The Number System
Identify, understand and use positive and negative
fractions, decimals, and whole numbers
•
Identify on number line position of positive/
negative fractions, decimals, whole numbers
Numbers and Operations in Base Ten
Generalize place value understanding for
multi-digit whole numbers
•
Recognize that in a multi-digit whole number, a
digit in one place represents ten times what it
represents in the place to its right
•
Read and write multi-digit whole numbers
using base-ten numerals, number names, and
expanded form
•
Use place value understanding to round multi-
digit whole numbers to any place
•
Use place value understanding and properties
of operations to perform multi-digit arithmetic
•
Fluently add and subtract multi-digit whole
numbers using the standard algorithm
•
Multiply a whole number of up to four digits
by a one-digit whole number, and multiply two
two-digit numbers, using strategies based on
place value and the properties of operations
•
Find whole-number quotients and remainders
with up to four-digit dividends and one-digit
divisors, using strategies based on place value,
and properties of operations
•
Understand and use standard algorithms
for multiplication and division of multi-digit
numbers
Numbers and Operations – Fractions
Extend understanding of fraction equivalence and
ordering
•
Explain why a fraction a/b is equivalent to a
fraction (n × a)/(n × b) by using visual fraction
models, with attention to how the number and
size of the parts differ even though the two
fractions themselves are the same size. Use this
principle to recognize and generate equivalent
fractions
•
Compare two fractions with different numerators
and different denominators, e.g., by creating
common denominators or numerators, or by
comparing to a benchmark fraction such as
1/2 Recognize that comparisons are valid only
when the two fractions refer to the same whole;
record the results of comparisons with symbols
>, =, or <, and justify the conclusions, e.g., by
using a visual fraction model
Build fractions from unit fractions
•
Understand a fraction a/b with a > 1 as a sum of
fractions 1/b
•
Understand addition and subtraction of fractions
as joining and separating parts referring to the
same whole
•
Decompose a fraction into a sum of fractions
with the same denominator in more than one
way, recording each decomposition by an
equation; justify decompositions
•
Add and subtract mixed numbers with like
denominators
•
Solve word problems involving addition and
subtraction of fractions referring to the same
whole and having like denominators
•
Extend previous understandings of
multiplication to multiply fraction by whole
number
•
Understand a fraction a/b as a multiple of 1/b
•
Understand a multiple of a/b as a multiple of
1/b, and use this understanding to multiply a
fraction by a whole number
•
Solve word problems involving multiplication of
a fraction by a whole number
Understand decimal notation for fractions, and
compare decimal fractions
•
Express a fraction with denominator 10 as an
equivalent fraction with denominator 100, and
use this technique to add two fractions with
respective denominators 10 and 100.2
•
Use decimal notation for fractions with
denominators 10 or 100
•
Compare two decimals to hundredths by
reasoning about their size, and recognize that
comparisons are valid only when the two decimals
refer to the same whole; record the results
59
Fourth Grade
Measurement and Data
Solve problems involving measurement and
conversion of measurements
•
Know relative sizes of measurement units within
one system of unit and within single system of
measurement, express measurements in a larger
unit in terms of a smaller unit
•
Use the four operations to solve word problems
involving distances, intervals of time, liquid
volumes, masses of objects, and money
•
Apply the area and perimeter formulas for
rectangles in real world and mathematical
problems
•
Apply strategies and formulas to estimate and
calculate area and perimeter of complex shapes
•
Explore what happens to measurements of two
dimensional shapes when the shape is changed
Represent and interpret data
•
Make a line plot to display a data set of
measurements in fractions of a unit
•
Solve problems involving addition and
subtraction of fractions by using information
presented in line plots
Geometric measurement: understand concepts of
angle and measure angles
•
Recognize angles as geometric shapes that are
formed wherever two rays share a common
endpoint, and understand concepts of angle
measurement
•
Know that an angle that turns through one-
degree angles is said to have an angle measure
of n degrees
•
Measure angles in whole-number degrees using
protractor; sketch angles of specified measure
•
Recognize angle measure as additive
Geometry
Draw and identify lines and angles, and classify
shapes by properties of their lines and angles
•
Draw points, lines, line segments, rays, angles
and perpendicular and parallel lines
•
Classify two-dimensional figures based
on presence or absence of parallel or
perpendicular lines
•
Recognize a line of symmetry for a two-
dimensional figure as a line across the figure
such that the figure can be folded along the line
into matching parts
Data Analysis and Probability
•
Label and use different parts of a graph
accurately
•
Collect and represent data on a number line
and on coordinate graphs, tables, and charts
•
Use technology to compute, represent, and
evaluate
•
Predict, test, and represent all possible
outcomes for a simple probability situation
•
Use statistical data to identify trends and to
make and justify generalization
SCIENCE
Land Features
•
Identify properties of the three types of rocks
•
Explain the stages of the rock cycle and how it
is used to identify rocks
•
Identify common minerals using the table of
diagnostic properties
•
Understand the differences between physical
and chemical weathering
•
Describe how the plates of the Earth can move
to create earthquakes
•
Know the properties of different soils
Water Features
•
Understand how the water cycle is influenced
by temperature and land features and how the
water cycle can influence them
•
Understand that the freezing and thawing of
water can cause rocks to break down
•
Understand the solvent nature of water
Natural Resources
•
Identify natural resources found in their state
•
Explain how soil is renewed
•
Identify ways that the misuse of natural
resources affect the quality of life
•
Provide examples of conservation
Earth and Space
•
Explain how the tilt of the Earth and the shape
60
Nobel Learning Curriculum Reference Guide
