I liked the comments about hoping to keep the POTW going. All we need is a few people to keep rolling with it each week and as you do, convince and remind others too.
POTW #20 Solution:
POTW #21 Gr. 7 Question:
POTW Gr. 8 Question:
Thursday, February 14, 2019
POTW #21 - Happy Valentine's Day
Happy Valentine's Day to those who are celebrating. The Gr. 7 question will be our last Measurement-specific POTW for the unit and we will start with more algebraic, patterning, using variables-type-questions next week.
I liked the comments about hoping to keep the POTW going. All we need is a few people to keep rolling with it each week and as you do, convince and remind others too.
POTW #20 Solution:
POTW #21 Gr. 7 Question:
POTW Gr. 8 Question:
I liked the comments about hoping to keep the POTW going. All we need is a few people to keep rolling with it each week and as you do, convince and remind others too.
POTW #20 Solution:
POTW #21 Gr. 7 Question:
POTW Gr. 8 Question:
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Try to solve both questions algebraically too
ReplyDeleteGrade 8 POTW:
ReplyDeleteSo, we can see that there are 6 numbers given in ratio format and only 5 ticket colours. This means that one of the colours would be overlapping both equations, and look here, green is shown as a ratio of 2 in relation to blue and red , and 1 in relation to yellow and orange. This means the following:
Since b:g:r = 1:2:4
And g:y:o = 1:3:6,
Then, y:o in relation to b:r is…
b:g:r:y:o = 1:2:4:6:12
So,
x+2x+4x+6x+12x = 400
25x = 400
x = 16
(x = blue)
(2x = green)
(4x = red)
(6x = yellow)
(12x = orange)
Red = 4x = 16 x 4 = 64
Blue = 16
Green = 2x = 2 x 16 = 32
Yellow = 6x = 6 x 16 = 96
Orange = 12x =12 x 16 = 192
Check:
64+16+32+96+192 = 400
Therefore, there are 64 red tickets, 16 blues, 32 green, 96 yellow and 192 oranges.
Grade 7 POTW:
ReplyDeleteSince this container does not have any other open areas to expand, the only way the water can expand is going upwards, this means that the water will expand in area, upwards.
Just to make sure that the height will indeed increase by 10% and it isn’t just the area, I plugged in 10 as a possible height and multiply it by 99 (9 x 11). Then, I increased this area by 10% (99) and got to 1089. Then, I divided this area by 99 and got 11. This 11 is the new height. The height does grow by 10%, and it isn’t just the area.
Algebraically, we can form this equation:
Let x be the height of the water before freezing.
1.1x = 38.5
x = 38.5/1.1
x = 35
Therefore, the height must be 35 cm before freezing so that the ice does not overflow.
(I don’t mean to be THAT person, but did I do something wrong? This seems too…. straight-forwards)
Do you mean straightforward? Misdisirregardless, I think you may have done it last year.
DeleteAhhhh, I think my "sticky notes" may have autocorrected to "straight-forwards". Or I just can't spell. c:
DeleteCan't spell...yet, Fiona. Yet.
DeleteHi.
ReplyDeleteGr. 8 Question:
So this one was easy, I just combined the ratios, so I ended up with the ratio of (Blue:Green:Red:Yellow:Orange) 1:2:4:6:12 I added those values up and I got 25. Now I divide the total number of tickets (400) by 25, and I got 16.
So now I just multiply the values of of the original ratio by 16. I got the ratio of (Blue:Green:Red:Yellow:Orange) 16:32:64:96:192. To double check I added those values up and I got 400.
Hi.
ReplyDeleteGr.7 Question:
So I tried to make an algebraic expression, so I came up with this:
n (volume of water that we need to fill)
n=9*11*38.5*(10/11)
9*11*38.5 is the total volume of the container
the 10/11 is to make sure when it freezes, the container doesn't leak or explode (11 is 110% of 10).
Now to solve:
n=99*38.5*(10/11)
n=3811.5*(0.909090909)
n=3465
Now the question asks for the height of the content, so I just divide it by the area of the base.
So the height of the contents should be 35 cm tall at max.
ReplyDeleteIf it increases by 10%, it will be 110% when frozen. You can divide it by 11 and multiply the quotient by 10 to find the original height of the water.
38.5/11x10=35cm
3.5x10=35cm
It can be filled to 35cm without it overflowing.
Maruti
Grade 8 POTW
ReplyDeleteThere are 400 tickets. The ratio of blue:green:red is 1:2:4. The ratio of green:yellow:orange is 1:3:6. If green is 2 in the previous ratio, then yellow would be 3 x 2 = 6 and orange would be 6 x 2 = 12 in the first ratio. In other words the ratio of blue:green:red:yellow:orange is 1:2:4:6:12. 1 + 2 + 4 + 6 + 12 = 25. 400/25 = 16.
Now we just need to multiply each color by 16 to get the number of that color.
Blue: 1 x 16 = 16
Green: 2 x 16 = 32
Red: 4 x 16 = 64
Yellow: 6 x 16 = 96
Orange: 12 x 16 = 192
Therefore, the number of tickets for each color is 16 blue, 32 green, 64 red, 96 yellow, and 192 orange.
Just in case, we can add them all and see if we get 400:
16 + 32 + 64 + 96 + 192 = 400
which we do.
Grade 7 POTW
ReplyDeleteWe know that the water expands by 10% when froze. To determine the maximum height, we can just find out how much water there is before that 10% was added (divide by 1.1). However, due to the fact that we are just solving for the height and not the volume and the base area is consistent, we just need to divide the height by 1.1 and not find out the amount of water.
38.5/1.1 = 35
The container can be filled up to 35cm so that when frozen, the ice would not go above the top of the container.
POTW:
ReplyDeleteAfter the water freezes, it increases by %10. So after freezing, the depth will be 110% of the height.
38. 5 / 1.1 = 35 cm.