ELED 471 EXAM 1 QUESTIONS ANSWERED CORRECTLY LATEST UPDATE 2026
conceptual understanding - Answers comprehension of mathematical concepts, operations, and
relations
strategic competence - Answers ability to formulate, represent, and solve mathematical problems
procedural fluency - Answers skill in carrying out procedures flexibly, accurately, efficiently, and
appropriately
adaptive reasoning - Answers capacity for logical thought, reflection, explanation, and justification
productive disposition - Answers habitual inclination to see mathematics as sensible, useful, and
worthwhile, coupled with a belief in diligence and one's own efficacy
join problems - Answers Addition problems that can have an unknown at the start, change, or result.
Physical action
Example: Lou had 12 toy cars, Mia gave him 6 more. How many cars does Lou have altogether?
separate problems - Answers Subtraction problems that can have an unknown at the start, change or
result. Physical action
Some bears were at a campfire, 3 bears left, there were 2 bears left, how many bears were there at
the start?
part-part whole problems - Answers 2 different parts but the same subject. No physical action.
George has 4 pennies and 8 nickels, how many coins does he have?
compare problems - Answers Looking at two different things, comparing them to one another.
Usually, situations of how many more. No physical action. George has 12 pennies and Sandra has 8
pennies. How many more pennies does George have than Sandra.
Cardinal Numbers - Answers designate the quantity of a set
Tells "how many"
Also known as the counting numbers
What is not one of the 5 strands of mathematical proficiency?
A. Conceptual understanding
B. Strategic competency
C. Problem solving
D. Procedural fluency - Answers C
What is the difference between a part-part whole word problem and a compare word problem? -
Answers A compare problem compares two things and involves looking at two different subjects or
things, while a part part whole problem is looking at parts of the same subject or thing.
Conservation of number - Answers the ability to conserve number quantities arranged in different
ways
ordinal numbers - Answers orders of numbers in a set. rank or position
nominal numbers - Answers name or identify objects
What grade are fractions introduced? - Answers 3
Describe seriation and how it is used - Answers being able to focus on an attribute and then arranging
or ordering a set of objects according to that attribute. Used for organization.
Example: Colors of the rainbow, tv show episodes, measuring cups smallest to larges
Prenumber activities: Classification - Answers process of determining an attribute or characteristic of
a selected set of objects and then grouping those objects according to the characteristic
Prenumber activities: seriation - Answers being able to focus on an attribute and then arranging or
ordering a set of objects according to that attribute. Used for organization.
Prenumber activities: patterns - Answers being able to recognize concrete and number patterns and
then later translating patterns from one medium to another.
Prenumber activities: one to one correspondence - Answers Process of comparing sets of objects by
using one to one correspondence strategy. (Comparison)
Prenumber activities: conservation of number - Answers Ability to conserve number quantities
arranged in different ways.
Name one shift in the classroom environment and what we are moving towards? - Answers 3 shifts of
mathematics: focus, coherence, rigor.
Problem solving
Which is not an implication of constructivist and sociocultural theory?
a. Build new knowledge from prior knowledge
, b. Scaffold new content c. Honor diversity
d. Knowing does not equal understanding - Answers C
What are Polya's four steps in problem solving? - Answers 1. Understand the problem
2. Devise a plan to solve the problem
3. Implement a solution plan
4. Reflect on the problem
When changing the difficulty of problems, which two problem contexts are the easiest to
differentiate?
a. Abstract and personalized setting b. Concrete and hypothetical setting
c. Abstract and concrete
d. Concrete and personal - Answers A
What grade do you stop teaching numbers and operations/fractions. - Answers 6
____ is the ability to formulate, represent and solve mathematic problems - Answers strategic
competence
problem solving strategies - Answers Drawing a picture
Constructing table/chart
Finding a pattern
Solving simpler problem
Guessing and checking
Working backwards
Considering all possibilities
Logical reasoning
Changing point of view
give and example of a compare problem - Answers Kate had 6 more pets than Liz, Liz has 2 pets. How
many pets does Kate have?
2+6=8
Which is not a type of problem?
a. Translation
b. Application
c. Process
d. Transition - Answers D
Types of problems: Process - Answers require solution processes other than computational
procedures
Example: At an air show, 8 skydivers were released from a plane. Each skydiver was connected to
each of the other skydivers with a separate piece of ribbon. How many pieces of ribbon were used in
the skydiving act?
Types of problems: translation - Answers include the one- and two-step story problems typically
found in textbooks.
A school auditorium can seat 648 people in 18 rows. How many people are in each row?
types of problems: application - Answers Involve gathering data and then making a decision about
the solution process. These problems are generally solved using computation.
types of problems: puzzle - Answers
Sarah baked 24 cookies for her class. 18 were chocolate chip. The rest were peanut butter. How many
were peanut butter? Solve the problem and identify what type of word problem it is. - Answers
Whole: 24 18: CC Unkown: PB
_+18=24
6 are peanut butter
Part-Part whole problem
Model for introducing operations with real world problems - Answers 1. Real-world setting or
problem
2. Models
-Concrete
-Pictorial
-Mental images
-Language
3. Symbols
conceptual understanding - Answers comprehension of mathematical concepts, operations, and
relations
strategic competence - Answers ability to formulate, represent, and solve mathematical problems
procedural fluency - Answers skill in carrying out procedures flexibly, accurately, efficiently, and
appropriately
adaptive reasoning - Answers capacity for logical thought, reflection, explanation, and justification
productive disposition - Answers habitual inclination to see mathematics as sensible, useful, and
worthwhile, coupled with a belief in diligence and one's own efficacy
join problems - Answers Addition problems that can have an unknown at the start, change, or result.
Physical action
Example: Lou had 12 toy cars, Mia gave him 6 more. How many cars does Lou have altogether?
separate problems - Answers Subtraction problems that can have an unknown at the start, change or
result. Physical action
Some bears were at a campfire, 3 bears left, there were 2 bears left, how many bears were there at
the start?
part-part whole problems - Answers 2 different parts but the same subject. No physical action.
George has 4 pennies and 8 nickels, how many coins does he have?
compare problems - Answers Looking at two different things, comparing them to one another.
Usually, situations of how many more. No physical action. George has 12 pennies and Sandra has 8
pennies. How many more pennies does George have than Sandra.
Cardinal Numbers - Answers designate the quantity of a set
Tells "how many"
Also known as the counting numbers
What is not one of the 5 strands of mathematical proficiency?
A. Conceptual understanding
B. Strategic competency
C. Problem solving
D. Procedural fluency - Answers C
What is the difference between a part-part whole word problem and a compare word problem? -
Answers A compare problem compares two things and involves looking at two different subjects or
things, while a part part whole problem is looking at parts of the same subject or thing.
Conservation of number - Answers the ability to conserve number quantities arranged in different
ways
ordinal numbers - Answers orders of numbers in a set. rank or position
nominal numbers - Answers name or identify objects
What grade are fractions introduced? - Answers 3
Describe seriation and how it is used - Answers being able to focus on an attribute and then arranging
or ordering a set of objects according to that attribute. Used for organization.
Example: Colors of the rainbow, tv show episodes, measuring cups smallest to larges
Prenumber activities: Classification - Answers process of determining an attribute or characteristic of
a selected set of objects and then grouping those objects according to the characteristic
Prenumber activities: seriation - Answers being able to focus on an attribute and then arranging or
ordering a set of objects according to that attribute. Used for organization.
Prenumber activities: patterns - Answers being able to recognize concrete and number patterns and
then later translating patterns from one medium to another.
Prenumber activities: one to one correspondence - Answers Process of comparing sets of objects by
using one to one correspondence strategy. (Comparison)
Prenumber activities: conservation of number - Answers Ability to conserve number quantities
arranged in different ways.
Name one shift in the classroom environment and what we are moving towards? - Answers 3 shifts of
mathematics: focus, coherence, rigor.
Problem solving
Which is not an implication of constructivist and sociocultural theory?
a. Build new knowledge from prior knowledge
, b. Scaffold new content c. Honor diversity
d. Knowing does not equal understanding - Answers C
What are Polya's four steps in problem solving? - Answers 1. Understand the problem
2. Devise a plan to solve the problem
3. Implement a solution plan
4. Reflect on the problem
When changing the difficulty of problems, which two problem contexts are the easiest to
differentiate?
a. Abstract and personalized setting b. Concrete and hypothetical setting
c. Abstract and concrete
d. Concrete and personal - Answers A
What grade do you stop teaching numbers and operations/fractions. - Answers 6
____ is the ability to formulate, represent and solve mathematic problems - Answers strategic
competence
problem solving strategies - Answers Drawing a picture
Constructing table/chart
Finding a pattern
Solving simpler problem
Guessing and checking
Working backwards
Considering all possibilities
Logical reasoning
Changing point of view
give and example of a compare problem - Answers Kate had 6 more pets than Liz, Liz has 2 pets. How
many pets does Kate have?
2+6=8
Which is not a type of problem?
a. Translation
b. Application
c. Process
d. Transition - Answers D
Types of problems: Process - Answers require solution processes other than computational
procedures
Example: At an air show, 8 skydivers were released from a plane. Each skydiver was connected to
each of the other skydivers with a separate piece of ribbon. How many pieces of ribbon were used in
the skydiving act?
Types of problems: translation - Answers include the one- and two-step story problems typically
found in textbooks.
A school auditorium can seat 648 people in 18 rows. How many people are in each row?
types of problems: application - Answers Involve gathering data and then making a decision about
the solution process. These problems are generally solved using computation.
types of problems: puzzle - Answers
Sarah baked 24 cookies for her class. 18 were chocolate chip. The rest were peanut butter. How many
were peanut butter? Solve the problem and identify what type of word problem it is. - Answers
Whole: 24 18: CC Unkown: PB
_+18=24
6 are peanut butter
Part-Part whole problem
Model for introducing operations with real world problems - Answers 1. Real-world setting or
problem
2. Models
-Concrete
-Pictorial
-Mental images
-Language
3. Symbols
