Please find the latest POTW questions and solutions below. There is some great patterning practice in there.
POTW #21 Gr 8 Solution:
POTW #21 Gr. 7 Solution:
POTW #22 Gr. 8 Question:
POTW #22 Question (do the extension, too!):
Thursday, February 21, 2019
POTW #22 - Great Caribou Scores!
Great job on the latest Caribou everyone. Special shout-out to Seayrohn for finishing tops in the school, again!
Please find the latest POTW questions and solutions below. There is some great patterning practice in there.
POTW #21 Gr 8 Solution:
POTW #21 Gr. 7 Solution:
POTW #22 Gr. 8 Question:
POTW #22 Question (do the extension, too!):
Please find the latest POTW questions and solutions below. There is some great patterning practice in there.
POTW #21 Gr 8 Solution:
POTW #21 Gr. 7 Solution:
POTW #22 Gr. 8 Question:
POTW #22 Question (do the extension, too!):
Subscribe to:
Post Comments (Atom)
The gr 7 question: This one is pretty easy, I basically just calculate each year's numbers and then average them.
ReplyDeleteY1:
100-25=75
75*2=150
Y2:
150-25=125
125*2=250
Y3:
250-25=225
225*2=450
Y4:
450-25=425
425*2=850
Now, I just average it out.
850-100=750 (# employees that company hired)
750/4=187.5
So the company gained an average of 187.5 employees every year
New phone who 'dis?
DeleteGrade 8 POTW:
ReplyDelete(I’m going…. bananas)
Anyways….
Since it takes 3 seconds to from a maple to another tree and vice versa, and only 2 seconds to swing from a pine to a palm, it would be ideal to skip over the maple as many times as possible. And since it takes 7 seconds to swing between two pines and two pam without the maple, we would have to swing to the maple at least once to avoid wasting the monkey’s time.
In the PQSRTRP sequence, we can see that there is a “RTR” near the end of the sequence. This would mean that the monkey is swinging back and forth from one tree, to another and back to that same tree. It would be ideal for these two trees to not be a maple, therefore reducing the total time.
Since swinging to and from the maple tree would cost a total of 6 seconds and is necessary or else, more time would be wasted, we know that the minimum time would involve 3*2 = 6. Then, four other swings would happen between the pine and palms, causing a minimum time of 14 seconds.
Going back to the “RTR”, we know that R cannot be the maple tree because it would involve much more swings towards the maple than necessary. This would take too much time, logistically.
And if the maple were Q, it would involve a long distance travel between two opposing trees, which would add an extra 7 seconds to the clock. This wouldn’t work either, logistically.
This means that….
Therefore, the maple tree can only have Pananas (P), Sananas (S) and Tananas (T)
Yes Fiona! You know as they say, a Tanana a day keeps the doctor away.
DeleteI posted my answer for the other POTW, the one about the company. Did it not go through, or...
Delete....or....did Mr. Milette have an oopsie. I posted it now, thanks Fiona.
DeleteOther question that does not have a grade-specific number:
ReplyDeleteWhat I’m understanding is that after each year, 25 employees say “nope, I’m outta here” and to get back at them, the company grows in size depending on the number of employees that are still loyal to the company and don’t just leave randomly.
So, for the zeroth term, we would have:
0 years = 100
This would be the starting number of employees. The pattern would continue
0 years = 100
1 year = (100-25) x 2 = 150
2 years = (150-25) x 2 = 250
3 years = 450
4 years = 850
As for the average, we can take the ending number (850), subtract the 100 to give us 750, then divide by 4. This gives us 187.5.
Therefore, there will be 850 employees and they hire an average of 187.5 members per year,
AHHH, AFTER 10 MINUTES OF FINDING THE ALGEBRAIC EXPRESSION TO GET OUTPUT FROM INPUT, I FINALLY GOT ITTT.
So, let’s say we want to find the nth term, we basically have to apply the (100-25) x 2 n number of times. This gives us:
n x ((100-25) x 2), which simplifies to n((100-25) x 2).
Yay, time to do the extension.
EXTENSION
- Finding 10th term
n((100-25) x 2)
=10((100-25) x 2))
=10 (75 x 2)
=10 (150)
= 1500
Therefore, they will be a bigger company and have 1500 employees. Now, the ones who left regret their decision.
This formula only works for year 1. Every other year results in a totally different answer including the tenth year.
DeleteWell... then I found a formula for year one :)
DeleteGrade 7 POTW
ReplyDeleteIn order to solve this POTW, I will have to subtract the number of employees retiring and multiply the employees left by 2 for each year. I will start with the first year.
Year 1:
100-25=75 75x2=150 employees +75 employees
Year 2: 150-25=125 125x2=250 +125 employees
Year 3: 250-25=225 225x2=450 +225 employees
Year 4 450-25=425 425x2=850 +425 employees
Now, I will have to add all of the new employees for each year and divide by the number of years to find the average.
75+125+225+425=850 employees 850/4=212.5
The company gained an average of 212.5 employees every year.
Extension:
Year 4: 425
Year 5: 825
Year 6: 1,625
Year 7: 3,225
Year 8: 6,425
Year 9: 12,825
Year 10: 25,625 x2=51,250
The company will have 51,250 new employees by the end of the tenth year
For the garde 7 question the avarage growth per year was 187.5. Calculations below.
ReplyDelete2018: 100-25+75=150 Growth: 50
2019: 150-25+125=250 Growth: 100
2020: 250-25+225=450 Growth: 200
2021: 450-25+425=850 Growth: 400
Growth total = 750
750/4= 187.5
The growth from each year added together (50+100+200+400) is 750. 750 divided by 4 (because 4 years) is 187.5 The average growth for each year is 187.5
We can represent the business growth as a pattern. The pattern rule:
ReplyDeleteStart at 100, subtract 25, then multiply by 2 each time.
Repeating this process 4 times,
100-25=75 75*2=150 growth=50
150-25=125 125*2=250 growth=100
250-25=225 225*2=450 growth=200
450-25=425 425*2=850 growth=400
At this point, a pattern has become apparent. The company grows by 50*(2^x) every term. We can use this to find the tenth term by adding up the growth and by adding 100 to it.
50+100+200+400+800+1600+3200+100=6450 people by the tenth year.
To find the average of the company growth, we divide 50+100+200+400 by 4.
(50+100+200+400)/4= 750/4 = 187.5.
Therefore, the company will grow by an average of 187.5 people each year, and will reach a total of 6450 people by the last year.
Grade 8 POTW
ReplyDeleteOkay, so we have 1 maple tree, 2 pine trees, and 2 palm trees. We also have bananas P, Q, R, S, and T. Each are equal in terms of time to eat it. Each tree also has only one type of banana. From maple to any tree and vice versa is 3 seconds. From pine to palm and vice versa is 2 seconds. From pine to pine or palm to palm is 7 seconds. First, we know that swinging from one tree to the same tree takes 7 seconds, so it is better to try to not do this. We also know that traveling to or from a maple would take 3 seconds, and since we are trying to get the minimum time, we should try not to do this too many times either. In that case, we should try going from pine to palm and vice versa as much as possible.
The order is P,Q,S,R,T,R,P. Each letter is present here, so we know that the monkey has to swing to a maple tree, and off a maple tree. We know it must be both ways as even if the maple is a P, the sequence starts and ends with it. For every other swing, we can just go from palm to pine or vice versa and not get an extra seven seconds. In this case, the minimum time must be at least: 2(3) + 4(2) = 6 + 8 = 14 seconds.
Now we can try performing the route for each possible maple banana. Note, it doesn't matter too much of which type of tree (other than maple) has which banana type as long as it doesn't involve going into the same tree (7 seconds instead of 2).
These are just examples of a possible sequence that may work. No two letters next to each other can be the same tree type.
Maple Banana P: WORKS
3 + 2 + 2 + 2 + 2 + 3 = 14
P Maple
Q Pine
R Pine
S Palm
T Palm
Maple Banana Q: DOESN'T WORK
There is no possible way to have any two bananas not to be the same type causing an extra 7 seconds instead.
3 + 3 + 2 + 7 + 7 + 2 = 24
P Palm
Q Maple
R Pine
S Palm
T Pine
Maple Banana R: DOESN'T WORK
There is no way to stop 4 3 second swings.
2 + 2 + 3 + 3 + 3 + 3 = 16
P Palm
Q Pine
R Maple
S Palm
T Pine
Maple Banana S: WORKS
2 + 3 + 3 + 2 + 2 + 2 = 14
P Palm
Q Pine
R Pine
S Maple
T Palm
Maple Banana T: WORKS
2 + 2 + 2 + 3 + 3 + 2 = 14
P Palm
Q Pine
R Pine
S Palm
T Maple
Therefore, the maple tree can be a P, S, or T so the monkey can swing for the least amount of time.
Grade 7 POTW
ReplyDeleteI will just go straight into the math.
Year 0: 100
Year 1: 2(100 - 25) - 25 = 200 - 50 = 150
Year 2: 2(2(100 - 25) - 25) = 2(200 - 50 - 25) = 400 - 100 - 50 = 250
Year 3: 2(2(2(100 - 25) - 25) - 25) = 2(2(200 - 50 - 25) - 25) = 2(400 - 100 - 50 - 25) =
800 - 200 - 100 - 50 = 450
Year 4: 2(2(2(2(100 - 25) - 25) - 25) - 25) = 2(2(2(200 - 50 - 25) - 25) - 25) =
2(2(400 - 100 - 50 - 25) - 25) = 2(800 - 200 - 100 - 50 - 25) = 1600 - 400 - 200 - 100 - 50 = 850
A faster way to solve for the value with any year is with the equation (2^x)50 + 50 = y where x is the year and y is the number of employees.
Now we can find the average (mean). We just need to subtract the end amount by the original amount or 850 - 100 = 750. This is the total growth. 750/4 (4 years) = 187.5 people.
Therefore, the average growth was 187.5 people.
Extension:
We can just use the formula from before:
(2^x)50 + 50 = y
(2^10)50 + 50 = (1024)50 + 50 = 51200 + 50 = 51250
Therefore, there will be 51250 employees after the tenth year.
POTW:
ReplyDeleteTo determine average number the employees grow by each year, we...
We know that after each year 25 employees leave, and are then replaced by 25 employees.
To solve this problem, we would subtract 25 (employees leaving) and multiply the remaining employees by two to recieve total amount per year.
1: 100 - 25 = 75, 75 x 2 = 150..... 150 - 100 = 50
2: 150 - 25 = 125, 125 x 2 = 250.... 250 - 150 = 100
3: 250 - 25 = 225, 225 x 2 = 450..... 450 - 250 = 200
4: 450 - 25 = 425, 425 x 2 = 850..... 850 - 450 = 400
(50 + 100 + 200 + 400) / 4 = 187.5
187.5 is the average growth.
10th Year: 50, 100, 200, 400, 800, 1600, 3200, 6400, 12800, 25600, 51200.
There will be 51200 employees after 10 years.
(I just followed the pattern rule, multiply the previous term by 2).