1) List three things in nature that understand how numbers work.
2) How many cubes were used to make the base of the pyramid built by Robert and the number devil?
3) Why does Robert tell the number devil, "It'll never be a pyramid."?
4) Which number does the triangles of numbers begin with?
5) How are the values for each cube calculated?
6) If you calculate the sum of each row, which type of numbers do you get?
7) Identify the numbers revealed along the diagonals of the multicolored triangle.
8) What happens when the number devil turns off the odd numbered cubes? Describe the diagram.
9) Compare and contrast the diagram with multiples of 2 and the diagram with the multiples of 5.
10) Using the diagram on page 146, predict what the triangle will look like with multiples of highlighted.
When answering questions in a post, be sure to answer them in complete sentences. In order to avoid echoing someone else's comment, each student will be required to answer one of the questions above. Utilize more of the questions, for more points. In class on Monday, students will share their posts and respond to at least one of the someone's response to a question. When answering a question, remember to expand your thinking and think of mathematical examples that will make your response richer.
Your task this week is to choose one of the following questions and post an intelligent response. I have extended the deadline to next Monday, December 21st. We will continue our discussion at this time. Use the bookmark to help guide your comments. Then continue reading through Chapter 8.
Let's get reacquainted with important parts of the rubric. Follow this rubric to achieve the highest scores possible.
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Ideas & Content
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The student expresses some original ideas. The majority of ideas are related to the subject matter.
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The student has many original ideas and expresses them clearly. The great majority of ideas are related to the subject matter. Student makes connections to real-world situations and prior mathematical concepts learned.
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Commenting
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Student offers constructive comments and/or asks questions that provide assistance in reaching the solution of the problem.
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Student offers constructive comments and/or asks questions of at least two classmates that clarify the problem solving process and/or provides assistance in reaching the solution of the problem with examples and counter examples.
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Writing Quality
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Posts show above average writing style.
The content demonstrates that the student reads moderately, and attempts to synthesize information and form new meaning.
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Posts are well written, and are characterized by elements of a strong writing style. The content demonstrates that the student is well read, synthesizes learned content and constructs new meaning.
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Mathematical
Communication
Clarity of
Explanation
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There is a clear
explanation.
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There is a clear, effective explanation detailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made.
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Mathematical
Communication
Representation
(when appropriate
or required)
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There is appropriate
use of accurate mathematical
representation.
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Mathematical representation is actively used as a means of communicating ideas related to the solution of the problem.
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Writing Conventions
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There is one spelling or
grammatical error in the explanation or comments.
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There are no spelling or grammatical
errors in either explanation or comments.
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In nature many things understand how numbers work and they use them. The three things that are mentioned are rabbits, trees, and tigers. All animals use math when they reproduce and make babies. They also make a certain amount of babies in a certain amount of months. So that is another form of math that they will use. In the book they use the example of rabbits and there reproduction. In two months rabbits make two babies. Then they make two more babies in two more months. Then the first babies have babies and they will have a grandchild. This is how nature uses math.
ReplyDeleteI like how you mentioned something from the last chapter. It shows that you're actually comprehending, what you're reading. Can you come up with your own examples of things in nature that understand numbers and how they work?
DeleteI agree and I complement the way you described the the example but you didn't list the other examples only rabbits,so try elaborating on the trees and tiger idea
DeleteI agree with Ibrahim and I would like to point out is that you should use the outside resources Ms. Brown gave us in class like the starfish. Another thing I would like to pint out is what does the continuous reproduction of rabbits mean in the math world. You could elaborate a little more.
DeleteThere were some good aspects in your response such as using the last chapter as your preference but I would like to add on what you said earlier how to the numbers and the pyramids relate to math.
DeleteI like the way you stated your claim and used direct evidence from the last chapter to support this new question.
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Delete3) Why does Robert tell the number devil, "It'll never be a pyramid."?
ReplyDeleteRobert tells the number devil it'll never be a pyramid because the figure was not triangular or rectangular at the base. I know this because on page 128 it says "but it'll never be a pyramid. Pyramids are triangular or rectangular at the base, and this things is flat.It won't be a pyramid, but it can be a triangle. This is Robert making a educated guess about the figure. In math you constantly do this. Making educated guesses helps you understand the problem, because it helps you point out the essential parts of the question you're trying to answer. This is because when your're making an educated guess you need information from what you're trying to predict and you need background knowledge. In order to get that information, you need to find it in the problem. Making a prediction or educated guess is an important tool, that is used in your daily classroom.
I liked how you include a example and explained it also how you connected to the real world
DeleteI complement the way you responded to the question with evidence but I think when you were discussing about educated guesses you should've gone back and explain how it related Robert's claim. Like what background knowledge did he use.
DeleteI loved how you gave an example and how it relates to the question your answering. Great,great answer Vianny.
DeleteI would like to add on that a triangle and a pyramid are 2 different dimensions. Triangles are 2-D figures, and pyramids are 3-D figures.
DeleteAdding that information would make your answer stronger. But I still agree with everything you said.
DeleteI like the way you stated your answer, used background info for the book, good hook and the way you have an example to help people understand what you are trying to say better.
DeleteBut don't forget to get right to the point or else the reader might be tired or thrown off.
DeleteThe volume of a cube is found by multiplying the length of any edge by itself twice
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DeleteI think you have responded to the question yet you missed some pretty big key elements needed in a short response. You didn't have evidence to support your claim and you didn't explain your claim very well. This may get the readers confused.
DeleteYes. I agree with Maimouna because you answered how to calculate VOLUME instead of the VALUES of the cubes in the pyramid that the Number Devil and Robert built. Also, please use evidence to support your answer.
DeleteI agree with maimouna.Julio,however there is no evidence to support your claim. You cant just say something and not back it up.
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DeleteI agree with Luis. Without evidence the reader might not be sure about the question. You should add evidence so that the reader has a clear understanding of what you are writing about.
Deletei Agree with vianny lara beacause in the book number deveil it clarly said that the rectangular shape would never be a pyramid because the shape is not even triangular.Also that in page 128 it states that this shape would never be a pyramid because this shap has 4 sides and a pyramid has 3 sides. Another thing is that this figure can not be a pyrimad but it can probally be a triangle.
ReplyDeleteI like how you helped Vianny with the background information on why Robert said it could never be a pyramid. I think you can explain on what would happen if a pyramid had 4 sides.
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DeleteI agree,but try to be more specific and to come up with your own claims and ideas.
Delete1) In nature it is possible to understand numbers work and how they are used. In nature their are 3 things in the wild and their are rabbits trees and tigers. All animals make math when they reduce and has children. They also do math when they produce children in every month. In math their is a book that has math with examples of rabbits every time they reproduce. Also rabbits make math when they make two babies each month and when they make two more babies in two months.
ReplyDeleteThis is the same thing I told Lenny, I think that you should use some outside resources and also that you should give an example of how they reproduce and how that relates to mathematics. Challenge yourself more.
DeleteI would like to answer question number 2 which is How many cubes were used to make the base of the pyramid built by Robert and the number devil? The answer to the question is 17. In the book the number devil on page 127 it shows a picture of a row that Robert and the number devil both made together. This is how i know that the number at the end is 17.
ReplyDeleteYou should of include a detail but overall great work.
DeleteI think you answered the question but you didn't really elaborate on your explanation.
DeleteI agree with you Shishawna but I think that you could extend this answer by giving an example from previous chapters, or researched any information that you would like to share, that will really match your answer.
DeleteCan you tie this back to a real world situation?
DeleteI agree with you Shishawna, I also like the way you concluded/explained the context of where you found your information but would also like to ask that if there is an way for you to show your answer in a different way.
Delete4) Which number does the triangles of numbers begin with? Well according to the number Devil it states that " The number devil then climbed up one side of the triangle and wrote the number one on the top cube. "You and your ones," Robert muttered " Right", the number devil replied spiritedly. "Because in the end everything always goes back to one." This states how the number devil choose 1 to be the first number on the triangle .
ReplyDeleteI agree with you Mia but I think you should've went back to the fifth night and related this question to that to show your level of comprehension.
DeleteI agree with Maimouna. You should've gone back to the 5th night. But, I also agree with you Mia that the answer is 1. I would like to give an example from the previous chapter, the 5th night on page 93. This is something that I included in my response. When Robert threw the "coconuts" it started to form triangular numbers. But before he did this, he started with only 1 coconut. Another example is on page 146. The number on the very top of the triangular pyramid is 1.
DeleteSometimes you might not always find the answer in one chapter so try to go back and use the other chapters. It will strengten your claim. Try to compare and contrast your claim to other situations.
DeleteQuestion #7: Identify the numbers revealed along the diagonals of the multicolored triangle?
ReplyDeleteResponse:
The first diagonal with the red 1's I found out that as I went down it had 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,. It was all 1's. On the second diagonal starting with a blue 1's, as I went down I saw numbers such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16. The numbers started changing and this time it was going in sequence. As I reached the next diagonal with the red 1's on top once again I saw the numbers, 1, 3, 6, 10, 15, 21, 28, 36, 45, and........ These were triangle numbers, I know this because on pg 94 it states, "All right. But the first is no triangle at all. It's just a dot." "Or just a triangle that shrunk so small that all you can see of it is a dot." The second triangle has 3 coconuts, the third 6, the fourth 10.." This shows why these numbers are triangle numbers because they form triangles and as they increase, the digit that is being added is being increased by 1. To go on, on the next diagonal is 1, 4, 10, 20, 35, 56, and so on till the cows come home. At first I was confused about this particular set of numbers but after some research, "Tetrahedral numbers are the sum of consecutive triangular numbers." As you can see form the diagonals of the multicolored triangle is tthat each diagnal hold different patterns.
5
1
Row 5
1
6
15
20
15
6
1
Row 6
1
7
21
35
35
21
7
1
Row 7
1
8
28
56
70
56
28
8
1
Row 8
I agree with you Maimouna, and I like how you went back to a previous chapter to add on to your response
DeleteThank you for the comment.
DeleteCan you explain how you saw triangle numbers in the diagram.Was it because the entire diagram is a triangle?
DeleteIf you go look at the pyramid and you look at the cubes diagonally thats how I saw the triangle numbers on the third diagonal line. I think that because it was a triangle that contributed part of why there were triangle numbers in the diagram. Because triangle numbers make up triangles. But because the number on the cubes were being added up it allowed different patterns to show. I hope that answered your question.
DeletePlease excuse the thing below my response. Please ignore it.
ReplyDelete10) Using the diagram on page 146, predict what the triangle will look like with multiples of highlighted.
ReplyDeleteThe right side and left sides of the pyramid will always include 1, and the inside of the pyramid will never include the number "1" because it doesn't go with the pattern. I would like to give an example from the previous chapter on page 93. The model is also familiar to a "tetrahedral number", which is something I researched on google. A tetrahedral number, or triangular pyramidal number, is a figurative number that represents a pyramid with a triangular base and three sides, called a tetrahedron. Going back to the example, each dot or "coconut" adds 1 more increasing number of coconuts. So the pattern starts from 1, adding 2, which is 3. Then 3 adding 3 is 6, then 6 adding another 4 is 10. Notice, the amount of coconuts increases by 1 more number, making the pyramid bigger. If you look at the 3rd row of the pyramid at 2, you will see 3,4,5,6,7,8... on both left side and right side. This shows the increasing number of coconuts. Then everything else inside the coconut is a triangular number. I predict that the multiples of highlighted numbers are the number of "coconuts" being thrown, and the 1 is what we started off with. Everything else is the total amount of "coconuts" Robert has thrown.
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ReplyDeleteGood use of details.
DeleteBut you must not add irrelevant things. GET RIGHT TO THE POINT!
DeleteThe number of cubers Robert and the Number Devil used to make the base was 17 because on page #127-128 it said' "He took a few cubes and laid them out in a row along the floor...Stop! the number devil called out suddenly. How many cubes have we got now? Robert counted them up.Seventeen he said"
ReplyDeleteCan you explain more elaborately? I'm still a little confused.
DeleteInstead of only using the book try to make up your own solution to these questions.
DeleteWhen the number devil turned off the odd number the diagram had triangle after triangle but they were upside down. Each triangle had 1 cube above its middle, and 2 cubes 1 black cube away at the very bottom of each triangle.
ReplyDeleteI like your response but I think you should've added evidence to really make it stand out and make it stronger.
Deletethe number that the triangles of numbers starts with is 1.two ones to be exact and the it the side plus side equals middle of the pyramid
ReplyDeleteI liked how you answered the question but you have to put some evidence from the text. There is some good evidence on page 131.
DeleteActually I disagree with you David. I think you should go back to page 137. On the very top, there is a cube with the number 1 on it. So, it is not 2 ones. There is only one 1. So, I disagree based on the chart.
DeleteI also agree with Ndeye but liked your attempt on the problem. I would like to comment on how Ndeye corrected you that was very noble.
DeleteI agree with both of them but even if your answer was not accurate you still tried to add evidence. 😁Good Job!
DeleteI disagree with you David. It was one 1. Not TWO! also add EVIDENCE!! I also feel as if you don't understand what your saying. Clarify your answer.
DeleteThe triangle of numbers begins with the number 1. This is because as seen on page 137, the one cube on the top is 1. And then, there are 2 1s and then the next row has a 1, 2 3s, and another 1. To conclude, I know that the first number on the number pyramid is 1.
ReplyDeleteYes, I agree that the ones are the thing that start of the pyramid. But why isn't the top of the pyramid start with a 0. If 0 comes first than 1.
DeleteI would like to answer your question Jairo. The pyramid doesn't start with 0 because 0 is a forbidden number. If you look at pg 54 of the Number Devil it states, " O is forbidden." This show why 0 is forbidden thus why the pyramid should start with one not 0.
DeleteNdeye I think you should refer to the first few chapters and how we talked about 1's alot to help better support your response, thus making your claim stronger.
DeleteTry not to confuse with explaining the whole pyramid. Get right to the pattern. I still liked the way you used direct evidence.
DeleteThe pyramid is calculated with it`s the first positive value. It starts with a row of ones. Now when you add the ones you get two, two is below both of the ones. This pattern should keep going on as long as you keep on adding the two numbers together. If you look at it closely it looks like carrots going up instead of down. Between each pair of numbers there is a line that goes down. The number that the line goes to is the sum of the pair of number. For example, the ninth row of the pyramid has the numbers 1,8,28,56,70,56,28,8,1. The first pair is 1 and 8. If you add them you should get 9. 9 is right below. Another pair could be 70 and 56, you should get 126. If you look 126 is right below. You might question why do the numbers repeat themselves in a row. This happens because of the ones on the top and side of the pyramid.
ReplyDeleteI like how you you think out of the box.you come up with your own ideas.I like how creative you are. You make up your own strategies and you end up with the same answer but in a unique way. You really do live up as mathematician of the month.
DeleteGood way of thinking, I absolutely love your strategy I might even use it myself. Good job Jairo!
Deletethree thing in nature that humans,flower,tree because their pattern is goes in numbers
ReplyDeleteI believe you need to be more specific. What numbers? Hopping numbers, Bonacci numbers, or others? You should get specific details from a website to support.
DeleteI also agree with Ndeye and would like to add on what other things in nature deal with numbers and why they deal with numbers.
DeleteYou should be more specific. Ask yourself why are they the three things in nature. Add evidence to what are they used for,what they do.
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DeleteI saw a really cool pattern when you add up all of the numbers in a row in order. For example, the first row has a sum of 1. Then, the following row has a sum of 2. 2 is double 1. The next row has a sum of 4. And 4 is double 2. The row after that has a sum of 8. 8 is double 4. That pattern continues throughout the whole triangle. Basically, they are doubling. Because every rows sum is the prior rows sum to the second power. For example, the 6th row has a sum of 32. THE 7th row has a sum of 64. 32 doubled is 64.
ReplyDeleteI agree with you Ndeye, and I would also, like to say that i thought it was cool too, how the value of each row just HAPPENED to be double the value of the previous row.
DeleteThose are really cool observations. What I observe is that all these numbers are all different kinds of numbers if you go across diagonally. Like on the 4th diagonal ine I discovered that it wasn't a type of number said in the Number Devil Book. As I searched it up I realized the numbers 1, 4, 10, 20, 35 are all "Tetrahedral numbers are the sum of consecutive triangular numbers." I was able to learn something new and expand my horizons on math.
DeleteI agree and I too found that cool and interesting. Nobody so far explained that.
Delete7) If you were to calculate all the numbers in each row, you'd get an even number for every single row. To show this, here's some of the rows. 1+3+3+1=8.1+4+6+4+1=16. Now when you calculate some more rows you'll see EXACTLY what I mean.
ReplyDeleteCan you be more elaborate? Because you are answering the question not us.
DeleteI like how you brought about your claim by getting right to the point. Be more specific even though it was good. I believe you can strengthen your answer.
DeleteI actually have a question for YOU all. What is a faster way to get the sums of the rows on the pyramid Robert and the Number Devil made?
ReplyDeleteAlso, here's a little hint: you have to use a different operation that is not addition. I repeat is NOT addition.
DeleteI know! It is multiplication. You just multiply the prior's rows total by 2. For example, the 1st row has 1. Multiply by 2, and you get the total for the second row, since 1 x 2= 2. And so on. So, a faster way is to multiply by 2, or doubling the total.
DeleteThose are really good observations.
DeleteChris good question. It's good because you thought of it by yourself and you did it and tried to check it by asking us for our opinion.
Delete3) Why does Robert tell the number devil, "It'll never be a pyramid."?
ReplyDeleteAccording to page 128 of "the Number Devil" Robert tells the number devil that it will never be a pyramid because "Pyramids are triangular or rectangular at the base, and this thing is flat. It won't be a pyramid, but it can be a triangle." So instead of building a number pyramid, they built a number triangle.
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5) How are the values for each cube calculated?
According to page 130 of the book, you can calculate the value of each cube by, adding the value of the two cubes directly above it. "On each cube we'll write the sum of the cubes directly above it."
For example above a cube labeled "12,870", there are 2 cubes both labeled "6435", and 6435 + 6435 = 12,870.
I like how you answered two questions at once! The responses are amazing and the work and quotes you used were fantastic! Keep up the great responses!
DeleteI agree with Christopher but I thought that you could do more challenging questions because these seems way to easy for your type of level. So challenge yourself and your brain to better help yourself.
DeleteBut you did well explaining. Unlike anybody else you did 2 in one and did well in both of them. Even if it was easy you can be a row model to the people who need help with questions like this.
DeleteThe diagram with multiples of 2 and the diagram with multiples of 5 are similar. This is because they both have numbers that end in zero. for example, both diagrams have numbers such as 10, 210, and 560 lit up. On the other hand, the two diagrams are also different. This is because the 2 diagram also had numbers that ended in 2,4,6, and 8. The 5 diagram had only had numbers that ended in 5 besides 0. So, they do not share many of the same numbers because 2 is even and 5 is odd. These are the similarities and differences between the multiples of 2 diagram and the multiples of 5 diagram.
ReplyDeleteI like your response but how does this have anything to do with the Number Devil Book. How do they connect? Clarify your answer more.
DeleteTrue,your answer does not compute to any of the questions . But, you stated background information. Somebody might have a question about this in the future, so they can read this answer to help them. Good work. To conclude, people can use this response to strengthen the A answers to A+ answers.
Delete
ReplyDeleteFor the base of the pyramid it was 17 cubes for the base then the number devil said stop and 17 is unexciting number but if you subtract it by one you get 16. Sixteen is a hopping number. A two that's been made to hop 2 exponet 4. This means that if you times 4 by it's self you get 16 and not 17
Good use of information but elaborate on it and try to strengthen your response.
DeleteThe diagram of the multiples of 2 and the multiples of 5 are similar yet different. Both diagrams have triangles within them and don't start with 1.About the triangles,within them are triangle numbers (THE sum of the diagonal rows are triangles.) For example,you see the triangle (pg 141) below the 2.the sum of the 3rd row is 38 a triangular number.Also,with the 5 multiples 125 is a triangular number.The difference is the multiples that existed in the triangles.
ReplyDeleteI like how you fluently constructed your response and used interesting vocab to sound more mature.
DeleteYou cleary stated your claim and used accurate evidence to back it up.
DeleteBut still try to make it more understandable.
DeleteI have found a way to calculate triangular numbers. xn = n(n+1)/2. n is the number of the triangular sequence like if you want to find the fifth number. For example, x5= 5(5+1)/2 5+1 is 6 multiplied by 5 is 30 and half of it is 15.So,15 is the 5th number.
ReplyDeleteWhat does the +1 represent? What does the /2 mean? If you don't explain those simple things readers may not understand what you are trying to convey.
DeleteYou should be more specific and don't put signs. Put it in words. Some people might not even know what you are talking about.
DeleteI like your example, however you have to be more specific and explain your example more specific and clear.
DeleteThe number of triangles begin with is 1.In earlier chapters,we saw that 1 began the triangles with the coconuts,and we see in the diagrams the very top it is 1.
ReplyDeleteI agree with you Ibrahim and I would like to add on, for those who don't know why it does not start with 0 here is why. If you look back at previous chapters and go to page 54, "O is forbidden." Also you can't divide by 0 because you'll either end up with 0.000000....... or 00.0000000....... Therefore it is forbidden and that's why it can't start the number of triangles.
DeleteI agree with both of you and basically you can't use zero because you have nothing
DeleteThe three things are trees rabbits and tigers. They way of life animals have of giving birth is bascically a math problem in progress. In the number devil a pair of rabbits give birth to 2 babies every two months. In the next 2 months, it's another 2 babies. The first babies have babies of their own. This is how these three things understand how numbers work.
ReplyDeleteI would like to answer question #6. When you add the sum of each row you get hopping twos. For example when Robert summed up the 3rd row 1+2+1=4,the next line would be 2x2x2 or two to the third power in other words eight.This example clearly shows the number devils old friend hoping numbers.
ReplyDelete#4) Well in the book I see that the triangle starts with the number 1 then it starts form in to a triangle of one's. Then it starts changing number until it forms a bigger triangle.
ReplyDelete1)Three things in nature that understand how numbers work are 1)rabbits
ReplyDelete2)trees
3)tigers
For example as it states in the last paragraph of page 121 it represents the tree and the rabbits then heading into chapter 7 2) How many cubes were used to make the base of the pyramid built by Robert and the number devil? The number of cubes used to build the bottom of the pyramid is 17 but for instance if you subtract one you would get 16 an hopping number which would equal 2`4 As it states on page 127~128.
3) Why does Robert tell the number devil, "It'll never be a pyramid."? Robert tells the number devil it will never be an pyramid because pyramids are triangular or rectangular at the base and the base are flat so it could not be an pyramid but an triangular it states on page 128
1)List three things in nature that understand how numbers work.
ReplyDelete1.Lions
2.Rabbits
3.Birds
The lions, rabbits, and birds reproduce and make babies like a pattern, there is a different amount of babies each time.
1)List three things in nature that understand how numbers work.
ReplyDelete1.Lions
2.Rabbits
3.Birds
The lions, rabbits, and birds reproduce and make babies like a pattern, there is a different amount of babies each time.
you need to explain more details in your answer
Deletethe numbers that the triangle start with is 1 16 120 560 1820 4368 8008 11440 and 12870
ReplyDelete