Fourth Grade Math
|
Standard
1: The student uses numerical and computational concepts and
procedures in a variety of situations. |
Fourth Grade Knowledge Base Indicators
The student:
1.
compares and orders whole numbers to 1,000,000, simple fractions (halves,
fourths, eighths, sixteenths, thirds, tenths, hundredths), mixed numbers and
decimals to the thousandths place.
ND 2. knows,
explains, and uses addition, subtraction, multiplication, and division and other
equivalent representations for whole numbers, decimals, time, and money, and
addition, subtraction, and pictorial representations for simple fractions such
as 12¸2=4+2
or 7¢=$.07=7/100 of a dollar.
Fourth
Grade Application Indicators
The
student:
1.
uses appropriate representations of whole numbers to formulate and solve
real-world problems.
ND
2. determines reasonableness of numerical values involving whole numbers
to 1,000,000, simple fractions, and decimals to the thousandths.
Benchmark
2: NUMBER SYSTEMS AND THEIR PROPERTIES - The student demonstrates
an understanding of whole numbers with a special emphasis on place value,
recognizes, uses, and explains their properties, and extends these properties to
simple fractions, mixed numbers, decimals and money.
Fourth
Grade Knowledge Base Indicators
The
student:
1.
recognizes the need for whole numbers, simple fractions, mixed numbers,
and decimals to thousandths.
2.
classifies various types of numbers as whole numbers, mixed numbers, or
fractions and decimals; identifies the place value of various digits from
thousandths up to millions.
3.
identifies, models, writes, and reads numbers using numerals, words, and
expanded form from thousandths to millions such as four million sixty-two
thousand two hundred eighty-four = 4,062,284 = 4x1,000,000 + 6x10,000 + 2x1,000
+ 2x100 + 8x10 + 4x1.
ND
4. uses the concepts of the
following whole number properties: commutative
property of addition and multiplication; associative properties of addition and
multiplication such as
4+(2+3)=(4+2)+3 or 2x(3x4)=(2x3)x4,
additive and multiplicative identity properties (zero property of addition and
multiplicative property of one); the distributive property; the symmetric
property of addition and multiplication such as 100=20+80 is the same as
20+80=100; and the multiplicative property of zero with two factors
such as 9x0=0 or 112x0=0.
5.
identifies odd and even numbers.
Fourth
Grade Application Indicators
The
student:
ND
1. uses place value and properties
of the whole number system and money to explain his/her reasoning, and to
formulate and solve real-world problems.
|
Standard
1: The student uses numerical and computational concepts and
procedures in a variety of situations. |
Fourth Grade Knowledge Base Indicators
The student:
1.
compares and orders whole numbers to 1,000,000, simple fractions (halves,
fourths, eighths, sixteenths, thirds, tenths, hundredths), mixed numbers and
decimals to the thousandths place.
ND 2. knows,
explains, and uses addition, subtraction, multiplication, and division and other
equivalent representations for whole numbers, decimals, time, and money, and
addition, subtraction, and pictorial representations for simple fractions such
as 12¸2=4+2
or 7¢=$.07=7/100 of a dollar.
Fourth
Grade Application Indicators
The student:
1. uses appropriate representations of whole numbers to
formulate and solve real-world problems.
ND
2. determines
reasonableness of numerical values involving whole numbers to 1,000,000, simple
fractions, and decimals to the thousandths.
Benchmark
2: NUMBER SYSTEMS AND THEIR PROPERTIES - The student demonstrates
an understanding of whole numbers with a special emphasis on place value,
recognizes, uses, and explains their properties, and extends these properties to
simple fractions, mixed numbers, decimals and money.
Fourth
Grade Knowledge Base Indicators
The student:
1.
recognizes the need for whole numbers, simple fractions, mixed numbers,
and decimals to thousandths.
2.
classifies various types of numbers as whole numbers, mixed numbers, or
fractions and decimals; identifies the place value of various digits from
thousandths up to millions.
3.
identifies, models, writes, and reads numbers using numerals, words, and
expanded form from thousandths to millions such as four million sixty-two
thousand two hundred eighty-four = 4,062,284 = 4x1,000,000 + 6x10,000 + 2x1,000
+ 2x100 + 8x10 + 4x1.
ND
4. uses the
concepts of the following whole number properties:
commutative property of addition and multiplication; associative
properties of addition and multiplication such
as 4+(2+3)=(4+2)+3 or 2x(3x4)=(2x3)x4,
additive and multiplicative identity properties (zero property of addition and
multiplicative property of one); the distributive property; the symmetric
property of addition and multiplication such as 100=20+80 is the same as
20+80=100; and the multiplicative property of zero with two factors
such as 9x0=0 or 112x0=0.
5.
identifies odd and even numbers.
Fourth
Grade Application Indicators
The student:
ND
1. uses
place value and properties of the whole number system and money to explain
his/her reasoning, and to formulate and solve real-world problems.
For the purpose of assessing this indicator on the
a) use
place value from thousandths up to
millions.
b) use
concepts of the following whole number properties:
commutative property of addition and multiplication; associative
properties of addition and multiplication such
as 4+(2+3)=(4+2)+3 or 2x(3x4)=(2x3)x4,
additive and multiplicative identity properties (zero property of addition and
multiplicative property of one); the distributive property; the symmetric
property of addition and multiplication such as 100=20+80 is the same as
20+80=100; and the multiplicative property of zero with two factors
such as 9x0=0 or 112x0=0.
2. uses
place value and whole number properties to perform various computational
procedures, extends these properties to simple fractions, mixed numbers and
decimals and explains how the properties are used.
Benchmark
3: ESTIMATION - The student uses
numerical estimation with whole numbers, simple fractions, decimals, and money
in a variety of situations.
Fourth Grade Knowledge Base Indicators
The student:
1.
uses a variety of computational methods including mental mathematics,
paper and pencil, concrete materials, and technological tools such as
calculators and computers to estimate quantities involving whole numbers, simple
fractions (halves, thirds, fourths) decimals (.1, .01, .001) and money.
2.
explains and uses various estimation techniques, such as:
front-end with adjustment, rounding, special numbers, clustering, and
compatible numbers to estimate quantities using whole numbers, decimals, money,
and simple fractions (halves, thirds, fourths).
3.
recognizes and explains the difference between exact and approximate
values.
Fourth
Grade Application Indicators
The student:
1. uses estimation to check reasonableness of results, and
makes predictions in situations involving whole numbers, simple fractions
(halves, thirds, fourths) decimals and money.
2. adjusts original whole number estimates based on
additional information (estimation from a frame of reference).
ND
3. determines if a
problem situation calls for an exact or approximate answer and performs the
appropriate computation.
For the purpose of assessing this indicator on the
Benchmark
4: COMPUTATION - The student explains
and performs computation with whole numbers,
addition and subtraction of proper fractions with like denominators, and
money in a variety of situations.
Fourth
Grade Knowledge Base Indicators
The student:
1.
uses a variety of computational methods including mental arithmetic
(doubles and neighbors), paper and pencil, concrete materials, and technological
tools such as calculators and computers.
2.
states and uses multiplication and corresponding division facts for
numbers up to twelve times twelve with efficiency and accuracy.
3.
selects, explains and uses appropriate whole number operations.
ND 4. explains
and performs computational procedures involving whole numbers, proper fractions
with like denominators and money.
For the purpose of assessing this indicator on the
whole number addition and subtraction.
whole number multiplication up to a three-digit
whole number by a two-digit whole number.
whole number division using dividends with up to
three digits and a one-digit divisor.
addition and subtraction of monetary amounts using
dollar and cents notation such as $47.07
+ $356.96.
multiplication of whole dollar money amounts by a
one - or two-digit whole number such as $45x16.
multiplication of money by whole numbers less than
ten such as $14.12 x 7.
make correct change.
Although not assessed on the Kansas Assessment, the student also explains
and performs the following computations:
whole number division using dividends with up to
three-digits and the multiples of ten up to 100 as divisors.
division of three-digit whole dollar amounts by a
one-digit whole number such as $999¸9.
addition and subtraction of
proper fractions with like denominators.
ND 5. knows
different ways to read and write the same addition, subtraction, multiplication
or division expression such as: 6•4
is the same as 6x4,
10 divided by 2 is the same as 10÷2 or 10 / 2.
6.
uses concrete materials to show the relationship between whole number
addition and multiplication, and between whole number multiplication and
division.
7.
finds multiples of whole numbers.
Fourth
Grade Application Indicators
The student:
ND 1. uses
computational procedures to formulate and solve real-world problems involving
whole numbers, proper fractions and money.
For the purpose of assessing this indicator on the
whole number addition and subtraction.
whole number multiplication up to a three-digit
whole number by a two-digit whole number.
whole number division using dividends with up to
three digits and a one-digit divisor.
addition and subtraction of monetary amounts using
dollar and cents notation such as $47.07
+ $356.96.
multiplication of whole dollar money amounts by a
one - or two-digit whole number such as $45x16.
multiplication of money by whole numbers less than
ten such as $14.12 x 7.
make correct change.
|
Standard
2: The student uses algebraic
concepts and procedures in a variety of situations. |
Fourth
Grade Knowledge Base Indicators
Using concrete materials, drawings, or other
representations, the student:
ND 1. identifies
and continues patterns presented in a variety of formats:
numeric, visual, oral, written, kinesthetic, pictorial, tabular,
graphical, or listing.
For the purpose of assessing this indicator on the
whole number patterns both increasing and
decreasing such as 20, 15, 10 . . . .
money and time patterns such as $.25, $.50, $.75 or
number theory patterns, such as
odds, evens, or multiples
through 5’s.
visual patterns involving two attributes.
measurement and geometric patterns such as 3 ft., 6
ft., 9 ft...
patterns occurring in daily life such as sports
scores, longitude and latitude, elections, eras and other patterns, appropriate
to grade level curriculum.
number theory patterns such as multiples and
factors through 12 or multiplying by 10, 100, and 1000.
kinesthetic patterns such as clapping.
2.
creates a pattern.
Special
Note: Working with various types of
patterns is an important precursor to working with functions and sequences in
middle school and high school.
Fourth
Grade Application Indicators
The student:
1.
generalizes patterns using written descriptions.
ND 2. recognizes
the same general pattern presented in different representations such as skip
counting by five's to sixty, whole number multiples of five to sixty, and the
five times tables give the same numerical pattern 5, 10, 15, . . . 60.
For the purpose of assessing this indicator on the
whole number patterns both increasing and
decreasing such as 20, 15, 10 . . . .
money and time patterns such as $.25, $.50, $.75 or
number theory patterns, such as
odds, evens, or multiples
through 5’s.
visual patterns involving two attributes.
measurement and geometric patterns such as 3 ft., 6
ft., 9 ft...
patterns occurring in daily life such as sports
scores, longitude and latitude, elections, eras and other patterns appropriate
to grade level curriculum.
number theory patterns such as multiples and
factors through 12 or multiplying by 10, 100, and 1000.
kinesthetic patterns such as clapping.
Benchmark
2: VARIABLES, EQUATIONS, AND
INEQUALITIES - The student uses symbols and whole numbers to solve simple
equations and inequalities in a variety of situations.
Fourth
Grade Knowledge Base Indicators
The student:
1.
solves one-step equations in one unknown with a whole number solution
such as finding any missing number in a multiplication or division equation
based on the multiplication and division facts for numbers up to 12 times 12,
equations involving time and money such as 8 quarters + 10 dimes =
∆ dollars or 180 minutes = ∆ hours and 100 x ∆ = 600.
2.
reads and writes whole number equations and inequalities using correct
mathematical vocabulary and notation such as 15=3x5, fifteen equals three times
five; 4<6, five is greater than three, 14,564>10,000, or fourteen thousand
is greater than thirteen thousand twenty-five.
Fourth
Grade Application Indicators
The student:
1.
uses symbols to represent problem situations which involve unknown
quantities.
ND 2. formulates
and solves problem situations involving one-step equations in one unknown with a
whole number solution.
For the purpose of assessing this indicator on the
Kansas Assessment the student should be able to solve one-step equations in one
unknown with a whole number solution such as finding any missing number in a
multiplication or division equation based on the multiplication and division
facts for numbers up to 12 times 12, equations
involving time and money such as 8 quarters + 10 dimes = ∆ dollars or 180
minutes = ∆ hours and 100 x ∆ = 600.
Benchmark
3: FUNCTIONS - The student recognizes
and describes relationships between whole numbers in a variety of situations.
Fourth
Grade Knowledge Base Indicators
The student:
1.
uses a variety of methods to recognize relationships between whole
numbers including mental mathematics, paper and pencil, concrete materials, and
graphing utilities or other technological tools.
2.
uses a T-table to find ordered pairs in a relationship.
ND
3. finds
values and determines rules involving operations of whole numbers using
input/output machines or T-tables.
4.
identifies and graphs ordered pairs in the first quadrant.
Fourth
Grade Application Indicators
The student:
ND 1. uses
concrete items, symbols and equations, tables, graphs, pictures and written
descriptions to represent and describe mathematical relationships.
2.
generalizes patterns by stating the rule using symbol notation.
Benchmark
4: MODELS - The student develops and
uses models to represent and justify mathematical relationships found in a
variety of situations.
Fourth
Grade Knowledge Base Indicators
The student:
ND 1. uses
mathematical models to represent and explain mathematical concepts and
procedures.
For the purpose of assessing this indicator on the
diagrams and pictures to model problem situations.
tables, charts, and graphs to organize and display
data.
place value models to compare, order and represent
whole numbers.
process models for whole number operations such as
multiplication arrays, division sets, the
number line, and the hundreds chart.
money (coins), fraction models (fraction strips),
decimal models (base ten blocks, coins) and mixed number models (pattern blocks)
to compare, order or represent numerical quantities
Venn Diagrams to sort up to three attributes.
T-tables to find and show relationships between
numbers.
2. creates
mathematical models to show the relationship between two or more things.
Although not assessed on the Kansas Assessment, an additional model
the student knows, explains, and uses simple tree diagrams for organizing
attributes of sets and determining the number of possible combinations.
Fourth
Grade Application Indicators
The student:
ND 1. recognizes
the same situation can be represented in more than one way.
For the purpose of assessing this indicator on the
a) represent the number of
items in a specific category for a given data set by a horizontal bar graph, a
vertical bar graph, a frequency table or a written description.
b) use
process models for whole number operations such as multiplication arrays,
division sets, the number line, and the hundreds chart.
c) use
different combinations of coins or bills to represent a monetary amount.
Special Note: The
mathematical modeling process involves:
a) selecting
key features and relationships within the real world situation and representing
these concepts in mathematical terms through some sort of mathematical model;
b) performing
manipulations and mathematical procedures within the mathematical model;
c) interpreting
the results of the manipulations within the mathematical model and using these
results to make inferences about the original real-world situation.
|
Standard
3: The student uses
geometric concepts and procedures in a variety of situations. |
Benchmark
1: GEOMETRIC FIGURES AND THEIR
PROPERTIES - The student recognizes or investigates properties of simple
geometric figures in a variety of situations.
Fourth
Grade Knowledge Base Indicators
The student:
1.
uses appropriate technology, manipulatives, and drawings to recognize and
investigate properties of simple geometric figures.
2.
recognizes and describes the following geometric figures and their basic
properties: rhombus, octagon, pentagon, circle, square, rectangle, triangle, and
ellipse (oval).
3.
recognizes and describes the
following geometric solids: pyramid, triangular prism, rectangular prism,
cylinder, cone, sphere and cube.
4.
identifies faces, edges, vertices (corners) and bases on
three-dimensional objects.
5.
recognizes and describes similar and congruent figures.
6.
identifies the radius and diameter of a circle.
Fourth
Grade Application Indicators
The student:
1.
formulates and solves real-world problems by applying basic properties of
simple geometric figures.
ND 2. categorizes
a composite figure into the shapes used to form it.
For the purpose of assessing this indicator on the
Benchmark
2: MEASUREMENT AND ESTIMATION - The
student estimates and measures using standard and nonstandard units in a variety
of situations.
Fourth
Grade Knowledge Base Indicators
The student:
1.
uses appropriate estimation techniques to find whole number
approximations of area, perimeter, length, width, distance, weight, temperature,
capacity, or time.
2.
finds the perimeter of two-dimensional figures given the measure of all
the sides.
3.
applies appropriate measurement techniques to find accurate
representations for area, perimeter, length, width, distance, weight, volume,
temperature and time.
ND 4. selects,
explains the selection of, and uses measurement tools, units of measure, and
degrees of accuracy appropriate to the given situation to measure length to the
nearest fourth of an inch, nearest centimeter; volume to the nearest pint, cup,
quart, gallon or liter and nonstandard units of measure to the nearest whole
unit; weight to the nearest pound or ounce and nonstandard units of measure to
the nearest whole unit; and temperature to the nearest degree; and units of
time.
5.
performs conversions within the same measurement system such as inches to
feet, feet to yards, inches to yards, quarts to gallons, pints to quarts, cups
to pints, pounds to ounces, or centimeters to meters.
Fourth
Grade Application Indicators
The student:
ND 1. formulates
and solves real-world problems by applying measurements and measurement
formulas.
For the purpose of assessing this indicator on the
a) area
of rectangles and squares.
b) perimeter.
c) length to the nearest fourth of an inch,
nearest centimeter and nonstandard
units of measure to the nearest whole unit; volume to the nearest pint, cup,
quart, gallon or liter; temperature to the nearest degree; and weight to the
nearest pound or ounce.
d)
conversions within the same measurement system such as going back and
forth between inches and feet, feet and yards, inches and yards, quarts and
gallons, pints and quarts, cups and pints, pounds and ounces, or centimeters and
meters.
e) units of
time
2. uses
estimation to check reasonableness of measurements and calculations.
3.
adjusts original measurements based on additional information (estimation
from a frame of reference).
4.
uses map scales to measure distance between locations.
Benchmark
3: TRANSFORMATIONAL GEOMETRY - The
student recognizes up to two transformations of basic geometric figures in a
variety situations.
Fourth
Grade Knowledge Base Indicators
The student:
ND 1. recognizes
and performs up to two transformations (rotation/turn, reflection/flip,
translation/slide) on simple two-dimensional shapes and uses cardinal or
positional directions to describe translations such as move the triangle three
units to the right and two units up.
Fourth
Grade Application Indicators
The student:
1.
describes or draws two-dimensional shapes as they would appear after
undergoing a specified transformation without actually performing the
transformation with concrete objects.
2. discusses
what properties of basic shapes stay the same and what changes when a
transformation is performed.
3.
recognizes how pyramids, triangular prisms, and rectangular prisms would
appear from a variety of visual perspectives (top, bottom, side, and corners).
4.
gives or uses directions to move from one location to the another on a
map or grid.
Benchmark
4: GEOMETRY FROM AN ALGEBRAIC
PERSPECTIVE - The student relates geometric concepts to the number line and the
first quadrant of the coordinate plane in a variety of situations.
Fourth
Grade Knowledge Base Indicators
The student:
1.
uses the number line to represent the distance between two whole numbers.
2.
graphs and identifies points in the first quadrant of the coordinate
plane.
3.
uses points on coordinate grids to identify locations.
Fourth
Grade Application Indicators
The student:
ND 1. uses
coordinate grids and maps to formulate and solve real world problems involving
distance and location such as identifying locations and giving or following
directions to move from one location to another.
For the purpose of assessing this indicator on the Kansas Assessment the
student should be able to use maps and grids which have positive whole number or
letter coordinates.
|
Standard
4: The student uses concepts
and procedures of data analysis in a variety of situations. |
Benchmark
1: PROBABILITY - The student uses
probability to make predictions and decisions in a variety of situations.
Fourth
Grade Knowledge Base Indicators
The student:
1.
lists the possible outcomes of a simple experiment.
2.
identifies the probability of a single event within a simple experiment such as
three chances
out of eight.