Summarize the Mathematics & Check Your Understanding (p. 15)
*Please post your answers as a comment.*
Summarize the Mathematics:
The sum of any two consecutive odd numbers is divisible by 4.
a) How could you arrive at this conjecture by using inductive reasoning?
b) Write this conjecture in if-then form.
i. What is the hypothesis of your statement?
ii. What is the conclusion?
c) How could you use deductive reasoning to prove this conjecture?
Check Your Understanding:
Make a conjecture about what happens when you choose four consecutive whole numbers, add the middle two, and then subtract the smallest of the four from that sum.
a) Describe the procedure you used to create your conjecture.
b) Write your conjecture in if-then form.
c) If n represents the smallest of four consecutive whole numbers, how would you represent each of the next three numbers?
d) Use your representations in Part c to write an argument that proves your conjecture is always true.
Summarize the Mathematics:
ReplyDeleteThe sum of any two consecutive odd numbers is divisible by 4.
a) How could you arrive at this conjecture by using inductive reasoning?
-by using formulas, such as (a+b), to solve so it would be general.
b) Write this conjecture in if-then form.
-If the sum of two consectutive odd numbers are divisable by 4 then the sum is an even number.
i. What is the hypothesis of your statement?
-the sum of two consecutive odd nubers are divisable by 4.
ii. What is the conclusion?
-the sum is an even number.
c) How could you use deductive reasoning to prove this conjecture?
-you would be more specific because there are facts to support the answer.
Check Your Understanding:
Make a conjecture about what happens when you choose four consecutive whole numbers, add the middle two, and then subtract the smallest of the four from that sum.
_(What do you do with the left over number?!?!?!?)_
a) Describe the procedure you used to create your conjecture.
- I just read the problem then thought of a question i had and thats how i got it
b) Write your conjecture in if-then form.
-if you choose four consecutive whole numbers, add the middle two, and then subtract the smallest of the four from that sum you will have some of your four numbers left over
c) If n represents the smallest of four consecutive whole numbers, how would you represent each of the next three numbers?
-a,b,c
d) Use your representations in Part c to write an argument that proves your conjecture is always true
- when you add a+b then subtract n you still have c when you add b+c then subtract n you still add a+c the subtract n you still have b
when you add b+n then subtract n you still have a and c when you add a+n the subtract n you still have b and c left over when you add c+n and subtract n you still have a and b leftover. there is always numbers left over no matter what you do.
Ebonique Knighton, 1st period 1/18/11
ReplyDeleteSTM:
a)You would arrive at that answer by using a specific answer.
b)If sum is divisible by 4, then it is the sum of two consecutive odd #'s.
i) divisible by 4
ii) sum of two consecutive odd #'s
c)By being vague and saying any two odd numbers are divisible by 4.
CYU:
Conjecture- when you choose any four consecutive whole #'s, add the middle two, and subtract the smallest of the four from the sum, the answer will be the last number of the group of #'s you chise.
a)I chose 12,13,14,15 and added the middle #'s 13 to 14 and got 27. I took the smallest number and subtracted that from the sum 27 and I got 15.
b)If you choose any four consecutive whole numbers, add the middle two, subtract the smallest of the four from that sum, then the answer will be the number that is the last number in your group of numbers.
c) n=smallest
o=1st middle number
p= 2nd middle number
q= last number (largest)
d) (o+ p)-n=q
Summarize the Mathematics:
ReplyDeleteThe sum of any two consecutive odd numbers is divisible by 4.
a) How could you arrive at this conjecture by using inductive reasoning?
~ You could write it as an specific reasoning or general reasoning.
b) Write this conjecture in if-then form.
~ If the sum of any two odd numbers is divisible by 4, then it a specific or general reasoning.
i. What is the hypothesis of your statement?
~ The sum of any two odd numbers is divisible by 4
ii. What is the conclusion?
~ Then it is a specific or general reasoning.
c) How could you use deductive reasoning to prove this conjecture?
~ Work it out and prove that it is a true reasoning.
Check Your Understanding:
Make a conjecture about what happens when you choose four consecutive whole numbers, add the middle two, and then subtract the smallest of the four from that sum.
a) Describe the procedure you used to create your conjecture.
~ To find four whole numbers then adding the two middle numbers and then subtracting them by the smallest number to get the biggest number.
b) Write your conjecture in if-then form.
~ If 32,33,34,35 are whole numbers, then you add the two middle numbers then subtract them by 32, you should get 35
c) If n represents the smallest of four consecutive whole numbers, how would you represent each of the next three numbers?
~ with opqrs
d) Use your representations in Part c to write an argument that proves your conjecture is always true.
~ N=32 O=33 p=34 r=35 (33o + 34p)=67s - 32n = 35 r
STM
ReplyDeletea) To arrive at this conjecture by using inductive reasoning you would have to be specific in your premise and general in your conclusion.
b) If two consecutive odd numbers have a sum, then it must be divisible by 4.
i. If two consecutive odd numbers have a sum
ii. then the sum must be divisible by 4
c) To prove this conjecture by using deductive reasoning you would have to start with a general premise and then a specific conclusion.
CYU
Conjecture: When you choose four consecutive whole numbers, add the middle two, and then subtract the smallest of the four from that sum you always receive the highest number of the four you picked.
a) I picked four consecutive integers; 2,3,4,5. I then added 3 and 4 because they are the middle two. Next, I subtracted 2 because that is the smallest of the four consecutive numbers and the number I got was the fourth number, 5.
b) If you choose four consecutive integers, add the middle two and subtract by the smallest of the four, then the highest number will always be your difference.
c) If n represents the smallest number I will make the next 3 (n+1, n+2, n+3).
d) (n+1 + n+2)- n=n+3