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STANDARDS INSTRUCTION
CONTENT STANDARDS FOR CALIFORNIA SCHOOLS
STUDENTTRACKING
Mathematics
Individual Student Profile for Kindergarten: Mathematics Standards
Student's Name
Number Sense Measurement and Geometry1.0 Numbers and Quantities 1.0 Measurement
1.1 Compare sets of objects to 10 1.1 Compare length, weight, ... of objects
1.2 Count, name, & order numbers to 30
1.2 Know time (morning, yesterday, etc.)
1.3 Larger numbers = larger sets 1.3 Name days of the week1.4 Identify time to nearest hour
2.0 Addition and Subtraction2.1 Use concrete objects to add &
subt. 2.0
Geometry
2.1 Identify/describe geometric objects
3.0 Estimation 2.2 Compare plane/solid objects3.1 Recognize reasonable
estimatesStatistics, Data Analysis, and Probability
Algebra and Functions 1.0 Collecting Information1.0 Sorting and Classifying
Objects1.1 Record data using picture
graphs1.1 Identify, sort, classify by
attribute1.2 Describe, extend simple
patterns
Mathematical Reasoning1.0 Make Decisions about a
Problem1.1 Determine strategies to be used1.2 Use tools to model problems
2.0 Solve Problems/Justify Reasoning2.1 Use concrete objects/pictorial
repres.2.2 Make precise
calculations/validity
Individual Student Profile for First Grade: Mathematics Standards
Student's Name
Number Sense Statistics, Data Analysis, and Probability
1.0 Place Value 1.0 Data1.1 Count/read/write numbers to
1001.1 Sort objects/data by attributes
1.2 Compare/order numbers to 100 1.2 Represent data on bar graphs ....
1.3 Equivalent forms of numbers to 100
1.4 Count/group object in ones and tens
2.0 Patterning
1.5 Identify and know the value of coins
2.1 Extend next element in patterns
2.0 Addition and Subtraction Mathematical Reasoning2.1 Know add./subt. facts to 20 1.0 Make Decisions about a
Problem2.2 Use the inverse relationship 1.1 Determine approach to be used2.3 Identify 1 more than/less, 10
more ...1.2 Use tools to model problems
2.4 Count by 2s, 5s, and 10s to 1002.5 Showing meaning of add. and
subt.2.0 Solve Problems/Justify
Reasoning2.6 Solve add. and subt. with 1 & 2
digits2.1 Explain the reasoning used
2.7 Find sum of 3 one-digit numbers 2.2 Make precise calculations/validity
3.0 Estimation 3.0 Make Connections3.1 Make reasonable estimates
w/numbers 3.1 Make connections between
problems
Algebra and Functions1.0 Number Sentences
1.1 Write/solve number sentences1.2 Know meaning of symbols +, -,
=1.3 Create problem situations/#
sent.
Measurement and Geometry1.0 Measurement
1.1 Compare length .... 2 or more objects
1.2 Tell time to nearest half hour
2.0 Geometry2.1 Identify/describe/compare
shapes2.2 Classify plane and solid objects2.3 Give and follow directions to
location2.4 Describe objects in space by
position
Individual Student Profile for Second Grade: Mathematics Standards
Student's Name
Number Sense Measurement and Geometry1.0 Place Value 1.0 Measurement
1.1 Count/read/write numbers to 1,000
1.1 Measure lengths of objects
1.2 Use expanded forms to represent #s
1.2 Use diff. units/measure same object
1.3 Order/compare numbers to 1,000
1.3 Measure to nearest inch/centimeter
1.4 Tell time to nearest 1/4 hour2.0 Addition and Subtraction 1.5 Duration of time intervals in
hrs. 2.1 Inverse relationship between +
& -2.2 Add./subt. 3-digit numbers 2.0 Geometry2.3 Use mental math/+ & - 2-digit
#s2.1 Classify plane/solid geom.
shapes2.2 Form other shapes from
shapes3.0 Multiplication and Division
3.1 Use repeated addition to multiply
Statistics, Data Analysis, and Probability
3.2 Use repeated subtraction to divide
1.0 Data
3.3 Know mult. facts of 2s, 5s, and 10s
1.1 Record numerical data
1.2 Represent same data in diff. ways
4.0 Fractions and Decimals 1.3 Identify range/mode of data sets
4.1 Name/compare fractions 1/12 - 1/2 1.4 Ask/answer questions about data
4.2 Recognize fractions of a whole group
4.3 Know what fractions equal a whole
2.0 Patterning
2.1 Recognize/describe/extend patterns
5.0 Computation - Money 2.2 Solve problems using # patterns
5.1 Solve problems with coins/bills5.2 Use decimal notation/ $ and ¢
signMathematical Reasoning
1.0 Make Decisions about a Problem
6.0 Estimation 1.1 Determine approach to be used
6.1 Recognize reasonable estimates
1.2 Use tools to model problems
Algebra and Functions 2.0 Solve Problems/Justify Reasoning
1.0 Number Relationships 2.1 Explain the reasoning used1.1 Use commutative/associative
rules2.2 Make precise
calculations/validity1.2 Relate problems to + & - no.
sent.1.3 Solve + & - problems from
charts3.0 Make Connections
3.1 Make connections between problems
Individual Student Profile for Third Grade: Mathematics Standards
Student's Name
Number Sense Measurement and Geometry1.0 Place Value 1.0 Measurement
1.1 Count/read/write numbers to 10,000
1.1 Choose appropriate tools to measure
1.2 Order whole numbers to 10,000 1.2 Find area & volume of solid figures
1.3 Identify place value to 10,000 1.3 Find perimeter of a polygon1.4 Round to nearest 10, 100, 1,000 1.4 Find unit conversions within a
system1.5 Use expanded notation
2.0 Geometry2.0 Computation - Whole
Numbers2.1 Identify, describe, classify
polygons2.1 Add/subt. numbers from 0 -
10,0002.2 Identify attributes of triangles
2.2 Memorize mult. tables to 10 X 10
2.3 Identify attributes of quadrilaterals
2.3 Use inverse of X and ÷ to check results
2.4 Identify right angles in geom. figures
2.4 Multiply whole numbers by one-digit
2.5 Identify/classify 3-dimensional objects
2.5 Divide whole numbers by one-digit
2.6 Identify components of a solid object
2.6 Understand properties of 0 and 1
2.7 Determine unit cost from total cost
Statistics, Data Analysis, and Probability
2.8 Solve problems using above skills
1.0 Data1.1 Common events/certain/unlikely,
etc.3.0 Fractions and Decimals 1.2 Record outcomes of a simple
event3.1 Compare fractions using
drawings1.3 Display results/probability
experim.3.2 Add and subtract simple
fractions1.4 Predict future events from
experiment3.3 Add/subt./mult./div. money
amounts3.4 Fractions/decimals show same
amount Mathematical Reasoning
1.0 Make Decisions about a Problem
Algebra and Functions 1.1 Analyze problems1.0 Number Relationships 1.2 Show when/how to break apart
problem1.1 Write numerical expressions ...1.2 Solve numeric 2.0 Solve Problems/Justify
equations/inequalities Reasoning1.3 Insert symbols/make expression
true2.1 Use estimation/verify results
1.4 Express unit conversions by equations
2.2 Apply strategies to complex problems
1.5 Commutative/associative properties
2.3 Use methods to explain math reasoning
2.4 Express solutions clearly2.0 Functional Relationships 2.5 Advantage of exact/approximate
results2.1 Find total cost of multiple items 2.6 Make precise calculation/validity2.2 Extend/recognize linear patterns
3.0 Make Connections 3.1 Evaluate reasonableness of a
result3.2 Note methods of deriving
solution3.3 Develop generalization of the
result
Individual Student Profile for Fourth Grade: Mathematics Standards
Student's Name:Number Sense 2.0 Coordinate Grids1.0 Place Value 2.1 Draw points on a graph (y=3x)
1.1 Read/write numbers to millions 2.2 Understand horizontal line on graph
1.2 Order whole #s/two place decimals
2.3 Understand vertical line on graph
1.3 Round numbers to nearest 100,000
1.4 Decide when rounded solution is good
3.0 Geometry
1.5 Divide whole number by whole no.
3.1 Parallel/perpendicular lines
1.6 Write 10ths/100ths in decimal/fract.
3.2 Radius/diameter of a circle
1.7 Write fraction from drawing of parts
3.3 Identify congruent figures
1.8 Use concepts of negative numbers
3.4 Bilateral/rotational symmetry
1.9 Show fractions on a number line
3.5 Know right/acute/obtuse angles
3.6 Make models of geometric solids2.0 Computation - Decimals 3.7 Definition/attributes of triangles
2.1 Add./subt. whole nos./2-place decimal
3.8 Definition of quadrilaterals
2.2 Round two-place decimalsStatistics, Data Analysis, and Probability
3.0 Computation - Whole Numbers
1.0 Data
3.1 Add and subtract multidigit numbers
1.1 Collect and represent data
3.2 Mult. by two digits/Divide by one digit
1.2 Identify mode/medium of data sets
3.3 Multiply multidigits by two digit no.
1.3 Interpret 1 & 2-variable data graph
3.4 Divide multidigits by one digit number
2.0 Making Predictions4.0 Factoring 2.1 State outcomes/probability
situations4.1 Factor whole numbers 2.2 Express outcomes/probability
exper.4.2 Certain numbers do not have
factorsMathematical Reasoning
Algebra and Functions 1.0 Make Decisions about a Problem
1.0 Number Sentences/Expressions
1.1 Identify relationships in problems
1.1 Letters/symbols may represent 1.2 When/how to break apart
#s problems1.2 Math expressions using
parentheses1.3 Order of operations using
parentheses2.0 Solve Problems/Justify
Reasoning1.4 Use and interpret formulas 2.1 Use estimation to verify results1.5 Equations are prescriptions to find
a #2.2 Apply strategies to complex
problems2.3 Use methods to explain math
reasoning2.0 More Equations 2.4 Express solutions clearly
2.1 Equals added to equals are equal
2.5 Advantage of exact/approximate results
2.2 Equals multiplied by equals are equal
2.6 Make precise calculations/validity
Measurement and Geometry 3.0 Make Connections1.0 Area and Perimeter 3.1 Evaluate reasonableness of a
result1.1 Measure area of rectangular
shapes3.2 Note methods of deriving solution
1.2 Compare rectangles with same area
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 Statistics, Data Analysis, and Probability
1.0 Relative Magnitude of Numbers
1.0 Data
1.1 Round very large/small numbers 1.1 Compute mean/medium/mode1.2 Find and compute percent 1.2 Organize/display single-variable
data1.3 Compute positive integer
powers1.3 Compare data sets with
fract./percent.1.4 Determine prime factors of #s to
501.4 Identify/interpret data from a
graph1.5 Order
decimals/fract/positive/neg. #1.5 Write ordered pairs correctly
2.0 Computation Mathematical Reasoning2.1 Compute decimals, neg.
integers, etc.1.0 Make Decisions about a Problem
2.2 Divide by multidigit divisor/decimals
1.1 Identify relationships in problems
2.3 Add/Subtract fractions and mixed no.
1.2 When/how to break problems into parts
2.4 Understand mult. and div. of fractions
2.5 Multiply and divide fractions 2.0 Solve Problems/Justify Reasoning2.1 Use estimation to verify results
Algebra and Functions 2.2 Apply strategies to complex problems
1.0 Simple Expressions 2.3 Use methods to explain math reasoning
1.1 Use graphs/equations to answer quest.
2.4 Express solutions clearly
1.2 Write/evaluate simple algebraic exp.
2.5 Advantage of exact/approximate results
1.3 Use the distributive property 2.6 Make precise calculations/validity
1.4 Identify and graph ordered pairs1.5 Linear functions with integer
values3.0 Make Connections
3.1 Evaluate reasonableness of a result
Measurement and Geometry 3.2 Note methods of deriving solution
1.0 Area and Volume 3.3 Develop generalization of the result
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 Geometry2.1 Draw angles, lines, shapes with
tools2.2 Know sum of angles of shapes2.3 Draw 3-dimensional objects
Individual Student Profile for Sixth Grade: Mathematics Standards
Student's Name:
Number Sense Statistics, Data Analysis, and Probability
1.0 Comparing and Ordering Numbers
1.0 Data
1.1 Order fractions/decimals/mixed #s
1.1 Compute range/mean/median/mode
1.2 Use ratios to show relative sizes of #s
1.2 Additional data affects data sets
1.3 Use proportions to solve problems
1.3 Outliers/measure of central tendency
1.4 Calculate given percentages of #s
1.4 Central tendency provides useful info.
2.0 Calculating 2.0 Limitations2.1 Compute positive fractions 2.1 Determine use of a sample data
set2.2 Explain mult./div. of positive
fract.2.2 Identify ways of selecting a
sample2.3 Compute positive & negative
integers2.3 Analyze ways results are
influenced2.4 Find LCM and GCF of whole
numbers2.4 Identify data sampling errors
2.5 Claims based on statistical dataAlgebra and Functions1.0 Writing Expressions 3.0 Probabilities
1.1 Solve one-step linear equations 3.1 Represent outcomes of events1.2 Algebraic expression / 3
variables3.2 Use data to estimate future
events1.3 Evaluate expressions using
tools3.3 Represent probabilities as
ratios, etc.1.4 Use order of operations to solve
prob.3.4 Understand probabilities
3.5 Independent/dependent events2.0 Rates and Proportions
2.1 Convert 1 unit of measure to another
Mathematical Reasoning
2.2 Define and use rate 1.0 Make Decisions about a Problem
2.3 Rates/average speed/distance/time
1.1 Identify relationships in problems
1.2 Justify mathematical conjectures3.0 Patterns 1.3 When/how to break apart
problems3.1 Use expressions/ describe
quantities3.2 Express geometric relationships 2.0 Solve Problems/Justify
Reasoning2.1 Use estimation to verify results
Measurement and Geometry 2.2 Apply strategies to complex problems
1.0 Area and Volume 2.3 Estimate unknown quantities graphically
1.1 Find circumference/area of circle
2.4 Use methods to explain math reasoning
1.2 Use value of pi/area/circum. of circle
2.5 Express solutions clearly
1.3 Find volume/triangular prism/cyl.
2.6 Advantage of exact/approximate results
2.7 Make precise calculations/validity
2.0 Geometry2.1 Identify angles as vertical, etc. 3.0 Make Connections2.2 Solve problems/unknown angle 3.1 Evaluate reasonableness of a
result2.3 Draw quadrilaterals/triangles 3.2 Note methods of deriving
solution3.3 Develop generalization of the
result
Individual Student Profile for Seventh Grade: Mathematics Standards
Student's Name:Number Sense1.0 Computing 2.0 Perimeter and Area
1.1 Read/write/compare rational nos. 2.1 Area/perimeter/2-dimensional shapes
1.2 Compute rational numbers 2.2 Area of complex 2 and 3D shapes1.3 Convert
fractions/decimals/percent2.3 Compute area/perimeter/volume
1.4 Differentiate rational/irrational #s
2.4 As meas. changes/scale meas. change
1.5 Nos../terminating/repeating decimal
1.6 Calculate percent increase/decrease
3.0 Geometry
1.7 Compute simple/compound interest
3.1 Use tools/construct geometric figures
3.2 Plot figures using coordinate graphs
2.0 Fractions 3.3 Know/use the Pythagorean theorem
2.1 Mult./div. expressions with exponents
3.4 How two geom. figures are congruent
2.2 Add. and subt. unlike fractions 3.5 Construct 2D patterns from 3D models.
2.3 Mult./div. rational nos./exponent rule
3.6 Identify elements of 3D figures
2.4 Raising to a power, extracting the root
2.5 Understand absolute value of a no.
Statistics, Data Analysis, and Probability1.0 Dat
aAlgebra and Functions 1.1 Various forms to display data sets1.0 Writing Expressions 1.2 Draw 2 no. variables on
scatterplot1.1 Write expressions/use variables 1.3 For a data set, computer median,
etc.1.2 Order of operations/algebraic
express.1.3 Simplify numerical expressions Mathematical Reasoning1.4 Use Algebraic terminology 1.0 Make Decisions about a
Problem1.5 Graph quantitative relationships 1.1 Identify relationships in problems
1.2 Justify mathematical conjectures2.0 Evaluating Expressions 1.3 When/how to break apart
problems2.1 Whole no. powers as repeated
mult.2.2 Multiply/divide monomials 2.0 Solve Problems/Justify
Reasoning2.1 Use estimation to verify results
3.0 Linear and Nonlinear Functions
2.2 Apply strategies to complex problems
3.1 Graph functions of the form y=nx2
2.3 Estimate unknown quantities graphically
3.2 Plot value/vol. /3-dimensional shapes
2.4 Test conjectures using reasoning skills
3.3 Graph linear functions 2.5 Use methods to explain math reasoning
3.4 Plot value with same ratio 2.6 Express solutions clearly2.7 Advantage of exact/approximate
results4.0 Linear Equations 2.8 Make precise calculations/validity
4.1 Solve 2-step linear equat./inequalities
4.2 Rate/average speed/dist./time prob.
3.0 Make Connections
3.1 Evaluate reasonableness of a result
Measurement and Geometry 3.2 Note methods of deriving solution1.0 Measurement 3.3 Develop generalization of the
result1.1 Compare
weight/time/capacity/temp.1.2 Construct/read scale drawings1.3 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 value4.0 Simplify expressions before solving linear equations and inequalities
with 1 variable5.0 Solve multistep problems involving linear equations and inequalities
in one variable6.0 Graph a linear equation and compute the x- and y-intercepts7.0 Verify that a point lies on a line, given an equation of the line8.0 Understand the concept of parallel and perpendicular lines and how
slopes are related9.0 Algebraically solve a system of two linear equations in two variables
10.0 Add, subtract, multiply, and divide monomials and polynomials11.0 Apply basic factoring techniques to second- and third-degree
polynomials12.0 Simplify fractions with polynomials13.0 Compute rational expressions and
functions14.0 Solve a quadratic equation15.0 Apply algebraic techniques to solve a rate problem16.0 Understand the concept of a relation and a function17.0 Determine domain of independent variables and range of dependent
variables18.0 Determine whether a relation is a
function19.0 Know the quadratic formula and be familiar with its proof20.0 Use quadratic formulas to solve quadratic equations21.0 Graph quadratic functions22.0 Determine if the graph of a quadratic function will intersect x-axis in 0,
1, or 2 points23.0 Apply quadratic equations to
physical problems24.0 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 deductions24.3 Use counter examples to show that an assertion is false
25.0 Use properties of the number system to judge the validity of results25.1 Use properties of numbers to construct simple valid arguments25.2 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 contradiction3.0 Construct and judge the validity of a logical argument4.0 Prove basic theorems involving congruence and similarity5.0 Prove that triangles are congruent6.0 Use the triangle inequality
theorem7.0 Use theorems involving properties of parallel lines, quadrilaterals,
and circles8.0 Find the perimeter, circumference, area, volume, lateral area, and surface
area of shapes9.0 Compute the volume and surface area of geometric shapes
10.0 Compute the area of polygons11.0 Know that changes in dimensions affect the perimeter, area, and
volume of shapes12.0 Classify figures using the measurement of the sides and angles of
triangles and polygons13.0 Prove relationships of angles using properties of angles14.0 Prove the Pythagorean theorem15.0 Use the Pythagorean theorem to find missing lengths of sides of a
right triangle16.0 Perform basic constructions with a straight edge and compass17.0 Prove theorems by using coordinate
geometry18.0 Know definitions of basic trigonometric functions defined by angles
of a right triangle19.0 Use trigonometric functions to solve for an unknown length of a side
of a right triangle20.0 Use angle and side relationships in problems with special right
triangles21.0 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 Solve equations and inequalities involving absolute value2.0 Solve linear equations and inequalities by
substitution/graphs/matrices3.0 Use operations with polynomials including long division4.0 Factor polynomials 5.0 Know how real and complex numbers are related6.0 Add, subtract, multiply, and divide complex numbers7.0 Add, subtract, multiply, divide, reduce, and evaluate rational
expressions8.0 Solve and graph quadratic
equations9.0 Explain the effect that changing a coefficient has on the graph of
quadratic functions10.0 Graph quadratic functions and determine the maxima, minima, and
zeros of the function11.0 Prove laws of logarithms
11.1 Understand inverse relationship between exponents and logarithms
11.2 Judge the validity of an argument
12.0 Know the laws of fractional exponents
13.0 Use the definition of logarithms to translate between logarithms in any base
14.0 Use the properties of logarithms to simplify logarithmic numeric expressions
15.0 Determine if a specific algebraic statement is sometimes true, always true, never true
16.0 Know that the graph of a conic section depends on coefficients of the quadratic equation
17.0 Given a quadratic equation, put equation in standard form and graph18.0 Use counting principles to compute combinations and permutations19.0 Use combinations and permutations to compute probabilities20.0 Use binomial theorem to expand binomial expressions21.0 Apply mathematical induction to prove statements about positive
integers22.0 Find the general term and the sums of arithmetic and geometric
series23.0 Derive the summation formulas for arithmetic and geometric series24.0 Solve problems involving functional
concepts25.0 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 variable6.0 Understand and compute mean, median, and mode of a distribution of
data7.0 Compute variance and the standard deviation of a distribution of data8.0 Organize and describe distributions of data by using a number of
different methods
