3 - DoDEA

Transcription

3 - DoDEA

DoDEA CCRSM Gap Analysis
DOMAIN
Third Grade
College and Career Ready Standards for Mathematics (CCRSM)
OPERATIONS AND ALGEBRAIC THINKING
3.OA.A.1
3.OA.A.2
3.OA.A.3
DoDEA Standards
Alignment Notes
CLUSTER: Represent and solve problems involving multiplication and division.
Demonstrate and explain
Interpret products of whole numbers, e.g., interpret 5
multiplication and division
× 7 as the total number of objects in 5 groups of 7
DoDEA numbers are much bigger, but
through the use of
objects each. For example, describe a context in
3.M.1i
representations and mathematical context is missing.
which a total number of objects can be expressed as 5
symbols where factors are 99 or
× 7.
less.
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.
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 the
unknown number to represent the problem.
Alignment of DoDEA CCRSM with the DoDEA Academic Standards
3.M.1i
through the use of
representations and mathematical
less.
4.M.1f
Use models to represent division
problems as the inverse of
multiplication, as partitioning, or
as successive subtraction and
describe the meaning of
remainders.
3.M.1h
Explain and solve problems
involving the multiplication of two
whole numbers where factors are
99 or less.
DoDEA numbers are much bigger.
Division emphasis for DoDEA increases in
Grade 4.
Solving problems with division and the
explicit use of variables do not appear
until Grade 4. The numbers included in
DoDEA standards are much larger.
DODEA standards don’t mention
measurement quantities nor do they
address the conceptual move from
groups to arrays.
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DOMAIN
DoDEA Standards
3.M.1i
3.OA.A.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 the
unknown number to represent the problem.
4.M.1i
4.M.1j
4.M.2f
3.OA.A.4
3.OA.B.5
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 = ?
3.M.1f
Alignment Notes
through the use of
less.
Divide two-digit whole numbers
by one-digit divisors.
Use the inverse relationships of
addition and subtraction, and
multiplication and division to solve
problems and verify solutions.
Write and solve algebraic
equations or inequalities using
variables that represent problem
situations.
Explain the relationship between
multiplication and division as
inverse operations.
The Grade 3 standard uses the word
"explain" but the example shows this to
be a very close match.
CLUSTER: Understand properties of multiplication and the relationship between multiplication and division.
Apply properties of operations as strategies to
Although DoDEA standards contain all
multiply and divide. Examples: If 6 × 4 = 24 is known,
the necessary components, the intent of
Solve open sentences by
then 4 × 6 = 24 is also known. (Commutative property
using the strategies flexibly with
representing an expression in
of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15,
decomposition of number prior to fact
3.M.2d more than one way using the
then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30.
memory is not present. The "higher" is an
commutative and associative
(Associative property of multiplication.) Knowing that
issue here. The Grade 5 standard was a
properties of multiplication.
8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 +
much better match to the computation
2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive
issue than the Grade 4 standard.
property.)
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DOMAIN
3.OA.B.5
3.OA.B.6
3.OA.C.7
Apply properties of operations as strategies to
multiply and divide. Examples: If 6 × 4 = 24 is known,
then 4 × 6 = 24 is also known. (Commutative property
of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15,
then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30.
(Associative property of multiplication.) Knowing that
8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 +
2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive
property.)
DoDEA Standards
4.M.2e
Use and interpret variables,
mathematical symbols, and
properties of addition and
multiplication (e.g., commutative,
associative, and the distributive
property) to write and simplify
mathematical expressions and
sentences.
5.M.1f
Identify and use the distributive
property to simplify and/or
perform computations.
through the use of
3.M.1i
Understand division as an unknown-factor
problem. For example, find 32 ÷ 8 by finding the
number that makes 32 when multiplied by 8.
less.
Explain the relationship between
3.M.1f multiplication and division as
inverse operations.
CLUSTER: Multiply and divide within 100.
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.
By the end of Grade 3, know from memory all
products of two one-digit numbers.
4.M.1j
4.M.1m
Demonstrate mastery in sums to
20 and related subtraction facts
and multiplication through 12X12
and related division facts.
Alignment Notes
Although the missing factor is not
specified, the two DoDEA standards
would logically include this.
DoDEA expects fact mastery for all
operations in Grade 4, but it is not
required earlier. CCRSM connects fluency
with strategies based on properties of
number and operations, which are not
specified in DODEA.
Page 50
DOMAIN
DoDEA Standards
Alignment Notes
CLUSTER: Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.M.1k
3.M.1j
3.OA.D.8
Solve two-step word problems using the four
operations. Represent these problems using
equations with a letter standing for the unknown
quantity. Assess the reasonableness of answers using
mental computation and estimation strategies
including rounding.
3.M.2c
Solve multi-step problems for
using mathematical tools and
strategies involving addition,
subtraction, and multiplication.
Later problem solving with division and
use of variables in DoDEA. It should be
noted that rounding is not explicitly
mentioned in DoDEA estimation
strategies.
Develop and use strategies to
estimate the results of whole
number addition and subtraction
and verify this.
Demonstrate mathematical
relationships of quantity in the
form of numeric expressions,
equations, or inequalities with
mathematical symbols.
4.M.1j
4.M.1k
Use estimation to make
predictions and check the
reasonableness of result.
4.M.2f
Write and solve algebraic
equations or inequalities using
variables that represent problem
situations.
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DOMAIN
3.OA.D.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 addends.
DoDEA Standards
3.M.2a
Identify, describe using their own
words, and extend the rules of
repeating, number, and growing
patterns.
3.M.2e
Organize and order data in tables
to discover patterns and make
predictions.
Alignment Notes
The level of justification in CCRSM is not
found in DoDEA standards (no "why"
required). There is preliminary pattern
work in DoDEA standards that does not
occur in CCRSM. 3.M.2a seems to
encapsulate earlier DoDEA numeric
patterns.
NUMBER AND OPERATOINS IN BASE TEN
CLUSTER: Use place value understanding and properties of operations to perform multi-digit arithmetic.
3.NBT.A.1
Use place value understanding to round whole
numbers to the nearest 10 or 100.
3.NBT.A.2
Fluently add and subtract within 1000 using strategies
and algorithms based on place value, properties of
operations, and/or the relationship between addition
and subtraction.
3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10
in the range 10-90 (e.g., 9 × 80, 5 × 60) using
strategies based on place value and properties of
operations.
not aligned
Rounding is not explicitly treated in
DoDEA standards.
3.M.1g
Explain and solve problems
involving the sum or difference of
two whole numbers up to 10,000.
DoDEA standard goes to larger values.
Strategies in CCRSM are not referenced.
DODEA does not reference use of
algorithms or use of properties, etc.
3.M.1i
through the use of
less.
CCRSM is included in the "factors are 99
or less." The emphasis on the pattern in
the CCSSM may be developed while
teaching multiplication ideas and
algorithms. Not specified in DODEA
standard, and not “straight-forward
computation.”
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DOMAIN
3.NF.A.1
NUMBERS AND OPERATIONS - FRACTIONS
3.NF.A.2
3.NF.A.2.A
3.NF.A.2.B
DoDEA Standards
CLUSTER: Develop understanding of fractions as numbers.
Understand a fraction 1/b as the quantity formed by 1
part when a whole is partitioned into b equal parts;
not aligned
understand a fraction a/b as the quantity formed
by a parts of size 1/b.
Identify, compare, and order the
Understand a fraction as a number on the number
4.M.1l relative position of fractions and
line; represent fractions on a number line diagram.
decimals on a number line.
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. Recognize that each
4.M.1l relative position of fractions and
part has size 1/b and that the endpoint of the part
based at 0 locates the number 1/b on the number
line.
Represent a fraction a/b on a number line diagram by
marking off a lengths 1/b from 0. Recognize that the
resulting interval has size a/b and that its endpoint
locates the number a/b on the number line.
4.M.1l
3.M.1c
3.NF.A.3
Explain equivalence of fractions in special cases, and
compare fractions by reasoning about their size.
4.M.1c
relative position of fractions and
Identify and generate equivalent
forms of common fractions less
than one whole, e.g., halves,
thirds, quarters, fifths, and tenths;
and explain their relationship to a
whole.
Judge the size of fractions by using
benchmarks, e.g., 0, ½, 1; and use
the terms greater than, less than,
or equal to or appropriate
mathematical symbols >, <, or = to
compare a fraction to the
benchmark.
Alignment Notes
This specific definition is not explicit in
DoDEA standards.
DoDEA standards do not include the
partitioning of the number line.
See comments linked to parts 3.M.1.A-D.
Page 53
DOMAIN
3.NF.A.3
3.NF.A.3.A
Explain equivalence of fractions in special cases, and
compare fractions by reasoning about their size.
Understand two fractions as equivalent (equal) if they
are the same size, or the same point on a number
line.
DoDEA Standards
4.M.1l
3.M.1c
whole.
DoDEA standard includes concept of
equivalence. Fractions are compared to
the whole not to each other. Referencing
the same point on the number line is not
mentioned in this standard (an equality
on the same point not mentioned in
4.M.1l.)
Use of visual model is included in DoDEA
standard example as well.
Number line is not mentioned in DoDEA
standard but "another way of
representing three thirds" is in 2.M.1j.
3.NF.A.3.B
Recognize and generate simple equivalent fractions,
e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions
are equivalent, e.g., by using a visual fraction model.
3.M.1c
whole.
3.NF.A.3.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.
2.M.1j
Use words, numerals, and physical
models to represent fractions and
their relationship to the whole.
Alignment Notes
Page 54
DOMAIN
3.NF.A.3.D
MEASUREMENT AND DATA
3.MD.A.1
3.MD.A.2
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 same whole. Record the
results of comparisons with the symbols >, =, or <, and
justify the conclusions, e.g., by using a visual fraction
model.
DoDEA Standards
4.M.1c
Judge the size of fractions by using
benchmarks, e.g., 0, ½, 1; and use
the terms greater than, less than,
or equal to or appropriate
mathematical symbols >, <, or = to
compare a fraction to the
benchmark.
4.M.1l
Alignment Notes
Although benchmarks and number lines
are used, reasoning is based on number
of equal parts or same number of
unequal parts not explicitly included in
DoDEA standards.
CLUSTER: Solve problems involving measurement and estimation.
Tell and write time to the nearest minute and
Tell time to the nearest minute
measure time intervals in minutes. Solve word
3.M.4h and find how much time has
problems involving addition and subtraction of time
elapsed.
intervals in minutes, e.g., by representing the problem
on a number line diagram.
Measure and estimate liquid volumes and masses of
objects using standard units of grams (g), kilograms
(kg), and liters (l). Add, 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.
2.M.4d
Make and use estimates of
measurement, including time
volume, weight, and area; verify
results.
3.M.4b
Use accurate vocabulary to
describe measurements of length,
volume, and weight.
4.M.4b
Measure with accuracy using both
customary and metric systems of
measurement.
Word problems specifically related to
measures and reading measurements are
not included in DoDEA standards.
Page 55
DOMAIN
DoDEA Standards
Alignment Notes
CLUSTER: Represent and interpret data.
3.MD.B.3
3.MD.B.4
Draw a scaled picture graph and a scaled bar graph to
represent a data set with several categories. 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.
Generate measurement data by measuring lengths
using rulers marked with halves and fourths of an
inch. Show the data by making a line plot, where the
horizontal scale is marked off in appropriate units—
whole numbers, halves, or quarters.
3.M.5b
Translate information from one
data representation to a graph or
table, e.g., frequency table, bar
graph, picture graph, line plot.
3.M.5c
Analyze and interpret information
by writing at least one statement
to support a conclusion or
prediction with evidence from
data.
3.M.5d
Organize and graphically display
data using categories and
intervals.
1.M.4c
Estimate and measure a variety of
attributes of objects using
standard and nonstandard units.
3.M.5b
Translate information from one
data representation to a graph or
table, e.g., frequency table, bar
graph, picture graph, line plot.
4.M.1l
Specificity about scale or key is not
present in DoDEA standards and needs to
be addressed for alignment. It is not clear
that one- and two-step problems are
included in 3.M.5c. This would need to
be spelled out.
The first mention of fractions on a
number line in DoDEA is in Grade 4.
Page 56
DOMAIN
3.MD.C.5
3.MD.C.5.A
3.MD.C.5.B
3.MD.C.6
3.MD.C.7
3.MD.C.7.A
DoDEA Standards
Alignment Notes
CLUSTER: Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Select units, strategies, and tools
See comments for parts A and B. Area as
to estimate and calculate
a concept is not formalized in the
3.M.4c
perimeter and area of twostandards until Grade 4.
dimensional shapes.
Recognize area as an attribute of plane figures and
understand concepts of area measurement.
Recognize that the area is the
measure of the space enclosed by
4.M.4c a two-dimensional figure and that
angles are figures made by two
rays with the same endpoint.
A square with side length 1 unit, called "a unit
Unit squares are not specifically
square," is said to have "one square unit" of area, and 3.M.4c
perimeter and area of tworeferenced in DoDEA standards.
can be used to measure area.
dimensional shapes.
A plane figure which can be covered without gaps or
Covering or tiling not explicit in DoDEA
overlaps by n unit squares is said to have an area
3.M.4c
perimeter and area of twostandards.
of n square units.
dimensional shapes.
DoDEA standards do not specify units or
Measure areas by counting unit squares (square cm,
3.M.4c
perimeter and area of twocounting unit squares.
square m, square in, square ft, and improvised units).
dimensional shapes.
See comments linked to parts A-D. Many
Relate area to the operations of multiplication and
of the concepts and methods are in
3.M.4c
perimeter and area of twoaddition.
DoDEA Grade 4.
dimensional shapes.
DoDEA standards do not specify tiling,
Find the area of a rectangle with whole-number side
but that is a common beginning strategy.
lengths by tiling it, and show that the area is the same 3.M.4c
perimeter and area of twoas would be found by multiplying the side lengths.
relationship between tiling and
dimensional shapes.
multiplication explicitly.
Page 57
DOMAIN
3.MD.C.7.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.
3.MD.C.7.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. Use
area models to represent the distributive property in
mathematical reasoning.
3.MD.C.7.D
Recognize area as additive. Find areas of rectilinear
figures by decomposing them into non-overlapping
rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve
real world problems.
3.MD.D.8
3.MD.D.8
DoDEA Standards
3.M.4c
4.M.4i
perimeter and area of twodimensional shapes.
Solve problems involving
perimeter and areas of rectangles.
not aligned
3.M.4c
perimeter and area of twodimensional shapes.
Describe strategies for estimating
the area of irregular shapes.
4.M.4i
CLUSTER: Geometric measurement: recognize perimeter.
Solve real world and mathematical problems involving
perimeters of polygons, including finding the
perimeter given the side lengths, finding an unknown
3.M.4c
side length, and exhibiting rectangles with the same
perimeter and area of twoperimeter and different areas or with the same area
dimensional shapes.
and different perimeters.
Solve real world and mathematical problems involving
Select units and develop strategies
perimeters of polygons, including finding the
3.M.4f for estimating the perimeter of
perimeter given the side lengths, finding an unknown
irregular two-dimensional shapes.
side length, and exhibiting rectangles with the same
perimeter and different areas or with the same area
Alignment Notes
DoDEA standards do not include using
rectangular areas to represent products.
They do not specify solving by
multiplication, but this is inferred.
Although DoDEA standards include
finding area and using the distributive
property, they do not contain a
combination of the two at the PK-8 level.
CCRSM specifies rectilinear so DoDEA
standards listed seem to span the
content requirements.
4.M.4h
All situations included except the case for
fixed perimeter (which is a fairly
important idea for the characteristics of
squares).
Page 58
DOMAIN
and different perimeters.
DoDEA Standards
4.M.4d
Determine the possible
dimensions of rectangles when
the area is constant.
4.M.4i
Alignment Notes
GEOMETRY
CLUSTER: Reason with shapes and their attributes.
3.G.A.1
Understand that shapes in different categories (e.g.,
rhombuses, rectangles, and others) may share
attributes (e.g., having four sides), and 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.
3.G.A.2
Partition shapes into parts with equal areas. 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
1/4 of the area of the shape.
3.G.A.2
Partition shapes into parts with equal areas. 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
1/4 of the area of the shape.
not aligned
1.M.1i
Recognize wholes and parts of
wholes, i.e., 1/2, 1/3, and 1/4.
2.M.1j
Use words, numerals, and physical
models to represent fractions and
their relationship to the whole.
DoDEA 3.M.3a includes comparison
based on attributes but the idea of
categories and shared attributes is not
developed.
The example from 1.M.1i is very close
except not all parts are labeled as 1/4.
2.M.1j adds the actual making of the
model. DODEA standard does not
mention “equal areas” in the context of
partitioning shapes.
Page 59
Third Grade Alignment Sorted by DoDEA Standards
X = grade level with similar alignment to current DoDEA standards
Gray shading = no alignment with CCRSM at specified grade levels
DoDEA Standards
Third Grade
3.M.1a: read, write, and interpret the place value for each digit in whole numbers up to
10,000
3.M.1b: read, write, and interpret the place value for each digit in decimal numbers between
0 and 1 through hundredths
3.M.1c: identify and generate equivalent forms of common fractions less than one whole,
e.g., halves, thirds, quarters, fifths, and tenths; and explain their relationship to a whole
3.M.1d: identify odd and even numbers up to 10,000, identify factors or multiples of a given
number, and describe their characteristics
3.M.1e: compare whole numbers, up to 10,000, using mathematical symbols (>, <, =) and
words (greater than, less than, equal to) and arrange them in numerical order
CCRSM
Gr 1
Gr 2
Gr 4
Gr 5
X
X
X
X
X
X
3.M.1f: explain the relationship between multiplication and division as inverse operations
3.M.1g: explain and solve problems involving the sum or difference of two whole numbers
up to 10,000
3.M.1h: explain and solve problems involving the multiplication of two whole numbers
where factors are 99 or less
3.M.1i: demonstrate and explain multiplication and division through the use of
representations and mathematical symbols where factors are 99 or less
3.M.1j: develop and use strategies to estimate the results of whole number addition and
subtraction and verify
3.M.1k: solve multi-step problems for using mathematical tools and strategies involving
addition, subtraction, and multiplication
3.M.2a: identify, describe using their own words, and extend the rules of repeating, number,
and growing patterns
Gr 3
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Page 60
DoDEA Standards
Third Grade
CCRSM
Gr 1
Gr 2
Gr 3
3.M.2b: make predictions, identify relationships, and solve problems by using a relationship
between two quantities
3.M.2c: demonstrate mathematical relationships of quantity in the form of numeric
expressions, equations, or inequalities with mathematical symbols
3.M.2d: solve open sentences by representing an expression in more than one way using the
commutative and associative properties of multiplication
X
3.M.2e: organize and order data in tables to discover patterns and make predictions
X
Gr 4
Gr 5
X
3.M.2f: identify and describe the difference between qualitative and quantitative changes
3.M.3a: identify and compare two-dimensional shapes and three-dimensional objects using
attributes and properties, e.g., sides and angles in two-dimensional shapes, faces and edges
in three-dimensional objects
X
X
3.M.3b: identify and describe the relative size of angles using right angles as a reference
X
3.M.3c: use coordinate systems to specify locations and describe paths
3.M.3d: verify if two-dimensional shapes have symmetry by drawing vertical, horizontal, and
diagonal drawing lines
3.M.3e: build, draw, and analyze two-dimensional shapes
X
X
3.M.4a: describe the relationship of units within the customary and metric measurement
systems
X
3.M.4b: use accurate vocabulary to describe measurements of length, volume, and weight
X
3.M.4c: select units, strategies, and tools to estimate and calculate perimeter and area of
two-dimensional shapes
X
Page 61
DoDEA Standards
Third Grade
CCRSM
Gr 1
Gr 2
Gr 3
Gr 4
Gr 5
3.M.4d: use measurement tools and techniques to construct a figure
3.M.4e: select standard units and tools to compare the attributes of two-dimensional shapes
and three-dimensional objects
3.M.4f: select units and develop strategies for estimating the perimeter of irregular twodimensional shapes
X
X
3.M.4g: measure temperature in Celsius and Fahrenheit
3.M.4h: tell time to the nearest minute and find how much time has elapsed
3.M.5a: develop and implement a plan to collect and organize data to address a given
question
3.M.5b: translate information from one data representation to a graph or table, e.g.,
frequency table, bar graph, picture graph, line plot
3.M.5c: Analyze and interpret information by writing at least one statement to support a
conclusion or prediction with evidence from data
3.M.5d: organize and graphically display data using categories and intervals
X
X
X
X
X
X
X
X
X
X
3.M.5e: describe characteristics of graphically represented data
3.M.5f: examine graphs and tables that display the same set of data to identify what each
representation contributes to the interpretation of data and conclusions drawn
3.M.5g: represent the possible outcomes for a simple probability situation
Page 62

3 - DoDEA

Transcription

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