Math Curriculum for Above Grade Level Math
Welcome to the third grade advanced math class. This compacted math class attempts to combine the curriculum of third and fourth
grade so that students will be prepared for the rigorous challenges of 5th grade math while in fourth grade. This curriculum places an
emphasis on multiplication and division with whole numbers and solving problems involving addition and subtraction of fractions and
decimals. Students will learn and use the basic multiplication facts as they become proficient in multiplying larger numbers. Students
also will refine their estimation skills for computations and measurements and investigate relationships between and among simple
two-dimensional (plane) figures and three-dimensional (solid) figures. Students will identify and draw representations of points, lines,
line segments, and rays. Students will graph points in the first quadrant in the coordinate plane and extend and duplicate patterns.
Concrete materials and two-dimensional representations will be used to solve problems involving perimeter, patterns, probability, and
equivalence of fractions and decimals. Students will recognize a geometric transformation, such as reflection (flip), translation (slide),
and rotation (turn).
While learning mathematics, students will be actively engaged, using concrete materials and appropriate technologies such as
calculators and computers. However, facility in the use of technology shall not be regarded as a substitute for a student’s
understanding of quantitative concepts and relationships or for proficiency in basic computations.
Mathematics has its own language, and the acquisition of specialized vocabulary and language patterns is crucial to a student’s
understanding and appreciation of the subject. Students should be encouraged to use correctly the concepts, skills, symbols, and
vocabulary identified in the following set of standards.
Problem solving has been integrated throughout the six content strands (1. Number and Number Sense, 2. Computation and
Estimation, 3. Measurement, 4. Geometry, 5. Probability and Statistics, 6. Patterns, Functions, and Algebra). The development
of problem-solving skills should be a major goal of the mathematics program at every grade level. Instruction in the process of
problem solving will need to be integrated early and continuously into each student’s mathematics education. Students must be helped
to develop a wide range of skills and strategies for solving a variety of problem types.
Marking Period 1
Number and Number Sense
Marking
Period 2
Number and Number Sense
Students will be able to:
a)
identify (orally and in
The student will
writing) the place value for each
a) identify, model, and compare rational
digit in a whole number expressed
numbers (fractions[proper/improper] and mixed
through millions;
numbers), using concrete objects and pictures;
b)
compare two whole
b) represent equivalent fractions; and
numbers expressed through millions,
c) relate fractions to decimals, using concrete
using symbols ( >, <, or = ); and
objects.
c)
round whole numbers
expressed through millions to the
The student will compare the numerical value of
nearest thousand, ten thousand, and
fractions (with like and unlike denominators) having
hundred thousand.
denominators of 12 or less, using concrete materials.
The student will recognize and use
the inverse relationships between
addition/subtraction and
multiplication/division to complete
basic fact sentences. Students will
use these relationships to solve
problems such as 5 + 3 = 8 and 8 – 3
= ____.
Marking
Period 3
Number and Number Sense
The student will...
recognize and use the inverse relationships
between addition/subtraction and
multiplication/division to complete basic fact
sentences. Students will use these relationships
to solve problems such as 5 + 3 = 8 and 8 – 3 =
____.
Computation and Estimation
The student will...
estimate whole-number
products and quotients
The student will
and describe the method
a) read, write, represent, and identify decimals
of estimation.
expressed through hundredths;
b) round to the nearest whole number, tenth,
hundredths, and
c) compare the value of two decimals, using
symbols (<, >, or =), concrete materials,
drawings, and calculators.
The student will identify the ordinal
The students will
positions first through twentieth,
a) recognize and use the inverse relationships
using an ordered set of objects.
between addition/subtraction and
multiplication/division to complete basic fact
Computation and Estimation
sentences. Students will use these relationships
to solve problems such as 5 + 3 = 8 and 8 – 3 =
The student will estimate whole____.
refine estimates, using terms
such as closer to, between,
and a little more than.
multiply and divide whole numbers
written in vertical and horizontal
form, choosing appropriately
between paper and pencil methods
and calculators.
find the product of two whole
numbers when one factor has two
number sums and differences and
digits or fewer and the other factor
describe the method of estimation.
has three digits or fewer, using
Students will refine estimates, using Computation and Estimation
estimation and paper and pencil.
terms such as closer to, between, and
For larger products (a two-digit
The student will
a little more than.
numeral times a three-digit
a) add and subtract with fractions having like
numeral), estimation and
and unlike denominators of 12 or less, using
The student will solve problems
calculators will be used.
concrete
materials,
pictorial
representations,
and
involving the sum or difference of
paper and pencil;
two whole numbers, each 9,999 or
estimate and find the quotient of
b)
add
and
subtract
with
decimals
through
less, with or without regrouping,
two whole numbers, given a onethousandths, using concrete materials, pictorial
written in vertical and horizontal
digit divisor.
representations,
and
paper
and
pencil;
and
form, using various computational
c) solve problems involving addition and
methods, including calculators,
subtraction with fractions having like and unlike
paper and pencil, mental
Measurement
denominators of 12 or less and with decimals
computation, and estimation.
expressed through hundredths, using various
computational methods, including calculators,
The student will be introduced to
The student will...
paper and pencil, mental computation, and
and asked to recall the multiplication
estimation.
facts through the nines table.
identify and describe situations
d) solve problems involving addition or subtraction
representing the use of
with
decimals
through
the
tenths
or
money
to
the
The student will create and solve
perimeter and area; and
cent and/or explain the solution. This will be
problems involving addition,
limited
to
two-step
problems.
subtraction, and multiplication of
use measuring devices to find perimeter in
whole numbers, using paper and
The student will
both standard and nonstandard units of
pencil, estimation, mental
a)
recall
the
multiplication
and
division
facts
measure.
computation, and calculators.
through the nines table.
b) represent multiplication and division, using area
Geometry
Measurement
and set models, and create and solve problems
that involve multiplication of two whole
-not assessed this marking period.
The student will
numbers, one factor 99 or less and the second
a) determine by counting the value
factor 5 or less.
of a collection of bills and coins
Probability and Statistics
whose total value is $20.00 or less.
b) compare the value of the coins
or bills;
c) make change.
Geometry
Not instructed/assessed this
marking period.
Probability and Statistics
Not instructed/assessed this
marking period.
Patterns, Functions, and
Algebra
Measurement
Patterns, Functions, and Algebra
The student will
a) tell time to the nearest five-minute interval and The student will...
to the nearest minute, using analog and digital
clocks.
recognize, create, and
extend numerical and
The student will
geometric patterns, using
a) identify equivalent periods of time, including
concrete materials,
relationships among days, months, and years, as
number lines, symbols,
well as minutes and hours.
tables, and words.
The students will
a) determine and compare elapsed times.
The student will
a) estimate and measure length, using actual
measuring devices, and describe the results in
both metric and U.S. Customary units, including
part of an inch (1/2, and 1/4), inches, feet, yards,
millimeters, centimeters, and meters;
b) identify equivalent measurements between
units within the U.S. Customary system (inches
and feet; feet and yards; inches and yards) and
The student will recognize and
between units within the metric system
demonstrate the meaning of equality,
(millimeters and centimeters; centimeters and
using symbols representing numbers,
meters; and millimeters and meters); and
operations, and relations [e.g., 3 + 5
c) estimate the conversion of inches and
= 5 + 3 and 15 + (35 + 16) = (15 +
centimeters, yards and meters, and miles and
35) + 16].
kilometers, using approximate comparisons (1
inch is about 2.5 centimeters, 1 meter is a little
The student will
longer than 1 yard, 1 mile is slightly farther than
a)
investigate and create
1.5 kilometers, or 1 kilometer is slightly farther
The student will recognize and
describe a variety of patterns formed
using concrete objects, numbers,
tables, and pictures, and extend the
pattern, using the same or different
forms (concrete objects, numbers,
tables, and pictures).
-not assessed this marking period.
recognize and demonstrate the
meaning of equality, using symbols
representing numbers, operations,
and relations
patterns involving numbers,
than half a mile). *
operations (addition and
multiplication), and relations that
The student will
model the identity and commutative
a) estimate and measure liquid volume, using
properties for addition and
actual measuring devices and using metric and
multiplication; and
U.S. Customary units, including cups, pints,
b)
demonstrate an
quarts, gallons, milliliters, and liters;
understanding of equality by
b) identify equivalent measurements between
recognizing that the equal sign (=)
units within the U.S. Customary system (cups,
links equivalent quantities, such as 4
pints, quarts, and gallons) and between units
• 3 = 2 • 6.
within the metric system (milliliters and liters);
and
The student will create a problem
c) estimate the conversion of quarts and liters,
situation based on a given open
using approximate comparisons (1 quart is a
sentence using a single variable.
little less than 1 liter, 1 liter is a little more than 1
quart).*
The student will
a) estimate and measure weight/mass, using
actual measuring devices, and describe the
results in U.S. Customary/metric units as
appropriate, including ounces, pounds, grams,
and kilograms;
b) identify equivalent measurements between
units within the U.S. Customary system (ounces
and pounds) and between units within the metric
system (grams and kilograms); and
c) estimate the conversion of ounces and grams
and pounds and kilograms, using approximate
comparisons (1 ounce is about 28 grams, or 1
gram is about the weight of a paper clip; 1
kilogram is a little more than 2 pounds). *
* The intent of this standard is for students to make
ballpark comparisons and not to memorize
conversion factors between U.S. Customary and
metric units.
The student will
a) identify and describe situations representing
the use of perimeter, area, and volume; and
b) use measuring devices to find these
dimensions in both standard and nonstandard
units of measure.
Geometry
The student will investigate and describe the
relationships between and among points, lines, line
segments, and rays.
The student will
a) identify and draw representations of points,
lines, line segments, rays, and angles, using a
straightedge or ruler; and
b) describe the path of shortest distance
between two points on a flat surface.
The student will identify and draw
representations of lines that illustrate intersection,
parallelism, and perpendicularity.
The student will
a) analyze and compare the properties of twodimensional (plane) geometric figures (circle,
square, rectangle, triangle, pentagon, hexagon,
octagon, parallelogram, and rhombus) and threedimensional (solid) geometric figures (sphere,
cube, pyramid and rectangular solid [prism]);
b) identify congruent and noncongruent shapes;
and
c) investigate congruence of plane figures after
geometric transformations such as reflection
(flip), translation (slide) and rotation (turn),
using mirrors, paper folding, and tracing.
d) identify and create figures that have one, two
or no lines of symmetry.
Probability and Statistics
Not instructed this marking period.
Patterns, Functions, and Algebra
The student will recognize and describe a
variety of patterns formed using concrete objects,
numbers, tables, and pictures, and extend the pattern,
using the same or different forms (concrete objects,
numbers, tables, and pictures).
The student will
a) investigate and create patterns involving
numbers, operations (addition and
multiplication), and relations that model the
identity and commutative properties for addition
and multiplication; and
b) demonstrate an understanding of equality by
recognizing that the equal sign (=) links
equivalent quantities, such as 4 • 3 = 2 • 6.