MATH 110 FINAL EXAM
1. 5 NCTM Process Standards
*Answer* -problem solving
-connections
-communication
-reasoning & proof
-representation
2. What does NCTM stand for and when was it made/updated?
*Answer* National Council of Teachers of Mathematics (1989) (2000)
3. Problem Solving
*Answer* Have students try multiple ditterent strategies; open ended problems, non-routine problems
4. 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
1/
31
,-connections to the real world
5. Communication
*Answer* Student discussion, have students write sentences;
How would you explain today's concept to a student that was absent? (students answer)
6. 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
7. Representation
*Answer* Represent ideas in as many ditterent ways that you can think of
8. Inductive Reasoning
*Answer* specific -> general
ex. eyeglasses some people wear eyeglasses, everyone wears eyeglasses (conjecture is false)
9. Deductive Reasoning
*Answer* general -> specific ex. if right triangle,
then a2+b2=c2 (general proven fact) 5^2+12^2=c2 ->
2/
31
,13=c
10. Conjecturing
*Answer* Inferring or predicting from incomplete evidence; making a statement
11. Investigation
*Answer* uses reasoning to find answers ex.
odd+odd=even
even+even=even
even+odd=odd
12. Counterexample
*Answer* an example that disproves a statement
13. Negation
*Answer* ~A; NOT; S: Today is Thursday; N: Today is NOT Thursday
14. conditional statement
*Answer* If A, then B (-_>) (double bar arrow means implies)
3/
31
, 15. 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.
16. Inverse
*Answer* If not A, then not B
ex. S- If today is TH, then tomorrow is F.
Inverse- If today is not TH, then tomorrow is not F.
17. Contrapositive
*Answer* If not B, then not A ex. S-If
today is TH, then tomorrow is F.
Contrapositive- If tomorrow is not F, then today is not TH.
18. everyday language to conditional language
*Answer* Every dog is a mammal -> If it is a dog, then it is a mammal
19. not all vs. all not
4/
31
1. 5 NCTM Process Standards
*Answer* -problem solving
-connections
-communication
-reasoning & proof
-representation
2. What does NCTM stand for and when was it made/updated?
*Answer* National Council of Teachers of Mathematics (1989) (2000)
3. Problem Solving
*Answer* Have students try multiple ditterent strategies; open ended problems, non-routine problems
4. 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
1/
31
,-connections to the real world
5. Communication
*Answer* Student discussion, have students write sentences;
How would you explain today's concept to a student that was absent? (students answer)
6. 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
7. Representation
*Answer* Represent ideas in as many ditterent ways that you can think of
8. Inductive Reasoning
*Answer* specific -> general
ex. eyeglasses some people wear eyeglasses, everyone wears eyeglasses (conjecture is false)
9. Deductive Reasoning
*Answer* general -> specific ex. if right triangle,
then a2+b2=c2 (general proven fact) 5^2+12^2=c2 ->
2/
31
,13=c
10. Conjecturing
*Answer* Inferring or predicting from incomplete evidence; making a statement
11. Investigation
*Answer* uses reasoning to find answers ex.
odd+odd=even
even+even=even
even+odd=odd
12. Counterexample
*Answer* an example that disproves a statement
13. Negation
*Answer* ~A; NOT; S: Today is Thursday; N: Today is NOT Thursday
14. conditional statement
*Answer* If A, then B (-_>) (double bar arrow means implies)
3/
31
, 15. 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.
16. Inverse
*Answer* If not A, then not B
ex. S- If today is TH, then tomorrow is F.
Inverse- If today is not TH, then tomorrow is not F.
17. Contrapositive
*Answer* If not B, then not A ex. S-If
today is TH, then tomorrow is F.
Contrapositive- If tomorrow is not F, then today is not TH.
18. everyday language to conditional language
*Answer* Every dog is a mammal -> If it is a dog, then it is a mammal
19. not all vs. all not
4/
31
