Sundogs are small rainbows that appear when you look towards the sun. Jack has noticed that when he sees sundogs in the evening when the sun is setting, it often rains or snows the next day.
Jack saw sundogs as the sun was setting yesterday so he decided to where a rain jacket to work today.
Fill in the blanks in the statement below:
Jack is using _________________ reasoning to make a ___________________ regarding the weather.
Select one:
a.
deductive, conclusion
b.
inductive, conjecture
c.
inductive, premise
d.
deductive, conjecture
c.
inductive, premise
Conjecture: The product of an even number and an odd number is an odd number.
Choose the appropriate counterexample from the options below.
Select one:
a.
7 is odd
3 is odd
7 cross times 3 equals 21
b.
6 is even
3 is odd
6 cross times 3 equals 18
c.
6 is even
8 is even
6 cross times 8 equals 48
d.
7 is odd
2 is even
7 plus 2 equals 9
c.
6 is even
8 is even
6 times 8 equals 48
Example 1: 9 is an odd number because 9 cannot be divided into two equal parts. An even number can be divided into two equal parts.
Example 2: Mae cannot go to school today because she is sick.
Example 3: When Declan drinks a lot of water in the morning he does not get cramps when he runs later that day. Declan wants to have a great run tonight so he should drink lots of water this morning.
Classify the statements in each of these examples as a premise or conclusion by dragging and dropping in the corresponding blanks below.
Statement Premise or Conclusion
9 is a odd number blank
9 cannot be divided into two equal parts blank
an even number can be divided into two equal parts blank
Mae cannot go to school today blank
she is sick blank
When Declan drinks a lot of water in the morning
he does not get cramps when he runs later that day blank
Declan wants to have a great run tonight blank
Declan needs a good sleep tonight blank
He should drink lots of water this morning blank
Premise Conclusion
Statement Premise or Conclusion
9 is an odd number Premise
9 cannot be divided into two equal parts Premise
An even number can be divided into two equal parts Premise
Mae cannot go to school today Premise
She is sick Premise
When Declan drinks a lot of water in the morning, he does not get cramps when he runs later that day Premise
Declan wants to have a great run tonight Premise
Declan needs a good sleep tonight Conclusion
He should drink lots of water this morning Conclusion
Choose a number
Double it
Add 6
Divide your result by 2
Subtract the original number
Try this sequence of calculations with 2 as your chosen number. The result is Answer
.
Try this sequence of calculations with 4 as your chosen number. The result is Answer
.
Try this sequence of calculations with 10 as your chosen number. The result is Answer
.
A conclusion regarding the "magic number" at the end of this number trick that is based on these examples is the result of Answer
Reasoning.
The result of this number trick is always 3, regardless of the chosen number.
A conclusion regarding the "magic number" at the end of this number trick that is based on these examples is inductive reasoning.
Conjecture: The sum of 3 consecutive integer is divisible by 3.
Test this conjecture with 1, 2 and 3. The sum is Answer
which Answer
divisible by 3.
Test this conjecture with 5, 6 and 7. The sum is Answer
which Answer
divisible by 3.
Test this conjecture with -3, -4 and -5. The sum is Answer
which Answer
divisible by 3.
These examples Answer
the conjecture.
Test this conjecture with 1, 2 and 3. The sum is 6, which is divisible by 3.
Test this conjecture with 5, 6 and 7. The sum is 18, which is divisible by 3.
Test this conjecture with -3, -4 and -5. The sum is -12, which is divisible by 3.
These examples support the conjecture.
A student started to prove that the sum of 3 consecutive even integers is divisible by six. Pick up where the student left off and complete the proof and the conclusion.
Student Work
Let 2n, 2n+2, 2n+4 represent the 3 consecutive even integers.
2n + (2n+2) + (2n+4)
= blank -- Combine like terms
= blank -- Factor out GCF
Conclusion:
The sum is equal to blank times something so that means it can be evenly divided by blank and thus is divisible by blank .
6n + 6 6(n + 1) n + 1 6 2n 2n + 2 2n + 4 6n + 8
Student Work:
Let 2n, 2n+2, 2n+4 represent the 3 consecutive even integers.
2n + (2n+2) + (2n+4)
= 6n + 6 (Combine like terms)
= 6(n + 1) (Factor out GCF)
Conclusion:
The sum is equal to 6 times (n + 1), so that means it can be evenly divided by 6 and thus is divisible by 6.
A student attempted to prove that the sum of four consecutive whole numbers is odd but they got stuck and did not finish the proof. Their work is shown below.
Student work
• Let x comma space x plus 1 comma space x plus 2 space a n d space x plus 4 represent the consecutive whole numbers.
• The sum of the four numbers is:
x space plus space left parenthesis x plus 1 right parenthesis space plus space left parenthesis x plus 2 right parenthesis space plus space left parenthesis x space plus space 4 right parenthesis
equals space bold italic x space plus space bold italic x space plus space bottom enclose 1 space plus space bold italic x space plus space bottom enclose 2 space plus space bold italic x space plus space bottom enclose 4
equals space 4 x space plus space 7
equals space ? ? ? ?
What advice would you give to Jerry regarding his work?
Select one:
a.
You made an error when you got rid of the brackets.
b.
Great work, keep going!
c.
You made an error when you combined the like terms.
d.
You made an error when you defined the 4 consecutive integers.
c.
You made an error when you combined the like terms.
Kostis put on his winter jacket, therefore it must be snowing outside.
This statement is best described as:
Select one:
a.
circular reasoning
b.
flawed reasoning
c.
correct reasoning
d.
a paradox
b.
flawed reasoning
Peacocks are beautiful birds because they look spectacular.
This statement is best described as:
Select one:
a.
circular reasoning
b.
false premise
c.
correct reasoning
d.
a paradox
b.
false premise
Fill in the next number in the pattern.
2, 4, 6, 8, Answer
7, -14, 28, -56, 112, Answer
1, 4, 9, 16, 25, Answer
2, 4, 6, 8, Answer: 10
7, -14, 28, -56, 112, Answer: -224
1, 4, 9, 16, 25, Answer: 36
There are 4 food trucks at the county fair. Use the clues below to determine the owner of each food truck.
Marla does not sell burgers or BBQ.
Kit's truck sells vegetables only.
Dara's truck was last in the alphabetical listing on the sign at the fair.
Owner Food Truck
Marla
Burger Bus Veggie Chomp Urban BBQ The Ice Queen
Benji
Burger Bus Veggie Chomp Urban BBQ The Ice Queen
Kit
Burger Bus Veggie Chomp Urban BBQ The Ice Queen
Dara
Burger Bus Veggie Chomp Urban BBQ The Ice Queen
Owner Food Truck
Marla The Ice Queen
Benji Veggie Chomp
Kit Veggie Chomp
Dara Urban BBQ
Reasoning is based on observations. It can be used to form Answer
.
All it takes is a single Answer
to prove a conjecture is false.
Answer
Reasoning can produce a certain Answer
provided your premises are true and your reasoning is correct.
Reasoning is based on observations. It can be used to form conclusions.
All it takes is a single counterexample to prove a conjecture is false.
Inductive reasoning can produce a certain interpretation provided your premises are true and your reasoning is correct.