MAE4310 Critical Task Description
This is the critical task for this course. This assignment will be submitted in TK20 and will
represent one-quarter of your final grade. You will use knowledge and skills acquired from
class discussions, problem based activities, manipulative papers, and the textbook to
demonstrate a clear understanding of mathematics subject area competencies and skills. You
will show your knowledge of instruction and assessment by identifying a variety of appropriate
instructional strategies (e.g., cooperative learning, peer tutoring, think alouds) for teaching
specific concepts and ways that manipulatives, mathematical and physical models, and
technology can be used in instruction for the following concepts:
 Numbers and Operations
 Geometry and Measurement
 Algebra
 Data Analysis





Knowledge of numbers and operations
 Compare the relative size of integers, fractions, decimals, numbers
expressed as percents, and numbers with exponents.
 Represent numbers in a variety of equivalent forms, including whole
numbers, integers, fractions, decimals, percents, and exponents.
 Perform operations on rational numbers (e.g., whole numbers, fractions,
decimals, integers) using multiple representations and algorithms and
understand the relationships between these operations (i..e., addition,
subtraction, multiplication, and division).
 Select the appropriate operations(s) to solve problems involving rations
and percents and the addition, subtraction, multiplication, and division of
rational numbers.
 Apply number theory concepts (e.g., primes, composites, multiples,
factors, number sequences, number properties, rules of divisibility).
Knowledge of geometry and measurement
 Analyze properties of two-dimensional shapes (e.g., area, sides, angles).
 Apply the geometric concepts of symmetry, congruency, similarity, and
transformations.
 Determine how a change in length, width, height, or radius affects
perimeter, circumference, area, surface area, or volume.
 Select appropriate measurement units to solve problems.
Knowledge of algebra
 Extend and generalize patterns or functional relationships.
Knowledge of data analysis
 Make accurate predictions and draw conclusions from data.
Knowledge of instruction and assessment
 Identify a variety of appropriate instructional strategies (e.g., cooperative
learning, peer tutoring, think alouds) for teaching specific concepts

Identify ways that manipulatives, mathematical and physical models, and
technology can be used in instruction.
Critical Task Assignment Rubric: MAE4310 Teaching Mathematics in the Elementary School
Assignment: Culminating Manipulative and Mathematics Concept Reflection Paper
Program SLO: 2.2 Develop a repertoire of realistic projects and problem solving activities that will enable students to improve their
life skills and creative thinking abilities.
NCATE Standard: 1b. Pedagogical Content Knowledge
Conceptual Framework Outcome: Critical Thinker
Competency Rubric
Evaluation of the Course Student Learning Outcome (SLO) listed below is determined based on performance on the corresponding
Assignment Grading Rubric as follows: 100-90% = Exceeds Expectations, 89-70% = Meets Expectations, 69% & below = Does Not
Meet Expectations
Exceeds
Meets
Does not
FEAPS
Subject Area
ESOL Performance
Reading
Expectatio Expectatio
Meet
Competencies
Standards
Endorsemen
ns
ns
Expectatio
t
ns
Competenci
es
1.5, 2.2, 2.5, 2.6, 2.7, 60.28.1, 60.
N/A
N/A
2.8, 2.9, 3.3, 4.1, 4.2, 28.2, 60.28.4,
4.3, 4.4, 4.7, 4.9,
60.28.5, 60.28.6,
Course
4.10,
5.2,
5.4,
7.2,
60.28.8, 60.29.1,
SLO
7.3, 7.5, 7.6, 7.7, 8.2, 60.29.3, 60.29.7,
4. Students will produce
8.3, 8.4, 9.1, 9.5,
60.29.10,
developmentally appropriate
10.10,
10.13,
12.5
60.30.1, 60.31.3,
activity-based lessons, selecting
60.32.1, 60.32.2
and using appropriate teaching
tools and materials for teaching
mathematics.
PEC 00.1.3,
00.2.1, 00.2.2,
00.2.4, 00.3.2,
00.4.1, 00.4.2,
00.5.1, 00.7.2,
00.7.3, 00.7.4,
00.8.2, 00.8.3,
00.8.4, 00.9.1,
00.9.2, 00.10.2,
00.12.1, 00.13.2
Criteria
Numbers and
Operations
Appropriate
instructional
strategies
Exceptional
(20 points) Identifies a variety of
appropriate instructional
strategies for at least three out
of the five concepts (1) compare
relative size of integers,
fractions, decimals, percents,
and exponents; (2) represent
numbers in a variety of
equivalent forms, including
whole numbers, integers,
fractions, decimals, percents,
and exponents; (3) Perform
Assignment Grading Rubric
Performance Descriptors
Proficient
(14 points) Identifies a variety
of appropriate instructional
strategies for two out of the
five concepts (1) compare
relative size of integers,
fractions, decimals, percents,
and exponents; (2) represent
numbers in a variety of
equivalent forms, including
whole numbers, integers,
fractions, decimals, percents,
and exponents; (3) Perform
Limited
Needs
Improvement
(8 points) Identifies a
variety of appropriate
instructional strategies for
one out of the five
concepts (1) compare
relative size of integers,
fractions, decimals,
percents, and exponents;
(2) represent numbers in a
variety of equivalent
forms, including whole
numbers, integers,
(0 points) Didn’t
identify any.
Manipulatives
and Models
operations on rational numbers
(e.g., whole numbers, fractions,
decimals, integers) using
multiple representations and
algorithms and understand the
relationships between these
operations (i..e., addition,
subtraction, multiplication, and
division); (4) Select the
appropriate operations(s) to
solve problems involving rations
and percents and the addition,
subtraction, multiplication, and
division of rational numbers; (5)
Apply number theory concepts
(e.g., primes, composites,
multiples, factors, number
sequences, number properties,
rules of divisibility).
operations on rational
numbers (e.g., whole
numbers, fractions, decimals,
integers) using multiple
representations and
algorithms and understand the
relationships between these
operations (i..e., addition,
subtraction, multiplication,
and division); (4) Select the
appropriate operations(s) to
solve problems involving
rations and percents and the
addition, subtraction,
multiplication, and division of
rational numbers; (5) Apply
number theory concepts (e.g.,
primes, composites, multiples,
factors, number sequences,
number properties, rules of
divisibility).
fractions, decimals,
percents, and exponents;
(3) Perform operations on
rational numbers (e.g.,
whole numbers, fractions,
decimals, integers) using
multiple representations
and algorithms and
understand the
relationships between
these operations (i..e.,
addition, subtraction,
multiplication, and
division); (4) Select the
appropriate operations(s)
to solve problems
involving rations and
percents and the addition,
subtraction, multiplication,
and division of rational
numbers; (5) Apply
number theory concepts
(e.g., primes, composites,
multiples, factors, number
sequences, number
properties, rules of
divisibility).
(10 points) Identifies and
explains how specific (by name)
manipulatives, mathematical
(7 points) Identifies and
explains how specific (by
name) manipulatives,
(4 points) Identifies and
explains how specific (by
name) manipulatives,
(0 points) Didn’t
identify and
explain any.
Geometry and
Measurement
Appropriate
instructional
strategies
Manipulatives
and Models
and physical models, and or
technology can be used to teach
numbers and operations.
Identifies and explains at
minimum one of each for a total
of 3.
mathematical and physical
models, and or technology can
be used to teach numbers and
operations. Identifies and
explain two out of three.
mathematical and physical
models, and or technology
can be used to teach
numbers and operations.
Identifies and explain one
out of three.
(20 points) Identifies a variety of
appropriate instructional
strategies for at least three out
of the following concepts: (1)
Analyze properties of twodimensional shapes (e.g., area,
sides, angles).
(2) Apply the geometric
concepts of symmetry,
congruency, similarity, and
transformations. (3) Determine
how a change in length, width,
height, or radius affects
perimeter, circumference, area,
surface area, or volume. (4)
Select appropriate
measurement units to solve
problems.
(14 points) Identifies a variety
of appropriate instructional
strategies for at least two out
of the following concepts: (1)
Analyze properties of twodimensional shapes (e.g., area,
sides, angles).
(2) Apply the geometric
concepts of symmetry,
congruency, similarity, and
transformations. (3)
Determine how a change in
length, width, height, or radius
affects perimeter,
circumference, area, surface
area, or volume. (4) Select
appropriate measurement
units to solve problems.
(8 points) Identifies a
variety of appropriate
instructional strategies for
at least one out of the
following concepts: (1)
Analyze properties of twodimensional shapes (e.g.,
area, sides, angles).
(2) Apply the geometric
concepts of symmetry,
congruency, similarity, and
transformations. (3)
Determine how a change
in length, width, height, or
radius affects perimeter,
circumference, area,
surface area, or volume.
(4) Select appropriate
measurement units to
solve problems.
(0 points) Didn’t
identify any.
(10 points) Identifies and
explains how specific (by name)
(7 points) Identifies and
explains how specific (by
(4 points) Identifies and
explains how specific (by
(0 points) Didn’t
identify and
Algebra
Appropriate
instructional
strategies
Manipulatives
and Models
Data Analysis
Appropriate
instructional
strategies
manipulatives, mathematical
and physical models, and or
technology can be used to teach
geometry and measurement.
Identifies and explains at
minimum one of each for a total
of 3.
name) manipulatives,
mathematical and physical
models, and or technology can
be used to teach geometry
and measurement. Identifies
and explains two of the three.
name) manipulatives,
mathematical and physical
models, and or technology
can be used to teach
geometry and
measurement. Identifies
and explains one of the
three.
explain any.
(10 points) Identifies an
appropriate instructional
strategy and explains how it can
be used to teach student to
generalizing patterns or
functional relationships.
(2 points) Identified an
inappropriate instructional
strategy.
(0 points) Didn’t
identify any.
(10 points) Identifies and
explains how specific (by name)
manipulatives, mathematical
and physical models, and or
technology can be used to teach
algebra. Identifies and explains
at minimum one of each for a
total of 3.
(5 points) Identifies an
appropriate instructional
strategy but doesn’t explain
how it can be used to teach
students to generalize
patterns or functional
relationships.
(7 points) Identifies and
explains how specific (by
name) manipulatives,
mathematical and physical
models, and or technology can
be used to teach algebra.
Identifies and explains two of
the three.
(4 points) Identifies and
explains how specific (by
name) manipulatives,
mathematical and physical
models, and or technology
can be used to teach
algebra. Identifies and
explains one of the three.
(0 points) Didn’t
identify and
explain any.
(10 points) Identifies an
appropriate instructional
strategy and explains how it can
be used to teach student to
make accurate predictions and
draw conclusions from data.
(5 points) Identifies an
appropriate instructional
strategy but doesn’t explain
how it can be used to teach
students to make accurate
predictions and draw
(2 points) Identified an
inappropriate instructional
strategy.
(0 points) Didn’t
identify any.
Manipulatives
and Models
(10 points) Identifies and
explains how specific (by name)
manipulatives, mathematical
and physical models, and or
technology can be used to teach
data analysis. Identifies and
explains at minimum one of
each for a total of 3.
conclusions from data.
(7 points) Identifies and
explains how specific (by
name) manipulatives,
mathematical and physical
models, and or technology can
be used to teach data analysis.
Identifies and explains two of
the three.
(4 points) Identifies and
explains how specific (by
name) manipulatives,
mathematical and physical
models, and or technology
can be used to teach data
analysis. Identifies and
explains one of the three.
(0 points) Didn’t
identify and
explain any.