Dots can be arranged to form diamonds. Here are the first three diamond patterns.
A. Make a drawing of the next diamond pattern. Hand that in the basket for me to look at. 1 pt.
B. How many dots will be in the sixth diamond pattern? 1 pt
C. Make a table with data up to and including diamond 6 and hand that in with your drawing. 1 pt
D. Could a diamond pattern have 70 dots? Explain why or why not. 2 pts
E. How many dots would be in the nth diamond pattern? Clearly explain your process. 2 pts
53 comments:
B. The 6th diamond pattern would have 24 dots in it.
D. There could not be 70 dots because it goes up bye 4 each time and 4 does not go into 70 so no.
E.36 dots because if u take 4 times 9 you get 36 and in the problem it goes up by 4 each time so if you add 4 each time 9 times then you would get 36.
B. there are 24 dots in the 6th diamond
D. there can't be a diamong with 70 because 4 does't go into 70
E. in the n you would multiple it by 4 then the number you get would be the number of dots n x 4 = dots
B. There will be 24 dots in the sixth diamond pattern. D. No because for each pattern you add 4 more dots and 4 plus 4 plus 4 and so on. It will never equal or add up to 70. E. I don't really know how to understand this one. So I am going to put that you take the number of the problem and multiply that by 4 and you will get your answer. For example pattern number 10 will have 40 dots because you add 4 each time the pattern increases by one.
A: in the basket
B: 24 dots
C: also in the basket
D: No because all of the diamonds add 4 dots to it so if you divide 4 into 70 it would come out unevenly so, no you can't have 70 dots in a triangle.
E: in the 9th triangle there would be 36 dots cause like i said before each triangle contains 4 dots so if you multiply 9 and 4 you would get the product of 36 dots.
9 would have 41 dots. For 70 dots it wouldn't be posable because if you add it it woiuld be 1 off of 70.
b. there would be 24 dots, becuase if you take 4 x 6 =24
d. No, because 4 cannot go into 70 so it would be uneven.
e.You would take 4, because thats the number in the 1st pattern and take it times the number step you would get your answer
a. In the basket
b. 20
c. in the basket
d. no, because 20 doesn't go into 70 evenly.
e. 4(n)
B. 7x4=28 dots
D. No, because a diamond is a sqaure except turned. So you twould take 4 divided by 9 and you get an uneven number.
E. 13x4=54 You just take 13x 4
B. 24
D. No b/c seventy doesn't go into four evenly and I figured out it needed to go into four to be as dimondb/c there is 4 sides
E. I dont get it
B. the 6th one will have 24 dots.
D.No 4 doesn't go in to 4.
E.nx4 because n= number of steps.
D.no because it isn't a root of something.
E.100,because you take 10x10=100
B. 24dots in the sixth dimond
D. no because you can not divide 70/4 and that is what you need to do so you can get a dimond.
E. 37 dots will be in the ninth diamond because all you do is to add 4 form 6 then from 7 then from 8 and you would get 37.
B. 24
D. no because 4 doesnt go into 70
E. in the nineth prosess there would be 36 because if you multiply 4 and nine you would get 36 dots
D. No, a dimond pattern couldn't have 70 dots because if you take 70/4, 4 doesn't go into 70. For this pattern it is increasing by 4 dots everytime so, no a dimond pattern could not have 70 dots.
E. 36 dots would be in the 9th pattern because if you multipy 9 (# of dimonds) x 4 (which is how much it is increasing everytime)you will get your answer, 36 dots for the 9th dimond pattern.
B. 24
D. Yes, because you go up by adding four dots each time, so therefor, you just keep adding 4 until you get 70.
E. 36, because at 6 you had 24, and you add four 3 more times.
there would be 24 in 6th
and no you cant make one with 70 because it is going by 4s
and say if the number 12 diamond you have to take that times four to get the answer
B.28 dots in the sixth pattern
D.No it would not work because 70 can not be divided into 4 sides evenly
E. What I do is I mulitpiy the step and add 4 more dots to to it.
B.) There will be 24 dots in the sixth diamond.
D.) No because 70 divided by 4=17.5.
E.)Every time you want a new diamond you add 4 dots. So 9x4=36,or 4+4+4+4+4+4+4+4+4=36
or 9+9+9+9=36
B.) There will be 24 dots in the sixth diamond.
D.) No because 70 divided by 4=17.5.
E.)Every time you want a new diamond you add 4 dots. So 9x4=36,or 4+4+4+4+4+4+4+4+4=36
or 9+9+9+9=36
20 dots will be in the sixth pattern.
since each corner shares the fifth diamond and so on you minus 4 because they all share the fifth diamond. So you can take the 6th daimond and multiple 6 times 4 because of the four sides, and you get 24, so you take 24-4 and = 20.
YOu do the same thing for all the other ones
B.26
D.No, nomatter how many dots you use on each side each side has to be the same and there are 4 sides in a diamond and the sides must add up to 70 and 70 can't be divided by 4.
E.there would be 34 dots I made a model on the other piece of paper I handed in.
24 will be in the 6tyh diamond because 6 times 4 equals 24. No ther can not be 70 dots because 70 divided by 4 does not come out evenly. 36 in the nineth because 9 times 4 equals 36. you just multiply 4 each time.
b.24 would be in pattern sixth.
d. no it could not because it would go to 72 NOT 70.
e.36 because you add four each time so 9x4=36
A. In basket.
B. 24 dots.
C. In basket.
D. Yes because if you add 4 each time you will eventually get 70 dots.
E. 40 dots because if the 1 pattern has 4 dots and the 2 pattern has 8 dots then you keep adding 4. The 8 pattern has 34 dots then the 9 pattern has 40 dots.
A. On paper
B. 21 dots
C. On paper
D. No you cant. Because if you took 70 minus four( The sides and top dots) and divide that number b four, and you cant divide 66 by 4 evenly.
D. Okay, you take 9 times four and get 36. Then you take 36 minus four because of the top and side dots. and you get 32, then divide that by four for the sides, and that gives you your side lenghths.
yes you can have 70 dots cuz it the number is 17 and the
yes there is a patern in the dots in the problem
for the 6 one will be 28
20 IN 6 TH DIAMOND
YES
33 IN TH NINTH
B. 24 dots
D. No, because 70 cannot be divided by 4 without having a remainder.
E. Formula-d*4=n
d=diamond n=dots
The diamond number times four equals the total number of dots it will take to build the diamond.
A.)[on paper]
B.) 24 dots
C.)[on paper]
D.) No. Because on the ninth step there is 44 dots so in 5 more diamond steps there would be 64 dots and if you add four for the next diamond there would be 68 dots so you can't make 70 because the next number would be 72 dots.
E.) 44 dots because with each pattern they add 1 more dot to each side so is there is 24 on the forth diamond pattern then you just add 20 because 5 x 4 = 20 (the five would be the difference between diamond 4 & 9. The four because a diamond has four sides.)
In the sixth diamond there will be 24 dots.
No becasue there are only even number amounr of dots in the diamond.
There is 40 dots in the tenth didamond, becasue 10 x 49 = 40.
36 in the ninth because you add 4 every time.
A. 16 dots.
B. 24 dots.
C. keeps adding 4.
D. No, because if you keep adding 4 you do not come up with 70, you get either 68 or 72.
E. just keep adding 4 on to the next number.
B)25 dots
D)yes, because 70 can go into 5 evenly
B.20
D.it wouldnt work cause the number needs to be even
E.I don't know
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a.^
1/4
2/8
3/12
4/16
5/20
6/24
c.^
~32 dot in the the 6th diamonds
~no beacuase 70 isnt divisible by 4
b.24
D.no, because it has to be a multible of 4
E. 36, because 9 times 4 = 6
~ the 6th diamond will have 32 dots
~ no beacuase 70 isnt divisible by 4
B. There would be 24 dots.
D. No there could not be 70 dots in a diamond becuase every new diamond they add 4 more dots, and 4 does not go into 70.
E. There would be 36 dots. I used a table to find out the ninth diamond. Every new diamond they add four dots.
B) 20 dots
D) NO the number of dots must be divisible by 4 and 70 isn't
E) you would go step times 4 and that would give you the number of dots
B.-24 dots will be in the diamond.
D.- No because it will make a giant circle.
E.- I don't know I'm not good at expressions I don't get how to do expressions.
B)24 dots
D)becsuse the number of dots as to be a multipule of 4
E)you multiply the number of the dimond by 4
b.) 24 dots
d.) no it could not have 70 dots because each time you go up by 4 and 4 can't go into 70 evenly.
e.)take your number of the pattern like i'll call that "a" and the expression would be a x 4 = the number of dots you would have for that pattern.
B. 24
D.no bacause 4 does not go into 70 evenly and 4 has to be able to go into it because each time you add 4 to the diamond.
E. 4x or the number times four
B)I think in sixth diamond will 24 dots
D- No because you add 4 dots to each dimond. 4 does not go into 70.
E- there would be 36 dots. you add 4 dots each time.
b. 24
d. yes but it would be a big dimond.
e. first you add one triangle and you add 4 dots for example 9th triangle = 36 dots.
B.24 dots
D.No, because each diamond adds 4 dots on to it so 70 is a odd number and that is why it doesn't work.
E.36 dots, because you take the diamond number times 4
B. 24 dots
D. No. Two of the sides would be inequal to the rest.
E. Each step, a dot is added to each side of the diamond which makes 4 more dots each step.
B. 24 dots
D.No, 4 wont go evenly into 70
E. N(4)You multiply it by 4 because thats how the pattern is
B. 22dots
D.no, because you would can't use half dots other wise you would have 17.5 dots in a line.
E.16 b/c it is an evan # and ti will work.
B. 24 dots
D. No because when i looked at my chart that i made, i saw that every number of dots was divisible by 4. So then i took 70 and divided it by 70 and i got 17.5 and it is not a whole number so... their can not be a pattern with 70 dots.
E. i can not figure this one out but i tried my hardest but i just could not get the answer. :( :( :( :( :( :( :(
B. there would be 24 dots
D. no, because 70 i not divisible by 4
E. each time the pattern incerses by 4 so take four by n to equal the number of dots n*4
D. Answer- No, because it goes by 4, and 70 divided by 4 will not come out equally.
E. Answer- you would times it by 4 and then that would be your answer.
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