California State Mathematics Content Standards.
Kindergarten

By the end of kindergarten, students understand
small numbers, quantities, and simple shapes in their
everyday environment. They count, compare,
describe and sortobjects, and develop a sense of
properties and patterns.

Number Sense
1.0 Students understand the relationship
between numbers and quantities (i.e., that a
set of objects has the same number of objects
in different situations regardless of its position
or arrangement):
1.2 Count, recognize, represent, name, and order a
number of objects (up to 30).
“Counting by Ones” allows students to count and
sing.
2.0 Students understand and describe simple
additions and subtractions:
2.1 Use concrete objects to determine the answers
to addition and subtraction problems (for two
numbers that are each less than 10).
In general, the songs; “Columns”, “Odd and Even”,
and“The months” gives students an increased
awareness of number sense.

Measurement and Geometry
1.0 Students understand the concept of time
and units to measure it; they understand that
objects have properties, such as length,
weight, and capacity, and that comparisons
may be made by referring to those properties:
1.2 Demonstrate an understanding of concepts of
time (e.g., morning, afternoon, evening, today,
yesterday, tomorrow, week, year) and tools that
measure time (e.g., clock, calendar).
“The Clock Song” gives students an opportunity to
see time in action while internalizing conceptual
understanding.
1.3 Name the days of the week.
“The Days of the Week” songs address this
standard.
1.4 Identify the time (to the nearest hour) of
everyday events (e.g., lunch time is 12 o'clock;
bedtime is 8 o'clock at night).
“The Clock Song” gives students an opportunity to
see time in action while internalizing conceptual
understanding.

Grade One
By the end of grade one, students understand and
use the concept of ones and tens in the place value
number system. Students add and subtract small
numbers with ease. They measure with simple units
and locate objects in space. They describe data and
analyze and solve simple problems.

Number Sense
1.0 Students understand and use numbers up
to 100:
1.1 Count, read, and write whole numbers to 100.
The skip counting songs and “Columns song”
address the above two standards in that they allow
students to count to a hundred by twos, fives and
tens.
2.0 Students demonstrate the meaning of
addition and subtraction and use these
operations to solve problems:
2.4 Count by 2s, 5s, and 10s to 100.
The skip counting songs and “Columns song””
address the above standards in that they allow
students to count to a hundred by twos, fives and
tens.
2.5 Show the meaning of addition (putting together,
increasing) and subtraction (taking away, comparing,
finding the difference).
2.6 Solve addition and subtraction problems with
one-and two-digit numbers (e.g., 5 + 58 = __).
“You Carry Over” and the “Subtraction Song”
address the two above standards.
1.0 Students use number sentences with
operational symbols and expressions to solve
problems:
1.1 Write and solve number sentences from problem
situations that express relationships involving
addition and subtraction.
1.2 Understand the meaning of the symbols +, -, =.
1.3 Create problem situations that might lead to
given number sentences involving addition and
subtraction.
“You Carry Over” and the “Subtraction Song”
addresses the above standards.

Measurement and Geometry
1.0 Students use direct comparison and
nonstandard units to describe the
measurements of objects:
1.2 Tell time to the nearest half hour and relate time
to events (e.g., before/after, shorter/longer).
The “Clock song” illustrates telling time.

Grade Two
By the end of grade two, students understand place
value and number relationships in addition and
subtraction, and they use simple concepts of
multiplication. They measure quantities with
appropriate units. They classify shapes and see
relationships among them by paying attention to
their geometric attributes. They collect and analyze
data and verify the answers.

Number Sense
1.0 Students understand the relationship
between numbers, quantities, and place value in
whole numbers up to 1,000:
1.1 Count, read, and write whole numbers to 1,000
and identify the place value for each digit.
“You Carry Over”, the “Subtraction Song”, “Columns”,
and the “Odd and Even” songs address the above
standard.
3.0 Students model and solve simple problems
involving multiplication and division:
3.1 Use repeated addition, arrays, and counting by
multiples to do multiplication.
The selection “Times Table Blues,” addresses
automaticity of the times tables with the focus on
arrays.
3.2 Use repeated subtraction, equal sharing, and
forming equal groups with remainders to do division.
The selection “Long Division” gives a glimpse into
this operation.
3.3 Know the multiplication tables of 2s, 5s, and 10s
(to "times 10") and commit them to memory.
The selections “Times Table Blues,” “Count by
twos,” and “Count By Fives” address automaticity of
the times tables.
6.0 Students use estimation strategies in
computation and problem solving that involve
numbers that use the ones, tens, hundreds, and
thousands places:

Measurement and Geometry
1.0 Students understand that measurement is
accomplished by identifying a unit of measure,
iterating (repeating) that unit, and comparing it
to the item to be measured:
1.4 Tell time to the nearest quarter hour and know
relationships of time (e.g., minutes in an hour, days in
a month, weeks in a year).
The “Clock Song” addresses the telling time process.

Statistics, Data Analysis, and Probability
2.0 Students demonstrate an understanding of
patterns and how patterns grow and describe
them in general ways:
2.2 Solve problems involving simple number
patterns.
“Count by twos,” Count By Fives,” and “Even and
Odd” address skip counting skills.

Grade Three
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.

Number Sense
1.0 Students understand the place value of
whole numbers:
1.1 Count, read, and write whole numbers to 10,000.
“Count by twos,” “Count By Fives,” “Even and Odd,”
“Round It Off,” and “Columns” all address counting
skills.
1.2 Compare and order whole numbers to 10,000.
The selection “Round It Off,” “Decimals,” and
“Columns” address number ordering.
1.3 Identify the place value for each digit in numbers
to 10,000.
The selection “Decimals” addresses the concept of
column values.
1.4 Round off numbers to 10,000 to the nearest
ten, hundred, and thousand.
The selection “Round It Off” addresses the rounding
off process.
2.0 Students calculate and solve problems
involving addition, subtraction, multiplication,
and division:
2.1 Find the sum or difference of two whole numbers
between 0 and 10,000.
“Subtraction” and “You Carry Over” address the
addition and subtraction reordering process.
2.2 Memorize to automaticity the multiplication table
for numbers between 1 and 10.
The selection “Times Table Blues” addresses
automaticity of the times tables.

Grade Four
By the end of grade four, students understand large
numbers and addition, subtraction, multiplication, and
division of whole numbers. They describe and
compare simple fractions and decimals. They
understand the properties of, and the relationships
between, plane geometric figures. They collect,
represent, and analyze data to answer questions.

Number Sense
1.0 Students understand the place value of
whole numbers and decimals to two decimal
places and how whole numbers and decimals
relate to simple fractions. Students use the
concepts of negative numbers:
1.2 Order and compare whole numbers and decimals
to two decimal places.
The selection “Decimals” addresses the concept.
1.3 Round whole numbers through the millions to the
nearest ten, hundred, thousand, ten thousand, or
hundred thousand.
The selection “Round It Off” addresses the rounding
off process.
3.0 Students solve problems involving addition,
subtraction, multiplication, and division of whole
numbers and understand the relationships
among the operations:
3.1 Demonstrate an understanding of, and the ability
to use, standard algorithms for the addition and
subtraction of multi digit numbers.
“Subtraction” and “You Carry Over” address the
addition and subtraction reordering process.

Grade Five
By the end of grade five, students increase their
facility
with the four basic arithmetic operations applied to
fractions, decimals, and positive and negative
numbers. They know and use common measuring
units to determine length and area and know and use
formulas to determine the volume of simple
geometric figures. Students know the concept of
angle measurement and use a protractor and
compass to solve problems. They use grids, tables,
graphs, and charts to record and analyze data.

Number Sense
1.0 Students compute with very large and very
small numbers, positive integers, decimals, and
fractions and understand the relationship
between decimals, fractions, and percents.
They understand the relative magnitudes of
numbers:
1.1 Estimate, round, and manipulate very large (e.g.,
millions) and very small (e.g., thousandths) numbers.
The selection “Round It Off” addresses the rounding
off process.
2.2 Demonstrate proficiency with division, including
division with positive decimals and long division with
multi digit divisors.
The selection “Long Division” addresses this
operation.

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