1) How many possibilities are there of seating arrangements for two students? Three students? Four students?
2) How do you read the exclamation point in a mathematics problem?
3) What is the mathematical term for vroom?
4) If each of 5 students shook hands with another student before leaving, how many handshakes would occur?
5) Identify at least two ways to solve the handshake problem without counting each handshake.
6) What type of data display is used to show the number of group consisting of 3 students?
7) If there are 11 students in the broom brigade, how many groups consisting of 3 students exist?
8) How many groups would there be if 8 people volunteered for the broom brigade quartet?
9) Use the number triangle to determine the number of groups there would be if there were 6 people volunteering for the broom brigade duo.
10) If you have 14 volunteers taken 9 at a time, how many groups do you have?
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 weekend is to choose one of the following questions and post an intelligent response. The deadline to post for the Seventh night and Eighth night is Monday, December 21st. We will continue our discussion at this time. Use the bookmark to help guide your comments. Then continue reading through Chapter 9 and 10 which will be due by January 2. We will discuss these two chapters on Monday, January 4th.
Let's get reacquainted with important parts of the rubric. Follow this rubric to achieve the highest scores possible.
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3
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4
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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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The way that you would read the exclamation point in mathematics, a factorial is a function applied to natural numbers greater than zero, the symbol for the factorial function is an exclamation mark after a number
ReplyDeleteI agree with your answer and would also like to add on that a factorial also signifies that a certain number of consecutive numbers are being multiplied. For example, 5! is the same as 1x2x3x4x5. Using the factorial is a way to simplify the equation.
Deletei agree with aliana but with symbol it shows which nubers are factorial and non-factorial numbers in a diversity
DeleteCan you explain what a factorial is?
DeleteI agree with you but could you give an example of a factorial # to help u readers better understand what you're trying to display. Also could you use the Number Devil or an outside resource for evidence.
DeleteI would like to agree with Aliana because to read the exclamation point is to use the factorial function. But next time you should clarify what a factorial function is (for those who don't know).
DeleteIf five students shook hands before leaving there would be 10 handshakes because when doing the work ABCDE, five letters and comparing the number of handshakes and people it would be concluded to be AB,AC,AD,AE,BC,BD,BE,CD,CE,ED, ending with 10 handshakes with 5 students
ReplyDeleteI disagree with Aliana. Let me give an example. If you and I shaked hands, that is one handshake. And I think that you misinterpreted the question. It said the handshakes, not possible combinations. 10 people would be engaging in handshakes, but only 5 handshakes would happen.
DeleteThat was a great noticing Ndeye, it could really help others understand this question more thoroughly.
Deletethe number of possibilities for 4 students were student =1,student 2=1*2=2,student 3=1*2*3=6,student 4=1*2*3*4=4 and so on untill the line of kids stops (hopefully).
ReplyDeleteI would like to disagree with your answer and say that the number of possibilities for 2 students would be 2, because 2! equals 2 x 1, which is 2 The number of possibilities for 3 students is 6 because 3! is equivalent to 1 x 2 x 3, which equals 6. The number of possibilities for 4 students would be 24 because 4! is equivalent to 1 x 2 x 3 x 4 equals 24.
DeleteI agree with Janaidy and I think you should've elaborated more on your idea to support it .
DeleteI also agree with Fatou and I would like to say that in all the responses I have seen you've done it dosen't seem like your showing evidence and having a explanation to go with it. You should really work on that if you want to get a good score.
DeleteQuestion 4: The mathematical term for vroom is factorial. A factorial is a way of showing the products of a 1 through a number. For examples, 3 factorial is 1 x 2 x 3, which is equal to 6.
ReplyDeleteI agree with you Janaidy because throughout the rest of the book the number devil, uses this term to explain a problem to Robert
DeleteI agree with Janaidy because factorial means products, indicated by an exclamation mark. For instance, "four factorial" is written as "4!" and means 1×2×3×4 = 24.
DeleteWhat is the formula for factorial? What is the 1 useful for, what is the 2 useful for, what id the 3 useful for? Lastly, couuld be more elaborate on what you mean by a factorial is a way of showing the products of a 1 through a number.
DeleteI agree with Janaidy and I would like to add on. The specific definition of factorial is to multiply all of a numbers factors together to get a product. A simple way of finding the factorial of a number is: n!= 1 x 2 x 3 x 4 x ....n.
DeleteThe seating arrangement for two students is two possibilities. For three students there would be 5 possibilities, i know this because then it would be ABC,CBA,BCA,BAC,CAB, for four students there would be 24 opportunities I know this because it would then be ABCD,ABDC,ABDC,ACDB,ADBC,ADCB, and so on...
ReplyDeleteCan you think of anything that is similar to this, that you have done in past math classes?
DeleteIs there another way you could've have known that for two students there were two possibilities?
DeleteCould you relate this to real life and how life would be like without it?
Delete1) How many possibilities are there of seating arrangements for two students? Three students? Four students?
ReplyDeleteThere are only two possibilities of seating arrangements for two students. While for three students there are 6 possibilities of seating arrangements. For four students however, there are 24 possibilities for seating arrangements. This seating arrangement example shown in the number devil reminds me of how, when your solving a math problem sometimes you find multiple strategies to solve the one problem. This is because in every example there were the same letters, there was just different ways to put them. In math sometimes there is the same one problem that you can solve in multiple ways.
I love how you related this to the real world but how else do you know that there is only two possibilities and why it is a useful method.
DeleteI love how you did some connections to the real world and how you said " This seating arrangement example shown in the number devil reminds me of how, when your solving a math problem sometimes you find multiple strategies to solve the one problem." This shows a connection with a method we already know
DeleteMorayma, I really think you need to come up with some original ideas. It just looks like you are repeating what Maimouna said, and that is a waste of time. I want to see your own ideas.
DeleteAccording to the Number Devil book,the seating arrangement for 2 students is 2 possibilities. 3 students will have 6 possibilities and 4 will have 24 possibilities. This is because it is just like you have to count by 1's but you put a multiplication sign in between the numbers. For example , if you want to count to 8 . It would be 1x2x3x4x5x6x7x8=40,320.
ReplyDeleteI like how you gave an example to help clarify your response.
DeleteBasically, each of the answers of the seating possibilities can be found using factorials. I think you could have been specific and added how and why you know the answers.
DeleteI also want to add that this process is called factorials . Factorials are products, indicated by an exclamation mark.
ReplyDeleteCould be more elaborate and what is the formula for factorial?
DeleteI agree and like to add on that if you see my post it says that " The factorial function (symbol: !) means to multiply a series of descending natural numbers For example: 4! = 4 × 3 × 2 × 1 = 24 "
DeleteThanks for the example Morayma.
DeleteIn a mathematics problem, you read the exclamation mark as vroom.
ReplyDeleteIn the book the number devil gave Robert this example: 4!=24 Then the number devil told Robert that he read it correctly. 4vroom(page 156)
I'm confused on what question you're trying to answer and what is vroom in its mathematical form? You really should've been more explanatory in this response.
DeleteCan you elaborate and say what does Robert example show and what does the number devil means by '4vroom'
DeleteI would like to clarify Jose's answer. By vroom he means factorial. And by 4 vroom the number devil means 1 times 2 times 3 times 4 which equals to 24. So, the mathematical term for vroom is factorial.
DeleteAlso, Morayma, you did not have to repeat what Maimouna said about Jose clarifying.
Deletethe you read an explanation point in math is a factorial is a function applied to natural numbers greater than zero, the symbol for the factorial function is an exclamation mark after a number.factorial means to multiply a series of descending natural numbers.
ReplyDeleteCan you give an example? And how are factorial numbers used in real life? Why are they important? How would life be like without them.
DeleteThis comment has been removed by the author.
ReplyDeleteIf each of 5 students shook hands with another student before leaving, 10 hand shakes will occur .
ReplyDeleteHow does that relate to factorial? Why does it relate to factorial?
DeleteAlso I think you could've challenged yourself more by doing 2 questions or at least attempting a challenging question.
DeleteAlso why do you say that 10 handshakes occur?
Deleteif 5 students shook hand with another student 5 handshakes occurred.
ReplyDeleteI disagree with you Ibrahim because if the 5 students each shook hands with another student 10 shakes could occur because 1*2*5=10! Therefore I disagree with your answer. I also think you should've tried to answer one of the difficult questions in order to challenge yourself.
DeleteI would like to correct myself on the 1*2*5=10! That should've only been used when trying to find how many ways 5 students can be switched around. But I still disagree with Ibrahima and think it is 10 handshakes.
DeleteI actually now agree with Ibrahima because of the previous comments Ndeye posted I see that the reason why it was 5 handshakes was because when 2 students encountered one another that = 1 handshake. Now that each of the 5 students encountered another student in a handshake it = 5 handshakes. I see why I thought it was 10 because I thought it was like contact at hand counted as a handshake from each child. I compliment on how you figured it out, but I think you should've been more explanatory because people like me may have gotten confused and say your answer was wrong, when in truth it wasn't.
Deleteyou read the exclamation point in a mathematics problem is a factorial is a function applied to natural numbers greater than zero.
ReplyDeleteThe factorial function (symbol: !) means to multiply a series of descending natural numbers For example: 4! = 4 × 3 × 2 × 1 = 24
Why are factorials an important factor in the math world? How do we use it in real life?
Deleteif the 5 students each shook hands with another student 10 shakes could occur because 1*2*5=10!
ReplyDeleteI actually disagree with you Morayma because in previous comments, Ndeye said that the reason there were only 5 handshakes among the students was because when each student encountered another the 2 students produced 1 handshake. So when each of the students had encountered another student they produced 5 handshakes in total. To add on, I don't really think that this had anything to do with factorials honestly. My reasons behind this claim is because we are not trying to find the number of ways the students could've encountered with another student. Therefore I disagree with you Morayma and I think you should've been more explanatory.
DeleteI respectfully disagree with Morayma because on page 156 there is a picture that shows how you keep the pattern goin. So it would be 1*2*3*4*5=120
DeleteAccording to the number devil in page 158 it says " Two people-one handshake. Three people-three handshakes. Four people-six handshakes. Five people- ten handshakes" This shows how 2people=1handshakes,3people=3hankshakes, 4people=6handshakes, 5people=10handshakes
ReplyDeleteBut why does 2 people=1 handshake, 3 people=3 handshakes, 4 people=6 handshakes, 5 people=10 handshakes? Be more clear.
DeleteHow do you know if the Number Devil is correct?
DeleteThe way that you would read the exclamation point in mathematics, a factorial is a function applied to natural numbers greater than zero, the symbol for the factorial function is an exclamation mark after a number
ReplyDeleteCould you give an example? And why is it used in the math world? For what purpose?
DeleteIf the five students shook hand then there would be 10 handshakes in total. I say this because since there's five letters there would be 10 possibilities. AB,AC,AD,AE,BC,BD,BE,CD,CE,ED,
ReplyDeleteThe mathematical term for vroom is factorial. For example 5,1x2x3x4x5=120
ReplyDeleteI was wondering why did the Number Devil call the mathematical term factorial vroom?
DeleteI agree with Luis, but can you explain what a factorial is?
DeleteI disagree with anyone who said for question 4 that 10 handshakes would occur. The reason is pure logic. I did a little research, and two people shaking hands is ONE handshake, not two. So, this was a question of common sense. When you think about it, when two people shake hands, it is not 2 separate handshakes. It is 1. This was not related to factorials at all. It was easy to just multiply 2 people by 5 and get 10. To conclude, when 5 students shake hands with another student, 5 handshakes occur.
ReplyDeleteI agree with Ndeye and I compliment on how you challenged against the Number Devil book.
DeleteFor those of you who are wondering, the definition of vroom is used to express or imitate the sound of an engine or to suggest speed or acceleration. I think vroom was used as factorial because vroom shows how factorials can increase the number of ways something can be written or accelerate it. Vroom is also related to factorials because it imitates a sound like factorials imitating numbers by including it into the situation. For example, 1*2=2!. You are including the 1 and 2, showing how two numbers can be switched 2 ways. Another example, 1*2*3=6=3!, imitating the 1 and 2 from the previous example, showing that 3 numbers could be switched around 6 ways. This is why instead of using the correct mathematical term the Number Devil used vroom as a relation to factorial.
ReplyDeleteThere are 2 possibilities of seating arrangements for two students. There are 6 possibilities of seating arrangements for three students, and there are 24 possibilities of seating arrangements for 4 sudents. I know this because in the book there is a picture that shows all the seating arrangements possible for different amounts of students.
ReplyDeleteBut how do you know the book is correct because in some of the previous chapters we have shown how the Number Devil was incorrect sometimes.
DeleteI agree with you Tamia can you compare this to an real world situation also can you show me more evidence stated from the text
DeleteAccording to page 156 it shows how to pronounce exclamation mark in a problem is "4!=24 And you read it four vroom!".An example to prove that point is eleven vroom=1x2x3x4x5x6x7x8x9x10x11
ReplyDeleteWhat is the mathematical term for vroom?
Delete#2) In the book I see that theres a problem which is 4! = 24 and under that problem it states that you read a exclamation mark (!) as four vroom.
ReplyDeleteCan you be more specific and give more examples?
DeleteQuestion #4: The mathematical term for vroom is factorial. The factorial function (symbol: !) means to multiply series of descending natural numbers. For example, 4! = 4 x 3 x 2 x 1 = 24. Another example is, 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
ReplyDeleteI like how you used an example that wasn't in the Number Devil Book.
DeleteQuestion #2: To read the exclamation point in mathematics, we have to use the factorial function. The symbol for the factorial function is an exclamation (!) mark after a number greater then zero.
ReplyDeleteCan you give an example? I like your approach on 2 questions.
DeleteExample: 3! = 3 x 2 x 1 = 6
DeleteHow do you read the exclamation point in a mathematics problem?
ReplyDeleteWell for starters, what does an exclamation point in math show? An exclamation point in a math problem shows factorial. A factorial is the product of an integer and all the numbers below it. For example:
1!=1=1
2!= 2 x 1=2
3!= 3 x 2 x 1=6
4!= 4 x 3 x 2 x 1= 24
5!= 5 x 4 x 3 x 2 x 1= 120
6!= 6 x 5 x 4 x 3 x 2 x 1= 720
7!= 7 x 6 x 5 x 4 x 3 x 2 x 1= 5040
and so on.
To read the exclamation point you have to use the factorial function which is the exclamation point. An exclamation point is only to be used after a number greater than 0 because any number multiplied by 0 gives you 0 so it would make mo sense to do a factorial of 0 if the product of the integers are just going to be 0.
I compliment on how you incorporated why 0 can't be used and how you were explanatory in your response.
Delete(10. if you have 14 kids taken 9 at a time you have 1 5/9 groups.
ReplyDeletethere are only 2 possibilities for an arrangement of 2. This is because 2 only has 2 factors and it can only be put in a column and row differently in 2 ways.
ReplyDeleteMuhamadou I like how you related the 2 possibilities to how 2 is used in multiplication and in factors. Well done!
Delete2) How do you read the exclamation point in a mathematics problem?
ReplyDeleteThe examination point in an math problem is an factorial a factorial is a function applied to natural numbers greater than zero. The symbol for the factorial function is an exclamation mark after a number, like this: 2!The first handful of factorial values from positive integers are: 1! = 1; 2! = 2; 3! = 3*2 = 6; 4! which is what the number devil states on page 163 also you can do an number triangle 3) Vroom! – Factorial. Vroom! is the visual description of the speed at which factorial numbers grows.
2)How do you read the exclamation point in a mathematics problem?
ReplyDeleteIn mathematic problems the exclamation point is referred to as factorial. Thus 5! is read "five factorial." The factorial operation indicatfactorsproduct of all the integers less than and equal to the given number. For example:
5!:5*4*3*2*1=120
The mathematical term for vroom is factorial is the factor of an integer and the integers before it.For example.4 factorial is 24 since 4x3x2x1 is equal to 24.
ReplyDeleteThe possibilities of arrangements varies on the number of variables in the current scenario.For example,if there is two people there is only 2 arrangements is possible.but that doesn't mean that there is 3 arrangements possible.According to the Number Devil,when Charlie came into play there was 6 arrangements but is not because 3x2 but a new equation I came up with x square - x. I'll show you how to us later when there is 4 people.When there is 4 people there is 12 possible ways since 4 square is 16 and 16-4 is 12.My other arrangements prove it.2 square is 4 and 4-2 is 2.3 square is 9 and 9-3 is 6.
ReplyDelete3) What is the mathematical term for vroom?
ReplyDeleteThe mathematical term for vroom is the visual description of the speed at which factorial numbers grows
The mathematical term for vroom is to describe the speed of the factorial number grows or increases
ReplyDeleteI agree with kiara because as the number devil said is the mathematical term of vroom is to show the speed of the increasing numbers
ReplyDelete