the sunday that he had off as one of the days he waited for a day off.
Connor Nile North Math.
If i had to count from 1 to 150 and clap on multiples of six and numbers that end with six. First i counted all of the multiples of six and got 28. Next i counted all the numbers between 1 and 150 that ended in six and werent multiples and got 10. Finally i added 28 plus 10 and got my final answer of 38. you could also clap on multiples and numbers that end with six and have some one write down how many times you clap. I wouldn't use this method it would take too long.
If a bus driver got this sunday off and works 5 days before getting the sixth day off he would have to wait 41 days to get another sunday off. First i made a chart and put an x on every day he got off. Then i counted all the days untill i got to his next sunday off. My answer was 41 days. I would use this method because it is organized and easy to follow.
kyle d
east
35 days
i drew a pictue but you cold of made a list
yes i would still use the stragety
Problem 2 A bus driver works according to the following schedule: he works for 5 consecutive days and has the sixth 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? well he will have Mon Tues wed Thur Fri the off saterday then sun Mon Tue wed Thur off Friday so in 4 weeks he will have a day off on sunday again
erika silveira
south math
11/6/11
problem 1
multiples 6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150 there are 25 multiples
numbers with last digit of 6
16,26,46,56,76,86,106,116,136,146
10 numbers that end in six
25 multiples
+10 numbers that end in 6
--------------------------
35 claps
In total I will clap my hands 35 times.
Skye N. North math
problem 1 35 claps
Problem 2 41 days
I used the following strategy for problem 1. 150/6 for the claps for multiples=25+numbers ending in 6, 15-number that overlap 6 36 66 96 126 5= 35 claps. I did this because I figured it would be the quickest way without actually clapping and counting. It could also be used for almost any number if I changed it a little bit. You could count instead.
For problem 2 I used the strategy of a chart.
6 Saturday
12 Friday
18 Thursday
24 Wednesday
30 Tuesday
36 Monday
42 Sunday- 1 for Sunday = 41 days.
I wouldn't use this strategy again with a larger number because you have to do each number instead of using an equation and I used this strategy now because it wasn't a large number and it would be the easiest way without a huge reasoning. I just used 6 for the days and went back one day for each 6. I could use the days in the week and days for each day off and make it an equation.
Lindsey.B
South
First I knew I had to clap my hands on the multiples of 6 and the numbers that had 6 in 150. So I stared clapping my hands up to 150 butthen i relized i could do this a more simpler way. I grabbed a paper and i wroted 165 divided by 6 which would eaqual to 27.5. so the highest i could go was to 27*6 which would equals to 162. So my answer to the question how many times i would clap my hands up to 150 would be 27 times for the multiples of 6 and the numbers that end with 6 in it.
Jared Faria north math
Question 1) the answer is 35 times that you would clap. I got my answer by making an organized list then crossing out the pair that match in each list that i made. one list was of the multiples of 6 and the other was the last digit being 6. The other way that you could have possibly done this was to make a table with the multiples of six and the 6 as the last digit inside of the table. I would do the same method for the numbers even if they were higher because it was an easy metod to work with.
Question 2) The answer is 42 days that he would have until he would have another sunday off again. For this problem i used the same method as before and made an organized list. I kept on writing out the days then when i felt like i had enough i started to cross out 5 in a row then left the 6th one blank every time. I kept on doing this until I ened up crossing out a sunday which ment that was the day that he had it off. the other method that you could use is to create a table to put the numbers in and cross them out in the table. Even if the numbers were larger i would still use this metod because i thought that it was fast and an easy method to use.
Blog Assignment #2
Neil T
West
Problem 1
Answer=35 claps to 150
The way I solve the problem was I counted by sixes to one hundred fifty. Every time I added six I clapped. When I cam to 12 six does not reach 16 so I added one more clap for that situation.
Another way I could of solved this problem is I could of counted to 150 by ones. Every time I cam up on 6 or the next multiple I'd clap.
I would try my strategy with bigger numbers because if the number was 50 and I had to get to 1000 it would be simple.
I kinda thought this problem was a little easy but took long and a lot of thinking.
Hey it is Tori Z from North math. For the first problem if you were to clap from 1 to 150 only clapping the numbers that end in either 6 or the multiples of 6 you would clap 34 times. I got my answer my making a list of the numbers 1 to 150 but when i got to the multiples or any number that ended in 6 i would put it in a differnent coloum so that way I would know how many times to clap.
Another way of solving this problem is having a recorder and a clapper and then while 1 person is capping the other is keeping tally of how many times they clap.
No I would not use this strategy if the numbers were much larger because I think that it would take too long to do.
I really dont have any other thoughts about this problem.
The answer to the second problem is 7 days. i got this answer by making a calender type thing. Then i colored in every 5 consecutive days pink and the 6th day blue.
Im sure that there are other ways of solving this problem but i could not find it.
Yes i would use this stategy if the numbers were much larger because this way was very efficient for my i found it simple and easy.I think that this problem could have been worded differently.
Taa Taa for now, tori
Leah Medeiros
North
Problem #1
Answer; 34 claps
I wrote out the numbers from 1-150 on grid paper. And I circled all the numbers that are multiples of 6. Then I went back to number 1 and circled all the numbers that end with 6 that weren’t already circled. When I finished circling I counted how many circled numbers there were in all and received a total of 34 circled numbers, therefore if you were to clap every time a multiple of 6 or a number ending with 6 was said while counting to 150, you would clap 34 times total.
Another way to solve this problem is to act it out. Count to 150 and clap whenever a multiple of 6 or a number ending with 6 is said, and have someone mark down on paper whenever you clap. Then count the number of tallies.
If the numbers were larger, I would still be willing to use this method. I would because having a visual view of the problem and my work, makes it easier for me to solve it.
My additional thoughts on this problem is that making a number grid was the most helpful strategy in my opinion.
Problem #2
Answer; 42 days
I sort of used a chart for #2 as well, I used the calendar in my agenda and started to count on Monday. I counted 5 days then stared the 6th, I repeated this until I got a star on a Sunday. It took 42 days until the driver got another Sunday off.
I don’t think there’s another strategy that will work well for this problem. Counting and marking days on paper is the best way.
If the numbers were larger I still would be willing to use this strategy. As I said before, I like to be able to have a visual view of the problem and my work.
My additional thoughts are that this problem was some what similar to the first and because I used “charts” of some sort to solve the problems,they weren’t very challenging.
Leah Medeiros
North
Problem #1
Answer; 34 claps
I wrote out the numbers from 1-150 on grid paper. And I circled all the numbers that are multiples of 6. Then I went back to number 1 and circled all the numbers that end with 6 that weren’t already circled. When I finished circling I counted how many circled numbers there were in all and received a total of 34 circled numbers, therefore if you were to clap every time a multiple of 6 or a number ending with 6 was said while counting to 150, you would clap 34 times total.
Another way to solve this problem is to act it out. Count to 150 and clap whenever a multiple of 6 or a number ending with 6 is said, and have someone mark down on paper whenever you clap. Then count the number of tallies.
If the numbers were larger, I would still be willing to use this method. I would because having a visual view of the problem and my work, makes it easier for me to solve it.
My additional thoughts on this problem is that making a number grid was the most helpful strategy in my opinion.
Problem #2
Answer; 42 days
I sort of used a chart for #2 as well, I used the calendar in my agenda and started to count on Monday. I counted 5 days then stared the 6th, I repeated this until I got a star on a Sunday. It took 42 days until the driver got another Sunday off.
I don’t think there’s another strategy that will work well for this problem. Counting and marking days on paper is the best way.
If the numbers were larger I still would be willing to use this strategy. As I said before, I like to be able to have a visual view of the problem and my work.
My additional thoughts are that this problem was some what similar to the first and because I used “charts” of some sort to solve the problems,they weren’t very challenging.
Jared Faria
Question 1) the answer is 35 times that you would clap. the method that i used for this problem was an organized list. when ever there was a multiple of six and a number with last digit as six in each i would right down on the list. another way that you could do this problem is by using people to clap every time that I said a multiple of six or a number with the last digit of six. I would use this method even if the numbers were larger because it was an easy method.
Question 2) The answer is 42 days until he would have another sunday off again. The method that I used for this problem was also an organized list. I wrote down a bunch off the days until I felt like there was enough then I crossed out each day five times then left the sixth day off. Another method that I would use is to use a table and write down that information in the table. I would continue to use this method even with larger numbers because it was an easy one to use.
Sam Campanella~North
1. 134 times
2. 40 days
I used a table and chart to figure out my problem. There is another way to solve the problem. I would be willing to use the same strategy. i enjoyed the problems.
Sarah Ricks North Math
Blog
Problem 1 My answer to problem one was 35 times. The first thing I did was write out all the multiples of 6, from 6 to 150. Then, on a sheet of paper, I counted from 6 to 150, and tallied all the times I got to a factor of 6 or a number that ended in 6. Another way I could have done this problem was act it out. I could have had my mom and my sister stand next to me as I counted. Every time they clapped, my dad could write it down. I would use the same method I used to answer the same problem with bigger numbers. With that strategy, I could just skip the numbers that I don’t necessarily need to count.
Problem 2 My answer for problem 2 was 34 days. To answer problem two, I drew a chart. I drew at the top the days of the week, like a calendar without the dates. I drew circles in the days he had work off, and crosses when he was working. It was almost 7 weeks, before he got a Sunday off again. Instead of this strategy, I could have tallied all the days he worked, and then tallied all the days he had off until I got to a Sunday. I would use my original strategy to answer the same problem with bigger numbers, because after finding how many days it took him to get the next Sunday off, I would then be able to use my past work to figure out the answer easier.
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