PUBLISHER:
SUBJECT:
SPECIFIC GRADE:
COURSE:
TITLE:
COPYRIGHT DATE:
SE ISBN:
TE ISBN:
GENERIC EVALUATION CRITERIA
20013-2016 – Off Cycle Year Adoption
Grade 3 Mathematics
Yes
R-E-S-P-O-N-S-E
No
N/A
CRITERIA
NOTES
I. INTER-ETHNIC
The instructional material meets the
requirements of inter-ethnic: concepts,
content and illustrations, as set by West
Virginia Board of Education Policy (Adopted
December 1970).
II. EQUAL OPPORTUNITY
The instructional material meets the
requirements of equal opportunity: concept,
content, illustration, heritage, roles
contributions, experiences and achievements
of males and females in American and other
cultures, as set by West Virginia Board of
Education Policy (Adopted May 1975).
1
III. FORMAT
The resource is available as an option for
adoption in an interactive electronic format.
INSTRUCTIONAL MATERIALS ADOPTION: 21st CENTURY LEARNING EVALUATION CRITERIA
GENERAL EVALUATION CRITERIA
20013-2016 – Off Cycle Year Adoption
Grade 3 Mathematics
INSTRUCTIONAL MATERIALS ADOPTION: GENERAL EVALUATION CRITERIA
The general evaluation criteria apply to each grade level and are to be evaluated for each grade level unless otherwise specified. These criteria consist of
information critical to the development of all grade levels. In reading the general evaluation criteria and subsequent specific grade level criteria, e.g. means
“examples of” and i.e. means that “each of” those items must be addressed. Eighty percent of the general criteria must be met with I (In-depth) or A
(Adequate) in order to be recommended.
2
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
(IMR Committee) Responses
I=In-depth
A=Adequate
M=Minimal
N=Nonexistent
I
A
M
N
For student mastery of content standards and objectives, the instructional materials will provide students with the opportunity to
apply:
A. MATHEMATICAL PRACTICES
1. Make sense of problems and persevere in solving them.
 Explain to themselves the meaning of a problem and looking for
entry points to its solution.
 Analyze givens, constraints, relationships, and goals
 Make conjectures about the form and meaning of the solution
attempt.
 Plan a solution pathway rather than simply jumping into a
solution.
 Consider analogous problems and try special cases and simpler
forms of insight into its solution.
 Monitor and evaluate their progress and change course if
necessary.
 Transform algebraic expressions or change the viewing window
on their graphing calculator to get information.
 Explain correspondences between equations, verbal descriptions,
tables, and graphs.
 Draw diagrams of important features and relationships, graph
data, and search for regularity or trends.
 Use concrete objects or pictures to help conceptualize and solve
a problem.
 Check their answers to problems using a different method.
 Ask themselves, “Does this make sense?”
 Understand the approaches of others to solving complex
3
problems and identify correspondences between approaches.
2. Reason abstractly and quantitatively.
 Make sense of quantities and their relationships in problem
situations.
 Bring two complementary abilities to bear on problems involving
quantitative relationships:
o Decontextualize (abstract a given situation and represent it
symbolically and manipulate the representing symbols as if
they have a life of their own, without necessarily attending
to their referents and
o Contextualize (pause as needed during the manipulation
process in order to probe into the referents for the symbols
involved).
 Use quantitative reasoning that entails creating a coherent
representation of the problem at hand, considering the units
involved, and attending to the meaning of quantities, not just how
to compute them
 Know and flexibly use different properties of operations and
objects.
3. Construct viable arguments and critique the reasoning of others.
 Understand and use stated assumptions, definitions, and
previously established results in constructing arguments.
 Make conjectures and build a logical progression of statements to
explore the truth of their conjectures.
 Analyze situations by breaking them into cases
 Recognize and use counterexamples.
 Justify their conclusions, communicate them to others, and
respond to the arguments of others.
 Reason inductively about data, making plausible arguments that
take into account the context from which the data arose.
 Compare the effectiveness of plausible arguments.
 Distinguish correct logic or reasoning from that which is flawed
4

and, if there is a flaw, explain what it is
o Elementary students construct arguments using concrete
referents such as objects, drawings, diagrams, and
actions.
o Later students learn to determine domains to which an
argument applies.
Listen or read the arguments of others, decide whether they
make sense, and ask useful question to clarify or improve
arguments.
4. Model with mathematics.
 Apply the mathematics they know to solve problems arising in
everyday life, society, and the workplace.
o In early grades, this might be as simple as writing an
addition equation to describe a situation. In middle grades,
a student might apply proportional reasoning to plan a
school event or analyze a problem in the community.
o By high school, a student might use geometry to solve a
design problem or use a function to describe how one
quantity of interest depends on another.
 Make assumptions and approximations to simplify a complicated
situation, realizing that these may need revision later.
 Identify important quantities in a practical situation
 Map their relationships using such tools as diagrams, two-way
tables, graphs, flowcharts and formulas.
 Analyze those relationships mathematically to draw conclusions.
 Interpret their mathematical results in the context of the situation.
 Reflect on whether the results make sense, possibly improving the
model if it has not served its purpose.
5. Use appropriate tools strategically.
 Consider available tools when solving a mathematical problem.
(these tools might include pencil and paper, concrete models, a
ruler, protractor, calculator, spreadsheet, computer algebra
system, a statistical package, or dynamic geometry software.
5





Are sufficiently familiar with tools appropriate for their grade or
course to make sound decisions about when each of these tools
might be helpful, recognizing both the insight to be gained and
their limitations.
o High school students analyze graphs of functions and
solutions generated using a graphing calculator
Detect possible errors by using estimations and other
mathematical knowledge.
Know that technology can enable them to visualize the results of
varying assumptions, explore consequences, and compare
predictions with data.
Identify relevant mathematical resources and use them to pose or
solve problems.
Use technological tools to explore and deepen their understanding
of concepts.
6. Attend to precision.
 Try to communicate precisely to others.
 Try to use clear definitions in discussion with others and in their own
reasoning.
 State the meaning of the symbols they choose, including using the
equal sign consistently and appropriately.
 Specify units of measure and label axes to clarify the
correspondence with quantities in a problem.
 Calculate accurately and efficiently, express numerical answers with
a degree of precision appropriate for the problem context.
o In the elementary grades, students give carefully formulated
explanations to each other.
o In high school, students have learned to examine claims and
make explicit use of definitions.
7. Look for and make use of structure.
 Look closely to discern a pattern or structure.
o Young students might notice that three and seven more is the
same amount as seven and three more or they may sort a
6


collection of shapes according to how many sides the shapes
have.
o Later, students will see 7 x 8 equals the well remembered 7 x 5 +
7 x 3, in preparation for the distributive property.
o In the expression x2 + 9x + 14, older students can see the 14 as
2 x 7 and the 9 as 2 + 7. They recognize the significance of an
existing line in a geometric figure and can use the strategy of
drawing an auxiliary line for solving problems.
Step back for an overview and can shift perspective.
See complicated things, such as some algebraic expressions, as
single objects or composed of several objects.
8. Look for and express regularity in repeated reasoning.
 Notice if calculations are repeated.
 Look both for general methods and for shortcuts.
o Upper elementary students might notice when dividing 25 by 11
that they are repeating the same calculations over and over
again, and conclude they have a repeated decimal.
o Middle school students might abstract the equation (y-2)/((x-1)=3
by paying attention to the calculation of slope as they repeatedly
check whether the points are on the line through (1,2) with a
slope 3.
o Noticing the regularity in the way terms cancel when expanding
(x-1)(x+1)(x2+1) and (x-1)(x3+x2+x+1) might lead high school
students to the general formula for the sum of a geometric
series.
 Maintain oversight of the process of solving a problem, while
attending to the details.
 Continually evaluate the reasonableness of intermediate results.
7
SPECIFIC EVALUATION CRITERIA
20013-2016 – Off Cycle Year Adoption
Grade 3 Mathematics
In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100;
(2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and
(4) describing and analyzing two-dimensional shapes.
1. Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays and area
models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the
unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies
based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship
between multiplication and division.
2. Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along
with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a
small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal
parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They
solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.
3. Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the
shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into
identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication and justify using multiplication to
determine the area of a rectangle.
4. Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions
of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.
8
(IMR Committee) Responses
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
I=In-depth
A=Adequate
M=Mi
nimal
N=Nonexistent
I
A
M
N
For student mastery of content standards and objectives, the instructional materials will provide students with the
opportunity to
A. Operations & Algebraic Thinking
Represent and solve problems involving multiplication and division.
1. interpret products of whole numbers, e.g., interpret 5 × 7 as the total
number of objects in 5 groups of 7 objects each. For example,
describe context in which a total number of objects can be expressed
as 5 × 7.
2. interpret whole-number quotients of whole numbers, e.g., interpret 56
÷ 8 as the number of objects in each share when 56 objects are
partitioned equally into 8 shares, or as a number of shares when 56
objects are partitioned into equal shares of 8 objects each. For
example, describe a context in which a number of shares or a number
of groups can be expressed as 56 ÷ 8.
3. use multiplication and division within 100 to solve word problems in
situations involving equal groups, arrays and measurement
quantities, e.g., by using drawings and equations with a symbol for
9
the unknown number to represent the problem.
4. determine the unknown whole number in a multiplication or division
equation relating three whole numbers. For example, determine the
unknown number that makes the equation true in each of the
equations 8× ? = 48, 5 = ? ÷ 3, 6 × 6 = ?.
Understand properties of multiplication and the relationship between
multiplication and division.
5. interpret products of whole numbers, e.g., interpret 5 × 7 as the total
number of objects in 5 groups of 7 objects each. For example,
describe context in which a total number of objects can be expressed
as 5 × 7.
6. interpret whole-number quotients of whole numbers, e.g., interpret 56
÷ 8 as the number of objects in each share when 56 objects are
partitioned equally into 8 shares, or as a number of shares when 56
objects are partitioned into equal shares of 8 objects each. For
example, describe a context in which a number of shares or a number
of groups can be expressed as 56 ÷ 8.
Multiply and divide within 100.
7. fluently multiply and divide within 100, using strategies such as the
relationship between multiplication and division (e.g., knowing that 8 ×
5 = 40, one knows 40 ÷ 5 = 8) or properties of operations and by the
end of Grade 3, know from memory all products of two one-digit
numbers.
Solve problems involving the four operations, and identify and explain
patterns in arithmetic.
8. solve two-step word problems using the four operations, represent
these problems using equations with a letter standing for the
unknown quantity and assess the reasonableness of answers using
mental computation and estimation strategies including rounding.
(This standard is limited to problems posed with whole numbers and
having whole number answers; students should know how to perform
operations in the conventional order when there are no parenthesis to
specify a particular order (Order of Operations).)
9. identify arithmetic patterns (including patterns in the addition table or
multiplication table) and explain them using properties of operations .
For example, observe that 4 times a number is always even and
explain why 4 times a number can be decomposed into two equal
10
addends.
B. Number & Operations in Base Ten
Use place value understanding and properties of operations to perform multi-digit arithmetic.
1. understand a fraction 1/b as the quantity formed by 1 part when a
whole is partitioned into b equal parts and understand a fraction a/b
as the quantity formed by a parts of size 1/b.
2. understand a fraction as a number on the number line and represent
fractions on a number line diagram
a. represent a fraction 1/b on a number line diagram by defining
the interval from 0 to 1 as the whole and partitioning it into b
equal parts and recognize that each part has size 1/b and
that the endpoint of the part based at 0 locates the number
1/b on the number line.
b. represent a fraction a/b on a number line diagram by marking
off a lengths 1/b from 0 and recognize that the resulting
interval has size a/b and that its endpoint locates the number
a/b on the number line.
3. explain equivalence of fractions in special cases and compare
fractions by reasoning about their size
a. understand two fractions as equivalent (equal) if they are the
same size or the same point on a number line,
b. recognize and generate simple equivalent fractions, e.g., 1/2
= 2/4, 4/6 = 2/3) and explain why the fractions are equivalent,
e.g., by using a visual fraction model,
c. express whole numbers as fractions, and recognize fractions
that are equivalent to whole numbers (Examples: Express 3
in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at
the same point of a number line diagram.)
d. compare two fractions with the same numerator or the same
denominator by reasoning about their size, recognize that
comparisons are valid only when the two fractions refer to the
11
same whole, record the results of comparisons with the
symbols >, = or < and justify the conclusions, e.g., by using a
visual fraction model.
C. Measurement & Data
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of
objects.
1. tell and write time to the nearest minute, measure time intervals in
minutes and solve word problems involving addition and subtraction
of time intervals in minutes, e.g., by representing the problem on a
number line diagram.
2. measure and estimate liquid volumes and masses of objects using
standard units of grams (g), kilograms (kg) and liters (l) (Excludes
compound units such as cm3 and finding the geometric volume of a
container.) and subtract, multiply or divide to solve one-step word
problems involving masses or volumes that are given in the same
units, e.g., by using drawings (such as a beaker with a measurement
scale) to represent the problem. (Excludes multiplicative comparison
problems - problems involving notions of “times as much”.)
Represent and interpret data.
3. draw a scaled picture graph and a scaled bar graph to represent a
data set with several categories and solve one- and two-step “how
many more” and “how many less” problems using information
presented in scaled bar graphs. For example, draw a bar graph in
which each square in the bar graph might represent 5 pets.
4. generate measurement data by measuring lengths using rulers
marked with halves and fourths of an inch and show the data by
12
making a line plot, where the horizontal scale is marked off in
appropriate units—whole numbers, halves or quarters.
Geometric measurement: understand concepts of area and relate area to
multiplication and to addition.
5
recognize area as an attribute of plane figures and understand
concepts of area measurement
a. a square with side length 1 unit, called “a unit square,” is said
to have “one square unit” of area and can be used to
measure area,
b. a plane figure which can be covered without gaps or overlaps
by n unit squares is said to have an area of n square units.
6
measure areas by counting unit squares (square cm, square m,
square in, square ft and improvised units).
7
relate area to the operations of multiplication and addition
a. find the area of a rectangle with whole-number side lengths
by tiling it, and show that the area is the same as would be
found by multiplying the side lengths,
b. multiply side lengths to find areas of rectangles with whole
number side lengths in the context of solving real world and
mathematical problems and represent whole-number
products as rectangular areas in mathematical reasoning,
c. use tiling to show in a concrete case that the area of a
rectangle with whole-number side lengths a and b + c is the
sum of a × b and a × c and use area models to represent the
distributive property in mathematical reasoning,
d. recognize area as additive and find areas of rectilinear figures
by decomposing them into non-overlapping rectangles and
adding the areas of the non-overlapping parts, applying this
technique to solve real world problems.
Geometric measurement: recognize perimeter as an attribute of plane
figures and distinguish between linear and area measures.
13
8
solve real world and mathematical problems involving perimeters of
polygons, including finding the perimeter given the side lengths,
finding an unknown side length and exhibiting rectangles with the
same perimeter and different areas or with the same area and
different perimeters.
D. Geometry
Reason with Shapes and Their Attributes
1. understand that shapes in different categories (e.g., rhombuses,
rectangles and others) may share attributes (e.g., having four sides),
that the shared attributes can define a larger category (e.g.
quadrilaterals), recognize rhombuses, rectangles and squares as
examples of quadrilaterals and draw examples of quadrilaterals that
do not belong to any of these subcategories.
2. partition shapes into parts with equal areas and express the area of
each part as a unit fraction of the whole. For example, partition a
shape into 4 parts with equal area, and describe the area of each part
as ¼ or the area of the shape.
14