ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
KINDERGARTEN-MATHEMATICS
NUMBER SENSE
ALGEBRA AND FUNCTIONS
MEASUREMENT AND GEOMETRY
MEASUREMENT
GEOMETRY
STATISTICS, DATA ANALYSIS, AND PROBABILITY
MATHEMATICAL REASONING
FIRST GRADE – MATHEMATICS
NUMBER SENSE
PLACE VALUE
ADDITION AND SUBTRACTION
ESTIMATION
ALGEBRA AND FUNCTIONS
MEASUREMENT AND GEOMETRY
STATISTICS, DATA ANALYSIS, AND PROBABILITY
MATHEMATICAL REASONING
SECOND GRADE - MATHEMATICS
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development Team © Copyright January 2002
NUMBER SENSE
PLACE VALUE
ADDITION AND SUBTRACTION
MULTIPLICATION AND DIVISION
FRACTIONS AND DECIMALS
COMPUTATION--MONEY
ALGEBRA AND FUNCTIONS
MEASUREMENT AND GEOMETRY
MEASUREMENT
GEOMETRY
MATHEMATICAL REASONING
MAKE DECISIONS ABOUT A PROBLEM
SOLVE PROBLEMS/JUSTIFY REASONING
THIRD GRADE - MATHEMATICS
NUMBER SENSE
PLACE VALUE
COMPUTATION - WHOLE NUMBERS
FRACTIONS AND DECIMALS
MEASUREMENT AND GEOMETRY
MATHEMATICAL REASONING
FOURTH GRADE - MATHEMATICS
NUMBER SENSE
PLACE VALUE
COMPUTATION - DECIMALS
COMPUTATION - WHOLE NUMBERS
FACTORING
ALGEBRA AND FUNCTIONS
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development Team © Copyright January 2002
NUMBER SENTENCES AND EXPRESSIONS
MATHEMATICAL REASONING
FIFTH GRADE - MATHEMATICS
NUMBER SENSE
RELATIVE MAGNITUDE OF NUMBERS
COMPUTATION
ALGEBRA AND FUNCTIONS
SIMPLE EXPRESSIONS
MATHEMATICAL REASONING
DECISIONS ABOUT APPROACHING PROBLEMS
USE STRATEGIES, SKILLS, AND CONCEPTS IN FINDING SOLUTIONS
GENERALIZE TO OTHER SITUATIONS
SIXTH GRADE - MATHEMATICS
NUMBER SENSE
ALGEBRA AND FUNCTIONS
MEASUREMENT AND GEOMETRY
STATISTICS, DATA, ANALYSIS AND PROBABILITY
MATHEMATICAL REASONING
SEVENTH GRADE – MATHEMATICS
NUMBER SENSE
MEASUREMENT AND GEOMETRY
STATISTICS, DATA, ANALYSIS AND PROBABILITY
MATHEMATICAL REASONING
EIGHTH, NINTH, TENTH GRADE - MATHEMATICS
ALGEBRA I
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development Team © Copyright January 2002
MATHEMATICS SELECTED STANDARDS CHECKLIST
KINDERGARTEN
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)
K.1.2 Count recognizes, represent, name, and order a
number of objects (up to 30).
2.0
Students understand and describe
simple additions and subtractions
K 2.1 Use concrete objects to determine the answers to
addition and subtraction problems (for two
numbers that are each less than 10).
ALGEBRA AND FUNCTION
1.0 Students sort and classify objects
K 1.1 Identify, sort, and classify objects by attribute and
identify objects that do not belong to a particular
group (e.g., all these balls are green, those are red).
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:
K 1.1 Compare the length, weight, and capacity of objects
by making direct comparisons with reference
objects (e.g., note which object is shorter, longer,
taller, lighter, heavier, or holds more
K 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).
K 1.3 Name the days of the week.
K 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).
MEASUREMENT AND GEOMETRY-Cont
2.0 Students identify common objects in their
environment and describe the geometric
features
K 2.1 Identify and describe common geometric objects
(e.g., circle, triangle, square, rectangle, cube,
sphere, cone).
STATISTICS, DATA ANALYSIS AND PROB
1.0 Students collect information about objects
and events in their environment
K 1.1 Pose information questions; collect data; and record
the results using objects, pictures, and picture
graphs.
K 1.2 Identify, describe, and extend simple patterns (such
as circles or triangles) by referring to their shapes,
sizes, or colors.
MATHEMATICAL REASONING
2.0 Students solve problems in reasonable
ways and justify their reasoning.
K 2.1 Explain the reasoning used with concrete objects
and/ or pictorial representations.
K 2.2 Make precise calculations and check the validity of
the results in the context of the problem.
MATHEMATICS SELECED STANDARDS CHECKLIST
FIRST GRADE
NUMBER SENSE
1.0 Students understand and use numbers up to 100
1.1.1 Count, read, and write whole numbers to 100.
1.1.2 Compare and order whole numbers to 100 by using
the symbols for less than, equal to, or greater than
(<, =, >).
1.1.4 Count and group object in ones and tens (e.g., three
groups of 10 and 4 equals 34, or 30+4)
1.1.5 Identify and know the value of coins and show
different combinations of coins that equal the same
value.
MEASUREMENT AND GEOMETRY
1.0 Students use direct comparison and
nonstandard units to describe the
measurements of objects:
1.1.2 Tell time to the nearest half hour and relate time to
events (e.g., before/after, shorter/longer).
STATISTICS, DATA ANALYSIS AND PROB.
1.0 Students organize, represent, and
compare data by category on simple graphs
and charts
1.1.1 Sort objects and data by common attributes and
describe the categories.
2.0 Students demonstrate the meaning of
addition and subtraction and use these
operations to solve problems:
1.1.2 Represent and compare data (e.g., largest, smallest,
most often, least often) by using pictures, bar
graphs, tally charts, and picture graphs.
1.2.1 Know the addition facts (sums to 20) and the
corresponding subtraction facts and commit them
to memory.
MATHEMATICAL REASONING
1.0 Students make decisions about how to
set up a problem
1.2.4 Count by 2s, 5s, and 10s to 100.
1.1.1 Determine the approach, materials, and strategies
to be used.
1.2.5 Solve addition and subtraction problems with oneand two-digit numbers (e.g., 5+8=__).
1.2.7 Find the sum of three one-digit numbers.
3.0 Students use estimation strategies in
computation and problem solving that
involve numbers that use the ones, tens, and
hundreds places:
1.2.1 Use tools, such as manipulatives or sketches, to
model problems.
2.0 Students solve problems and justify their
reasoning
1.2.1 Explain the reasoning used and justify the
procedures selected.
1.3.1 Make reasonable estimates when comparing larger
or smaller numbers.
ALGEBRA AND FUNCTIONS
1.0 Students use number sentences with
operational symbols and expressions to
solve problems
1.1.1 Write and solve number sentences from problem
situations that express relationships involving
addition and subtraction.
1.2
Understand the meaning of the symbols +, -, =.
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development
Team © Copyright January 2002
MATHERMATICS SELECTED STANDARDS CHECKLIST
SECOND GRADE
NUMBER SENSE
1.0 Students understand the relationship
between numbers, quantities, and place value
in whole numbers up to 1,000
NUMBER SENSE – continued
5.0 Students model and solve problems by
representing, adding, and subtracting
amounts of money
2.1.1 Count, read, and write whole numbers to 1,000 and
identify the place value for each digit.
2.5.1 Solve problems using combinations of coins and bills.
2.1.2 Use words, models, and expanded forms (e.g.,
45=4tens+5) to represent numbers (to 1,000).
2.1.3 Order and compare whole numbers to 1,000 by using the
symbols <, =,>.
2.0 Students estimate, calculate, and solve
problems involving addition and subtraction
of two-and three-digit numbers
2.5.2 Know and use the decimal notation and the dollar and
cent symbols for money.
6.0 Students use estimation strategies in
computation and problem solving that
involve numbers that use the ones, tens,
hundreds, and thousands places
2.6.1 Recognize when an estimate is reasonable in
measurements (e.g., closest inch).
2.2.1 Understand and use the inverse relationship between
addition and subtraction (e.g., an opposite number
sentence for 8+6=14 is 14-6=8) to solve problems and
check solutions.
ALGEBRA AND FUNCTIONS
1.0 Students model, represent, and interpret
number relationships to create and solve
problems involving addition and subtraction
2.2.2 Find the sum or difference of two whole numbers up to
three digits long.
2.1.2 Relate problem situations to number sentences involving
addition and subtraction.
3.0 Students model and solve simple
problems involving multiplication and
division
2.1.3 Solve addition and subtraction problems by using data
from simple charts, picture graphs, and number
sentences.
2.3.1 Use repeated addition, arrays, and counting by multiples
to do multiplication.
2.3.2 Use repeated subtraction, equal sharing, and forming
equal groups with remainders to do division.
2.3.3 Know the multiplication tables of 2s, 5s, and 10s (to
"times 10") and commit them to memory.
4.0 Students understand that fractions and
decimals may refer to parts of a set and parts
of a whole
2.4.1 Recognize, name, and compare unit fractions from 1/12
to 1/2.
2.4.2 Recognize fractions of a whole and parts of a group (e.g.,
one-fourth of a pie, two-thirds of 15 balls).
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
2.1.1 Measure the length of objects by iterating (repeating) a
nonstandard or standard unit.
2.1.3 Measure the length of an object to the nearest inch and/
or centimeter.
2.1.4 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).
2.1.5 Determine the duration of intervals of time in hours (e.g.,
11:00a.m. to 4:00p.m.).
2.4.3 Know that when all fractional parts are included, such as
four-fourths, the result is equal to the whole and to one.
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development
Team © Copyright January 2002
MSRMNT & GEOMM continued
MATHEMATICAL REASONING Embedded
2.0 Students identify and describe the attributes of
common figures in the plane and of common objects in
space
1.0 Students make decisions about how to set up a problem
2.1.1 Determine the approach, materials, and strategies to be
used.
2.2.1 Describe and classify plane and solid geometric shapes
(e.g., circle, triangle, square, rectangle, sphere, pyramid,
cube, rectangular prism) according to the number and shape
of faces, edges, and vertices.
2.0 Students solve problems and justify their reasoning
2.2.1 Defend the reasoning used and justify the procedures
selected.
2.2.2 Put shapes together and take them apart to form other
shapes (e.g., two congruent right triangles can be arranged
to form a rectangle).
STATISTICS, DATA ANALYSIS, and
PROBABILITY
1.0 Students collect numerical data and record,
organize, display, and interpret the data on bar graphs
and other representations
2.1.1 Record numerical data in systematic ways, keeping track
of what has been counted.
2.1.2 Represent the same data set in more than one way (e.g.,
bar graphs and charts with tallies).
2.1.3 Identify features of data sets (range and mode).
2.0 Students demonstrate an understanding of
patterns and how patterns grow and describe them in
general ways
2.2.1 Recognize, describe, and extend patterns and determine a
next term in linear patterns (e.g., 4, 8, 12 ...; the number of
ears on one horse, two horses, three horses, four horses).
2.2.2 Solve problems involving simple number patterns.
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development
Team © Copyright January 2002
MATHEMATICS SELECTED STNADARDS CHECKLIST
THIRD GRADE
NUMBER SENSE
1.0 Students understand the place value of
whole numbers
3.1.1 Count, read, and write whole numbers to 10,000.
NUMBER SENSE-continued
3.0 Students understand the relationship
between whole numbers, simple fractions,
and decimals
3.1.2 Compare and order whole numbers to 10,000.
3.3.2 Add and subtract simple fractions (e.g., determine that
1/8 + 3/8 is the same as 1/2).
3.1.3 Identify the place value for each digit in numbers to
10,000.
3.1.4 Round off numbers to 10,000 to the nearest ten, hundred,
and thousand.
3.1.5 Use expanded notation to represent numbers (e.g., 3,206
= 3,000 + 200 + 6).
2.0 Students calculate and solve problems
involving addition, subtraction,
multiplication, and division
3.2.1 Find the sum or difference of two whole numbers
between 0 and 10,000.
3.2.2 Memorize to automaticity the multiplication table for
numbers between 1 and 10.
3.2.3 Use the inverse relationship of multiplication and
division to compute and check results.
3.2.4
Solve simple problems involving multiplication of
multiplication numbers by one-digit numbers (3,671 x 3
= __).
3.3.3 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.
3.3.4 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
3.1.1 Represent relationships of quantities in the form of
mathematical expressions, equations, or inequalities.
3.1.3 Select appropriate operational and relational symbols to
make an expression true
3.1.4 Express simple unit conversions in symbolic form (e.g.,
__ inches = __ feet x 12).
3.2.5 Solve division problems in which a multiplication
number is evenly divided by a one-digit number (135 ÷ 5
= __).
3.1.5 Recognize and use the commutative and associative
properties of multiplication (e.g., if 5 x 7 = 35, then what
is 7 x 5? and if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?).
3.2.6 Understand the special properties of 0 and 1 in
multiplication and division.
2.0 Students represent simple functional
relationships
3.2.7 Determine the unit cost when given the total cost and
number of units.
3.2
Solve simple problems involving a functional
relationship between two quantities (e.g., find the total
cost of multiple items given the cost per unit).
3.2.8 Solve problems that require two or more of the skills
mentioned above.
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).
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development
Team © Copyright January 2002
MEASUREMENT AND GEOMETRY
1.0 Students choose and use appropriate
units and measurement tools to quantify the
properties of objects
3.1.2 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.
3.1.3 Find the perimeter of a polygon with integer sides.
2.0 Students describe and compare the
attributes of plane and solid geometric
figures and use their understanding to show
relationships and solve problems
3.2.1 Identify, describe, and classify polygons (including
pentagons, hexagons, and octagons).
3.2.2 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).
STATISTICS, DATA ANALYSIS, AND
PROBABILITY
1.0 Students conduct simple probability
experiments by determining the number of
possible outcomes and make simple
predictions
3.1.2 Record the possible outcomes for a simple event (e.g.,
tossing a coin) and systematically keep track of the
outcomes when the event is repeated many times.
3.1.3 Summarize and display the results of probability
experiments in a clear and organized way (e.g., use a bar
graph or a line plot).
MATHEMATICAL REASONING Embedded
2.0 Students use strategies, skills, and
concepts in finding solutions
3.2.3 Use a variety of methods, such as words, numbers,
symbols, charts, graphs, tables, diagrams, and models, to
explain mathematical reasoning.
3.2.3 Identify attributes of quadrilaterals (e.g., parallel sides
for the parallelogram, right angles for the rectangle,
equal sides and right angles for the square).
3.2.4 Identify right angles in geometric figures or in
appropriate objects and determine whether other angles
are greater or less than a right angle.
3.2.5 Identify, describe, and classify common threedimensional geometric objects (e.g., cube, rectangular
solid, sphere, prism, pyramid, cone, cylinder ).
3.2.6 Identify common solid objects that are the components
needed to make a more complex solid object.
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development
Team © Copyright January 2002
MATHEMATICS SELECTED STANDARDS CHECKLIST
FOURTH GRADE
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
4.1.1 Read and write whole numbers in the millions
4.1.2 Order and compare whole numbers and decimals to two
decimal places.
4.1.3 Round whole numbers through the millions to the nearest
ten, hundred, thousand, ten thousand, or hundred
thousand.
4.1.5 Explain different interpretations of fractions, for
example, parts of a whole, parts of a set, and division of
whole numbers by whole numbers; explain equivalents
of fractions (see Standard 4.0).
4.1.6 Write tenths and hundredths in decimal and fraction
notations and know the fraction and decimal equivalents
for halves and fourths (e.g., 1/2 = 0.5 or .50; 7/4 = 1 3/4
= 1.75).
4.1.7 Write the fraction represented by a drawing of parts of a
figure; represent a given fraction by using drawings; and
relate a fraction to a simple decimal on a number line.
4.1.8 Use concepts of negative numbers (e.g., on a number
line, in counting, in temperature, in "owing").
4.1.9 Identify on a number line the relative position of positive
fractions, positive mixed numbers, and positive decimals
to two decimal places.
2.0 Students extend their use and
understanding of whole numbers to the
addition and subtraction of simple decimals
2.1 Estimate and compute the sum or difference of
whole numbers and positive decimals to two
places.
NUMBER SENSE-continued
3.0 Students solve problems involving
addition, subtraction, multiplication, and
division of whole numbers and understand
the relationships among the operations
4.3.1 Demonstrate an understanding of, and the ability to use,
standard algorithms for the addition and subtraction of
multi-digit numbers.
4.3.2 Demonstrate an understanding of, and the ability to use,
standard algorithms for multiplying a multi-digit number
by a two-digit number and for dividing a multi-digit
number by a one-digit number; use relationships between
them to simplify computations and to check results.
4.3.3 Solve problems involving multiplication of multi-digit
numbers by two-digit numbers.
4.3.4 Solve problems involving division of multi-digit
numbers by one-digit numbers.
4.0 Students know how to factor small
whole numbers
4.4.1 Understand that many whole numbers break down in
different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3).
4.4.2 Know that numbers such as 2, 3, 5, 7, and 11 do not have
any factors except 1 and them selves and that such
numbers are called prime numbers.
ALGEBRA AND FUNCTIONS
1.0 Students use and interpret variables,
mathematical symbols, and properties to
write and simplify expressions and sentences
4.1.1
Use letters, boxes, or other symbols to stand CAHSEE
for any number in simple expressions or equations
(e.g., demonstrate an understanding and the use of the concept
of a variable).
4.1.2
CAHSEE
Interpret and evaluate mathematical
expressions that now use parentheses.
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development
Team © Copyright January 2002
ALG. & FUNCTIONS-continued
1.0 Students use and interpret variables,
mathematical symbols, and properties to
write and simplify expressions and sentences
4.1.3
CAHSEE
4.1.4
CAHSEE
4.1.5
CAHSEE
Use parentheses to indicate which operation
to perform first when writing expressions
containing more than two terms and different
operations.
Use and interpret formulas (e.g., area =
length x width or A = l ) to answer questions
about quantities and their relationships.
Understand that an equation such as y = 3 x
+ 5 is a prescription for determining a second
umber when a first number is given.
MEASUREMENT AND GEOMETRY
1.0 Students understand perimeter and
area.
4.1.4
MEASUREMENT AND GEOMETRY
3.0 Students demonstrate an understanding
of plane and solid geometric objects and use
this knowledge to show relationships and
solve problems
4.3.1
Identify lines that are parallel and perpendicular.
4.3.2
Identify the radius and diameter of a circle.
4.3.3
Identify congruent figures.
4.3.4
Identify figures that have bilateral and rotational
symmetry.
4.3.5
Know the definitions of a right angle, an acute angle,
and an obtuse angle. Understand that 90°, 180°, 270°,
and 360° are associated, respectively, with 1/4, 1/2,
3/4, and full turns.
4.3.7
Visualize, describe, and make models of geometric
solids (e.g., prisms, pyramids) in terms of the number
and shape of faces, edges, and vertices; interpret twodimensional representations of three-dimensional
objects; and draw patterns (of faces) for a solid that,
when cut and folded, will make a model of the solid.
Understand and use formulas to solve problems
involving perimeters and areas of rectangles and
squares. Use those formulas to find the areas of more
complex figures by dividing the figures into basic
shapes.
2.0 Students use two-dimensional
coordinate grids to represent points and
graph lines and simple figures
4.2.1
Draw the points corresponding to linear relationships
on graph paper (e.g., draw 10 points on the graph of
the equation y = 3 x and connect them by using a
straight line).
4.2.2
Understand that the length of a horizontal line segment
equals the difference of the x- coordinates.
4.2.3
Understand that the length of a vertical line segment
equals the difference of the y- coordinates.
MATHEMATICAL REASONING
Embedded
1.0 Students make decisions about how to
approach problems
4.1.2
Determine when and how to break a problem into
simpler parts.
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development
Team © Copyright January 2002
MATHEMATICS SELECTED STANDARDS CHECKLIST
FIFTH GRADE
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
5.1.1
5.1.2
T*
5.1.4
5.1.5
Estimate, round, and manipulate very
large (e.g., millions) and very small (e.g.,
thousandths) numbers.
Interpret percents as a part of a hundred;
find decimal and percent equivalents for
common fractions and explain why they
represent the same value; compute a
given percent of a whole number.
Determine the prime factors of all
numbers through 50 and write the
numbers as the product of their prime
factors by using exponents to show
multiples of a factor (e.g., 24 = 2 x 2 x 2
x 3 = 23 x 3).
Identify and represent on a number line
decimals, fractions, mixed numbers, and
positive and negative integers.
2.0 Students perform calculations and solve
problems involving addition, subtraction,
and simple multiplication and division of
fractions and decimals
5.2.1
5.2.2
5.2.3
5.2.5
Add, subtract, multiply, and divide with
decimals; add with negative integers;
subtract positive integers from negative
integers; and verify the reasonableness of
the results.
Demonstrate proficiency with division,
including division with positive decimals
and long division with multi-digit
divisors.
Solve simple problems, including ones
arising in concrete situations, involving
the addition and subtraction of fractions
and mixed numbers (like and unlike
denominators of 20 or less), and express
answers in the simplest form.
Compute and perform simple
multiplication and division of fractions
and apply these procedures to solving
problems.
ALGEBRA AND FUNCTIONS
1.0 Students use variables in simple expressions,
compute the value of the expression for specific
values of the variable, and plot and interpret the
results
5.1.1
CAHSEE
5.1.2
CAHSEE
5.1.4
CAHSEE
5.1.5
CAHSEE
Use information taken from a graph or
equation to answer questions about a
problem situation.
Use a letter to represent an unknown
number; write and evaluate simple
algebraic expressions in one variable by
substitution.
Identify and graph ordered pairs in the
four quadrants of the coordinate plane.
Solve problems involving linear
functions with integer values; write the
equation; and graph the resulting ordered
pairs of integers on a grid.
MEASUREMENT AND GEOMETRY
1.0 Students understand and compute the volumes
and areas of simple objects
5.1.1
5.1.2
5.1.3
Derive and use the formula for the area of
a triangle and of a parallelogram by
comparing it with the formula for the area
of a rectangle (i.e., two of the same
triangles make a parallelogram with twice
the area; a parallelogram is compared
with a rectangle of the same area by
cutting and pasting a right triangle on the
parallelogram).
Construct a cube and rectangular box
from two-dimensional patterns and use
these patterns to compute the surface area
for these objects.
Understand the concept of volume and
use the appropriate units in common
measuring systems (i.e., cubic centimeter
[cm3], cubic meter [m3], cubic inch [in3],
cubic yard [yd3]) to compute the volume
of rectangular solids.
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development
Team © Copyright January 2002
MEASUREMENT AND GEOMETRY
2.0
Students identify, describe, and
classify the properties of, and the
relationships between, plane and solid
geometric figures
5.2.1
5.2.2
Measure, identify, and draw angles,
perpendicular and parallel lines, rectangles,
and triangles by using appropriate tools
(e.g., straightedge, ruler, compass,
protractor, drawing software).
Know that the sum of the angles of any
triangle is 180° and the sum of the angles of
any quadrilateral is 360° and use this
information to solve problems.
MATHEMATICAL REASONING Embedded
1.0 Students make decisions about how to
approach problems
5.1.2
2.0 Students use strategies, skills, and concepts in
finding solutions
5.2.3
5.1.1
5.1.4
5.1.5
Students use strategies, skills, and
concepts in finding solutions
3.0 Students move beyond a particular problem by
generalizing to other situations
5.3.2
STATISTICS, DATA ANALYSIS, AND
PROBABILITY
1.0
Students display, analyze, compare,
and interpret different data sets, including
data sets of different sizes
Determine when and how to break a
problem into simpler parts.
Note the method of deriving the solution
and demonstrate a conceptual
understanding of the derivation by
solving similar problems.
Know the concepts of mean, median, and
mode; compute and compare simple
examples to show that they may differ.
Identify ordered pairs of data from a graph
and interpret the meaning of the data in
terms of the situation depicted by the graph.
Know how to write ordered pairs correctly;
for example, ( x, y ).
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MATHEMATICS SELECTED STANDARDS CHECKLIST
SIXTH GRADE
NUMBER SENSE
1.0 Students compare and order positive
and negative fractions, decimals, and mixed
numbers. Students solve problems involving
fractions, ratios, proportions, and
percentages
6.1.4
CAHSEE
Calculate given percentages of
quantities and solve problems
involving discounts at sales, interest
earned, and tips.
2.0 Students calculate and solve problems
involving addition, subtraction,
multiplication, and division
6.2.1
6.2.2
6.2.3
CAHSEE
6.2.4
CAHSEE
Solve problems involving addition,
subtraction, multiplication, and
division of positive fractions and
explain why a particular operation
was used for a given situation.
Explain the meaning of
multiplication and division of
positive fractions and perform the
calculations (e.g., 5/8 ÷ 15/16 = 5/8
x 16/15 = 2/3).
Solve addition, subtraction,
multiplication, and division
problems, including those arising in
concrete situations, that use positive
and negative integers and
combinations of these operations.
Determine the least common
multiple and the greatest common
divisor of whole numbers; use them
to solve problems with fractions
(e.g., to find a common denominator
to add two fractions or to find the
reduced form for a fraction).
ALGEBRA AND FUNCTIONS
2.0 Students analyze and use tables, graphs,
and rules to solve problems involving rates
and proportions
6.2.1
CAHSEE
Convert one unit of measurement to
another (e.g., from feet to miles,
from centimeters to inches).
MEASUREMENT AND GEOMETRY
1.0 Students deepen their understanding of the
measurement of plane and solid shapes and use this
understanding to solve problems
6.1.1
CAHSEE
1 Understand the concept of a
constant such as ; know the
formulas for the circumference and
area of a circle.
STATISTIC, DATA ANALYSIS, and
PROBABILITY
1.0 Students compute and analyze statistical
measurements for data sets
6.1.1
CAHSEE
Compute the range, mean, median,
and mode of data sets.
2.0 Students use data samples of a population and
describe the characteristics and limitations of the
samples
6.2.5
CAHSEE
Identify claims based on statistical
data and, in simple cases, evaluate
the validity of the claims
3.0 Students determine theoretical and
experimental probabilities and use these to make
predictions about events
6.3.1
CAHSEE
6.3.5
CAHSEE
Represent all possible outcomes for
compound events in an organized
way (e.g., tables, grids, tree
diagrams) and express the
theoretical probability of each
outcome.
Understand the difference between
independent and dependent events.
MATHEMATICAL REASONING-Embedded
1.0 Students make decisions about how to
approach problems
6.1.3
Determine when and how to break a
problem into simpler parts.
2.0 Students use strategies, skills, and concepts in
finding solutions
6.2.5
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.
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Copyright January 2002
MATHEMATICS SELECTED STANDARDS CHECKSLIST
SEVENTH GRADE
NUMBER SENSE
ALGEBRA AND FUNCTIONS
1.0 Students know the properties of, and
1.0 Students express quantitative
compute with, rational numbers expressed in
relationships by using algebraic
a variety of forms
terminology, expressions, equations,
Read, write, and compare rational
inequalities, and graphs
7.1.1
CAHSEE
7.1.2
CAHSEE
7.1.3
CAHSEE
7.1.6
CAHSEE
T*
7.1.7
CAHSEE
T*
numbers in scientific notation
(positive and negative powers of 10)
with approximate numbers using
scientific notation.
Add, subtract, multiply, and divide
rational numbers (integers, fractions,
and terminating decimals) and take
positive rational numbers to wholenumber powers.
Convert fractions to decimals and
percents and use these
representations in estimations,
computations, and applications.
Calculate the percentage of
increases and decreases of a
quantity.
Solve problems that involve
discounts, markups, commissions,
and profit and compute simple and
compound interest.
2.0 Students use exponents, powers, and
roots and use exponents in working with
fractions
7.2.1
CAHSEE
7.2.2
CAHSEE
7.2.3
CAHSEE
7.2.4
7.2.5
CAHSEE
Understand negative whole-number
exponents. Multiply and divide
expressions involving exponents
with a common base.
Add and subtract fractions by using
factoring to find common
denominators.
Multiply, divide, and simplify
rational numbers by using exponent
rules
Use the inverse relationship between
raising to a power and extracting the
root of a perfect square integer; for
an integer that is not square,
determine without a calculator the
two integers between which its
square root lies and explain why.
Understand the meaning of the
absolute value of a number; interpret
the absolute value as the distance of
the number from zero on a number
line; and determine the absolute
value of real numbers.
7.1.1
CAHSEE
7.1.2
CAHSEE
7.1.5
CAHSEE
Use variables and appropriate
operations to write an expression, an
equation, an inequality, or a system
of equations or inequalities that
represents a verbal description (e.g.,
three less than a number, half as large
as area A).
Use the correct order of operations to
evaluate algebraic expressions such
as 3(2x + 5)2
Represent quantitative relationships
graphically and interpret the meaning
of a specific part of a graph in the
situation represented by the graph.
2.0 Students interpret and evaluate
expressions involving integer powers and
simple roots
7.2.1
CAHSEE
Interpret positive whole-number
powers as repeated multiplication
and negative whole-number powers
as repeated division or multiplication
by the multiplicative inverse.
Simplify and evaluate expressions
that include exponents.
3.0 Students graph and interpret linear
and some nonlinear functions
7.3.3
CAHSEE
Graph linear functions, noting that
the vertical change (change in yvalue) per unit of horizontal change
(change in x- value) is always the
same and know that the ratio ("rise
over run") is called the slope of a
graph.
4.0 Students solve simple linear
equations and inequalities over the
rational numbers
7.4.1
CAHSEE
Solve two-step linear equations and
inequalities in one variable over the
rational numbers, interpret the
solution or solutions in the context
from which they arose, and verify the
reasonableness of the results.
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Copyright January 2002
MEASUREMENT GEOMETRY
1.0 Students choose appropriate units of
measure and use ratios to convert within and
between measurement systems to solve
problems
7.1.1
CAHSEE
7.1.3
CAHSEE
1 Compare weights, capacities,
geometric measures, times, and
temperatures within and between
measurement systems (e.g., miles per
hour and feet per second, cubic inches
to cubic centimeters).
Use measures expressed as rates (e.g.,
speed, density) and measures
expressed as products (e.g., persondays) to solve problems; check the
units of the solutions; and use
dimensional analysis to check the
reasonableness of the answer.
2.0 Students compute the perimeter, area,
and volume of common geometric objects
and use the results to find measures of less
common objects. They know how perimeter,
area, and volume are affected by changes of
scale
7.2.1
CAHSEE
7.2.2
CAHSEE
Use formulas routinely for finding the
perimeter and area of basic twodimensional figures and the surface
area and volume of basic threedimensional figures, including
rectangles, parallelograms, trapezoids,
squares, triangles, circles, prisms, and
cylinders.
Estimate and compute the area of
more complex or irregular two-and
three-dimensional figures by breaking
the figures down into more basic
geometric objects.
STATISTICS, DATA ANALYSIS, and
PROBABILIITY
1.0 Students collect, organize, and represent
data sets that have one or more variables and
identify relationships among variables within
a data set by hand and through the use of an
electronic spreadsheet software program
7.1.1
CAHSEE
7.1.2
CAHSEE
7.1.3
CAHSEE
Know various forms of display for
data sets, including a stem-and-leaf
plot or box-and-whisker plot; use the
forms to display a single set of data or
to compare two sets of data.
Represent two numerical variables on
a scatterplot and informally describe
how the data points are distributed and
any apparent relationship that exists
between the two variables (e.g.,
between time spent on homework and
grade level).
Understand the meaning of, and be
able to compute, the minimum, the
lower quartile, the median, the upper
quartile, and the maximum of a data
set.
MATHEMATICAL REASONING-Embedded
1.0 Students make decisions about how to
approach problems
7.1.1
CAHSEE
7.1.3
CAHSEE
Analyze problems by identifying
relationships, distinguishing relevant
from irrelevant information,
identifying missing information,
sequencing and prioritizing
information, and observing patterns.
Determine when and how to break a
problem into simpler parts.
2.0 Students use strategies, skills, and
concepts in finding solutions
7.2.1
CAHSEE
7.2.3
CAHSEE
Use estimation to verify the
reasonableness of calculated results.
Estimate unknown quantities
graphically and solve for them by
using logical reasoning and arithmetic
and algebraic techniques.
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Copyright January 2002
MATHEMATICS SELECTED STANDARDS CHECKLIST
EIGHT, NINTH, TENTH GRADE
ALGEBRA 1
Symbolic reasoning and calculations with symbols are central in algebra.
Through the study of algebra, a student develops an understanding of the
symbolic language of mathematics and the sciences. In addition, algebraic skills
and concepts are developed and used in a wide variety of problem-solving
situations.
2.0
CAHSEE
3.0
CAHSEE
4.0
CAHSEE
5.0
CAHSEE
6.0
CAHSEE
7.0
CAHSEE
8.0
CAHSEE
9.0
CAHSEE
10.0
CAHSEE
12.0
CAHSEE
13.0
CAHSEE
15.0
CAHSEE
17.0
CAHSEE
21.0
CAHSEE
23.0
CAHSEE
24.2
CAHSEE
24.2
CAHSEE
Students understand and use such operations as taking the opposite, finding the reciprocal, taking a
root, and raising to a fractional power. They understand and use the rules of exponents.
Students solve equations and inequalities involving absolute values.
Students simplify expressions before solving linear equations and inequalities in one variable, such as
3(2x-5) + 4(x-2) = 12.
Students solve multi-step problems, including word problems, involving linear equations and linear
inequalities in one variable and provide justification for each step.
Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They
are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by
2x + 6y < 4).
Students verify that a point lies on a line, given an equation of the line. Students are able to derive
linear equations by using the point-slope formula.
Students understand the concepts of parallel lines and perpendicular lines and how those slopes are
related. Students are able to find the equation of a line perpendicular to a given line that passes through
a given point.
Students solve a system of two linear equations in two variables algebraically and are able to interpret
the answer graphically. Students are able to solve a system of two linear inequalities in two variables
and to sketch the solution sets.
Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step
problems, including word problems, by using these techniques.
Students simplify fractions with polynomials in the numerator and denominator by factoring both and
reducing them to the lowest terms.
Students add, subtract, multiply, and divide rational expressions and functions. Students solve both
computationally and conceptually challenging problems by using these techniques.
Students apply algebraic techniques to solve rate problems, work problems, and percent mixture
problems.
Students determine the domain of independent variables and the range of dependent variables defined
by a graph, a set of ordered pairs, or a symbolic expression.
Students graph quadratic functions and know that their roots are the x- intercepts.
Students apply quadratic equations to physical problems, such as the motion of an object under the
force of gravity.
Students identify the hypothesis and conclusion in logical deduction.
Students use counterexamples to show that an assertion is false and recognize that a single
counterexample is sufficient to refute an assertion.
25.1
CAHSEE
Students use properties of numbers to construct simple, valid arguments (direct and
indirect) for, or formulate counterexamples to, claimed assertions.
25.2
CAHSEE
Students judge the validity of an argument according to whether the properties of the real number
system and the order of operations have been applied correctly at each step.
Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or
equations or inequalities, students determine whether the statement is true sometimes, always, or
never.
25.3
CAHSEE
ACSA/CARS+ Goals & Objectives Project – (CAHSEE) Standards matching California High school Exit Exam – CDE/CAHSEE Development Team ©
Copyright January 2002
ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
KINDERGARTEN-MATHEMATICS
NUMBER SENSE
objects in different
situations, regardless of its position or arrangement).
and subtractions.
ESSENTIAL STANDARD
K.1.2 Count, recognize, represent, name, and order
a number of objects (up to 30).
GOAL
(Annual Goal) By (date), when given up to thirty
objects, (name) will count, recognize, represent,
name, order the number of objects with ___%
accuracy in ___ of ___ trials as measured by
teacher-made tests/teacher-charted data.
OBJECTIVE/BENCHMARK
1. By (date), when given up to ten objects
(name)will count, recognize, represent, name, order
the number of these objects with ___% accuracy in
___ of ___ trials as measured by teacher-made
tests/teacher-charted data.
2. By (date), when given up to twenty objects,
(name) will count, recognize, represent, name, order
the number of these objects with ___% accuracy in
___ of ___ trials as measured by
teacher-made
tests/teacher-charted data.
K.2.1 Use concrete objects to determine the
answers to addition and subtraction problems (for
two numbers that are each less than 10).
(Annual Goal) By (date), when given concrete
objects, (name) will use these objects to add and
subtract numbers (each number less than 10) with
___% accuracy in ___ consecutive trials as
measured by teacher-charted observation/data.
1. By (date), when given concrete objects, (name)
will use these objects to add sums to 18 with ___%
accuracy in ___ consecutive trials as measured by
teacher-charted observation/data.
2. By (date), when given concrete objects, (name)
will use these objects to subtract (two numbers less
than 10) with ___% accuracy in ___ consecutive
trials as measured by teacher- charted
observation/data.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
KINDERGARTEN-MATHEMATICS
ALGEBRA AND FUNCTIONS
ESSENTIAL STANDARD
GOAL
K.1.1 Identify, sort and classify objects by attribute
and identify objects that do not belong to a particular
group (e.g., all these balls are green, those are red).
(Annual Goal) By (date), when given objects,
(name) will identify, sort and classify objects by
attributes and identify objects that do not belong in a
set with ____% accuracy in ___ of ___ trials as
measured by teacher-charted observation/data.
OBJECTIVE/BENCHMARK
1. By (date), when given objects, (name) will
identify, sort and classify objects with ___%
accuracy in ___ of ___ trials as measured by
teacher-charted observation/data.
2. By (date), when given objects, (name) will
identify, sort and classify objects by attributes and
identify objects that do not belong in the set with
____% accuracy in ___ of ___ trials as measured
by teacher-charted observation/ data.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
KINDERGARTEN-MATHEMATICS
MEASUREMENT AND GEOMETRY
length, weight, and
capacity, and that comparisons may be made by referring to those properties
ects in their environment and describe the geometric features
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given objects to
compare, (name) will compare length, width, and
capacity of objects by making direct comparisons
with ___% accuracy in __ of ___ trials as measured
by teacher-made tests.
1. By (date), when given objects to compare,
(name) will compare length and width by making
direct comparisons with __% accuracy in ___ of ___
trials as measured by teacher made tests.
Measurement
K.1.1 Compare the length, weight, and capacity of
objects by making direct comparisons with
reference objects (e.g., note which object is shorter,
longer, taller, lighter, heavier, or holds more).
2. By (date), when given objects to compare,
(name) will compare length, width, and capacity
of objects by making direct comparisons with __%
accuracy in ___ of ___ trials as measured by
teacher-made tests.
K.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).
(Annual Goal) By (date), when given a choice of
morning/afternoon, today/tomorrow/yesterday and
early/late, (name) will identify time of day with ___%
accuracy in ___ consecutive trials as measured by
teacher-charted observation/data.
1. By (date), when given a choice of morning
/afternoon and today/tomorrow/yesterday, (name)
will identify time of day with ___% accuracy in ___
consecutive trials as measured by teacher-charted
observation/data.
2. By (date), when given a choice of
morning/afternoon, today/tomorrow/yesterday and
early/late, (name) will identify time of day with ___%
accuracy in ___ consecutive trials as measured by
teacher-charted observation/data.
HOME
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MEASUREMENT AND GEOMETRY – KINDERGARTEN CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Measurement - continued
K.1.3 Name the days of the week.
(Annual Goal) By (date), when given a directive,
(name) will state the days of the week with ____%
accuracy in ___ of ___ trials as measured by
teacher-charted observation/data.
1. By date), when given no more than two prompts,
(name) will state the days of the week with ___%
accuracy in ___ of ____ trials as measured by
teacher-charted observation/data.
2. By (date), when given no more than one prompt,
(name) will state the days of the week with ___%
accuracy in ___ of ____ trials as measured by
teacher-charted observation/data.
K.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).
(Annual Goal) By (date), when given clock shown to
the nearest hour (name) will tell the time to the
nearest hour with ___% accuracy in ___ of ___
trials as measured by teacher-charted
observation/data.
1. By (date), when given a clock set to the nearest
hour, (name) will identify 1-4 o’clock with ___%
accuracy in ___ of ___trials as measured by
teacher-charted observation/data.
2. By (date), when given a clock set to the nearest
hour (name) will identify 1-8 o’clock with ___%
accuracy in ___ of ____ trials as measured by
teacher-charted observation/data.
Geometry
K.2.1 Identify and describe common geometric
objects (e.g., circle, triangle, square, rectangle,
cube, sphere, cone).
(Annual Goal) By (date), when given models and/or
pictures of common geometric objects (circle,
triangle, square, rectangle, cube, sphere, cone),
(name) will identify the shape of the object with
____% accuracy in ___ of ___ trials as measured
by teacher-charted observation/data.
1. By (date), when given models and/or pictures of
common geometric objects (circle, triangle, square,
rectangle), (name) will identify the shape of the
object with ___% accuracy in ___ of ____ trials as
measured by teacher-charted observation/data.
2. By (date), when given models and/or pictures of
common geometric objects (cube, sphere, cone),
(name) will identify the shape of the object with
___% accuracy in ___ of ____ trials as measured
by teacher-charted observation/data.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
KINDERGARTEN-MATHEMATICS
STATISTICS, DATA ANALYSIS, AND PROBABILITY
objects and events in their environment.
ESSENTIAL STANDARD
K.1.1 Pose information questions; collect data; and
record the results using objects, pictures, and
picture graphs.
GOAL
(Annual Goal) By (date), when given a question
based on a real life scenario, (name) will collect
data and record that data as a picture or picture
graph with ___% accuracy in ___ of ___ trails as
measured by student work samples.
OBJECTIVE/BENCHMARK
1. By (date), when given a question based on a real
life scenario and data collected through a teacher
guided class/small group activity, (name) will record
that data as a picture or picture graph with __%
accuracy in __ of __ trials as measured by student
work samples.
1. By (date), when given a question based on a real
life scenario, (name) will collect data and record that
data as a picture or picture graph following no more
than one individual teacher prompt, with __%
accuracy in __ of __ trials as measured by student
work samples.
K.1.2 Identify, describe and extend simple patterns
(such as circles or triangles) by referring to their
shapes, sizes, or colors.
(Annual Goal) By (date), when give simple patterns,
(name) will identify, describe and extend patterns
using shape, size or color with ___% accuracy in
___ of ___ trials as measured by student work
samples/teacher records.
1. By (date), when given simple patterns, (name)
will identify and describe the patterns using shape
and size with ___% accuracy in ___ of ___ trials as
measured by student work samples/teacher-charted
observation.
2, By (date), when given simple patterns, (name)
will identify, describe and extend patterns using size
and color with ___% accuracy in ___ of ___ trials as
measured by student work samples/teacher-charted
observation.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
KINDERGARTEN-MATHEMATICS
MATHEMATICAL REASONING
2.0 Students solve problems in reasonable ways and justify their reasoning.
ESSENTIAL STANDARD
K.2.1 Explain the reasoning used with concrete
objects and/or pictorial representations.
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given ___math
problems, (name) will make calculations and explain
results using concrete objects and/or pictorial
representations with ___% accuracy in ___
consecutive trials as measured by student work
samples/teacher-charted observations.
1. By (date), when given ___ math problems
involving two numbers less than 5, (name) will make
the calculation and explain the results using
concrete objects and/or pictorial representations,
with ___% accuracy in ____consecutive trials as
measured by student work samples/teacher-charted
observations.
2. By (date), when given ___ math problems
involving two numbers less than 10, (name) will
make the calculation and explain the results with
concrete objects and/or pictorial representations,
with ___% accuracy in ___ consecutive trials as
measured by student work samples/ teachercharted observations.
K.2.2 Make precise calculations and check the
validity of the results in the context of the problem.
(Annual Goal) By (date), when given ___ math
problems, (name) will find a solution that is
accurate, makes sense and explain his/her
reasoning with ___% accuracy in ___ consecutive
trials as measured by student work samples.
1. By (date), when given ___ math problems,
(name) will find a solution with ___% accuracy in
____ consecutive trials as measured by student
work samples.
2. By (date), when given ___ math problems,
(name) will find a solution that makes sense and
explain his/her reasoning with ____% accuracy in
___ consecutive trials as measured by student work
samples.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FIRST GRADE – MATHEMATICS
NUMBER SENSE
action and use these operations to solve problems.
tens, and hundreds places.
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Place Value
1.1.1 Count , read, and write whole numbers to 100.
(Annual Goal) By (date), when given a teacher
direction, (name) will orally count/read/write whole
numbers to 100 with ____% accuracy on ___
consecutive trials as measured by teacher charted
work samples.
1. By (date), when given a teacher direction, (name)
will orally count/read/write whole numbers to 50 with
____% accuracy on ___ consecutive trials as
measured by teacher-charted work samples.
2. By (date), when given a teacher direction, (name)
will orally count/read/write whole numbers to 75 with
____% accuracy on ___ consecutive trials as
measured by teacher-charted work samples.
1.1.2 Compare and order whole numbers to 100
using the symbols for less than, equal to, or greater
than (<, =, >).
(Annual Goal) By (date), when given two random
numbers between 0 and 100, (name) will write the
correct symbol (less than, equal to, or greater than)
with ___ % accuracy on ___ consecutive trials as
measured by student work samples.
1. By (date), when given two random numbers
between 0 and 50, (name) will write the correct
symbol (less than, equal to, or greater than) with
___ % accuracy on ___ consecutive trials as
measured by student work samples.
2. By (date), when given two random numbers
between 0 and 75, (name) will write the correct
symbol (less than, equal to, or greater than) with
___ % accuracy on ___ consecutive trials as
measured by student work samples.
HOME
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NUMBER SENSE- FIRST GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Place Value - continued
1.1.4 Count and group objects in ones and tens
(e.g., three groups of 10 and 4 equals 34, or 30+4).
(Annual Goal) By (date), when given a random
group of objects, (name) will sort and count objects
by ones/tens with % accuracy in of trials as
measured by teacher-charted observation.
1. By (date), when given a group of objects, not to
exceed, (name) will sort and count objects by ones
with % accuracy in of trials as measured by teachercharted observations.
2. By (date), when given a group a objects, not to
exceed, (name) will sort and count objects by tens
with % accuracy in of trials as measured by teachercharted observations.
1.1.5 Identify and know the value of coins and show
different combinations of coins that equal the same
value.
(Annual Goal) By (date), when given ___ coins,
(name) will identify/state the value/show different
combinations of coins with the same value with
____% accuracy in ___ consecutive trials as
measured by teacher-charted observations.
1. By (date), when given ___ coins, (name) will
identify and state the value of coins with ___%
accuracy in ___ consecutive trials by teachercharted observations.
2. By (date), when given ___ coins, (name) will
identify/state the value/show different combinations
of coins with the same value with ___% accuracy in
___ consecutive trials by teacher-charted
observations.
Addition and Subtraction
1.2.1 Know the addition facts (sums to 20) and the
corresponding subtraction facts and commit them to
memory.
(Annual Goal) By (date), when given ___
addition/subtraction problems to 20, (name) will
write answers to problems with ____% accuracy in
__ of ___ trials as measured by teacher-charted
observations.
1. By (date), when given ___ addition problems to
10, (name) will write answers to problems with
___% accuracy in ___ of ___ trials as measured by
teacher-charted observations.
2. By (date), when given ___ subtraction problems
to 15, (name) will write answers to problems with
___% accuracy in ___ of ___ trials as measured by
teacher-charted observations.
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NUMBER SENSE- FIRST GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when asked to count by 2s,
5s, and 10s, (name) will orally count to 100 with
___% accuracy in ___ consecutive trials as
measured by teacher-charted observations.
1. By (date), when asked to count by 2s, (name) will
orally count to 100 with ___% accuracy in ___
consecutive trials as measured by teacher-charted
observations.
Addition and Subtraction - continued
1.2.4 Count by 2s, 5s and 10s to 100.
2. By (date), when asked to count by 5s, (name) will
orally count to 100 with ___% accuracy in ___
consecutive trials as measured by teacher-charted
observations.
1.2.5 Solve addition and subtraction problems with
one- and two digit numbers (e.g., 5_+_58=_).
(Annual Goal) By (date), when given ___ one and
two-digit addition/subtraction problems without
regrouping, (name) will write sums with ____%
accuracy in ___ consecutive trials as measured by
teacher-made tests.
1. By (date), when given ___ one-digit
addition/subtraction problems without regrouping,
(name) will write sums with ___% accuracy in ____
consecutive trials as measured by teacher-made
tests.
2. By (date), when given ____ 2 digit addition
problems without regrouping, (name) will write sums
with ___% accuracy in ____ consecutive trials as
measured by teacher-made tests.
1.2.7 Find the sum of three one-digit numbers.
(Annual Goal) By (date), when given ___ problems
of three numbers, (name) will write the sums with
___% accuracy in ___ of ___ trials as measured by
student work samples.
1. By (date), when given ___ problems of three
numbers, each no greater than 5, (name) will write
the sums with ___% accuracy in ___ of ___ trials as
measured by student work samples.
2. By (date), when given ___ problems of three
numbers, (name) will write the sums with ___%
accuracy in ___ of ___ trials as measured by
student work samples.
Estimation
1.3.1 Make reasonable estimates when comparing
larger or smaller numbers.
(Annual Goal) By (date), when given ___ oral
problems, (name) will make reasonable estimates
with ___% accuracy in ___ of ___ trials as
measured by teacher-charted observations.
1. By (date), when given __ oral problems
accompanied by picture or model cues, (name) will
make reasonable estimates with ___% accuracy in
___ of ___ trials as measured by teacher-charted
observations.
2. By (date), when given __ oral problems, (name)
will make reasonable estimates with ___% accuracy
in ___ of ___ trials as measured by teacher-charted
observations.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FIRST GRADE - MATHEMATICS
ALGEBRA AND FUNCTIONS
ESSENTIAL STANDARD
1.1.1 Write and solve number sentences from
problem situations that express relationships
involving addition and subtraction.
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given
manipulatives/pictures presenting a problem
situation, (name) will provide a story explaining that
situation and write an addition or subtraction
equation expressing the number relationship
depicted with ___% accuracy in __ consecutive
trials as measured by student work samples.
1. By (date), when given manipulatives/pictures
presenting a problem situation, (name) will provide a
story explaining that situation and write an addition
equation expressing the number relationship
depicted (e.g., 4 bears riding on a bus, two more
bears get on the bus, now there are six bears on the
bus (4+2=6) with ___% accuracy in __ consecutive
trials as measured by student work samples.
3. By date), when given manipulatives/pictures
presenting a problem situation, (name) will provide a
story explaining that situation and write a
subtraction equation expressing the number
relationship depicted ( e.g. five bears on a bus, two
bears get off the bus, three bears are left on the
bus 5-2=3) with____% accuracy in ____consecutive
trials as measured by student work samples.
1.1.2 Understand the meaning of the symbols +, -,
=.
(Annual Goal) By (date), when given pictorial
representations and matching number sentences
with a missing +, - , or = sign, (name) will write the
correct sign with ___ % accuracy in ___ of ___ trials
as measured by student work samples.
1. By (date), when given pictorial representations
and matching number sentences with a missing + or
= sign, (name) will write the correct sign with ___ %
accuracy in___ of ___ trials as measured by student
work samples.
2. By (date), when given pictorial representations
and matching number sentences with a missing - or
= sign, (name) will write the correct sign with ___ %
accuracy in ___ of ___ trials as measured by
student work samples.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FIRST GRADE- MATHEMATICS
MEASUREMENT AND GEOMETRY
ESSENTIAL STANDARD
1.1.2 Tell time to the nearest half hour and relate
time to events (e.g. before/after, shorter/longer).
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given clocks showing
time, (name) will identify the time to the nearest half
hour with ___% accuracy in ___ consecutive trials
as measured by teacher-charted observations.
1. By (date), when given clocks showing time to the
hour, (name) will identify the time with ____%
accuracy in ___ consecutive trials as measured by
teacher-charted observations.
2. By (date), when given clocks showing time to the
half hour, (name) will identify the time with ____%
accuracy in ___ consecutive trials as measured by
teacher-charted observations.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FIRST GRADE- MATHEMATICS
STATISTICS, DATA ANALYSIS, AND PROBABILITY
pare data by category on simple graphs and charts.
ESSENTIAL STANDARD
1.1.1 Sort objects and data by common attributes
and describe the categories.
GOAL
(Annual Goal) By (date), when given eight different
colored/shaped manipulatives, (name) will sort by
color or attribute with ___% accuracy in ___
consecutive trials as measured by teacher-charted
observations.
OBJECTIVE/BENCHMARK
1. By (date), when given four different colored
manipulatives, (name) will sort by color with ____%
accuracy in ___ consecutive trials as measured by
teacher-charted observations.
2. By (date), when given six different colored
/shaped manipulatives, (name) will sort by attribute
with ____% accuracy in ___ consecutive trials as
measured by teacher-charted observations.
1.1.2 Represent and compare data (e.g., largest,
smallest, most often, least often) by using pictures,
bar graphs, tally charts, and picture graphs.
(Annual Goal) By (date), when given ___ pictures of
different objects, (name) will cut out the objects and
sort the objects by at least five common attributes to
create graphs which determine the number of each
object with ___% accuracy in ___ consecutive trials
as measured by student work samples.
1. By (date), when given ___ pictures of different
objects, (name) will cut out objects and sort by at
least three common attributes to create a graph to
determine the number of each object with ___%
accuracy in ___ consecutive trials as measured by
student work samples.
2. By (date), when given ___ pictures of different
objects, (name) will cut out objects and sort by at
least four common attributes to create a graph to
determine the number of each object with ___%
accuracy in ___ consecutive trials as measured by
student work samples.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FIRST GRADE- MATHEMATICS
MATHEMATICAL REASONING
ESSENTIAL STANDARD
1.1.1 Determine the approach, materials, and
strategies to be used.
GOAL
(Annual Goal) By (date), when given ___ oral or
pictorial math problems, (name) will determine
which approach will be taken to solve the problem
with ___% accuracy in ___ consecutive trials as
measured by teacher-charted observations.
OBJECTIVE/BENCHMARK
1. By (date), when given ___ pictorial or
manipulative math problems, (name) will determine
which approach will be taken to solve the problem
with ___% accuracy in ___ consecutive trials as
measured by teacher-charted observations.
2. By (date), when given ___ oral or pictorial math
problems, (name) will determine which approach will
be taken to solve the problem with ___% accuracy
in ___ consecutive trials as measured by teachercharted observations.
1.1.2 Use tools, such as manipulatives or sketches,
to model problems.
(Annual Goal) By (date), when given ___ addition
and subtraction word problems, (name) will be able
to create a number sentence using drawings or
manipulatives to model the problems with ___%
accuracy in __ of __ trials as measured by student
work samples.
1. By (date), when given ___ addition word
problems, (name) will be able to create a number
sentence using drawings or manipulatives to model
the problems with ___% accuracy in ___ of ___
trials as measured by student work samples.
2. By (date), when given ___ subtraction word
problems, (name) will be able to create a number
sentence using drawings or manipulatives to model
the problems with ___% accuracy in ___ of ___
trials as measured by student work samples.
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MATHEMATICAL REASONING – FIRST GRADE CONTINUED
ESSENTIAL STANDARD
1.2.1 Explain the reasoning used and justify the
procedures selected.
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given ___ oral word
problems requiring addition or subtraction, (name)
will explain the reasoning used to determine the
appropriate operation and number sentence with
___% accuracy in ___ of ___ trials as measured by
teacher-charted observations.
1. By (date), when given ___ oral word problems
requiring addition, (name) will explain the reasoning
used to determine the appropriate operation and
number sentence with ___% accuracy in ___of ___
trials as measured by teacher-charted observations.
2. By (date), when given ___ oral word problems
requiring subtraction, (name) will explain the
reasoning used to determine the appropriate
operation and number sentence with ___%
accuracy in ___of ___ trials as measured by
teacher-charted observations.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
SECOND GRADE - MATHEMATICS
NUMBER SENSE
two- and three-digit numbers.
ems by representing, adding and subtracting amounts of money.
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a teacher
direction, (name) will orally count/read/write and
identify place value of each digit for whole numbers
to 1000 with ____% accuracy on ___ consecutive
trials as measured by teacher-charted work
samples.
1. By (date), when given a teacher direction, (name)
will orally count/read/write and identify place value
of each digit for whole numbers to 500 with ____%
accuracy on ____consecutive trials as measured by
teacher-charted work samples.
Place Value
2.1.1 Count, read, and write whole numbers to
1,000 and identify the place value for each digit.
2. By (date), when given a teacher direction, (name)
will orally count/read/write and identify place value
of each digit for whole numbers to 750 with ____%
accuracy on ___ consecutive trials as measured by
teacher-charted work samples.
2.1.2 Use words, models, and expanded forms
(e.g., 45 = 4 tens + 5) to represent numbers (to
1,000).
(Annual Goal) By (date), when given ____ numbers
up to 1000 and visual representations of place value
(1000, 100, 10 & 1, counters/cards), (name) will
construct a model representing the expanded form
of the number with ___% accuracy, in__ of __ trials
as measured by teacher-charted record.
1. By (date), when given ____ numbers up to 500
and visual representations of place value (100, 10 &
1, counters/cards), (name) will construct a model
representing the expanded form of the number with
___% accuracy, in__ of __ trials as measured by
teacher-charted record.
2. By (date), when given ____ numbers up to 750
and visual representations of place value (100, 10 &
1, counters/cards), (name) will construct a model
representing the expanded form of the number with
___% accuracy, in__ of ___ trials as measured by
teacher-charted record.
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NUMBER SENSE- SECOND GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Place Value - continued
2.1.3 Order and compare whole numbers to 1,000
by using the symbols <, =, >.
(Annual Goal) By (date), when given two numbers
less than 1000 (e.g., 975 ÿ 830), (name) will
correctly identify the missing sign (
___% accuracy, in __ of __ trials as measured by
teacher-charted records/work samples.
1. By (date), when given two numbers less than 500
(e.g., 350 ÿ 411), (name) will correctly identify the
missing sign (
) with ___% accuracy, in __ of __
trials as measured by teacher-charted records/work
samples.
2. By (date), when given two numbers less than 750
(e.g., 599 ÿ 533), (name) will correctly identify the
) with ___% accuracy, in __ of
__ trials as measured by teacher-charted
records/work samples.
Addition and Subtraction
2.2.2 Find the sum or difference of two whole
numbers up to three digits long.
(Annual Goal) By (date), when given ___ three-digit
addition and subtraction number sentences with
regrouping, (name) will calculate the correct
answers with ___% accuracy in __ of __ trials as
measured by teacher-made tests.
1. By (date), when given ___ three-digit addition
number sentences with regrouping, (name) will
calculate the correct answers with ___% accuracy,
in __ of __ trials as measured by teacher-made
tests.
2. By (date), when given ___ 3-digit subtraction
facts with regrouping, (name) will calculate the
correct answers with ___% accuracy, in __ of __
trials as measured by teacher-made tests.
Multiplication and Division
2.3.3 Know the multiplication tables of 2s, 5s, and
10s (to “times 10”) and commit them to memory.
(Annual Goal) By (date), when given ____
multiplication facts of 2's, 5's, & 10's, (name) will
calculate the correct products with ___% accuracy,
in __ of __ trials as measured by student work
samples.
1. By (date), when given ___ multiplication facts of
2s, (name) will calculate the correct answers with
___% accuracy, in __ of __ trials as measured by
student work samples.
2. By (date), when given ___ multiplication facts of
2s & 5's, (name) will calculate the correct answers
with ___% accuracy, in __ of __ trials as measured
by student work samples.
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NUMBER SENSE- SECOND GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Fractions and Decimals
2.4.2 Recognize fractions of a whole and parts of a
group (e.g., one-fourth of a pie, two-thirds of 15
balls).
(Annual Goal) By (date), when shown visuals of
fractions of a whole/parts of a group, (name) will
identify the correct fraction notation with ___%
accuracy, in __ of __ trails as measured by student
work samples.
1. By (date), when shown visuals of fractions of a
whole (one-fourth of a pie), (name) will identify the
correct fraction notation with ___% accuracy, in __
of __ trials as measured by student work samples.
2. By (date), when shown visuals of parts of a group
(one-third of 15 balls), (name) will identify the
fraction notation with ___% accuracy, in __ of __
trails as measured by student work samples.
2.4.3 Know that when all fractional parts are
included, such as four-fourths, the result is equal to
the whole and to one.
Computation--Money
2.5.1 Solve problems using combinations of coins
and bills.
(Annual Goal) By (date), when shown ____ visual
fraction models, (name) will identify each model
including all fractional parts (ex 4/4, 2/2) equaling
the whole with ____% accuracy, in ___ of ___ trials
as measured by teacher records.
(Annual Goal) By (date), when given addition and
subtraction problems involving both coins and bills
(not to exceed $9.99), (name) will calculate the
answers with ___% accuracy, in __ of __ trials as
measured by student work samples/teacher-charted
records.
1. By (date), when shown ____ visual fraction
models, (name) will identify each model including all
fractional parts (ex 4/4, 2/2) equaling the whole with
____% accuracy, in ___ of ___ trials as measured
by teacher records.
2. By (date), when shown ____ visual fraction
models, (name) will identify ____ models including
all fractional parts (ex 4/4, 2/2) equaling the whole
with ____% accuracy, in ___ of ___ trials as
measured by teacher records.
1. By (date), when given addition problems involving
coins and bills (not to exceed $9.99), (name) will
calculate the answers with ____% accuracy in __ of
__ trials as measured by student work
samples/teacher-charted records.
2. By (date), when given subtraction problems
involving coins and bills (not to exceed $9.99),
(name) will calculate the answers with ____%
accuracy in __ of __ trials as measured by student
work samples/teacher-charted records.
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NUMBER SENSE- SECOND GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when verbally given a
money amount including dollars and cents to $9.99,
(name) will write that amount using correct dollar
and decimal notation with ___% accuracy, in __ of
__ trials as measured by teacher-made tests.
1. By (date), when verbally given a dollar amount to
$9.00, (name) will write the amount using correct
dollar notation with ___% accuracy, in __ of __ trials
as measured by teacher-made tests.
Computation – Money – continued
2.5.2 Know and use the decimal notation and the
dollar and cent symbols for money.
2. By (date), when verbally given a money amount
including dollars and cents to $9.99, (name) will
write the amount using correct dollar and decimal
notation with ___% accuracy in __ of __ trials as
measured by teacher-made tests.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
SECOND GRADE - MATHEMATICS
ALGEBRA AND FUNCTIONS
action
ESSENTIAL STANDARD
2.1.3 Solve addition and subtraction problems by
using data from simple charts, picture graphs, and
number sentences.
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a simple chart
or graph created in a teacher-led activity, (name)
will use the data to solve addition and subtraction
number sentences with ___% accuracy in ___ of
____ trials as measured by student work samples.
1. By (date), when given a simple chart or graph
created in a teacher-led activity, (name) will use the
data to solve addition number sentences with ___%
accuracy in ___ of ____ trials as measured by
student work samples.
2. By (date), when given a simple chart or graph
created in a teacher-led activity, (name) will use the
data to solve subtraction number sentences with
___% accuracy in ___ of ____ trials as measured
by student work samples.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
SECOND GRADE - MATHEMATICS
MEASUREMENT AND GEOMETRY
that unit, and comparing it to the item to be measured.
nd of common objects in space.
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given ___objects and
a unit of measurement, (name) will measure the
objects and report the total number of measurement
units, with ___% accuracy, in __ consecutive trials
as measured by teacher-made tests.
1. By (date), when given ___ objects and a unit of
measurement, (name) will measure the objects and
report the total number of measurement units, with
___% accuracy, in__ consecutive trials as
measured by teacher-made tests.
Measurement
2.1.1 Measure the lengths of objects by iterating
(repeating) a nonstandard or standard unit.
2. By (date), when given __ objects and a unit of
measurement, (name) will measure the objects and
report the total number of measurement units, with
___% accuracy, in __ consecutive trials as
measured by teacher-made tests.
2.1.4 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.
(Annual Goal) By (date), when shown a face
clock/calendar, (name) will tell time to the nearest
quarter hour and state the relationships of time with
___% accuracy, in __ of __trials as measured by
teacher-charted observations.
1. By (date), when shown a face clock, (name) will
tell time to the nearest quarter hour with ___%
accuracy, in __ of __ trials as measured by teachercharted observations.
2. By (date), when shown a face clock/calendar,
(name) will state the relationships of time ( e.g.,
minutes in an hour, days in a month, weeks in a
year) with ___% accuracy, in __ of __ trials as
measured by teacher-charted observations.
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MEASUREMENT AND GEOMETRY – SECOND GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
2.2.1 Describe and classify plane and solid
Geometric shapes (e.g., circle, triangle, square,
rectangle, sphere, pyramid, cube, rectangular prism)
according to the number and shape of faces, edges
and vertices
(Annual Goal) By (date), when given
____models/pictures of plane and solid geometric
shapes, (name) will describe and classify them
according to the number and shape of faces, edges,
and vertices with ___% accuracy, in __ of __ trials
as measured by teacher-made tests.
1. By (date), when given ___models/pictures of
plane and solid geometric shapes, (name) will
describe and classify them according to the number
and shape of face and edges with ___% accuracy,
in __ of __ trials as measured by teacher-made
tests.
Geometry
2. By (date), when given ____models/pictures of
plane and solid geometric shapes, (name) will
describe and classify them according to the number
and shape of faces, edges, and vertices with ___%
accuracy, in __ of __ trials as measured by teachermade tests.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
SECOND GRADE - MATHEMATICS
MATHEMATICAL REASONING
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Make Decisions about a Problem
2.1.1 Determine the approach, materials, and
strategies to be used.
(Annual Goal) By (date), when given a word
problem orally, (name) will determine the approach
and operation needed (+, -) to successfully
complete the problem with ___% accuracy in __ of
__ trials as measured by teacher-charted
observation.
1. By (date), when given a word problem orally,
(name) will determine the approach and operation
needed to successfully complete the problem with
___% accuracy in __ of __ trials as measured by
teacher-charted observations.
2. By (date), when given a word problem orally,
(name) will determine the approach and operation
needed to successfully complete the problem with
___% accuracy in __ of __ trials as measured by
teacher-charted observations.
Solve Problems/Justify Reasoning
2.2.1 Defend the reasoning used and justify the
procedures selected
(Annual Goal) By (date), when given a word
problem orally, (name) will determine the approach
and operation needed (+, -) to successfully
complete the problem with ___% accuracy, in __ of
__ trials as measured by teacher-charted
observation.
1. By (date), when given a word problem orally,
(name) will determine the approach and operation
needed to successfully complete the problem with
___% accuracy in __ of __ trials as measured by
teacher-charted observations.
2. By (date), when given a word problem orally,
(name) will determine the approach and operation
needed to successfully complete the problem with
___% accuracy in __ of __ trials as measured by
teacher-charted observations.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
THIRD GRADE - MATHEMATICS
NUMBER SENSE
division
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Place Value
3.1.1 Count, read, and write whole numbers to
10,000.
(Annual Goal) By (date), when given a directive to
count, read and write numbers to 10,000, (name)
will count, read and write numbers to 10,000 with
___% accuracy in ___ consecutive trials as
measured by student work samples.
1. By (date), when given a directive, (name) will
count and read numbers to 10,000 with ___%
accuracy in ___ consecutive trials as measured by
student work samples.
2. By (date), when given a directive, (name) will
write numbers to 10,000 with ___%accuracy in ____
consecutive trials as measured by student work
samples.
3.1.3 Identify the place value for each digit in
numbers to 10,000.
(Annual Goal) By (date), when given numbers to
10,000, (name) will correctly state place values of
each digit to 10,000 with ___% accuracy in __ of
___ trials as measured by student work samples.
1. By (date), when given numbers to 10,000, (name)
will correctly state place values of numbers to 100
with ___% accuracy in ___ of ___ trials as
measured by student work samples.
2. By (date), when given numbers to 10,000, (name)
will correctly state place values of numbers to 1,000
with ___% accuracy in ___ of ___ trials as
measured by student work samples.
3.1.4 Round off numbers to 10,000 to the nearest
ten, hundred, and thousand.
(Annual Goal) By (date), when given numbers to
1,000, (name) will round to the nearest 10, 100 or
1,000 with ___% accuracy in ___ consecutive trials
as measured by student work samples.
1. By (date), when given numbers to 1,000, (name)
will round to the nearest 10 with ___% accuracy in
___ consecutive trials as measured by student work
samples.
2. By (date), when given numbers to 1,000, (name)
will round to the nearest 100 with ___% accuracy in
___ consecutive trials as measured by student work
samples.
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NUMBER SENSE- THIRD GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given numbers to
10,000, (name) will use expanded notation to
represent the number with ___% accuracy in ___ of
___ trials as measured by student work samples.
1. By (date), when given numbers to 100, (name)
will use expanded notation to represent the number
with ___% accuracy in ___ of ___ trials as
measured by student work samples.
Place Value - continued
3.1.5 Use expanded notation to represent Numbers
(e.g., 3,206 = 3,000 + 200 +6).
2. By (date), when given numbers to 1,000, (name)
will use expanded notation to represent the number
with ___% accuracy in ___ of ___ trials as
measured by student work samples.
Computation – Whole Numbers
3.2.2 Memorize to automaticity the multiplication
table for numbers between 1 and 10.
(Annual Goal) By (date), when given a blank
multiplication chart, (name) will complete
multiplication for numbers between 1 and 10 with
___% accuracy in ___ of ___ trials as measured by
student work samples.
1. By (date), when given a blank multiplication chart,
(name) will complete the multiplication facts for
numbers between 1 and 5 with ___% accuracy in
___ of ____ trials as measured by student work
samples.
2. By (date), when given a blank multiplication chart,
(name) will complete the multiplication facts for
numbers between 1 and 8 with ___% accuracy in
___ of ____ trials as measured by student work
samples.
3.2.4 Solve simple problems involving multiplication
of multi-digit numbers by one digit numbers (3,671 x
3 = __ ).
(Annual Goal) By (date), when given simple
multiplication problems of single digit by multiple
digit numbers, (name) will compute correct answers
with ___% accuracy in ___ consecutive trials as
measured by teacher-made tests.
1. By (date), when given simple multiplication
problems of single digit by two digit numbers,
(name) will compute correct answers with ___%
accuracy in ___ consecutive trials as measured by
teacher-made tests.
2. By (date), when given simple multiplication
problems of single digit by multiple digit numbers,
(name) will compute correct answers with ____%
accuracy in ___ consecutive trials as measured by
teacher-made tests.
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NUMBER SENSE- THIRD GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Computation-Whole Numbers - continued
3.2.5 Solve division problems in which a multi-digit
number is evenly divided by a one digit number
(135/5 = __ ).
(Annual Goal) By (date), when given even division
problems with multi-digit numbers divided by single
digit divisors, (name) will compute correct answers
with ___% accuracy in ___ of ___ trials as
measured by teacher-made tests.
1. By (date), when given even division problems
with two-digit numbers divided by single digit
divisors, (name) will compute the correct answers
with ___% accuracy in ___ of ___ trials as
measured by teacher-made tests.
2. By (date), when given even division problems
with three-digit numbers divided by single digit
divisors, (name) will compute the correct answers
with ___% accuracy in ___ of ___ trials as
measured by teacher-made tests.
3.2.8 Solve problems that require two or more of the
skills mentioned above.
(Annual Goal) By (date), when given word problems
requiring two or more processes (addition,
subtraction, multiplication, division) to solve, (name)
will compute the correct answer with ____%
accuracy in ___ consecutive trials as measured by
student work samples.
1. By (date), when given two step word problems
requiring addition and subtraction, (name) will
compute the correct answer with ___% accuracy in
___ consecutive trials as measured by student work
samples.
2. By (date), when given two step word problems
requiring addition, subtraction, and/or multiplication,
(name) will compute the correct answer with ___%
accuracy in ___ consecutive trials as measured by
student work samples.
Fractions and Decimals
3.3.1 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).
(Annual Goal) By (date), when given drawings or
concrete materials representing fractions, (name)
will correctly show fractional equivalents and add
and subtract fractions in context with ___%
accuracy in ___ of ___ trials as measured by
student work samples.
1. By (date), when given drawings or concrete
materials representing fractions, (name) will
correctly show fractional equivalents with __%
accuracy in ___ of ___ trials as measured by
student work samples.
2. By (date), when given drawings or concrete
materials representing fractions, (name) will add
and subtract fractions in context with ___%
accuracy in ___ of ___ trials as measured by
student work samples.
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NUMBER SENSE – THIRD GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Fractions and Decimals – continued
3.3.2 Add and subtract simple fractions (e.g.,
determine that 1/8 + 3/8 is the same as 1/2).
(Annual Goal) By (date), when given ___ simple
fractions, (name) will correctly add or subtract and
show answer in lowest terms with ___% accuracy in
___ of ___ trials as measured by student work
samples.
1. By (date), when given ___ simple fractions,
(name) will correctly add and show sum in lowest
terms with __% accuracy in ___ of ___ trials as
measured by student work samples.
2. By (date), when given ___ simple fractions to
subtract, (name) will correctly subtract and show
difference in lowest terms with __% accuracy in ___
of ___ trials as measured by student work samples.
3.3.3 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.
(Annual Goal) By (date), when given money
amounts in decimal notation to
add/subtract/multiply/divide, (name) will correctly
perform operations with ___% accuracy in __ of __
trials as measured by student work samples.
1. By (date), when given money amounts to
add/subtract, (name) will correctly perform
operations with ___% accuracy in ___of___ trials as
measured by student work samples.
2. By (date), when given money amounts to
multiply/divide, (name) will correctly perform
operations with ___% accuracy in ___of___ trials as
measured by student work samples.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
THIRD GRADE - MATHEMATICS
MEASUREMENT AND GEOMETRY
ESSENTIAL STANDARD
3.1.2 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.
GOAL
(Annual Goal) By (date), when given ___ solid
figures and square or cube counters, (name) will
use the counters to estimate or determine the
area/volume with ___% accuracy in ___
consecutive trials as measured by student work
samples/teacher-charted observations.
OBJECTIVE/BENCHMARK
1. By (date), when given ___ solid figures and
square counters, (name) will use the counters to
estimate or determine the area with ___% accuracy
in ___ consecutive trials as measured by student
work samples/teacher-charted observations.
2. By (date), when given ___ solid figures and cube
counters, (name) will use the counters to estimate
or determine the volume with ___% accuracy in ___
consecutive trials as measured by student work
samples/teacher-charted observations.
3.1.3 Find the perimeter of a polygon with integer
sides.
(Annual Goal) By (date), when given ___ polygons
with sides measured in whole numbers, (name) will
correctly compute the perimeter with ___%
accuracy in ___ consecutive trials as measured by
student work samples.
1. By (date), when given ___ polygons of no more
than four sides measured in whole numbers, (name)
will correctly compute the perimeter with ___%
accuracy in ___ consecutive trials as measured by
student work samples.
2. By (date), when given ___ polygons of four or
more sides measured in whole numbers, (name) will
correctly compute the perimeter with ___%
accuracy in ___ consecutive trials as measured by
student work samples.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
THIRD GRADE - MATHEMATICS
MATHEMATICAL REASONING
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
3.2.3 Use a variety of methods, such as words,
numbers, symbols, charts, graphs, tables, diagrams,
and models, to explain mathematical reasoning.
(Annual Goal) By (date), when given ___ problems,
(name) will use a variety of methods to explain math
reasoning with ___% accuracy in ___ of ___ trials
as measured by student work samples/teachercharted observations.
1. By (date), when given ___ problems, (name) will
use methods including words, numbers, symbols, or
charts to explain math reasoning with ___%
accuracy in ___ of ___ trials as measured by
student work samples/ teacher-charted
observations.
2. By (date), when given ___ problems, (name) will
use methods including graphs, tables, diagrams, or
models to explain math reasoning with ___%
accuracy in ___ of ___ trials as measured by
student work sample/ teacher-charted observations.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FOURTH GRADE - MATHEMATICS
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.
2.0 Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals.
3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships
among the operations.
4.0 Students know how to factor small whole numbers.
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a list of
____mixed whole numbers and decimals, (name)
will order/compare these numbers to two decimal
places with ___% accuracy in ___ consecutive trials
as measured by student work samples.
1. By (date), when given a list of ____whole
numbers and one decimal number, (name) will
order/compare these numbers with __% accuracy in
___ consecutive trials as measured by student work
samples.
Place Value
4.1.2 Order and compare whole numbers and
decimals to two decimal places.
2. By (date), when given a list of ___whole numbers
and decimal numbers, (name) will order/compare
these numbers to one decimal place with __%
accuracy in ___ consecutive trials as measured by
student work samples.
4.1.3 Round whole numbers through the millions to
the nearest ten, hundred, thousand, ten thousand,
or hundred-thousand
(Annual Goal) By (date), when given a list of __
numbers through the millions, (name) will round
each number to the nearest ten, hundred, thousand,
ten- thousand, or hundred thousand in __
consecutive trials with ___% accuracy as measured
by teacher-made tests.
1. By (date), when given a list of ___numbers
through the millions, (name) will round each number
to the nearest ten, hundred, or thousand in
___consecutive trials with ____ % accuracy as
measured by teacher-made tests.
2. By (date), when given a list of ___numbers
through the millions, (name) will round each number
to the nearest ten thousand or hundred thousand in
___ consecutive trials with ___ % accuracy as
measured by teacher-made tests.
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NUMBER SENSE- FOURTH GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Place Value - continued
4.1.5 Explain different interpretations of fractions, for
example, parts of a whole, parts of a set, and
division of whole numbers by whole numbers;
explain equivalents of fractions (see Standard 4.0)
(Annual Goal) By (date), when given a fraction,
(name) will explain the fraction as a part of a whole,
parts of a set, or division of whole number by whole
number and explain equivalents of the fraction with
___ % accuracy in __ out of __ trials as measured
by teacher-made tests/student work samples.
1. By (date), when given a fraction, (name) will
explain the fraction as a part of a whole, parts of a
set, or division of whole number by whole number
with ____% accuracy in ___ our of ___ trials as
measured by teacher-made tests/student work
samples.
2. By (date), when given a fraction, (name) will
explain equivalents of the fraction with ___%
accuracy as measured by teacher-made
tests/student work samples.
4.1.8 Use concepts of negative numbers (e.g., on a
number line, in counting, in temperature, in “owing”)
(Annual Goal) By (date), when given ___ negative
numbers, (name) will show what each negative
number would mean on a number line, in counting,
in temperature and in “owing “ with ____% accuracy
in __ of ___ trials as measured by teacher-made
tests/teacher-charted observations.
1. By (date), when given ___ negative numbers,
(name) will show what each negative number would
mean on a number line or in counting with ___ %
accuracy in ___ of ___ trials as measured by
teacher-made tests/teacher-charted observations.
2. By (date), when given ___ negative numbers,
(name) will show what each negative number would
mean in temperature and in “owing” with ___%
accuracy in ___ of ___ trials as measured by
teacher made tests/teacher-charted observations.
Computation --Decimals
4.2.1 Estimate and compute the sum or difference
of whole numbers and positive decimals to two
places.
(Annual Goal) By (date), when given a set of___
problems requiring addition/subtraction of whole
numbers and positive decimals to two places,
(name) will compute the answers with ___ %
accuracy in ___ out of ___ trials as measured by
teacher-made tests/student work samples.
1. By (date), when given a set of ___ problems
requiring addition of whole numbers and positive
decimals to two places, (name) will compute the
sums with ___% accuracy in ___ of ___ trials as
measured by teacher-made tests/student work
samples.
2. By (date), when given a set of ___ problems
requiring subtraction of whole numbers and positive
decimals to two places, (name ) will compute the
differences with ___% accuracy in ___ of ____ trials
as measured by teacher-made tests/student work
samples.
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NUMBER SENSE- FOURTH GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a set of ___
problems requiring the addition and subtraction of
multi-digit numbers greater than 10.000, (name) will
compute the answers with ___% accuracy in __ of
__ trials as measured by teacher-made
tests/student work samples.
1. By (date), when given a set of ____ problems
requiring the addition of multi-digit numbers greater
than 10,000, (name) will compute the sums with
___% accuracy in ___ of ____ trials as measured
by teacher-made tests/student work samples.
Computation –Whole Numbers
4.3.1 Demonstrate an understanding of, and the
ability to use, standard algorithms for the addition
and subtraction of multi-digit numbers
2. By (date), when given a set of ___ problems
requiring the subtraction of multi-digit numbers
greater than 10,000, (name) will compute the
differences with ___% accuracy in ___ of ___ trials
as measured by teacher-made tests/student work
samples.
Factoring
4.4.1 Understand that many whole numbers break
down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x
2 x 3).
(Annual Goal) By (date), when given ___ whole
numbers, (name) will list all factors of each whole
number with ____ % accuracy in___ of __ trials as
measured by student work samples/teacher-made
tests.
1. By (date), when given ___ whole numbers,
(name) will list a set of factors for each whole
number with ___ % accuracy in ___ of ___ trials as
measured by student work samples/teacher-made
tests.
2. By (date), when given ___ whole numbers,
(name) will list all factors for each whole number
with ___ % accuracy in ___ of ____ trials as
measured by student work samples/teacher-made
tests.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FOURTH GRADE - MATHEMATICS
ALGEBRA AND FUNCTIONS
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Number Sentences and Expressions
4.1.1 Use letters, boxes, or other symbols to stand
for any number in simple expressions or equations
(e.g., demonstrate an understanding and the use of
the concept of a variable).
(Annual Goal) By (date), when given __ math
problems requiring the use of letters, boxes, or other
symbols to represent numbers, (name) will
demonstrate knowledge of symbols representing
numbers in math problems with ___% accuracy in
__ consecutive trials as measured by student work
samples.
1. By (date), when given __ math problems
containing letters, boxes or other symbols to
represent numbers, (name) will solve for the value
of the symbol(s) with ___% accuracy in ___
consecutive trials as measured by student work
samples.
2. By (date), when given a word problem or teacher
directive, (name) will write and solve a three
element equation containing at least one letter, box,
or other symbol representing a number with ___%
accuracy in ___consecutive trials as measured by
student work samples.
4.1.2 Interpret and evaluate mathematical
expressions that now use parentheses.
(Annual Goal) By (date), when given mathematical
expressions/problems requiring the use of
parentheses, (name) will interpret and evaluate
them with ___% accuracy in ___ consecutive trials
as measured by student work samples.
1. By (date), when given a three-element
multiplication expression including parentheses,
(name) will rewrite the expression in two different
ways [associative property: 2 x (5 X 1) = (2 x 5) x 1)]
with ___% accuracy in ___ consecutive trials as
measured by student work samples.
2. By (date), when given a problem requiring the
use of parentheses, (name) will write the equation
with ___% accuracy in ___ consecutive trials as
measured by student work samples.
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ALGEBRA AND FUNCTIONS – FOURTH GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given ___ problems
with parentheses (to indicate which operation to
perform first) containing more than two terms and
different operations, (name) will perform operations
in correct order with ____% accuracy in ___
consecutive trials as measured by student work
samples.
1. By (date), when given ___ problems with
parentheses (to indicate which operation to
complete first) containing more than two terms and
one operation, (name) will perform each operation in
the correct order with ___% accuracy in __
consecutive trials as measured by student work
samples.
Number Sentences and Expressions-cont.
4.1.3 Use parentheses to indicate which operation
to perform first when writing expressions containing
more than two terms and different operations.
2. By (date), when given ___ problems with
parentheses (to indicate which operation to use first)
containing more than two terms and different
operations, (name) will perform the operations in the
correct order with ____% accuracy in ___
consecutive trials as measured by student work
samples.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FOURTH GRADE - MATHEMATICS
MATHEMATICAL REASONING
ESSENTIAL STANDARD
4.1.2 Determine when and how to break a problem
into simpler parts.
GOAL
(Annual Goal) By (date), when given a mixture of
___ math problems requiring both single and multistep solutions, (name) will determine how and when
to break a problem into simpler parts with ____%
accuracy in__ of __ trials as measured by student
work samples.
OBJECTIVE/BENCHMARK
1. By (date), when given a mixture of ___ math
problems requiring both single and multi-step
solutions, (name) will sort the problems based on
this criteria with ___% accuracy in ___ of ___ trials
as measured by student work samples.
2. By (date), when given ___ math problems
requiring multi-step solutions, (name) will determine
how to break a problem into simpler parts with
____% accuracy in ___ of ___ trials as measured
by student work samples.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FIFTH GRADE - MATHEMATICS
NUMBER SENSE
nts 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.
s and solve problems involving addition, subtraction, and simple multiplication and division of fractions and
decimals.
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Relative Magnitude of Numbers
5.1.1 Estimate, round, and manipulate very large
(e.g., millions) and very small (thousandths)
numbers.
(Annual Goal) By (date), when given a set of very
large (e.g., millions) or very small (e.g.,
thousandths) numbers, (name) will
estimate/round/manipulate those numbers with ___
% accuracy in ___ of ___ trials as measured by
student work samples/criterion assessment.
1. By (date), when given a set of very large (e.g.,
millions) numbers, (name) will
estimate/round/manipulate those numbers with
___% accuracy in ___ of___ trials as measured by
student work samples/criterion assessment.
2. By (date), when given a set of very small (e.g.,
thousandths) numbers, (name) will
estimate/round/manipulate those numbers with
___% accuracy in ___ of ___ trials as measured by
student work samples/criterion assessment.
5.1.2 Interpret percents as a part of a hundred; find
decimal and percent equivalents for common
fractions and explain why they represent the same
value; compute a given percent of a whole number.
(Annual Goal) By (date), when given ___ problems
involving percents and decimals, (name) will
interpret percents as a part of a hundred, compute a
given percent of a whole number, and find decimal
and percent equivalents for common
fractions/explain why they represent the same value
with ___ % accuracy in ___ of ___ trials as
measured by student work samples/criterion
assessment.
1. By (date), when given ___ problems involving
percents and decimals, (name) Will interpret
percents as a part of a hundred, and compute a
given percent of a whole number with ___ %
accuracy in ___ of ___ trials as measured by
student work samples/criterion assessment.
2. By (date), when given ___ problems involving
percents and decimals, (name) will find decimal and
percent equivalents for common fractions/explain
why they represent the same value with ___ %
accuracy in ___ of ___ trials as measured by
student work samples/criterion assessment.
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NUMBER SENSE- FIFTH GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a set of ___
numbers through 50, (name) will list the prime
factors of each number and write each number as
the product of their prime factors using exponents to
show multiples of a factor with ___ % accuracy in
___ of ___ trials as measured by student work
samples/criterion assessment.
1. By (date), when given a set of ___ numbers
through 50, (name) will list the prime factors of each
number with ___ % accuracy in ___ of ___ trials as
measured by student work samples/criterion
assessment.
(Annual Goal) By (date), when given ___ problems
requiring division with positive long division with
multi-digit divisors, (name) will find the quotients
with ___ % accuracy in ___ of ___ trials as
measured by student work samples/criterion
assessment.
1. By (date), when given ___ problems requiring
division with positive decimals, (name) will find the
quotients with ___ % accuracy in ___ of ___ trials
as measured by student work samples/criterion
assessment.
Relative Magnitude of Numbers – continued
5.1.4 Determine the prime factors of all numbers
through 50 and write the numbers as the product of
their prime factors by using exponents to show
multiples of a factor (e.g., 24 = 2 x 2 x 2 x 3 = 23 x
3).
Computation
5.2.2 Demonstrate proficiency with division,
including division with positive decimals and long
division with multi-digit divisors.
2. By (date), when given a set of ___ numbers
through 50, (name) will list the prime factors of each
number and write each number as the product of
their prime factors using exponents to show
multiples of a factor with ___ % accuracy in ___ of
___ trials as measured by student work
samples/criterion assessment.
2. By (date), when given ___ problems requiring
division with multi-digit divisors, (name) will find the
quotients with ___ % accuracy in ___ of___ trials as
measured by student work samples/criterion
assessment.
5.2.3 Solve simple problems, including ones arising
in concrete situations, involving the addition and
subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express
answers in the simplest form.
(Annual Goal) By (date), when given ___ problems,
including ___ real life scenarios, which require the
addition and subtraction of fractions and mixed
numbers, (name) will solve for the sum or
difference, expressed in simplest terms, with ___ %
accuracy in ___ of ___ trials as measured by
student work samples/criterion assessment.
1. By (date), when given ___ problems which
require the addition and subtraction of fractions and
mixed numbers, (name) will solve for the sum or
difference, expressed in simplest terms, with ___ %
accuracy in ___ of ___ trials as measured by
student work samples/criterion assessment.
2. By (date), when given ___ problems, including
real life scenarios, which require the addition and
subtraction of fractions and mixed numbers, (name)
will solve for the sum or difference, expressed in
simplest terms, with ___% accuracy in ___ of __
trials as measured by student work
samples/criterion assessment.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FIFTH GRADE - MATHEMATICS
ALGEBRA AND FUNCTIONS
and plot and interpret
the results.
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
Simple Expressions
5.1.1 Use information taken from a graph or
equation to answer questions about a problem
situation.
(Annual Goal) By (date), when given a graph or
equation, (name) will use information taken form
those sources to answer questions about a problem
situation with % ___ accuracy in ___of __ trails as
measured by student work samples/teacher-charted
records.
1. By (date), when given a graph, (name) will use
information from the graph to answer questions
about a problem situation with ___ % accuracy in
___ of ___ trials as measured by student work
samples/teacher-charted records.
2. By (date), when given an equation, (name) will
use information from the equation to answer
questions about a problem situation with ___%
accuracy in ___of ___trials as measured by student
work samples/teacher-charted records.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
FIFTH GRADE - MATHEMATICS
MATHEMATICAL REASONING
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a mixture of
___ math problems requiring both single and multistep solutions, (name) will determine how and when
to break a problem into simpler parts with ____%
accuracy in ____ of ____ trials as measured by
student work samples.
1. By (date), when given a mixture of ___ math
problems requiring both single and multi-step
solutions, (name) will sort the problems based on
this criteria with ____% accuracy in ___ of ___ trials
as measured by student work samples.
Decisions About Approaching Problems
5.1.2 Determine when and how to break a problem
into simpler parts.
2. By (date), when given ____ math problems
requiring multi-step solutions, (name) will determine
how to break a problem into simpler parts with___%
accuracy in ____ of ____ trials as measured by
student work samples.
Use Strategies, Skills, and Concepts in
Finding Solutions
5.2.3 Use a variety of methods, such as words,
numbers, symbols, charts, graphs, tables, diagrams,
and models to explain mathematical reasoning.
(Annual Goal) By (date), when given a grade five
level problem, (name) will use a variety of methods
(words, numbers, symbols, models, charts, graphs,
tables, and/or diagrams to explain the mathematical
reasoning necessary to find the solution with ___%
accuracy in ____ of ____ trials as measured by
teacher-made tests/student work samples.
1. By (date), when given a grade five level problem,
(name) will use words, numbers, symbols, or graphs
to explain the mathematical reasoning necessary to
find the solution with ___% accuracy in ___ of ____
trials as measured by teacher-made tests/student
work samples.
2. By (date), when given a grade five level problem,
(name) will use charts, graphs, tables, or diagrams
to explain the mathematical reasoning necessary to
find the solution with ___% accuracy in ___ of ___
trials as measured by teacher-made tests/student
work samples.
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MATHEMATICAL REASONING – FIFTH GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a grade five
level problem and its solution, (name) will explain
the method of deriving the solution and demonstrate
an understanding of this derivation by solving similar
problems with ____% accuracy in ____ of ____
trials as measured by teacher-made tests/student
work samples.
1. By (date), when given a grade five level problem,
a teacher-led explanation of its solution, and a
similar new problem, (name) will solve the new
problem with ___% accuracy in ____ of ____ trials
as measured by teacher-made tests/student work
sample.
Generalize to Other Situations
5.3.2 Note the method of deriving the solution and
demonstrate a conceptual understanding of the
derivation by solving similar problems.
2. By (date), when given a grade five level problem
and its solution, (name) will explain the method of
deriving the solution and demonstrate an
understanding of this derivation by solving similar
problems with ____% accuracy in ____ of ____
trials as measured by teacher-made tests/student
work samples.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
SIXTH GRADE - MATHEMATICS
NUMBER SENSE
d numbers. Students solve problems involving fractions,
ratios, proportions, and percentages.
ESSENTIAL STANDARD
GOAL
6.1.4 Calculate given percentages of quantities
and solve problems involving discounts at sales,
interest earned, and tips.
(Annual Goal) By (date), when given a set of interestrelated word problems at (name’s) independent reading
level, (name) will calculate sales discounts, interest
earned and tips with_______% accuracy in of trials
as measured by student work samples.
OBJECTIVE/BENCHMARK
1. By (date), when given a set of interest related
word problems from consumer materials
(newspapers, journal ads), (name) will calculate
sales discounts on single items and multiple
quantities with _______% accuracy in ____of ____
trials as measured by student work samples.
2. By (date), when given a set of interest related
word problems, at (name’s) independent reading
level, (name) will calculate the interest earned on a
savings account using multiple variables number of
days, simple interest, compound interest) with
_____% accuracy in ____of____ trials as measured
by student work samples.
6.2.1 Solve problems involving addition,
subtraction, multiplication, and division of
positive fractions and explain why a particular
operation was used for a given situation.
(Annual Goal) By (date), when given assorted addition,
subtraction, multiplication, and division problems of
rational numbers at (name’s) instructional level, (name)
will solve problems and create a visual representation of
what operation was used to calculate correct response
and why with _______% accuracy in
of trials as
measured by performance- based product.
1. By (date), when given assorted addition and
subtraction, problems using positive fractions,
(name) will list order of operations to correctly solve
each problem with ___% accuracy in
of
trials
as measured by performance-based product
2. By (date), when given assorted multiplication and
division problems of positive fractions, (name) will
solve and create a chart listing type of problem and
order of operations to solve each type of problem
with _____% accuracy in
of
trials as
measured by performance- based product.
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NUMBER SENSE - SIXTH GRADE CONTINUED
ESSENTIAL STANDARD
6.2.2 Explain the meaning of multiplication and
division of positive fractions and perform the
calculations (e.g. 5/8 divided by 5/16= 5/8 X16/15
=2/3).
6.2.3 Solve addition, subtraction, multiplication and
division problems, including those arising in concrete
situations, that use positive and negative integers
and combinations of these operations.
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a set of positive
fraction multiplication and division problems, at
(name’s) instructional level, (name) will write an
explanation of the operations using examples (e.g.
5/8 divided by 5/16 = 5/8/x 16/15 = 2/3) and correctly
solve the example problems with ____% accuracy as
measured by student work samples/criterion
assessment.
1. By (date), when given a set of positive fraction
multiplication problems at (name’s) instructional
level, (name) will write an explanation of the process
needed to solve the problems including examples
and the correct solutions with __% accuracy in
of
trials as measured by student work samples/criterion.
(Annual Goal) By (date), when given a visual model
of positive integers, their roots and rising to the next
power, (name) will solve varied addition, subtraction,
multiplication and division problems with two or more
operations with _____% accuracy as measured by
student work samples/criterion assessment.
1. By (date), when given a set of positive integers
and their roots, (name) will order the operations and
solve with ____% accuracy a series of addition and
subtraction problems in
of
trials as
measured by student work samples/criterion.
2. By (date), when given a set of positive fraction
division problems at (name’s) instructional level,
(name) will write an explanation of the process,
listing the steps needed to solve the problems
including examples and the correct solutions with
___% accuracy in
of
trials as measured by
student work samples/criterion.
2. By (date), when given a set of positive integers
and powers, (name) will order multiplication and
division problems with ____% accuracy in_ _ of___
trials as measured by student work samples.
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NUMBER SENSE - SIXTH GRADE CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
6.2.4 Determine the least common multiple and the
greatest common divisor of whole numbers; use them
to solve problems with fractions (e.g., to find a
common denominator to add to fractions or to find the
reduced form for a fraction.)
(Annual Goal) By (date), when given ____
multiplication and division of fractions problems,
(name) will determine the least common multiple and
the greatest common divisor in each problem and
use them to correctly calculate the answer with_
% accuracy in _ _ of __ trials as measured by
student work samples/criterion assessment.
1. By (date), when given ____multiplication of fraction
problems, (name) will determine the least common
multiple and greatest common divisor in each
problem and use them to correctly calculate the
answer with __% accuracy in ____of____ trials as
measured by student work samples/criterion
assessment.
2. By (date), when given ____division of fraction
problems, (name) will determine the greatest
common divisor and least common multiple to
correctly calculate the answer with ______%
accuracy in _____of_____ trials as measured by
student work samples/criterion assessment.
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ESSENTIAL CALIFORNIA STATE CONTENT STANDARDS
SIXTH GRADE - MATHEMATICS
ALBEBRA AND FUNCTIONS
rtions.
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
6.2.1 Convert one unit of measurement to another
(e.g., from feet to miles, from centimeters to inches).
(Annual Goal) By (date), when given a chart to be
analyzed, (name) will list the rules to solve problems
requiring conversion of units of measurements with
____% accuracy in ____of___ trials as measured by
work samples and criterion assessment.
1. By (date), when given a chart and a list of rules to
solve problems requiring conversion of units of
measurement, (name) will match rules to the
conversion tasks with ___% accuracy in ____ of ___
trials/criterion assessment as measured by work
samples and criterion assessment.
2. By (date), when given visual models (a chart and
rules), (name) will solve problems using models with
______% accuracy in ___of____ trials as measured
by work samples and criterion assessment.
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ESSENTIAL CALIFORNIA STATE CONTENT STANDARDS
SIXTH GRADE - MATHEMATICS
MEASUREMENT AND GEOMETRY
Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
6.1.1 Understand the concept of a constant such as
; know the formulas for the circumference and
area of a circle.
(Annual Goal) By (date), when given a teachermade model of a ”constant” formula (e.g. ),
(name) will memorize, list steps and solve problems
requiring the formulas for the circumference and
area of a circle with ____% accuracy in __of_ trials
as measured by work samples/criterion
assessment.
1. By (date), when given the formula for the
circumference of a circle, (name) will state the
formula, list the steps and solve problems using the
formula with _____% accuracy in
of___ trials
as measured by work samples/criterion
assessment.
2. By (date), when given the formula for the area of
a circle, (name) will state formula, list the steps and
solve ____of ____ problems in ____of____ trials as
measured by work samples/criterion assessment.
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ESSENTIAL CALIFORNIA STATE CONTENT STANDARDS
SIXTH GRADE - MATHEMATICS
STATISTICS, DATA, ANALYSIS AND PROBABILITY
dents use data samples of a population and describe the characteristics and limitations of the samples.
3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events.
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
6.1.1 Compute the range, mean, median and mode of
data sets. (CAHSEE)
(Annual Goal) By (date), when given a teacher-made
chart of the math terms, mean, median, and mode
with definitions and examples, (name) will solve word
problems at (name’s) independent reading level with
______% accuracy in ____of__ trials as measured
by work samples/criterion assessment.
1. By (date), when given a teacher-made chart of the
terms mean and mode, (name) will write definitions
and find an example of the term in ___of____ word
problems written at (name’s) independent reading
level with ____% accuracy as measured by work
samples/criterion assessment .
2. By (date), when given a set of “median” word
problems at (name’s) independent reading level,
(name) will define and solve ___of___ problems with
___% accuracy in as measured by work
samples/criterion assessment. (CAHSEE)
6.2.5 Identify claims based on statistical data and, in
simple cases evaluate the validity of claims.
(CAHSEE)
(Annual Goal) By (date), when given data samples of
a population, characteristics and limitations of the
samples, (name) will create a visual representation of
the data and identify statistical claims and whether
those claims are valid with ____% accuracy in
of
trials as measured by teacher-made rubric.
1. By (date), when given a data set of population
characteristics, (name) will chart characteristics and
differences with ___% accuracy as measured by
teacher-made rubric.
2. By (date), when given a set of data about a
populations characteristics and differences will
chart/visually represent data and it’s validity with
______% accuracy in ____of____ trials as measured
by teacher-made rubric.
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STATISTICS, DATA ANALYSIS, AND PROBABILITY - SIXTH GRADE CONTINUED
ESSENTIAL STANDARD
6.3.4 Understand the probability of either of two
disjoint events occurring is the sum of the two
individual probabilities and that the probability of
one event following another, in independent trials,
is the product of the two probabilities.
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a teacher–
made chart that shows the terminology, steps and
process for solving the probability of unrelated
events occurring, (name) will identify key terms,
listing examples and apply steps to determine and
predict the conditions required to solve word
problems at (name’s) independent reading level
with _
___% accuracy in
of
trials as
measured by work sample/teacher rubric.
1. By (date), when given a teacher–made chart that
shows the terminology, steps and process for
solving the probability of unrelated events
occurring, (name) will identify key terms and give
examples to determine conditions required to solve
problems with ___% accuracy in of trials as
measured by criterion assessment/work samples.
2. By (date), when given a chart that shows the
terminology, steps and process for solving the
probability of unrelated events occurring, (name)
will identify key terms and apply steps to predict
impact of conditions required to solve word
problems with ___% accuracy in
of
trials as
measured by work samples/criterion assessment.
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ESSENTIAL CALIFORNIA STATE CONTENT STANDARDS
SIXTH GRADE - MATHEMATICS
MATHEMATICAL REASONING
ESSENTIAL STANDARD
6.1.3 Determine when and how to break a problem
into simpler parts.
GOAL
(Annual Goal) By (date), when given a mixture of
____math problems requiring both single and multistep solutions, (name) will determine how and when
to break a problem into simpler parts with ______%
accuracy in ____of_____ trials as measured by
student work samples.
OBJECTIVE/BENCHMARK
1. By (date), when given a mixture of ____math
problems requiring both single and multi-step
solutions, (name) will sort the problems based on this
criteria with _____% accuracy in_____ of ______
trials as measured by student work samples.
2. By (date), when given _____math problems
requiring multi-step solutions, (name) will determine
how to break a problem into simpler parts with ____%
accuracy in____ of____ trials as measured by
student work samples.
6.2.5 Express the solutions clearly and logically by
using the appropriate mathematical notation and
terms and clear language; support solutions with
evidence in both verbal and symbolic work.
(Annual Goal) By (date), when given a set of mixed
number operation problems, (name) will use a variety
of methods (words, numbers, symbols, models,
charts, graphs, tables diagrams ) to explain the
mathematical reasoning necessary to derive the
solution with ____% accuracy in _____of_____ trials
as measured by teacher-made tests/rubric/student
work samples.
1. By (date), when given a grade level problem,
(name) will use words, numbers, symbols, or graphs
to explain the math reasoning necessary to find the
solution with _____% accuracy in __of__ trials as
measured by teacher-made tests/student work
samples.
2. By (date), when given a grade level problem,
(name) will use words, numbers, symbols, or graphs
to explain the math reasoning necessary to find the
solution with _____% accuracy in __of____ trials as
measured by teacher-made tests/student work
samples.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
SEVENTH GRADE – MATHEMATICS
NUMBER SENSE
ESSENTIAL STANDARD
7.1.1 Read, write and compare rational numbers in
scientific notation (positive and negative powers of
10) with approximate numbers using scientific
notation. (CAHSEE)
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a sample of
numbers in scientific notation, (name) will be able to
read orally and write them with at least ____%
accuracy in
of
trials as measured by
student work samples.
1. By (date), when given a sample of numbers in
scientific notation, (name) will read orally the
scientific numbers with ____% accuracy in ____of
____ trials as measured by student work samples.
2. By (date), when given a sample of a scientific
notation, (name) will write scientific numbers
with_____% accuracy in _____ of _____trials as
measured by student work samples.
7.1.2 Add, subtract, multiply and divide rational
numbers (integers, fractions and decimals) and
take positive rational numbers to whole number
powers. (CAHSEE)
(Annual Goal) By (date), when given assorted
addition, subtraction, multiplication, and division of
rational numbers at (name’s) instructional level,
(name) will calculate the correct response with
_____%accuracy in
of
trials as
measured by student work samples.
1. By (date), when given a series of addition,
subtraction, problems of rational numbers at
(name’s) instructional level, (name) will calculate
correct responses with ____% accuracy in
of
trials as measured by student work samples.
2. By (date), when given a series of multiplication
and division of rational numbers at (name’s)
instructional level, (name) will calculate responses
with ___% accuracy in
of
trials as
measured by student work samples.
7.1.3 Convert fractions to decimals and percents
and use these representations in estimation,
computation and applications. (CAHSEE)
(Annual Goal) By (date), when given a teachermade sample of fractions, (name) will convert them
to decimals and percents and create a visual
representation with ___% accuracy in
of
trials as measured by student work
samples/criterion assessments.
1. By (date), when given a teacher-made sample of
fractions, (name) will convert fractions to decimals
with ___% accuracy in____ of____ trials as
measured by student work samples/ criterion
assessments.
2. By (date), when given teacher-made sample of
fractions, (name) will convert fractions to percents
making a conversion chart for assignments with
___% accuracy in
of
trials as measured
by student work samples/criterion assessments.
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NUMBER SENSE – SEVENTH GRADE CONTINUED
ESSENTIAL STANDARD
7.1.6 Calculate percent of increases and
decreases of a quantity. (CAHSEE)
GOAL
(Annual Goal) By (date), when given a set of
quantity problems, (name) will compute a given
increase and decrease of a number expressed as
a percent with _____% accuracy in
of
trials as measured by student work
samples/criterion assessments.
OBJECTIVE/BENCHMARK
1. By (date), when given a set of quantity
problems, (name) will compute the percent of
increase in a quantity with __
_% accuracy in
of
trials as measured by student work
samples/criterion assessments.
2. By (date), when given a set of quantity
problems, (name) will compute the percent of
decrease in a quantity (number) with _____%
accuracy in
of
trials as measured by
student work samples/criterion assessments.
7.1.7 Solve problems that involve discounts,
markups, commissions, and profit and compute
Simple and compound interest. (CAHSEE)
(Annual Goal) By (date), when given a set of
interest-related word problems at (name’s)
independent reading level, (name) will calculate
the simple interest and monthly payments with _
_% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
1. By (date), when given a set of interest-related
word problems at (name’s) independent reading
level, (name) will calculate the simple interest
amount on a major purchase with ____% accuracy
in
of
trials as measured by student
work samples/criterion assessments.
2. By (date), when given a set of interest-related
problems at (name’s) independent reading level,
(name) will calculate the monthly payments using
simple interest calculations with _____% accuracy
in
of
trials as measured by student work
samples/criterion assessments.
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NUMBER SENSE – SEVENTH GRADE CONTINUED
ESSENTIAL STANDARD
7.2.1 Understand negative whole-number
exponents. Multiply and divide expressions
involving exponents with a common base.
(CAHSEE)
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a teachermade sample of numerical expressions with
exponents, (name) will multiply, divide and simplify
the expressions with _____% accuracy in
of
trials as measured by student work
samples/criterion assessment.
1. By (date), when given a teacher-made sample of
numerical expressions with exponents, (name) will
multiply and divide expressions with ______%
accuracy in
of
trials as measured by
student work samples/criterion assessment.
2. By (date), given a set of multiplication and
division problems with exponents, (name) will
simplify numerical expressions with _______%
accuracy in _____ of _____ trials as measured by
student work samples/criterion assessment.
7.2.2 Add and subtract fraction by using factoring to
find common denominators. (CAHSEE)
(Annual Goal) By (date), when given a teachermade sample of unlike fractions, (name) will add,
subtract, and simplify the fractions with at least
_____% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
1. By (date), when given a teacher-made sample of
unlike fractions, (name), will add and subtract the
unlike fractions with __% accuracy in of
trials
as measured by student work samples/criterion
assessment.
2. By (date), when given a set of unlike fractions,
(name) will correctly solve simplify fractions with
______% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
7.2.4 Use the inverse relationship between raising
to a power and extracting the root of a perfect
square integer; for an integer that is not square,
determine without a calculator the two integers
between which its square root lies and explain why.
(Annual Goal) By (date), when given a series of
perfect square integers, (name) will calculate the
roots and raise each integer to the next power with
_____% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
1. By (date), when given a series of perfect
integers, (name) will calculate the roots of the
integers with _____% accuracy in
of
trials
as measured by student work samples/criterion
assessment.
2. By (date), when given a series of perfect
integers, (name) will raise each integer to the next
power with _____% accuracy in
of
trials
as measured by student work samples/criterion
assessment.
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NUMBER SENSE – SEVENTH GRADE CONTINUED
ESSENTIAL STANDARD
7.2.5 Understand the meaning of the absolute
value of a number; interpret the absolute value as
the distance of the number from zero on a number
line; and determine the absolute value of real
numbers. (CAHSEE)
GOAL
(Annual Goal) By (date), when given a series of
positive whole numbers, (name) will be able to
express the number’s absolute value as the
distance of the number from 0 on the number line
with ____% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
OBJECTIVE/BENCHMARK
1. By (date), when given a series of positive whole
numbers, (name) will use a visual model (number
line) to mark the distance the number is from zero
with ______% accuracy in _____of____ trials as
measured by student work samples/criterion
assessment.
2. By (date), when given a series of positive whole
numbers, (name) will write the number that
expresses the distance of a positive whole number
from 0 with __% accuracy in
of trials as
measured by student work samples/criterion
assessment.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
SEVENTH GRADE – MATHEMATICS
MEASUREMENT AND GEOMETRY
problems.
ESSENTIAL STANDARD
7.1.1 Compare weights, capacities, geometric
measures, times, and temperatures within and
between measurement systems (e.g., miles per
hour and feet per second, cubic inches to cubic
centimeters). (CAHSEE)
GOAL
(Annual Goal) By (date), when given a set of data,
(name) will be able to compare local temperatures
over time and use ratios to compute the amount of
increase or decrease with __% accuracy of
trials as measured by student work
samples/criterion assessment.
OBJECTIVE/BENCHMARK
1. By (date), when given a set of data, (name) will
compare local temperatures over time and visually
graph the results with __% accuracy in of trials
as measured by student work samples/criterion
assessment.
2. By (date), when given a set of data, (name) will
compare data and compute amounts of increase
with ____% accuracy in ___of___ trials as
measured by student work samples/criterion
assessment.
7.1.3 Use measures expressed as rates (e.g.,
speed, density) and measures expressed as
products (e.g., person-days) to solve problems;
check the units of the solutions; and use
dimensional analysis to check the reasonableness
of the answer. (CAHSEE)
Annual Goal), By (date), when given a formula for a
measure, (name) will be able to identify the
numerical terms necessary to solve the equation
with ____% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
1. By (date), when given a formula for measure,
(name) will identify and list the numerical terms
necessary to solve an equation with____%
accuracy in
of
trials as measured by
student work sample/criterion assessment.
2. By (date), when given a formula for measure,
(name) will write and solve three problems at
(name’s) independent reading level that include a
need to measure a (room, baseball diamond,
cooking) with
% accuracy in
of
trials
as measured by student work samples/criterion
assessment.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
SEVENTH GRADE – MATHEMATICS
STATISTICS, DATA, ANALYSIS AND PROBABILITY
iables within a data
set by hand and through the use of an electronic spreadsheet software program.
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
7.1.1 Know various forms of display for data sets,
including a stem-and-leaf plot or box-and whisker
plot; use the forms to display a single set of data
or to compare two sets of data. (CAHSEE)
(Annual Goal) By (date), when given word problems at
(name’s) independent reading level with single set of
data, (name) will display the data using various forms
such as stem-and-leaf or box-and-whisker plots with
_____% accuracy in
of
trials as measured
by student work samples/criterion assessment.
1. By (date), when given word problems with a
single set of data at (name’s) independent reading
level, (name) will list the various forms of displaying
with ____% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
2. By (date), when given word problems with a
single set of data, (name) will compute the lower,
median and upper quartiles with ____% accuracy
in
of
trials as measured by student work
samples/criterion assessment.
7.1.2 Represent two numerical variables on a
scatter plot and informally describe how the data
points are distributed and any apparent
relationship that exists between the two variables
(e.g., between time spent on homework and
grade level). (CAHSEE)
(Annual Goal) By (date), when given a set of word
problems at (name’s) independent reading level which
involve two variables, (name) will represent the data
on a scatterplot and be able to write a sentence which
describes the relationship between the two variables
with _____% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
1. By (date), when given a set of word problems at
(name’s) independent reading level, involving two
variables, (name) will represent the data on a
scatterplot with ___% accuracy in
of
trials
as measured by student work samples/criterion
assessment.
2. By (date), when given a set of word problems at
(name’s) independent reading level, involving two
variables, (name) will write a sentence to describe
the relationship between the two variables with
___% accuracy in
of
trials as measured
by student work samples/criterion assessment.
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STATISTICS, DATA, ANALYSIS AND PROBABILITY – SEVENTH GRADE CONTINUED
ESSENTIAL STANDARD
7.1.3 Understand the meaning of, and be able to
compute, the minimum, the lower quartile, the
median, the upper quartile, and the maximum of a
data set. (CAHSEE)
GOAL
(Annual Goal) By (date), when given word
problems at (name’s) independent reading level
with a single set of data, (name) will compute the
lower, median, and upper quartiles with _____%
accuracy in of trials as measured by student
work samples/criterion assessment.
OBJECTIVE/BENCHMARK
1. By (date), when given word problems at
(name’s) independent reading level with a single
set of data, (name) will compute the lower, median,
and upper quartiles with _____% accuracy in
of
trials as measured by student work
samples/criterion assessment.
2. By (date), when given word problems at
(name’s) independent reading level with a single
set of data, (name) will compute the lower, median,
and upper quartiles with _____% accuracy in
of
trials as measured by student work
samples/criterion assessment.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
SEVENTH GRADE – MATHEMATICS
MATHEMATICAL REASONING
ESSENTIAL STANDARD
GOAL
7.1.1 Analyze problems by identifying relationships,
distinguishing relevant from irrelevant information,
identifying missing information, sequencing and
prioritizing information, and observing patterns
(CAHSEE)
(Annual Goal) By (date), when given a set of word
problems at (name’s) independent reading level,
(name) will distinguish relevant from irrelevant
information, identify missing information, and
sequence the information necessary to solve the
problems with _____% accuracy in
of
trials
as measured by student work samples/criterion
assessment.
OBJECTIVE/BENCHMARK
1. By (date), when given a set of word problems at
(name’s) independent reading level, (name) will
distinguish by listing all relevant information from
irrelevant information and phrase information as a
numerical expression with __
__% accuracy
in
of
trials as measured by student work
samples/criterion assessment.
2. By (date), when given a set of word problems at
(name’s) independent reading level, (name) will
identify in writing all missing information and
sequence information with __
__% accuracy in
of
trials as measured by student work
samples/criterion assessment.
7.1.3 Determine when and how to break a problem
into simpler parts.
(Annual Goal) By (date), when given a set of word
problems at his/her independent reading level,
(name) will underline key terms such as more than,
less than, of, times, etc. and identify the function
necessary to solve the problems with ___%
accuracy in of trials as measured by student
work samples/criterion assessment.
1. By (date), when given a set of word problems at
(name’s) independent reading level, (name) will
underline key terms for more than and less than
and identify the function necessary to solve the
problems with ___% accuracy in
of
trials
as measured by student work samples/criterion
assessment.
2. By (date), when given a set of word problems,
(name) will underline key terms for (of, times) and
identify the function necessary to solve problems
with ____% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
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MATHEMATICAL REASONING - SEVENTH GRADE CONTINUED
ESSENTIAL STANDARD
7.2.1 Use estimation to verify reasonableness of
calculated results. (CAHSEE)
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given an example of
estimation, (name) will use estimation as a
checking device to verify the validity of calculated
results in _____ out of ____ word problems with
% accuracy as measured by student work
samples/criterion assessment.
1. By (date), when given an example of estimation
problems, (name) will use estimation as a checking
device to verify the validity of calculated results in
___ of ___% accuracy in of
trials as
measured by student work samples/criterion
assessment.
2. By (date), when given an estimation chart,
(name) will use the chart to verify the validity of
calculated results for ____of____ word problems in
of
trials as measured by student work
samples/criterion assessment.
7.2.3 Estimate unknown quantities graphically and
solve for them by using logical reasoning and
arithmetic and algebraic techniques. (CAHSEE)
(Annual Goal) By (date), when given a set of word
problems at (name’s) independent reading level,
(name) will be able to create a visual representation
as an aid in estimating an unknown quantity and
solve the problems using algebraic techniques with
_____% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
1. By (date). when given a set of word problems at
(name’s) independent reading level, (name) will
underline words that represent number operations
and create a visual representation to aid in
calculation with ___% accuracy in
of
trials
as measured by student work samples/criterion
assessment.
2. By (date), when given a set of word problems at
(name’s) independent reading level, (name) will
solve the problems using algebraic strategies, with
% accuracy in
of
trials as measured by
student work samples/criterion assessment.
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ESSENTIAL STATE OF CALIFORNIA CONTENT STANDARDS
EIGHTH, NINTH, TENTH GRADE - MATHEMATICS
ALGEBRA I
t, multiply and divide monomials and polynomials. Students are able to solve problems using these techniques.
ESSENTIAL STANDARD
2.0 Students understand and use operations as
taking the opposite, finding the reciprocal, taking a
root and raising to a fractional power. They
understand and use the rules of exponents.
(CAHSEE)
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given the rules of
exponents, (name) will define (taking the opposite,
finding the reciprocal, taking a root and raising to a
power) and give written examples of each rule with
_____% accuracy in
of
trials as
measured by teacher-made assessment.
1. By (date,) when given the rules of exponents
(opposites, reciprocals, roots and power), (name)
will solve equations in four basic number operations
(+ accuracy in ___of____ trials
as measured by teacher-made and standardized
assessments.
2. By (date), when given the rules of exponents
(opposites, reciprocals, roots and powers), (name)
will solve equation in four basic number operations
(T –
___of
trials
as measured by teacher-made and standardized
assessments.
3.0 Students solve equations and inequalities
involving absolute values. (CAHSEE)
(Annual Goal) By (date), when given assorted
addition, subtraction, multiplication and division
equations and inequalities involving absolute
values, (name) will calculate the correct response
with ____% accuracy in
of
trials as
measured by student work samples/criterion
assessment.
1. By (date), when given addition and subtraction
equations involving absolute values, (name) will
calculate correct response ____% accuracy in ___
of ____trials as measured by classroom
assessment and charting.
equations involving inequalities in absolute
values, (name) will calculate correct response
_____% accuracy in ___of____ trials as measured
by classroom assessment and charting.
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ALGEBRA I – EIGHTH, NINTH, TENTH CONTINUED
ESSENTIAL STANDARD
4.0 Students simplify expressions before solving
linear equations and inequalities in one variable,
such as 3(2x-5) + 4(x-2) = 12. (CAHSEE)
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a teachermade sample of linear equations, (name) will
develop a chart listing the steps required to simplify
expressions before solving linear equations and
provide examples to demonstrate understanding
with ______% accuracy in
of
trials as
measured by performance-based assessment
criteria.
1. By (date), when given a teacher-made sample of
linear equations at (name’s) instructional level,
(name) will list the steps required to simplify
expressions and create a visual representation with
_____% accuracy in _____of ____trials as
measured by performance-based assessment
criteria.
2. By (date), when given a visual representation of
steps to simplify linear equations, (name) will
provide examples of equations for each step and
calculate correct response with %_____ accuracy
in _____of _____ trials as measured by
performance-based assessment criteria.
5.0 Students solve multi-step problems, including
word problems, involving linear equations and
linear inequalities in one variable and provide
justification for each step. (CAHSEE)
(Annual Goal) By (date), when given a series of
multi-step linear problems and word problems at
(name’s) independent reading level, involving one
variable, (name) will solve linear equations and
inequalities with ____% accuracy in
of
trials as measured by student work
samples/criterion assessment.
1. By (date), when given a series of multi-step
linear problems with one variable, (name) will
identify order of operations and calculate the
correct response with _____% accuracy in
of
trials as measured by student work
samples/criterion assessment.
2. By (date), when given a set of multi-step word
problems at (name’s) independent reading level,
(name) will identify order of expectation and
calculate the correct response with ______%
accuracy in ____of ____trials as measured by
student work samples/criterion assessment.
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ALGEBRA I – EIGHTH, NINTH, TENTH CONTINUED
ESSENTIAL STANDARD
6.0 Students graph a linear equation and compute
the x- and y intercepts (e.g., graph 2x + 6y = 4).
They are also able to sketch the region defined by
linear inequality (e.g., they sketch the region
defined by 2x + 6y< 4). (CAHSEE)
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a linear
equation, (name) will graph and compute the x and
y intercepts graphically showing the region of linear
inequality with ____% accuracy in
of
trials as measured by performance-based
products/assessment.
1. By (date), when given a teacher made graphic
model of a linear equation, (name) will graph and
compute x + y intercepts with _____% accuracy in
__ of ___ trials as measured by performance-based
products/assessment.
2. By (date), when given a set of graphs
representing different linear equations, (name) will
compute x+ y intercepts and graph inequalities
with____% accuracy in _____of_____ trials as
measured by performance-based
products/assessment.
7.0 Students verify that a point lies on a line, given
an equation of the line. Students are able to derive
linear equations by using the point-slope formula.
(CAHSEE)
(Annual Goal) By (date), when using the point-lope
formula, (name) will create written directions to
derive linear equations verifying that a point lies on
a line. (Name) will use criteria to compute correct
responses with _____% accuracy in
of
trials as measured by student- developed criteria.
1. By (date), when given a point-slope formula
calculation, (name) will create written directions to
derive linear equations with %____ accuracy in
of
trials as measured by student-developed
criteria.
2. By (date), when given a series of point-slope
derivation problems, (name) will use criteria to
compute correct responses with _____% accuracy
in _____of____ trials as measured by studentdeveloped criteria.
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ALGEBRA I – EIGHTH, NINTH, TENTH CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
8.0 Students understand parallel and perpendicular
lines and how those slopes are related. Students
are able to find the equation of a line perpendicular
to a given line that passes through a given point.
(CAHSEE)
(Annual Goal) By (date), when given a set of data
about parallel and perpendicular lines and how
slopes are related, (name) will find the equation of a
line perpendicular to a given line that passes
through a given point with ____% accuracy in
of
trials as measured by student work samples.
1. By (date), when given a set of data about parallel
and perpendicular lines and how slopes are related,
(name) will define terms and list steps to find
equations with ____% accuracy in ___ of ___ trials
as measured by student work samples.
2. By (date), when given a series of parallel and
perpendicular line and slope problems, (name) will
find the equation for a line perpendicular to a given
line that passes through a given point with _____%
accuracy in ___ of____ trials as measured by
student work samples.
9.0 Students solve a system of two linear equations
in two variables algebraically and are able to
interpret the answer graphically. Students are able
to solve a system of tow linear inequalities in tow
variables and to sketch the solution sets.
(CAHSEE)
10.0 Students add, subtract, multiply, and divide
monomials and polynomials. Students solve multistep problems, including word problems, by using
these techniques. (CAHSEE)
(Annual Goal) By (date), when given a problem with
two linear equations or inequalities, (name) will
solve and graph the correct response with ____%
accuracy in
of
trials as measured by
student work samples/criterion assessment.
1. By (date), when given a problem with two linear
equations, (name) will solve and graph the correct
response with ____% accuracy in ____of____ trials
as measured by student work samples/criterion
assessment.
2. By (date), when given a problem with two linear
inequalities, (name) will solve and graph the correct
response with ____% accuracy in ___ of____ trials
as measured by student work samples/criterion
assessment.
(Annual Goal) By (date), when given a teachermade model of monomials and set of ten basic
operation monomial problems, (name) will add,
subtract, multiply and divide monomials and
polynomials by correctly factoring and reducing
equations to lowest terms with ______% accuracy
in ___ of ___ trials as measured by student work
samples.
By (date), when given a teacher-made model
of monomials and set of ten basic operation
monomial problems, (name) will add, subtract,
multiply and divide monomials by correctly factoring
and reducing the solution to lowest terms with
______% accuracy in ___ of ____trials as
measured by student work samples.
1. By (date), when given a set of ten basic
operation polynomial problems, (name) will add,
subtract, multiply and divide polynomials by
correctly factoring and reducing the solution to
lowest terms with ____% accuracy in ___of ___
trials as measured by student work samples.
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ALGEBRA I – EIGHTH, NINTH, TENTH CONTINUED
ESSENTIAL STANDARD
15.0 Students apply algebraic techniques to solve
rate problems, work problems and percent mixture
problems. (CAHSEE)
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a set of raterelated word problems at (name’s) independent
reading level, (name) will write the algebraic
equation correctly and solve problem with ____%
accuracy in ___of___ trials as measured by student
work samples
1. By (date), when given a set of rate-related word
problems at (name’s) independent reading level,
(name) will underline words and list the factors that
represent number operations (e.g. + - x) in an
algebraic equation correctly with ____% accuracy
in ___ of ___ trials as measured by student work
samples.
2. By (date), when given a set of rate-related word
problems at (name’s) independent reading level,
(name) will write the algebraic equation correctly
with ____% accuracy in____ of____ trials as
measured by student work samples.
17.0 Students determine the domain of
independent variables and the range of dependent
variables defined by a graph, a set of ordered pairs,
or a symbolic expression.
(Annual Goal) By (date), when given a graph or a
set of ordered pairs, (name) will determine and plot
the domain of independent variables and the range
of dependent variables illustrated with ____%
accuracy in
of
trials as measured by
student work samples.
1. By (date), when given a set of ordered pairs,
(name) will determine and plot on a graph the
independent variables with ____% accuracy in
___of___ trials as measured by student work
samples.
2. By (date), when given a set of ordered pairs,
(name) will determine the range of dependent
variables and plot on a graph with ____% accuracy
in ____of ____ trials as measured by student work
samples.
21.0 Students graph quadratic functions and know
that their roots are the x-intercepts.
(Annual Goal) By (date), when given the steps and
a visual model of the quadratic formula, (name) will
create a mnemonic device to memorize the
quadratic formula and graph quadratic functions
that show their roots are the x intercepts with
____% accuracy in
of
trials as
measured by student work samples.
1. By (date), when given the steps and a visual
model of the quadratic formula, (name) will create a
mnemonic device to memorize the quadratic
formula and simplify the steps with _____%
accuracy in
of
trials as measured by
student work samples.
2. By (date), when given a series of five quadratic
formula problems, (name) will graph the quadratic
functions that show their roots are the x intercepts
with ____% accuracy in ____of ____ trials as
measured by student work samples.
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ALGEBRA 1 – EIGHTH, NINTH, TENTH CONTINUED
ESSENTIAL STANDARD
GOAL
OBJECTIVE/BENCHMARK
23.0 Students apply quadratic equations to physical
problems, such as the motion of an object under
the force of gravity.
(Annual Goal) By (date), when given a set of written
physical problems at (name’s) independent reading
level (e.g., motion of an object under the force of
gravity), (name) will apply quadratic equations to
correctly solve problems with _____% accuracy in
___ of ___ trials as measured by student work
samples. (Transition)
1. By (date), when given a set of physical word
problems at (name’s) independent reading level
(e.g. motion of an object under the force of gravity),
(name) will write the quadratic equation
representing the problem with ____% accuracy in
____of____ trials as measured by student work
samples.
2. By (date), when given a set of physical word
problems at (name’s) independent reading level,
(name) will use a student-generated mnemonic
device showing the steps of the quadratic equation
to correctly solve problem with ____% accuracy in
___of ___ trials as measured by student work
samples.
24.2 Students Identify the hypothesis and
conclusion in logical deduction.
(Annual Goal) By (date), when given a vocabulary
list about the elements of a logical argument
(hypothesis, assertion, counterexample and
conclusion) and a written logical argument at
(name’s) independent reading level, (name) will
underline and paraphrase all terms relating to
elements with ____% accuracy in ____ of _____
trials as measured by teacher-selected
assessment.
1. By (date), when given a list of vocabulary words
describing the elements of a logical argument
(hypothesis, assertion, counterexample, and
conclusion, (name) will define terms with__ %
accuracy in____ of _____trials as measured by
student work samples.
2. By (date), when given a written logical argument
at (name’s) independent reading level, (name) will
underline and paraphrase all terms relating to
elements of a logical argument with____ %
accuracy in ____ of _____trials as measured by
student work samples.
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ALGEBRA I– EIGHTH, NINTH, TENTH CONTINUED
ESSENTIAL STANDARD
24.3 Students use counterexamples to show that
an assertion is false and recognize that a single
counterexample is sufficient to refute an assertion.
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given a set of
counterexamples, (name) will use counterexamples
to show that an assertion is false and that a single
counterexample can prove an assertion invalid and
create a visual representation with ____% accuracy
in ____ of _____ trials as measured by
performance-based assessment.
1. By (date), when given a logical argument with
several counterexamples to show that an assertion
is false, (name) will underline and chart
counterexamples with _____% accuracy in ____ of
_____ trials as measured by performance-based
assessment.
2. By (date), when given a logical argument with
several counterexamples to show that an assertion
is false, (name) will prioritize in a visual
representation, counterexamples to show that a
single counterexample can disprove the assertion
with ____% accuracy in ____ of _____ trials as
measured by performance-based assessment.
25.1 Students use properties of numbers to
construct simple, valid arguments (direct and
indirect) for, or formulate counterexamples to,
claimed assertions.
(Annual Goal) By (date), when given a set of logical
assertions (statements), (name) will use a visual
model of the properties of numbers to construct
equations that represent simple valid arguments for
or counterexamples to disprove assertions
(statements) with _____% accuracy in ____ of
_____ trials as measured by performance-based
assessment.
1. By (date), when given a teacher-made sample of
the properties of numbers to construct equations
representing logical arguments, (name) will
construct equations that represent simple valid
arguments with ____% accuracy in ____ of _____
trials as measured by performance-based
assessment.
2. By (date), when given a set of three logical
assertions, (name) will construct equations for
counterexamples to disapprove assertions with
_____% accuracy in ____of____ trials as
measured by performance-based assessment.
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ALGEBRA I– EIGHTH, NINTH, TENTH CONTINUED
ESSENTIAL STANDARD
25.2 Students judge the validity of an argument
according to whether the properties of the real
number system and the order of operations have
been applied correctly at each step.
GOAL
OBJECTIVE/BENCHMARK
(Annual Goal) By (date), when given an argument,
(name) will determine the validity by charting
whether the properties of the real numbers and the
order of operations have been applied correctly with
____% accuracy in ____ of _____ trials as
determined by performance-based assessment.
1. By (date), when given a written argument at
name’s) independent reading level, (name) will
determine the argument’s validity by charting
whether the properties of the real number have
been correctly applied with____% accuracy in ____
of _____ trials as measured by performance-based
measures.
2. By (date), when given an argument, (name) will
underline terms representing the number
operations and determine if the order of operations
supports the argument’s validity with _____%
accuracy in ____ of _____ trials as measured by
performance-based assessment.
25.3 Given a specific algebraic statement involving
linear, quadratic, or absolute value expressions or
equations or inequalities, students determine
whether a statement is true sometimes, always or
never.
(Annual Goal) By (date), when given a series of
algebraic statements (linear, quadratic, absolute
value, equation or Inequalities), (name) will
correctly determine whether the statement is true
sometimes, always, or never with _____% accuracy
in ___ of ____ trials as measured by performancebased assessment.
1. By (date), when given two algebraic statements
(linear, quadratic), (name) will construct equations
to correctly determine whether the statement is true
sometimes, always or never with ____% accuracy
in ____ of _____trials as measured by
performance-based assessment.
2. By (date), when given a series of algebraic
statements (absolute value, equation or
inequalities), (name) will construct equations to
correctly determine whether the statement is true
sometimes, always or never with ___% accuracy in
____ of _____ trials as measured by performancebased assessment.
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