MATH 110 EXAM 3 2026 FINAL PAPER REVIEW
QUESTIONS ANSWERS BUNDLED PRACTICE
COLLECTION
◉ What does NCTM stand for and when was it made/updated?.
Answer: National Council of Teachers of Mathematics (1989) (2000)
◉ Problem Solving.
Answer: Have students try multiple different strategies; open ended
problems, non-routine problems
◉ Connections.
Answer: Show why it's useful in the real world. Why do they need to
know this?
-connections within math
-connections with other subjects
-connections to the real world
◉ Communication.
Answer: Student discussion, have students write sentences;
How would you explain today's concept to a student that was
absent? (students answer)
,◉ Reasoning & Proof.
Answer: WHY we do problems the way we do; have students make
conjectures; have students discover something; have students
support what they say
◉ Representation.
Answer: Represent ideas in as many different ways that you can
think of
◉ Inductive Reasoning.
Answer: specific -> general
ex. eyeglasses some people wear eyeglasses, everyone wears
eyeglasses (conjecture is false)
◉ Deductive Reasoning.
Answer: general -> specific
ex. if right triangle, then a2+b2=c2 (general proven fact)
5^2+12^2=c2 -> 13=c
◉ Conjecturing.
Answer: Inferring or predicting from incomplete evidence; making a
statement
, ◉ Investigation.
Answer: uses reasoning to find answers
ex. odd+odd=even
even+even=even
even+odd=odd
◉ Counterexample.
Answer: an example that disproves a statement
◉ Negation.
Answer: ~A; NOT; S: Today is Thursday; N: Today is NOT Thursday
◉ conditional statement.
Answer: If A, then B (-_>) (double bar arrow means implies)
◉ converse.
Answer: If B, then A
ex. S- If today is TH, then tomorrow is F.
Converse- If tomorrow is F, then today is TH.
◉ Inverse.
QUESTIONS ANSWERS BUNDLED PRACTICE
COLLECTION
◉ What does NCTM stand for and when was it made/updated?.
Answer: National Council of Teachers of Mathematics (1989) (2000)
◉ Problem Solving.
Answer: Have students try multiple different strategies; open ended
problems, non-routine problems
◉ Connections.
Answer: Show why it's useful in the real world. Why do they need to
know this?
-connections within math
-connections with other subjects
-connections to the real world
◉ Communication.
Answer: Student discussion, have students write sentences;
How would you explain today's concept to a student that was
absent? (students answer)
,◉ Reasoning & Proof.
Answer: WHY we do problems the way we do; have students make
conjectures; have students discover something; have students
support what they say
◉ Representation.
Answer: Represent ideas in as many different ways that you can
think of
◉ Inductive Reasoning.
Answer: specific -> general
ex. eyeglasses some people wear eyeglasses, everyone wears
eyeglasses (conjecture is false)
◉ Deductive Reasoning.
Answer: general -> specific
ex. if right triangle, then a2+b2=c2 (general proven fact)
5^2+12^2=c2 -> 13=c
◉ Conjecturing.
Answer: Inferring or predicting from incomplete evidence; making a
statement
, ◉ Investigation.
Answer: uses reasoning to find answers
ex. odd+odd=even
even+even=even
even+odd=odd
◉ Counterexample.
Answer: an example that disproves a statement
◉ Negation.
Answer: ~A; NOT; S: Today is Thursday; N: Today is NOT Thursday
◉ conditional statement.
Answer: If A, then B (-_>) (double bar arrow means implies)
◉ converse.
Answer: If B, then A
ex. S- If today is TH, then tomorrow is F.
Converse- If tomorrow is F, then today is TH.
◉ Inverse.
