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attributes:
a characteristic or distinctive feature—such as shapes, size, color—of an object or given
set of objects.
bar graph:
a graph that uses the height or lengthof rectangles to compare data.
classify numbers:
to group a set of numberstogether by an attribute, such as even or odd, less
than 20, more than 20, etc. recognizing that different
types of numbers have particular characteristics.
commonly used fractions
: halves, thirds,fourths, fifths, sixths, eighths, and tenths.
commutative property of addition:
the sumstays the same when the order of the addends is
changed.
Example: 6 + 4 = 4 + 6.
composing or decomposing numbers:
flexibly using or knowing numbers through creating
and breaking numbers apart to form equivalent
representations. For example, 36 can be thought of
as 32 + 4, 20 + 16, 40 – 4, 12 X 3, etc.
congruent:
objects that have the same shape andsize are congruent.
develop fluency:
developing the ability forefficient and accurate methods of computing and
being able to demonstrate flexibility in computational
methods chosen which result in students being able
to explain their methods and produce accurate
answers.
expression:
a mathematical phrase thatrepresents a number through the combination of
operation symbols, numbers and/or symbols.
Examples: 2 x 60; 3 + .
identity property of addition
: if you add azero to a number, the sum is the same as that given
number.
Example: 7 + 0 = 7
line graph:
a graph used to show change overtime with points connected by line segments.
line plot:
a diagram showing frequency of data ona number line.
model:
to represent a mathematical situation withmanipulatives (objects), pictures, numbers or
symbols.
number sentences:
equations or comparisons.Examples: 3 + 4 = 7, 8 – 2 = 6, 7 > 6
pictorial (picture) graph:
a graph that usespictures or symbols to show data.
quantitative:
relating to number or quantity;elements can be counted or measured.
referent:
a familiar object or place that a studentcan use as a basis for estimating the measurement
of something; students might think of the length of
their desks, the size of an orange, etc.
shape of data:
An overview of numerical data—the highest and lowest points (range) of the data,
where most of the data are clumped together, where
there are no data, where there are be data located
far from the rest of the data (outliers), as well as
what the mode and median are.
By
the end of grade three, students deepen their understanding of place value
and
their understanding of and skill with addition, subtraction, multiplication,
and
division of whole numbers. Students estimate, measure, and describe objects
in
space. They use patterns to help solve problems. They represent number
relationships
and conduct simple probability experiments.
Third
Grade Math - California State Standards Taught
Number
Sense
1.0
Students understand the place value of whole numbers:
1.1
Count, read, and write whole numbers to 10,000.
1.2
Compare and order whole numbers to 10,000.
1.3
Identify the place value for each digit in numbers to 10,000.
1.4
Round off numbers to 10,000 to the nearest ten, hundred, and thousand.
1.5
Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).
2.0
Students calculate and solve problems involving addition, subtraction, multi
plication,
and division:
2.1
Find the sum or difference of two whole numbers between 0 and 10,000.
2.2
Memorize to automaticity the multiplication table for numbers between 1 and 10.
2.3
Use the inverse relationship of multiplication and division to compute and check
results.
2.4
Solve simple problems involving multiplication of multidigit numbers by
one-digit
numbers
(3,671 ?3
= __).
2.5
Solve division problems in which a multidigit number is evenly divided by a
one-digit
number (135 ?5
= __).
2.6
Understand the special properties of 0 and 1 in multiplication and division.
2.7
Determine the unit cost when given the total cost and number of units.
2.8
Solve problems that require two or more of the skills mentioned above.
11
3.0
Students understand the relationship between whole numbers, simple fractions,
and
decimals:
3.1
Compare fractions represented by drawings or concrete materials to show
equivalency
and
to add and subtract simple fractions in context (e.g., 1/2
of a pizza is
the
same
amount as 2/4
of another
pizza that is the same size; show that 3/8
is larger than
1/4).
3.2
Add and subtract simple fractions (e.g., determine that 1/8
+ 3/8
is the same as 1/2).
3.3
Solve problems involving addition, subtraction, multiplication, and division of
money
amounts in decimal notation and multiply and divide money amounts in
decimal
notation by using whole-number multipliers and divisors.
3.4
Know and understand that fractions and decimals are two different
representations
of
the same concept (e.g., 50 cents is 1/2
of a dollar, 75
cents is 3/4
of a dollar).
Algebra
and Functions
1.0
Students select appropriate symbols, operations, and properties to represent,
describe,
simplify, and solve simple number relationships:
1.1
Represent relationships of quantities in the form of mathematical expressions,
equations,
or inequalities.
1.2
Solve problems involving numeric equations or inequalities.
1.3
Select appropriate operational and relational symbols to make an expression true
(e.g.,
if 4 __ 3 = 12, what operational symbol goes in the blank?).
1.4
Express simple unit conversions in symbolic form (e.g., __ inches = __ feet ?12).
1.5
Recognize and use the commutative and associative properties of multiplication
(e.g.,
if 5 ?7
= 35, then what is 7 ?5?
and if 5 ?7
?3
= 105, then what is
7
?3
?5?).
2.0
Students represent simple functional relationships:
2.1
Solve simple problems involving a functional relationship between two quantities
(e.g.,
find the total cost of multiple items given the cost per unit).
2.2
Extend and recognize a linear pattern by its rules (e.g., the number of legs on
a
given
number of horses may be calculated by counting by 4s or by multiplying the
number
of horses by 4).
Measurement
and Geometry
1.0
Students choose and use appropriate units and measurement tools to quantify
the
properties of objects:
1.1
Choose the appropriate tools and units (metric and U.S.) and estimate and
measure
the
length, liquid volume, and weight/mass of given objects.
1.2
Estimate or determine the area and volume of solid figures by covering them with
squares
or by counting the number of cubes that would fill them.
1.3
Find the perimeter of a polygon with integer sides.
1.4
Carry out simple unit conversions within a system of measurement (e.g.,
centimeters
and
meters, hours and minutes).
2.0
Students describe and compare the attributes of plane and solid geometric
figures
and use their understanding to show relationships and solve problems:
2.1
Identify, describe, and classify polygons (including pentagons, hexagons, and
octagons).
2.2
Identify attributes of triangles (e.g., two equal sides for the isosceles
triangle, three
equal
sides for the equilateral triangle, right angle for the right triangle).
2.3
Identify attributes of quadrilaterals (e.g., parallel sides for the
parallelogram, right
angles
for the rectangle, equal sides and right angles for the square).
2.4
Identify right angles in geometric figures or in appropriate objects and
determine
whether
other angles are greater or less than a right angle.
2.5
Identify, describe, and classify common three-dimensional geometric objects
(e.g.,
cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).
2.6
Identify common solid objects that are the components needed to make a more
complex
solid object.
Statistics,
Data Analysis, and Probability
1.0
Students conduct simple probability experiments by determining the number
of
possible outcomes and make simple predictions:
1.1
Identify whether common events are certain, likely, unlikely, or improbable.
1.2
Record the possible outcomes for a simple event (e.g., tossing a coin) and
systemati
cally
keep track of the outcomes when the event is repeated many times.
1.3
Summarize and display the results of probability experiments in a clear and orga
nized
way (e.g., use a bar graph or a line plot).
1.4
Use the results of probability experiments to predict future events (e.g., use a
line
plot
to predict the temperature forecast for the next day).
Mathematical
Reasoning
1.0
Students make decisions about how to approach problems:
1.1
Analyze problems by identifying relationships, distinguishing relevant from
irrel
evant
information, sequencing and prioritizing information, and observing patterns.
1.2
Determine when and how to break a problem into simpler parts.
2.0
Students use strategies, skills, and concepts in finding solutions:
2.1
Use estimation to verify the reasonableness of calculated results.
2.2
Apply strategies and results from simpler problems to more complex problems.
2.3
Use a variety of methods, such as words, numbers, symbols, charts, graphs,
tables,
diagrams,
and models, to explain mathematical reasoning.
2.4
Express the solution clearly and logically by using the appropriate mathematical
notation
and terms and clear language; support solutions with evidence in both
verbal
and symbolic work.
2.5
Indicate the relative advantages of exact and approximate solutions to problems
and
give answers to a specified degree of accuracy.
2.6
Make precise calculations and check the validity of the results from the context
of
the
problem.
3.0
Students move beyond a particular problem by generalizing to other situations:
3.1
Evaluate the reasonableness of the solution in the context of the original
situation.
3.2
Note the method of deriving the solution and demonstrate a conceptual understand
ing
of the derivation by solving similar problems.
3.3
Develop generalizations of the results obtained and apply them in other circum
stances.
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