CONTENT STANDARDS FOR
CALIFORNIA SCHOOLS
STUDENT
TRACKING
STANDARDS
INSTRUCTION
Mathematics
Individual Student Profile for Kindergarten: Mathematics Standards
Student's Name
Number Sense
1.0 Numbers and Quantities
1.1 Compare sets of objects to 10
1.2 Count, name, & order numbers to 30
1.3 Larger numbers = larger sets
Measurement and Geometry
1.0 Measurement
1.1 Compare length, weight, ... of
objects
1.2 Know time (morning, yesterday, etc.)
1.3 Name days of the week
1.4 Identify time to nearest hour
2.0 Addition and Subtraction
2.1 Use concrete objects to add & subt.
3.0 Estimation
2.0 Geometry
2.1 Identify/describe geometric objects
2.2 Compare plane/solid objects
3.1 Recognize reasonable estimates
Algebra and Functions
1.0 Sorting and Classifying Objects
1.1 Identify, sort, classify by attribute
Statistics, Data Analysis, and Probability
1.0 Collecting Information
1.1 Record data using picture graphs
1.2 Describe, extend simple patterns
Mathematical Reasoning
1.0 Make Decisions about a Problem
1.1 Determine strategies to be used
1.2 Use tools to model problems
2.0 Solve Problems/Justify Reasoning
2.1 Use concrete objects/pictorial repres.
2.2 Make precise calculations/validity
Individual Student Profile for First Grade: Mathematics Standards
Student's Name
Number Sense
1.0 Place Value
1.1 Count/read/write numbers to 100
1.2 Compare/order numbers to 100
1.3 Equivalent forms of numbers to 100
1.4 Count/group object in ones and tens
1.5 Identify and know the value of coins
2.0 Addition and Subtraction
2.1 Know add./subt. facts to 20
2.2 Use the inverse relationship
2.3 Identify 1 more than/less, 10 more ...
2.4 Count by 2s, 5s, and 10s to 100
2.5 Showing meaning of add. and subt.
2.6 Solve add. and subt. with 1 & 2 digits
2.7 Find sum of 3 one-digit numbers
3.0 Estimation
3.1 Make reasonable estimates w/numbers
Algebra and Functions
1.0 Number Sentences
1.1 Write/solve number sentences
1.2 Know meaning of symbols +, -, =
1.3 Create problem situations/# sent.
Measurement and Geometry
1.0 Measurement
1.1 Compare length .... 2 or more objects
1.2 Tell time to nearest half hour
2.0 Geometry
2.1 Identify/describe/compare shapes
2.2 Classify plane and solid objects
2.3 Give and follow directions to location
2.4 Describe objects in space by position
Statistics, Data Analysis, and Probability
1.0 Data
1.1 Sort objects/data by attributes
1.2 Represent data on bar graphs ....
2.0 Patterning
2.1 Extend next element in patterns
Mathematical Reasoning
1.0 Make Decisions about a Problem
1.1 Determine approach to be used
1.2 Use tools to model problems
2.0 Solve Problems/Justify Reasoning
2.1 Explain the reasoning used
2.2 Make precise calculations/validity
3.0 Make Connections
3.1 Make connections between problems
Individual Student Profile for Second Grade: Mathematics Standards
Student's Name
Number Sense
1.0 Place Value
1.1 Count/read/write numbers to 1,000
1.2 Use expanded forms to represent #s
1.3 Order/compare numbers to 1,000
2.0 Addition and Subtraction
2.1 Inverse relationship between + & 2.2 Add./subt. 3-digit numbers
2.3 Use mental math/+ & - 2-digit #s
Measurement and Geometry
1.0 Measurement
1.1 Measure lengths of objects
1.2 Use diff. units/measure same
object
1.3 Measure to nearest inch/centimeter
1.4 Tell time to nearest 1/4 hour
1.5 Duration of time intervals in hrs.
2.0 Geometry
2.1 Classify plane/solid geom. shapes
2.2 Form other shapes from shapes
3.0 Multiplication and Division
3.1 Use repeated addition to multiply
3.2 Use repeated subtraction to divide
3.3 Know mult. facts of 2s, 5s, and 10s
4.0 Fractions and Decimals
4.1 Name/compare fractions 1/12 - 1/2
4.2 Recognize fractions of a whole
group
4.3 Know what fractions equal a whole
5.0 Computation - Money
5.1 Solve problems with coins/bills
5.2 Use decimal notation/ $ and ¢ sign
6.0 Estimation
6.1 Recognize reasonable estimates
Algebra and Functions
1.0 Number Relationships
1.1 Use commutative/associative rules
1.2 Relate problems to + & - no. sent.
1.3 Solve + & - problems from charts
Statistics, Data Analysis, and
Probability
1.0 Data
1.1 Record numerical data
1.2 Represent same data in diff. ways
1.3 Identify range/mode of data sets
1.4 Ask/answer questions about data
2.0 Patterning
2.1 Recognize/describe/extend
patterns
2.2 Solve problems using # patterns
Mathematical Reasoning
1.0 Make Decisions about a Problem
1.1 Determine approach to be used
1.2 Use tools to model problems
2.0 Solve Problems/Justify Reasoning
2.1 Explain the reasoning used
2.2 Make precise calculations/validity
3.0 Make Connections
3.1 Make connections between
problems
Individual Student Profile for Third Grade: Mathematics Standards
Student's Name
Number Sense
1.0 Place Value
1.1 Count/read/write numbers to 10,000
1.2 Order whole numbers to 10,000
1.3 Identify place value to 10,000
1.4 Round to nearest 10, 100, 1,000
1.5 Use expanded notation
Measurement and Geometry
1.0 Measurement
1.1 Choose appropriate tools to measure
1.2 Find area & volume of solid figures
1.3 Find perimeter of a polygon
1.4 Find unit conversions within a system
2.0 Geometry
2.0 Computation - Whole Numbers
2.1 Add/subt. numbers from 0 - 10,000
2.2 Memorize mult. tables to 10 X 10
2.3 Use inverse of X and ÷ to check
results
2.4 Multiply whole numbers by one-digit
2.5 Divide whole numbers by one-digit
2.6 Understand properties of 0 and 1
2.7 Determine unit cost from total cost
2.8 Solve problems using above skills
3.0 Fractions and Decimals
3.1 Compare fractions using drawings
3.2 Add and subtract simple fractions
3.3 Add/subt./mult./div. money
amounts
3.4 Fractions/decimals show same amount
Algebra and Functions
1.0 Number Relationships
1.1 Write numerical expressions ...
1.2 Solve numeric equations/inequalities
1.3 Insert symbols/make expression true
1.4 Express unit conversions by
equations
1.5 Commutative/associative properties
2.0 Functional Relationships
2.1 Find total cost of multiple items
2.2 Extend/recognize linear patterns
2.1 Identify, describe, classify polygons
2.2 Identify attributes of triangles
2.3 Identify attributes of quadrilaterals
2.4 Identify right angles in geom. figures
2.5 Identify/classify 3-dimensional objects
2.6 Identify components of a solid object
Statistics, Data Analysis, and Probability
1.0 Data
1.1 Common events/certain/unlikely, etc.
1.2 Record outcomes of a simple event
1.3 Display results/probability experim.
1.4 Predict future events from experiment
Mathematical Reasoning
1.0 Make Decisions about a Problem
1.1 Analyze problems
1.2 Show when/how to break apart problem
2.0 Solve Problems/Justify Reasoning
2.1 Use estimation/verify results
2.2 Apply strategies to complex problems
2.3 Use methods to explain math
reasoning
2.4 Express solutions clearly
2.5 Advantage of exact/approximate
results
2.6 Make precise calculation/validity
3.0 Make Connections
3.1 Evaluate reasonableness of a result
3.2 Note methods of deriving solution
3.3 Develop generalization of the result
Individual Student Profile for Fourth Grade: Mathematics Standards
Student's Name:
Number Sense
1.0 Place Value
1.1 Read/write numbers to millions
1.2 Order whole #s/two place decimals
1.3 Round numbers to nearest 100,000
1.4 Decide when rounded solution is
good
1.5 Divide whole number by whole no.
1.6 Write 10ths/100ths in decimal/fract.
1.7 Write fraction from drawing of
parts
1.8 Use concepts of negative numbers
1.9 Show fractions on a number line
2.0 Computation - Decimals
2.1 Add./subt. whole nos./2-place decimal
2.2 Round two-place decimals
3.0 Computation - Whole Numbers
3.1 Add and subtract multidigit
numbers
3.2 Mult. by two digits/Divide by one digit
3.3 Multiply multidigits by two digit no.
3.4 Divide multidigits by one digit number
2.0 Coordinate Grids
2.1 Draw points on a graph (y=3x)
2.2 Understand horizontal line on graph
2.3 Understand vertical line on graph
3.0 Geometry
3.1 Parallel/perpendicular lines
3.2 Radius/diameter of a circle
3.3 Identify congruent figures
3.4 Bilateral/rotational symmetry
3.5 Know right/acute/obtuse angles
3.6 Make models of geometric solids
3.7 Definition/attributes of triangles
3.8 Definition of quadrilaterals
Statistics, Data Analysis, and Probability
1.0 Data
1.1 Collect and represent data
1.2 Identify mode/medium of data sets
1.3 Interpret 1 & 2-variable data graph
2.0 Making Predictions
4.0 Factoring
4.1 Factor whole numbers
4.2 Certain numbers do not have factors
Algebra and Functions
1.0 Number Sentences/Expressions
1.1 Letters/symbols may represent #s
1.2 Math expressions using parentheses
1.3 Order of operations using
parentheses
1.4 Use and interpret formulas
1.5 Equations are prescriptions to find a #
2.0 More Equations
2.1 Equals added to equals are equal
2.2 Equals multiplied by equals are
equal
Measurement and Geometry
1.0 Area and Perimeter
1.1 Measure area of rectangular shapes
1.2 Compare rectangles with same area
2.1 State outcomes/probability situations
2.2 Express outcomes/probability exper.
Mathematical Reasoning
1.0 Make Decisions about a Problem
1.1 Identify relationships in problems
1.2 When/how to break apart problems
2.0 Solve Problems/Justify Reasoning
2.1 Use estimation to verify results
2.2 Apply strategies to complex problems
2.3 Use methods to explain math
reasoning
2.4 Express solutions clearly
2.5 Advantage of exact/approximate
results
2.6 Make precise calculations/validity
3.0 Make Connections
3.1 Evaluate reasonableness of a result
3.2 Note methods of deriving solution
3.3 Develop generalization of the result
1.3 Rectangles with same perimeter
1.4 Formulas for perimeter and area
Individual Student Profile for Fifth Grade: Mathematics Standards
Student's Name:
Number Sense
1.0 Relative Magnitude of Numbers
1.1 Round very large/small numbers
1.2 Find and compute percent
1.3 Compute positive integer powers
1.4 Determine prime factors of #s to 50
1.5 Order decimals/fract/positive/neg.
#
2.0 Computation
2.1 Compute decimals, neg. integers, etc.
2.2 Divide by multidigit
divisor/decimals
2.3 Add/Subtract fractions and mixed
no.
2.4 Understand mult. and div. of
fractions
2.5 Multiply and divide fractions
Algebra and Functions
1.0 Simple Expressions
1.1 Use graphs/equations to answer
quest.
1.2 Write/evaluate simple algebraic exp.
1.3 Use the distributive property
1.4 Identify and graph ordered pairs
1.5 Linear functions with integer values
Measurement and Geometry
1.0 Area and Volume
1.1 Compare formulas of geometric
shapes
1.2 Compute surface area of cube, etc.
1.3 Compute volume of rectangular solid
1.4 Measure 2- & 3-dimensional objects
2.0 Geometry
2.1 Draw angles, lines, shapes with tools
2.2 Know sum of angles of shapes
2.3 Draw 3-dimensional objects
Statistics, Data Analysis, and Probability
1.0 Data
1.1 Compute mean/medium/mode
1.2 Organize/display single-variable data
1.3 Compare data sets with
fract./percent.
1.4 Identify/interpret data from a graph
1.5 Write ordered pairs correctly
Mathematical Reasoning
1.0 Make Decisions about a Problem
1.1 Identify relationships in problems
1.2 When/how to break problems into parts
2.0 Solve Problems/Justify Reasoning
2.1 Use estimation to verify results
2.2 Apply strategies to complex problems
2.3 Use methods to explain math
reasoning
2.4 Express solutions clearly
2.5 Advantage of exact/approximate results
2.6 Make precise calculations/validity
3.0 Make Connections
3.1 Evaluate reasonableness of a result
3.2 Note methods of deriving solution
3.3 Develop generalization of the result
Individual Student Profile for Sixth Grade: Mathematics Standards
Student's Name:
Number Sense
1.0 Comparing and Ordering Numbers
1.1 Order fractions/decimals/mixed #s
1.2 Use ratios to show relative sizes of #s
1.3 Use proportions to solve problems
1.4 Calculate given percentages of #s
2.0 Calculating
2.1 Compute positive fractions
2.2 Explain mult./div. of positive fract.
2.3 Compute positive & negative
integers
2.4 Find LCM and GCF of whole
numbers
Statistics, Data Analysis, and Probability
1.0 Data
1.1 Compute
range/mean/median/mode
1.2 Additional data affects data sets
1.3 Outliers/measure of central tendency
1.4 Central tendency provides useful
info.
2.0 Limitations
2.1 Determine use of a sample data set
2.2 Identify ways of selecting a sample
2.3 Analyze ways results are influenced
2.4 Identify data sampling errors
2.5 Claims based on statistical data
Algebra and Functions
1.0 Writing Expressions
1.1 Solve one-step linear equations
1.2 Algebraic expression / 3 variables
1.3 Evaluate expressions using tools
1.4 Use order of operations to solve
prob.
3.0 Probabilities
3.1 Represent outcomes of events
3.2 Use data to estimate future events
3.3 Represent probabilities as ratios, etc.
3.4 Understand probabilities
3.5 Independent/dependent events
2.0 Rates and Proportions
2.1 Convert 1 unit of measure to another
2.2 Define and use rate
2.3 Rates/average speed/distance/time
3.0 Patterns
3.1 Use expressions/ describe quantities
3.2 Express geometric relationships
Measurement and Geometry
1.0 Area and Volume
1.1 Find circumference/area of circle
1.2 Use value of pi/area/circum. of circle
1.3 Find volume/triangular prism/cyl.
Mathematical Reasoning
1.0 Make Decisions about a Problem
1.1 Identify relationships in problems
1.2 Justify mathematical conjectures
1.3 When/how to break apart problems
2.0 Solve Problems/Justify Reasoning
2.1 Use estimation to verify results
2.2 Apply strategies to complex
problems
2.3 Estimate unknown quantities
graphically
2.4 Use methods to explain math
reasoning
2.5 Express solutions clearly
2.6 Advantage of exact/approximate
results
2.7 Make precise calculations/validity
2.0 Geometry
2.1 Identify angles as vertical, etc.
3.0 Make Connections
2.2 Solve problems/unknown angle
2.3 Draw quadrilaterals/triangles
3.1 Evaluate reasonableness of a result
3.2 Note methods of deriving solution
3.3 Develop generalization of the result
Individual Student Profile for Seventh Grade: Mathematics Standards
Student's Name:
Number Sense
1.0 Computing
1.1 Read/write/compare rational nos.
1.2 Compute rational numbers
1.3 Convert fractions/decimals/percent
1.4 Differentiate rational/irrational #s
1.5 Nos../terminating/repeating decimal
1.6 Calculate percent increase/decrease
1.7 Compute simple/compound interest
2.0 Fractions
2.1 Mult./div. expressions with
exponents
2.2 Add. and subt. unlike fractions
2.3 Mult./div. rational nos./exponent
rule
2.4 Raising to a power, extracting the root
2.5 Understand absolute value of a no.
Algebra and Functions
1.0 Writing Expressions
1.1 Write expressions/use variables
1.2 Order of operations/algebraic
express.
1.3 Simplify numerical expressions
1.4 Use Algebraic terminology
1.5 Graph quantitative relationships
2.0 Evaluating Expressions
2.1 Whole no. powers as repeated mult.
2.2 Multiply/divide monomials
3.0 Linear and Nonlinear Functions
3.1 Graph functions of the form y=nx2
3.2 Plot value/vol. /3-dimensional
shapes
3.3 Graph linear functions
3.4 Plot value with same ratio
4.0 Linear Equations
4.1 Solve 2-step linear equat./inequalities
4.2 Rate/average speed/dist./time prob.
Measurement and Geometry
1.0 Measurement
2.0 Perimeter and Area
2.1 Area/perimeter/2-dimensional shapes
2.2 Area of complex 2 and 3D shapes
2.3 Compute area/perimeter/volume
2.4 As meas. changes/scale meas. change
3.0 Geometry
3.1 Use tools/construct geometric figures
3.2 Plot figures using coordinate graphs
3.3 Know/use the Pythagorean theorem
3.4 How two geom. figures are congruent
3.5 Construct 2D patterns from 3D
models.
3.6 Identify elements of 3D figures
Statistics, Data Analysis, and Probability
1.0 Data
1.1 Various forms to display data sets
1.2 Draw 2 no. variables on scatterplot
1.3 For a data set, computer median, etc.
Mathematical Reasoning
1.0 Make Decisions about a Problem
1.1 Identify relationships in problems
1.2 Justify mathematical conjectures
1.3 When/how to break apart problems
2.0 Solve Problems/Justify Reasoning
2.1 Use estimation to verify results
2.2 Apply strategies to complex problems
2.3 Estimate unknown quantities graphically
2.4 Test conjectures using reasoning skills
2.5 Use methods to explain math
reasoning
2.6 Express solutions clearly
2.7 Advantage of exact/approximate
results
2.8 Make precise calculations/validity
3.0 Make Connections
3.1 Evaluate reasonableness of a result
3.2 Note methods of deriving solution
3.3 Develop generalization of the result
1.1 Compare
weight/time/capacity/temp.
1.2 Construct/read scale drawings
1.3 Use measures to solve problems
Individual Student Profile for Algebra I: Mathematics Standards
Student's Name:
1.0 Identify and use properties of subsets of integers and rational, irrational & real
numbers
1.1 Use properties of numbers to demonstrate whether assertions are
true/false
2.0 Use such operations as taking the opposite and using rules of exponents
3.0 Solve equations and inequalities involving absolute value
4.0 Simplify expressions before solving linear equations and inequalities with 1
variable
5.0 Solve multistep problems involving linear equations and inequalities in one
variable
6.0 Graph a linear equation and compute the x- and y-intercepts
7.0 Verify that a point lies on a line, given an equation of the line
8.0 Understand the concept of parallel and perpendicular lines and how slopes are
related
9.0 Algebraically solve a system of two linear equations in two variables
10.0 Add, subtract, multiply, and divide monomials and polynomials
11.0 Apply basic factoring techniques to second- and third-degree polynomials
12.0 Simplify fractions with polynomials
13.0 Compute rational expressions and
functions
14.0 Solve a quadratic equation
15.0 Apply algebraic techniques to solve a rate problem
16.0 Understand the concept of a relation and a function
17.0 Determine domain of independent variables and range of dependent variables
18.0 Determine whether a relation is a
function
19.0 Know the quadratic formula and be familiar with its proof
20.0 Use quadratic formulas to solve quadratic equations
21.0 Graph quadratic functions
22.0 Determine if the graph of a quadratic function will intersect x-axis in 0, 1, or 2 points
23.0 Apply quadratic equations to physical
problems
24.0 Use and know simple aspects of a logical argument:
24.1 Know the difference between inductive and deductive reasoning
24.2 Identify the hypothesis and conclusion in logical deductions
24.3 Use counter examples to show that an assertion is false
25.0 Use properties of the number system to judge the validity of results
25.1 Use properties of numbers to construct simple valid arguments
25.2 Judge the validity of an argument
25.3 Determine whether algebraic statements are true sometimes, always, or
never
Individual Student Profile for Geometry: Mathematics Standards
Student's Name:
1.0 Identify undefined terms, axioms, theorems, and inductive/deductive
reasoning
2.0 Write geometric proofs/proofs with contradiction
3.0 Construct and judge the validity of a logical argument
4.0 Prove basic theorems involving congruence and similarity
5.0 Prove that triangles are congruent
6.0 Use the triangle inequality theorem
7.0 Use theorems involving properties of parallel lines, quadrilaterals, and circles
8.0 Find the perimeter, circumference, area, volume, lateral area, and surface area of
shapes
9.0 Compute the volume and surface area of geometric shapes
10.0 Compute the area of polygons
11.0 Know that changes in dimensions affect the perimeter, area, and volume of
shapes
12.0 Classify figures using the measurement of the sides and angles of triangles and
polygons
13.0 Prove relationships of angles using properties of angles
14.0 Prove the Pythagorean theorem
15.0 Use the Pythagorean theorem to find missing lengths of sides of a right triangle
16.0 Perform basic constructions with a straight edge and compass
17.0 Prove theorems by using coordinate
geometry
18.0 Know definitions of basic trigonometric functions defined by angles of a right
triangle
19.0 Use trigonometric functions to solve for an unknown length of a side of a right
triangle
20.0 Use angle and side relationships in problems with special right triangles
21.0 Solve problems with relationships among chords, secants, tangents, inscribed angles,
etc.
22.0 Understand the effect of rigid motions on figures in the coordinate plane and
space
Individual Student Profile for Algebra II: Mathematics Standards
Student's Name:
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
Solve equations and inequalities involving absolute value
Solve linear equations and inequalities by substitution/graphs/matrices
Use operations with polynomials including long division
Factor polynomials
Know how real and complex numbers are related
Add, subtract, multiply, and divide complex numbers
Add, subtract, multiply, divide, reduce, and evaluate rational expressions
Solve and graph quadratic equations
Explain the effect that changing a coefficient has on the graph of quadratic
functions
10.0 Graph quadratic functions and determine the maxima, minima, and zeros of the
function
11.0 Prove laws of logarithms
11.1 Understand inverse relationship between exponents and logarithms
11.2 Judge the validity of an argument
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
21.0
22.0
23.0
24.0
25.0
Know the laws of fractional exponents
Use the definition of logarithms to translate between logarithms in any base
Use the properties of logarithms to simplify logarithmic numeric expressions
Determine if a specific algebraic statement is sometimes true, always true, never
true
Know that the graph of a conic section depends on coefficients of the quadratic
equation
Given a quadratic equation, put equation in standard form and graph
Use counting principles to compute combinations and permutations
Use combinations and permutations to compute probabilities
Use binomial theorem to expand binomial expressions
Apply mathematical induction to prove statements about positive integers
Find the general term and the sums of arithmetic and geometric series
Derive the summation formulas for arithmetic and geometric series
Solve problems involving functional
concepts
Use properties of number systems to justify steps in combining/simplifying
fractions
Individual Student Profile for Probability and Statistics:
Mathematics Standards
Student's Name:
1.0 Use & apply addition, multiplication, and complementation rules to solve for
probabilities
2.0 Use the definition of conditional probability to solve for probabilities in finite
spaces
3.0 Use the notion of discrete random variables to solve for probabilities of outcomes
4.0 Use standard distributions to solve for events in problems
5.0 Determine the mean and standard deviation of a normally distributed random
variable
6.0 Understand and compute mean, median, and mode of a distribution of data
7.0 Compute variance and the standard deviation of a distribution of data
8.0 Organize and describe distributions of data by using a number of different
methods