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Humboldt Community Schools Mathematics Core Curriculum
Mathematics
Standard 1: Use a variety of strategies in the problem solving process.
ITP Indicator
A4.Demonstrate ways of
performing operations
A8.Use variable expressions to
model situations
A4.Demonstrate ways of
performing operations
C3.Choose a method for
Solving a problem
CODE
K.1.2
1.1.2
1.1.3
C2.Identify extraneous or
Insufficient information in
Problems
C3.Choose a method for
Solving a problem
A4.Demonstrate ways of
Performing operations
A8.Use variable expressions
To model situations
Page 1 of 51
Local Indicator
Analyze and solve problems using skills and
strategies
Uses models (e.g., pattern blocks, tiles,
or other manipulative) to represent
problems.
Analyze and solve problems using skills and
strategies
K.1.1
1.1.1
A8.Use a variable expressions
to model situations
BENCHMARK
Draws pictures to represent problems.
2.1.1
2.1.2
2.1.3
Restate problems in own words to
demonstrate understanding
Uses speaking, writing and drawing to
represent problem situations (e.g.,
translate from pictures of objects to
numerical expressions).
Uses models (e.g., pattern blocks, tiles,
or other manipulatives) to represent
problems.
Uses a variety of problem solving
strategies (e.g., identifying a pattern,
choosing an operation, using trial and
error, manipulatives, evaluating
methods of solution)
Explain to others the process used to
solve a problem.
Uses speaking, writing and drawing
forms to represent problem situations
(e.g., translate from pictures of objects
to numerical expressions).
Teacher Observation
Teacher Observation
Independent practice
Independent practice
Uses touchpoints
Uses counting up, counting back
Uses doubles
Uses 10 to add nine
Explains the process used to solve a
problem to another person
Uses white boards to solve a problem
Uses math journal
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
3.1.1
C3.Choose a method for
Solving a problem
C1.Solve single-step and
multiple-step math problems
C2.Identify extraneous or
Insufficient information in
Problems
C3.Choose a method for
solving a problem
C1.Solve single-step and
multiple-step math problems
C2.Identify extraneous or
insufficient information in
problems
C3.Choose a method for
solving a problem
3.1.2
4.1.1
4.1.2
5.1.1
5.1.2
5.1.3
6.1.1
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Knows information required to solve
Make tally tables to collect data for graphs
problems (e.g., make organized lists or
tables of information necessary).
Uses a variety of problem solving
Uses trial and error when creating an
strategies. (e.g., identifying a pattern,
invention that solves a problem
choosing an operation, using trial and
error, manipulatives, and evaluating
methods of solution).
Represent problem situations in a
Draw a picture to represent problems
variety of forms (e.g., translate from a
Guess and check and use estimation to test
diagram to a number or symbolic
reasonableness
expression.
Explain methods and reasoning behind Work together and talk about what it is that
the problem solution to determine its
you need to find out
reasonableness.
Does your answer made sense in the end
Check labels
Use a variety of problem-solving
strategies
Make an organized list
Draw pictures and diagrams
Use “guess and check”
Work backwards
Solves a simple problem
Understand basic valid and invalid
Using logical reasoning
arguments
Predict or estimate
Justify answers in verbal and written form
Understand that some ways of
State problems in own works to increase
representing a problem are more
understanding
helpful than others.
Distinguish between pertinent and irrelevant
information
Use a calculator to compare amounts and
larger numbers
Convert fractions into decimals
Use a variety of measuring processes to Exploring angles in a triangle
model and to solve problems.
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
C1.Solve single-step and
multiple-step math problems
6.1.2
Understand how to break a complex
problem into single parts
Finding area of irregular figures
A9.Explore numerical patterns
C3.Choose a method for
solving a problem
C2.Identify extraneous or
insufficient information in
problems
6.1.3
Uses multiple methods to solve
mathematical problems
Solving story problems
6.1.4
Construct informal logical arguments
to justify reasoning processes
Solving story problems
7.1.1
Uses a variety of strategies to
understand problem solving situations
7.1.2
Use a variety of strategies to
understand problem-solving situations
and processes
Solves real world problems by using
estimation strategies
Solves real world problems when given too
much or too little information
Solves real world problems by making a
table
Solves real world problems by finding a
pattern
Uses models to determine percents
Solves real world problems using multiple
strategies
Solves real world problems by drawing a
diagram
Solves real world problems by using a
“guess and test” strategy
Solves real world problems by using
estimation strategies
Solves real world problems when given too
much or too little information
Solves real world problems by making a
table
Solves real world problems by finding a
pattern
Uses models to determine percents
Solves real world problems using multiple
C1.Solve single-step and
multiple-step math probmens
C2.Identify extraneous or
insufficient information in
problems
C3.Choose a method for
solving a problem
Page 3 of 51
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
A9.Explore numerical patterns
7.1.3
C3.Chooose a method for
solving a problem
8.1.1
Generalize from a pattern of
observations made in particular cases,
make conjectures, and provide
supporting arguments for these
conjectures.
Formulate a problem, determine
information required to solve the
problem, choose methods for obtaining
this information, and set limits for
acceptable solutions.
strategies
Solves real world problems by drawing a
diagram
Solves real world problems by using a
“guess and test” strategy
Solves real world problems by making a
table
Solves real world problems by finding a
pattern
Accurately identifies corresponding sides
and angles in congruent triangles
Solves real world problems by looking for a
pattern
Solves real world problems by drawing a
diagram
Writes and evaluates expressions with
exponents
Solves real world problems by using a
“guess and test” strategy
Uses exponents to simplify numbers in
scientific notation
Solves one and two step equations and
inequalities using basic arithmetic
operations including combining like terms
Correctly simplifies variable expressions
A9.Explore numerical patterns
Understand the role of written symbols
in representing mathematical ideas and
the use of precise language in
conjunction with the special symbols of
mathematics.
Understand how to break a complex
problem into simpler parts or use a
similar problem type to solve a
problem [N].
Construct informal logical arguments
Page 4 of 51
Mathematics Alignment Results – November 5, 2003
8.1.2
8.1.3
Decides on appropriate strategy or strategies
to solve real world problems
Solves equations with two variables
Solves real world problems by using a
Humboldt Community Schools Mathematics Core Curriculum
C2.Identify extraneous or
insufficient information in
problems
8.1.4
to justify reasoning processes and
methods of solutions to problems (i.e.,
use informal deductive methods).
“guess and test” strategy
Solves real world problems using logical
reasoning
9-12.1.1
Understand, use, and construct a
mathematical proof. [Geometry]
IM2. Create a proof to show triangles or
parts of triangles are congruent
IM3. Write and/or compare coordinate and
synthetic proofs
IM3. Write indirect proofs using geometric
situations
IM3. Write and/or compare coordinate and
synthetic proofs
IM3. Write indirect proofs using geometric
situations
All. Translate real world problems into
variable equations
IM1. Interpret data in tables, graphs and
concept maps
IM1. Explore
Im1. Use coordinate systems to solve realworld problems
IM1. Explore and apply direct variation,
slope and tangent
IM2. Model real world situations in which
one quantity is proportional to the square or
cube of another quantity
IM3. Write simple algorithms for
mathematical and real-world problems
IM3. Explore the relationships between ifthen and its converse, inverse and
contrapositive
IM3. Write simple algorithms for
mathematical and real-world problems
All: Uses inductive reasoning to make
c.2. Reason quantitatively
9-12.1.2
9-12.1.3
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Apply the process of math modeling to
open-ended real-world problem
situations (i.e., problem formation,
math modeling, solve, interpret, and
justify use of technology when
appropriate). [All}
Construct logical arguments to test
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
conjectures and to justify solutions to
problems. [All }
9-12.1.4
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9-12.1.4a Construct equations for
simple problems. [All}
conjectures
IM1-3. Use a counter example to disprove
a statement
Trans-IM3. Verify or check for
reasonableness of answers
IM1. Investigate, write and graph equations
for horizontal and vertical lines
IM2. Calculate the odds of winning one of
the Iowa lottery games and make a decision
as to the intelligence of playing the game
IM2. Use a calculator to calculate
combinations, permutations and factorials
IM2. Apply the meaning of the works and,
or and not with a real life database
IM2. Graph algebraic sentences that sue the
words and and or
IM2. Represent if-then statements and their
converses with symbols and Venn diagrams
IM2. Use rules of logic, symbols and Venn
diagrams to reach conclusions and to decide
if an argument is valid or invalid
IM2. Write good definitions and make valid
arguments using “if and only if” statements
IM2. Recognize and write biconditionals
All. Translate real world problems into
variable equations, expressions or
inequalities, expressions or inequalities
IM1. Write rates and solve everyday
problems with ratios
IM1. Use proportions to model and solve
problems
IM1. Use direct variation models to make
predictions and find the slop of a line
Pass. Translate verbal phrase into algebraic
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
c.1. Solve math problems
requiring multiple steps and
operations
9-12-1.4b Construct equations for
multi-step problems. [All}
expressions
Pass. Translate verbal sentences into
algebraic equations
Pass. Use the Triangle Inequality to
estimate the length of the third side of a
triangle
APM. Read and write a formula
APM. Translate a problem into an equation
All. Translate real world problems into
variable equations
Standard 2: Understand and apply basic and advanced properties of the concepts of numbers.
ITP Indicator
CODE
K.2.1
BENCHMARK
Understand ordinal numbers (1st, 2nd,
3rd).
Local Indicators
Verbally identify positions
Assemble pictures in order
A16.Apply probability
concepts and counting rules
A1.Represent, compare and
order numbers
A5.Use place value and write
numbers
A9.Explore numerical patterns
A1.Represent, compare and
order numbers
A2.Describe and apply
properties of numbers
K.2.2
Count objects to 20.
1 to 1 correspondence
K.2.3
Understands a variety of
representations of whole numbers 0-20
(e.g., written numerals, objects in sets,
number lines).
Verbally recognize numbers represented in
different settings
K.2.4
Understands the order and relative
values of whole numbers 0-20.
Identify, compare, write and order numbers
to 20
1.2.1
Understand ordinal numbers 1st to 10th
1.2.2
Count numbers 0-100 (e.g., count by
1’s, 2’s, 5’s, and 10’s)
Teacher observation
Unit test
Teacher observation
A9.Explore numerical
problems
Page 7 of 51
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
A16.Apply probability
concepts and counting rules
A1.Represent, compare and
order numbers
A2.Describe and apply
properties of numbers
1.2.3
1.2.4
A5.Use place value and write
numbers
1.2.5
A1.Represent, compare and
order numbers
2.2.1
2.2.2
2.2.3
A6.Use and interpret
operational and relational
symbols
Page 8 of 51
2.2.4
Understands a variety of
representations of whole numbers 0100 (e.g., written numerals, objects in
sets, number lines) and the relationship
among them.
Understand the relationship of
fractional parts, 1/3, 1/2, and 1/4 to a
whole.
Independent practice
Chapter test
Understand the concept of place value
through the 10’s place (e.g., the
relationship between a quantity of
physical materials grouped by 10’s and
1’s and the corresponding written
numeral)
Count numbers 0-1000 (e.g., by 1’s,
2’s, 5’s, 10’s, 100’s).
Every day counts - opening
Understands a variety of
representations of whole numbers 01000 and the relationship among them
(e.g., relating written numerals to the
corresponding word, relating objects in
sets to the corresponding numeral).
Read and write numerals 0-1000 (e.g.,
standard and expanded form).
Spiral review
Teacher observation
ILS
Chapter test
Every Day counts
Write numbers to 1000
Use variety of methods to compare and Spiral review
order whole numbers (e.g. ordinal
numbers, “first” through “twentieth”,
symbols [<, >, =] and language, such as
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
A3.Classify numbers by
dividibility
2.2.5
A5.Use place value; write
numbers in standard, expanded
and exponential form
A5.Use place value; write
numbers in standard and
expanded form
2.2.6
3.2.1
3.2.2
3.2.3
A1.Represent, compare and
order numbers
A3.Classify numbers by
divisibility
A6.Use and interpret
operational and relational
symbols
3.2.4
3.2.5
A1.Represent, compare and
order numbers
A5.Use place value; write
numbers in standard and
expanded form
B1.Use standard rounding to
Page 9 of 51
4.2.1
4.2.2
“between”, “less than”, “greater than”,
or “equal to”).
Understand physical, verbal, and
symbolic representations of the
fractions of a whole number set. (e.g.
halves, fourths, thirds, eighths
Understand concept of place value for
whole numbers through hundreds place
(e.g., ones, tens, and hundreds).
Understands the concept of place
values of whole numbers through the
ten thousand place (e.g., 1’s, 10’s,
100’s, 1000’s, 10,000’s).
Understands the concept of odd and
even numbers
Understands decimals expressed
through the hundredths place (e.g., in
money)
3.2.4a Understands the comparison of
whole numbers (e.g., to a 1000).
3.2.4b Understands the comparison of
fractions (e.g., with denominators of 12
or less).
3.2.4c Understands the comparison of
commonly used decimals (e.g.,
monetary amounts).
Count, read, and write numbers from
1,000 to 999,999.
Understand the concept of place values
for whole numbers through the
millions.
Understand the concept of rounding
Problem of the day
Every Day counts
Base ten blocks
Board work
Daily deposit
Everyday counts
Works with money
Comp Dre and order numbers
Everyday counts calendar (spring)
Math 4 today
Greater than and less than with money
Practice on dry erase boards
Use place value
Write numbers in standard, expanded and
written form through millions
Play wipe out on calculators
Use standard rounding to express numbers
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
estimate
4.2.3
4.2.4
5.2.1
A1.Represent, compare and
order numbers
A5.Use place values; write
numbers in standard and
expanded form
A2.Describe and apply
properties of numbers
A3.Classify numbers by
divisibility
5.2.2
A5.Use place value; write
numbers in standard, expanded
and exponential form
6.2.2
6.2.1
6.2.3
A1.Represent, compare and
order numbers
A6.Use and interpret
operational and relational
Page 10 of 51
6.2.4
numbers expressed through the
thousands (e.g., nearest thousand).
Compare fractions (e.g., for halves,
thirds, fourths, eighths, tenths,
sixteenths).
through the thousands by estimating
Understand the concept of proportion
and the applications of proportional
reasoning (e.g. scale, similarity,
percentage, rate).
Read, write, order, and compare whole
numbers, fractions, decimals, percents
(using concrete and pictorial models)
Solving problems with proportions, rates
and percents
Represent, compare and order fractions
using fraction strips to identify halves,
thirds, fourths, eighths, tenths and
sixteenths
Identify fractions, decimals, mixed
Recognize fractions, decimals, mixed
numbers, and whole numbers.
numbers and who numbers in math
problems
Understands equivalent forms of basic Compare percentages, fractions, and
percents, fractions, and decimals (e.g.
decimals
1/2 = 50% = .5)
Use patterns to recognize and find
equivalent fractions
Understand the concept of place value
Name, compare and order whole numbers
for numbers from the thousandths place from the hundredths place to the one
to the hundred millions place
hundred millions
Explain the relationship between decimals
and whole numbers
Understand the relationships among
Identifies prime factors of whole numbers
factors, multiples, divisors, and
Use rules of divisibility
products (e.g. prime factorization,
GCF, LCM, rules of divisibility for
2,3,4,5,6,9,10)
Understand base-ten place value for
Uses place value to work with whole
whole numbers and decimals.
numbers and decimal numbers
Compares and orders fractions
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
symbols
A5.Use place values; write
numbers in standard, expanded
and exponential form
7.2.1
Understand the characteristics and
applications of scientific notation and
exponential notation
Accurately solves expressions with
exponents
A1.Represent, compare and
order numbers
7.2.2
Understand the relationships among
fractions,
decimals, and percents.
A2.Describe and apply
properties of numbers
7.2.3
Understand the concept of prime and
composite numbers
Accurately compares and orders decimals
Correctly compares and orders fractions
with like and unlike denominators
Writes mixed numbers as improper
fractions and improper fractions as mixed
numbers
Accurately converts fractions and decimals
Converts percents to fractions and decimals
and vice versa
Uses prime factorization to find the greatest
common factor or two numbers
A1.Represent, compare and
order numbers
A3.Classify numbers by
divisibility
8.2.1
Understand the relationships among
equivalent number representations (e.g.
whole numbers, positive and negative
integers, fractions, ratios, decimals,
percents, scientific notation,
exponential)
A5.Use place values; write
numbers in standard, expanded
and exponential form
8.2.2
9-12.2.1
Page 11 of 51
Solves real world problems by using a
“guess and test” strategy
Converts rational numbers from fractions to
decimals and vice versa
Decides appropriate units of measure to
measure a variety of real world objects and
situations
Understand the basic laws of exponents Writes and evaluates expressions with
exponents
Use discrete structures (finite graphs,
matrices, sequences) to represent and to
solve problems. [Algebra II, PreCalculus, Geometry
Trans. Construct and interpret bar graphs
IM1. Use a sequence to generalize the
pattern with a variable expression
IM2-3. Use a matrix to represent a system
of equations
IM2. Use matrices to represent data sets and
use matrix operations
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
9-12.2.2
9-12.2.3
Page 12 of 51
IM2. Use matrices to represent changes in
the size or position of a polygon
IM2. Recognize when matrices can be
multiplied and find the product of two
matrices
IM2. Use a graphing calculator to find the
inverse of a matrix and use the inverse to
solve a system of equations
Understand the properties of the real
Trans. Identify number as a whole number,
number system and its subsystems
or integer
(irrational numbers, natural numbers,
IM1. Identify number as whole, integers,
integers, rational numbers) [Algebra I, rationals or irrationals
II, Pre-Calculus, General Math,
IM2. Identify real numbers and imaginary
Geometry]
number
Pass. Model integers on a number line
Pass. Find the absolute value of a number
Pass. Use divisibility tests
Pass. Factor natural numbers, integers, and
algebraic expressions
Pass. Classify natural numbers as prime or
composite
Pass. Find the greatest common factor of
two numbers or expressions
Pass. Find the least common multiple of two
numbers or expressions
Pass. Classify real numbers as rational or
irrational
Pass. Represent real numbers with a number
line
Understand the properties and basic
All. Perform operations using basic roots
theorems of roots and exponents.
and exponents
[Algebra I, II, Pre-Calculus, Geometry, IM2. Convert fractional exponents to
General Math]
radical form and vice versa
IM3. Graph and use recursion with
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
9-12.2.4
Understand appropriate use and
corresponding notation of ratios,
proportions decimals, and percents and
scientific notation. [Algebra I, General
Math, Pre-Calculus]
exponential growth and decay functions
IM3. Explore exponential functions with
negative exponents
IM3. Apply and explore the relationship
between fractional exponents and radicals
IM3. Solve exponential and log equations
and use these in real-world applications
IM3. Model real-world situations using
exponential functions with base “e”
IM3. Solve exponential and log equations
and use these in real-world applications
IM3. Apply and explore the relationship
between fractional exponents and radicals
IM1-2, App. Apply ratios and proportions
to solve similar triangle problems
Pass. Write proportions as percents
Pass. Write percents as decimals
Pass. Write decimals and percents
Pass. Write fractions as percents
Pass. Write percents as fractions
Pass. Find a percent of a number
IM2. Find the surface area and volume of
spheres, and use the fact that all spheres are
similar to solve problems
Standard 3: Use basic and advanced procedures while performing the processes of computation
ITP Indicator
A6.Use and interpret
operational and relational
Page 13 of 51
CODE
K.3.1
BENCHMARK
K.3.1a Demonstrates addition problems
with real objects
Local Indicators
Use manipulatives to represent addition or
subtraction problems
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
symbols
A7.Solve equations and
inequalities
A4.Demonstrate ways of
performing operations
A6.Use and interpret
operational and relational
symbols
A4.Demonstrate ways of
performing operations
A6.Use and interpret
operational and relational
symbols
K.3.1b Demonstrates subtraction
problems with real objects
K.3.2
Develop understanding of more, less, and
same.
Identify and compare groups of objects;
equal, more, fewer, one more, one fewer
1.3.1
1.3.1a knows basic addition facts to 10.
1.3.1b knows basic subtraction facts to
10.
Chapter test
CBM
Chapter test
CBM
1.3.2
1.3.2a Add two digit numbers with no
Independent practice
regrouping
1.3.2b Subtract two digit numbers with no Independent practice
regrouping
2.3.1
2.3.1a Knows addition facts through 20.
2.3.1b Knows subtractions facts through
20.
2.3.2a Solves two digit addition with and
without regrouping
2.3.2b Solves two digit subtraction with
and without regrouping
Understand that addition and subtraction
are inverse operations.
Knows basic multiplication fats 0-9
Math timed tests
3.3.2
Use estimating strategies to the nearest 10
or 100 (e.g. rounding/front-end).
Practice problems on board and dry erase
boards
3.3.3
Solve multi-step problems (story
Keeps a mental math journal
C1.Solve single-step and
multiple-step math problems
2.3.2
A2.Describe and apply
properties of numbers
A2.Describe and apply
properties of numbers
C1.Solve single-step and
multiple-step math problems
B1.Use standard rounding to
estimate
B3.Use number sense to
estimate
C2.Identify extraneous or
2.3.3
Page 14 of 51
3.3.1
Solves two digit problems with regrouping
Solves two digit problems without
regrouping
Knows fact families
Timed tests
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
insufficient information in
problems
A4.Demonstrate ways of
performing operations
C1.Solve single-step and
multiple-step math problems
A2.Describe and apply
properties of numbers
A4.Demonstrate ways of
performing operations
A2.Describe and apply
properties of numbers
A3.Classify numbers by
divisibility
problems, parentheses).
3.3.4
Solve addition and subtraction problems
up to 4 digit.
Practice problems on board and dry erase
boards
4.3.1
Multiply 3 digit by a two-digit number.
4.3.2
Use all four operations with money.
4.3.3
4.3.3a Knows basic division facts 1-9.
4.3.3 Divides by a 1 digit divisor with or
without a remainder
A4.Demonstrate ways of
performing operations
4.3.4
Understand the relationships and
properties of the four operations.
Demonstrate the process of how to multiply
and three digit by a two digit number
Describe and apply properties of the four
operations with the use of money
Demonstrates an understanding of basic
multiplication and division facts of one
through nine
Understand the process of starting with a
total and sharing or dividing by a one digit
divisor with our without a remainder
Timed tests
Describe and apply properties of the four
operations
A7.Solve equations and
inequalities
B2.Use order of magnitude to
estimate
B3.Use number sense to
estimate
A14.Estimate measurements
with appropriate precision
B1.Use standard rounding to
estimate
B2.Use order of magnitude to
estimate
4.3.5
Use estimation strategies (rounding/front
end).
Use different strategies of estimation
(rounding and front end) to solve problems
5.3.1
Use a variety of estimation strategies (e.g.
front-end, standard rounding, order of
magnitude, compatible numbers,
compensation) to solve and to check the
reasonableness of results of computation
problems involving whole numbers and
Give high and low estimates of products
Find greatest common factors of numbers
Page 15 of 51
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
B3.Use number sense to
estimate
decimals (e.g. money)
A2.Describe and apply
properties of numbers
A3.Classify numbers by
divisibility
A4.Demonstrate ways of
performing operations
5.3.2
5.3.2aAdd, subtract, multiple, and divide
whole numbers.
5.3.2b Add, subtract, multiply and divide
decimals
A4.Demonstrate ways of
performing operations
5.3.3
A7.Solve equations and
inequalities
5.3.4
5.3.3a Add, subtract, and simplify
fractions and mixed numbers with like
denominators.
5.3.3b Add, subtract, and simplify
fractions and mixed numbers with unlike
denominators
Use appropriate operation and method of
calculation (e.g. mental math, paper and
pencil, calculator, computer) to solve
problems and to check the reasonableness
of results
5.3.5
B1.Use standard rounding to
estimate
B2.Use order of magnitude to
estimate
B3.Use number sense to
estimate
Page 16 of 51
6.3.1
6.3.2
Define what division is and parts of a
problem (divisor, dividend and quotient)
Use a variety of estimation strategies (e.g.
powers of ten, compatible numbers,
breaking numbers apart, front-end
estimation, rounding) to solve and to
check the reasonableness or results of
computation problems involving whole
Demonstrate how to multiply a three digit
by a two digit number
Add and subtract decimals through the
hundredths place
Insert zeros in products with decimals
Use multiples, prime numbers, factors and
properties of multiplication
Divide using two digit divisors
Solve problems by choosing a calculation
method
Analyze word problems by interpreting
remainders
Solve problems by making decisions about
whether an exact answer or an estimate is
needed
Identify divisors, dividends, quotients
Uses estimation skills to find sums,
differences, products and quantities with
decimals
Estimates sums and differences of mixed
numbers
Adds and subtracts using decimals
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
A4.Demonstrate ways of
performing operations
numbers, fractions, and decimals.
6.3.2a Add, subtract, multiply, and divide
whole numbers.
6.3.2b Add, subtract, multiply, and
divide, fractions and mixed numbers.
6.3.2c Add, subtract, multiply, and divide
decimals.
6.3.3
Understand the correct order of
operations for performing arithmetic
computations.
B1.Use standard rounding to
estimate
B2.Use order of magnitude to
estimate
B3.Use number sense to
estimate
7.3.1
Use a variety of estimation strategies to
solve and to check reasonableness of
computation problems involving whole
numbers, fractions, decimals, and
percents
A3.Classify numbers by
divisibility
A4.Demonstrate ways of
performing operations
A6.Use and interpret
operational and relational
symbols
7.3.2
Page 17 of 51
Multiplies and divides whole numbers
Multiplies and divides whole numbers by
decimals and decimals by decimals
Solving problems using the four rules of
order of operations
Solves real world problems by using
estimation strategies
Uses estimation strategies to find the sum,
difference, product or quotient of a fraction
problem with proper fractions and mixed
numbers
Estimates lengths
Understands computations with whole
Correctly performs basic arithmetic
numbers, fractions, decimals, and integers operations on decimals
Accurately classifies decimals as
terminating or repeating
Uses order of operations to simplify whole
number and decimal expressions
Uses the distributive property to simplify
expressions
Performs basic arithmetic operations on
integers
Uses the order of operations to evaluate
expressions
Solves addition and subtraction problems
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
7.3.3
involving proper fractions and mixed
numbers
Solves multiplication and division problems
involving proper fractions and mixed
numbers
Uses basic conversions between fractions, Writes mixed numbers as improper
percents, and decimals.
fractions and improper fractions as mixed
numbers
Accurately converts fractions and decimals
Converts percents to fractions and decimals
and vice versa
Use a variety of estimation strategies to
Solves real world problems by working
solve and to check reasonableness of
backwards
results of computation problems
involving rational numbers.
B1.Use standard rounding to
estimate
B2.Use order of magnitude to
estimate
B3.Use number sense to
estimate
A2.Describe and apply
properties of numbers
A4.Demonstrate ways of
performing operations
A6.Use and interpret
operational and relational
symbols
8.3.1
8.3.2
Perform operations on rational numbers
(e.g. add, subtract, multiply, divide, raised
to a power, extract roots, take opposites
and reciprocals)
A4.Demonstrate ways of
performing operations
8.3.3
Understand how different algorithms
work for arithmetic computations and
operations.
Page 18 of 51
Writes and simplifies variable expressions
Correctly performs basic arithmetic
operations on integers
Uses exponents to represent products of
factors
Identify the relative size of rational numbers
by comparing and ordering pairs and groups
of rational numbers, accurately performs
arithmetic operations (add, subtract,
multiply and divide) with rational numbers
Recognizes square numbers, and find square
roots
Uses the Pythagorean theorem formulas to
find lengths of sides of right triangles
Solves one and two step equations and
inequalities using basic arithmetic
operations including combining like terms
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
9-12.3.1
a.1. Understand and apply
number properties and
operations
Page 19 of 51
9-12.3.2
8.3.4 Find percents and percent of a
number.
Add, subtract, multiply, and divide
rational expressions. [All]
Use a variety of operations on
expressions containing real numbers (e.
g., adding, subtracting, multiplying,
dividing, finding a reciprocal, raising to a
power, taking a root, taking opposites and
reciprocals, determining absolute value).
[Algebra II, I]
Solves real world problems using area and
perimeter formulas
Writes ratios and rates in a multiple of ways
All. Add, subtract, multiply and divide
fractions
IM1. Add, subtract, multiply and divide
fractions with units and scientific notation
IM1-3, Add, subtract, multiply and divide
variable expressions
Pass. Add and subtract like fractions
Pass. Add and subtract unlike fractions
Pass. Combine fractions by writing the
fractions as decimals
Pass. Multiply rational numbers
Pass. Divide rational numbers
All. Compute opposites, reciprocals and
absolute values of numbers
All. Compute exponents and basic roots
All. Add, subtract, multiply and divide real
numbers
Pass. Evaluate expressions using the four
basic number operations
Pass. Evaluate powers and square roots
Pass. Evaluate numerical expressions using
the order of operations
Pass. Evaluate variable expressions using
the order of operations
Pass. Apply the distributive property
Pass. Add two or more integers
Pass. Subtract integers
Pass. Multiply integers
Pass. Divide integers
IM1. Explore, simplify and multiply square
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
9-12.3.3
9-12.3.4
b.1. Understand and apply
concepts and procedures of
standard rounding, order of
magnitude and number sense
b.2. Evaluate reasonableness
of solutions
Page 20 of 51
9-12.3.5
roots
IM1. Factor and multiply algebraic
equations
All. Use the distributive property and order
of operations
Solve problems using proportional
App, Trans. Find percent of a number
reasoning (e.g., Finding percent and
App, Trans. Find percent of increase or
percents of a number, finding percent
decrease
increase/decrease, using data from tables App, IM1. Use scales and proportions to
and graphs, use of scale). [General Math, solve problems
Algebra I]
Pass. Solve proportions
Pass. Find what percent one number is of
another
Pass. Solve a percent equation
Pass. Find a percent of increase or decrease
Pass. Find a percent of a number
Pass. Simplify and compare fractions
Pass. Show that a number is rational
Pass. Write a decimal as a fraction
Add, subtract, multiply, divide, and
IM1. Simplify radical expressions
simplify radical expressions containing
containing whole numbers
positive rational numbers. [Algebra II]
IM2. Simplify radical expressions
containing fractions
APM. Add, subtract, and simplify
expressions containing radicals
Use a variety of approximation and
All. Check reasonableness of answers,
estimation strategies to solve and to check verify answers
reasonableness and results of a variety of IM1. Estimate measurements
problems
Pass. Round decimals while solving
equations
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
Standard 4: Understand and apply basic and advanced properties of the concepts of measurement
ITP Indicator
A12.Apply the concepts of
volume
A13. Measure weight and
volume
A12.Apply the concepts of
perimeter
A13.Measure length, distance,
and weight
A15.Identify and use
appropriate units of
measurement
A13.Measure length/distance,
time, temperature, weight,
mass and volume
A13.Measure length/distance,
Page 21 of 51
CODE
K.4.1
BENCHMARK
Recognizes value of coins and their
names.
Local Indicators
Identify and count using pennies, nickels
and dimes
K.4.2
Read and write time to the hour.
Identify, compare and tell time
K.4.3
Use and recognize parts of the calendar
K.4.4
Read a calendar to recognize days of
week, sequence of days, months, and
seasons.
Compares objects by size and weight.
1.4.1
Read and write time to the hour-half-hour
1.4.2
Count money by pennies, nickels, and
dimes
Chapter test
ILS
Independent practice
1.4.3
Demonstrate measurement using familiar
objects (weight and length).
Demonstrate measurement using familiar
objects
2.4.1
Understands time by 5 minute intervals.
Every Day counts
Uses clocks
2.4.2
Counting money using quarters and half
dollars
Every Day counts
2.4.3
Understanding temperature and how it is
Every Day counts
Explore weight and size (includes
comparing and ordering)
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
time, temperature, weight,
mass and volume
A13.Measure length/distance,
time, temperature, weight,
mass and volume
A15.Identify and use
appropriate units of
measurement
A13.Measure length/distance,
time, temperature, weight,
mass and volume
A15.Identify and use
appropriate units of
measurement
A12.Apply the concepts of
perimeter, area and volume
A13.Measure length/distance,
time, temperature, weight,
mass and volume
A14.Estimate measurements
with appropriate precision
A15.Identify and use
appropriate units of
measurement
A13.Measure length/distance,
time, temperature, weight,
mass and volume
Page 22 of 51
measured.
2.4.4
Can measure and compare length, height,
and weight.
Uses rulers
Uses balances
3.4.1
Can tell time to the nearest minute, a.m.,
and p.m.
Work with clocks to compute the time
3.4.2
Counts, writes, and computes money up to Work with play money
$5.00.
3.4.3
Measure (perimeter) length, weight, and
volume to the nearest whole unit.
Math 4 Today activities
4.4.1
Able to figure elapsed time.
4.4.2
4.2.2a Count correct change
4.2.2b Make correct change
Choose the correct method to discover the
difference between the starting and stopping
time and whether it is AM or PM
Demonstrate an understanding of counting
and giving correct amount of change
Demonstrate an understanding of counting
on in order to make correct change
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
A12.Apply the concepts of
perimeter, area and volume
A13.Measure length/distance,
time, temperature, weight,
mass and volume
A14.Estimate measurements
with appropriate precision
A15.Identify and use
appropriate units of
measurement
A13.Measure length/distance,
time, temperature, weight,
mass and volume
A15.Identify and use
appropriate units of
measurement
A12.Apply the concepts of
perimeter, area and volume
4.4.3
4.4.3 a Uses appropriate units of
measurement of length, weight, volume,
temp. in the standard system to problem
solve (ex. perimeter, area).
4.4.3b Uses appropriate units of
measurement of length,. Weight, volume,
temp. in the metric system to problem
solve (ex. Perimeter, area)
Choose correct unit of measurement to
solve a problem (time, length, weight,
volume, perimeter and area)
Use labels in the answer
Identify and use the appropriate unit of
measurement
5.4.1
Uses appropriate units of measure and
basic conversions within the same system
(dimensional analysis)
Chooses between customary or metric
systems of measurement
Can choose appropriate size of
measurement
5.4.2
Understands and applies the basic
measures of perimeter, area, volume
Find perimeter, area and volume of shapes
and solids
A13.Measure length/distance,
time, temperature, weight,
mass and volume
A13.Measure length/distance,
time, temperature, weight,
mass and volume
A14.Estimate measurements
with appropriate precision
A15.Identify and use
appropriate units of
measurement
A12.Apply the concepts of
perimeter, area and volume
5.4.3
Understands and manipulates the concept
of time (add, subtract, convert)
6.4.1
Selects and uses appropriate tools for
given measurement situations
Measures angles using a protractor
6.4.2
Understands and applies measures of
perimeter, area, volume, and
circumference
Solves problems involving perimeter
Page 23 of 51
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
A12.Apply the concepts of
perimeter, area and volume
A13.Measure volume
7.4.1
Understands and applies measures of
surface area and volume of rectangular
prisms, perimeter and area of polygons.
A15.Identify and use
appropriate units of
measurement
A13.Measure length/distance,
time, temperature, weight,
mass and volume
A14.Estimate measurements
with appropriate precision
A15.Identify and use
appropriate units of
measurement
A12.Apply the concepts of
perimeter, area and volume
7.4.2
Selects and uses appropriate tools for
given measurement situations
8.4.1
Uses multi-step dimensional analysis
when converting within a system of
measurement
Converts measurements to different units in
both customary and metric systems
8.4.2
Understands and applies measures of
perimeter, area, volume, and
circumference.
9-12.4.1
Solve real world problems involving 2and 3-dimensional measures (e.g. area,
volume, perimeter). [Geometry]
Selects and uses formulas to find areas of
geometric figures
Selects appropriate formula and use to find
surface areas and volumes of threedimensional figures (prisms, pyramids,
cylinders and cones)
Decides on appropriate strategy or strategies
to solve real world problems
IM2. Calculate volume and surface area of
a sphere
All. Calculate area and perimeter of two
dimensional figures
Pass. Build and describe polyhedrons
Pass. Identify and draw 3D solids
Pass. Find the surface area of a prism and a
cylinder
Page 24 of 51
Selects and uses formulas to find areas of
plane geometric figures (parallelograms,
triangles, trapezoids, and circles)
Uses formulas to find circumferences of
circles
Uses formulas to find surface area and
volume of prisms and cylinders
Estimates lengths
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
9-12.4.2
9-12.4.3
9-12.4.4
9-13.4.5
Solve problems involving rate as a
measure (e.g., velocity). [Algebra and
Pre-Calculus]
Determine precision and accuracy of
measurement. [Algebra I]
Use the appropriate tools or units to
determine measurement. [General Math]
Uses multi-step dimensional analysis to
convert within and between systems of
measurement
Pass. Find the volume of a prism
Pass. Find the volume of a cylinder
Pass. Find the volume of a pyramid and a
cone
Pass. Find volumes of 2 solids put together
Pass. Find the volume of a sphere
IM1. Find surface areas of prisms,
cylinders, and pyramids
IM1. Find volumes of pyramids and cones
IM1. Solve problems using d=rt
Pass. Find rate and ratios
App. Students can measure to a set
accuracy level
App. Use scales, rulers, protractors,
micrometers and meter sticks to measure
All. Convert within a system of
measurement
IM1. Solve a problem by finding the point
of intersection of two lines
Standard 5: Understand and apply basic and advanced properties of the concepts of geometry.
ITP Indicator
A10.Identiify, classify, and
compare geometric figures
CODE
K.5.1
K.5.2
Page 25 of 51
BENCHMARK
Understand geometric patterns and
relationships (similarities/differences
among basic plane figures: circles, square,
rectangle, and triangle).
Understand the common language of
spatial sense (e.g., “inside”, “outside”,
“between”, “above”, “below”, and
“behind”.
Local Indicator
Identify 2 and 3 dimensional figures;
circle, triangle, square, rectangle,
rectangular prism, pyramid, sphere, and
cube
Identify and use positional words: top,
middle, bottom, in front, behind, over,
under, on, inside, outside, left and right
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
A11.Describe geometric
properties, patterns, and
relationships
K.5.3
Understands that patterns can be made by
putting different shapes together or taking
them apart.
A10.Identiify, classify, and
compare geometric figures
A11.Describe geometric
properties and patterns
A10.Identiify, classify, and
compare geometric figures
A11.Describe geometric
properties, patterns and
relationships
1.5.1
Knows basic characteristics and properties Chapter test
of basic plane figures (e.g., a square has
ILS
four equal sides, closed vs. open figures). Performance task
2.5.1
Understand properties of and similarities
and differences among basic solid figures
(e.g., spheres, cubes, rectangular prisms,
cylinders, pyramids, and cones) and basic
geometric terms (e.g., sides, edges, and
corners) associated with these figures.
Understand what makes a figure
symmetric.
Identifies plane figures and space figures:
parallelogram, trapezoid, sphere, and
cube.
Identifies space relationships (symmetry,
congruence).
Problem of the day
Understand characteristics of line (e.g.,
parallel, perpendicular, intersecting) and
angles (e.g., right, acute, obtuse).
Understand basic properties of figures
(e.g., two or three- dimensionality,
symmetry, number of faces, type of
angle).
Know basic geometric language for
Identify the different angles by
understanding the characteristics of lines
2.5.2
A10.Identiify, classify, and
compare geometric figures
3.5.1
A11.Describe geometric
properties, patterns, and
relationships
A10.Identiify, classify, and
compare geometric figures
3.5.2
A11.Describe geometric
properties, patterns, and
relationships
4.5.2
4.5.1
4.5.3
Page 26 of 51
Use a variety of manipulatives
Problem of the day
Every Day counts calendar
Make faces out of paper, fold and cut to
show symmetry, sides, flips and turns
Describe geometric properties, patterns
and relationships
Use geoboardes
Identify, classify and compare shapes by
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
4.5.4
describing and naming shapes (e.g.,
trapezoid, parallelogram, cube, sphere,
and polygon).
Understand basic geometric
transformations in a plane and the
relationships among transformed figures
(e.g., symmetry, congruency, similarity,
slide flip and turn).
Understands the characteristics of
(classification) and relationships among
(symmetry, congruence) points, lines, line
segments, rays, planes, and polygons.
A10.Identiify, classify, and
compare geometric figures
A11.Describe geometric
properties, patterns and
relationships
5.5.1
A10.Identiify, classify, and
compare geometric figures
A11.Describe geometric
properties, patterns and
relationships
A10.Identiify, classify, and
compare geometric figures
A11.Describe geometric
properties, patterns and
relationships
6.5.1
Understands the characteristics of
(classification) and relationships among
(parallel, perpendicular, congruence)
lines, angles, polygons and circles.
7.5.1
Understands the characteristics of
(classification) and relationships among
(parallel, perpendicular, congruence)
lines, angles, polygons, circles,
trapezoids, parallelograms, triangles
A10.Identiify, classify, and
8.5.1
Understands the characteristics of
Page 27 of 51
using appropriate geometric language
Flips, sides and turns
Use geoboards
Explain the difference between
congruence and symmetry
Recognize and classify quadrilaterals and
triangles
Count edges and faces on geometric
shapes and solids
Measure angles using a protractor
Identifies right, obtuse and acute angles
Classifies lines and angles
Identifies types of quadrilaterals and
polygons
Correctly classifies and measures angles
Correctly classifies triangles by their sides
and angles
Accurately identifies corresponding sides
and angles in congruent triangles
Correctly classifies polygons and
quadrilaterals
Accurately identifies parts of a circle
(chords, radii, diameter)
Selects and uses formulas to find areas of
plane geometric figures (parallelograms,
triangles, trapezoids and circles)
Identifies geometric figures and their parts
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
compare geometric figures
A11.Describe geometric
properties, patterns and
relationships
(classification) and relationships among
quadrilaterals, triangles, and circles.
(types of triangles, quadrilaterals and
other polygons)
Page 28 of 51
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
a.3. Understand and apply
concepts of geometry and
measurement
Page 29 of 51
9-12.5.1
Understand and use inductive and
deductive reasoning to make observations
about and to verify properties of and
relationships among figures (e.g., the
relationship among interior angles of
parallel lines cut by a transversal).
[Geometry]
All. Use inductive reasoning to make
conjectures about polygons
IM2. Use deductive reasoning to probe
angle and triangle relationships
IM1. Use inductive and deductive
reasoning to investigate the relationships
among the length of the sides of right
triangles
IM2. Write proofs using properties of
algebra
IM2. Use postulates, definitions, given
information, and proven theorems to write
proofs about angles
IM2. Write proofs for properties of
parallel lines
IM2. Apply converses of parallel lines
theorems in proofs
IM2. Explore angles related to triangles
and quadrilaterals and apply this
information to numerical problems
IM2. Use SSS, SAS, AAS, and ASA to
prove triangles are congruent
IM2. Apply properties of isosceles and
equilateral triangles
IM3. Find the interior and exterior angles
of polygons
IM3. Explore polygons inscribed in a
circle (central angles, arcs, chords)
IM3. Investigate and apply the
relationships between inscribed angles
and arcs of circles
IM3. Explore the relationships between
circumscribed polygons and inscribed
circles
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
9-12.5.2
9-12.5.2a Know and use the Pythagorean
Theorem and its converse to solve
mathematical and real-world problems.
[Geometry, Algebra]
9-12.5.2b Know and use the properties of
special right triangles (e.g., 30-60-90
degree right triangles) to solve
mathematical and real-world problems
(Geometry and Algebra)
9-12.5.3
Use properties of figures to solve
mathematical and real-world problems
(e.g., use understanding of arc and
properties of circles to interpret
information in circle graphs). [Geometry]
9-12.5.4
Use geometric constructions (e.g., the
parallel to a line through a given point not
on the line, line segment congruent to a
given line segment) to complete simple
proofs, to model, and to solve
mathematical and real-world problems.
[Geometry]
Understand that objects and relations in
geometry correspond directly to objects
and relations in algebra (e.g., a line in
9-12.5.5
Page 30 of 51
IM2. Review Pythagorean theorem
APM. Understand and know how to use
the Pythagorean Theorem
All. Use Pythagorean theorem and its
converse to solve real world problems
IM2. Use properties of special right
triangles to solve real world problems
Pass. Use the Pythagorean theorem
IM2. Identify similar right triangles and
apply right triangle theorems
IM2. Find the geometric mean between
two numbers
IM2. Use trigonometry and properties of
special right triangles to find angle
measures and segment lengths
IM1. Use properties of circles to interpret
information in circle graphs
IM1. Apply angle relationships found by
intersecting lines, in circles and triangles
IM1. Investigate, write and graph
equations for horizontal and vertical lines
IM1. Graph linear inequalities
IM2. Apply the properties of similar
triangles
IM1-3. Translate between tables,
equations and graphs
IM1. Write expressions for measures of
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
geometry corresponds to a set of ordered
pairs satisfying an equation of the form
ax+by =c) [Geometry, Algebra II]
Page 31 of 51
9-12.5.6
To understand and use geometric
transformations and their properties to
solve problems. [Geometry, Pre-Calculus]
9-12.5.7
Understand the basic concepts of right
triangle trigonometry (e.g., basic trig
ratios, such a sine, cosine, and tangent)
and use trigonometric ratio methods to
solve mathematical and real-world
problems. [Pre-Calculus]
geometric figures
IM2. Explain and use the relationships
between the slopes of parallel and
perpendicular lines
IM2. Describe characteristics of
quadrilaterals and develop classification
skills
IM2. Use the formula for slope and
distance to explore quadrilaterals and their
properties on the coordinate plane
IM2. Use the formula for midpoint of a
segment in a variety of situations
IM1. Identify transformations and
symmetry
IM2-3. Use transformations to solve real
world problems
IM1. Translate figures in a coordinate
plane
IM1. Rotate figures in a coordinate plane
and on polar graph paper
IM1. Explore properties of similar
polygons
IM1. Enlarge or reduce a figure
IM1. Draw a mirror image of object,
explore reflections
IM2. Use right triangle trigonometry
IM1. Investigate right triangle ratios
IM2. Use trigonometry and properties of
special right triangles to find angle
measures and segment lengths
IM3. Use the law of cosines to solve realworld problems
IM3. Use the law of sines to solve realworld problems
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
Page 32 of 51
9-12.5.8
Describe and use relationships among
figures to solve mathematical and realworld problems (e.g., congruent and
similar polygons, parallel and
perpendicular lines). [Geometry]
9-12.5.9
Understand the characteristics and uses of
vectors (e.g., representations of velocity
ad force) and basic operations on vectors
(e.g., vector addition, scalar
multiplication). [Pre-Calculus]
IM3. Use the law of sines to solve real
world problems
IM3. Use the law of cosines to solve real
world problems
APM. Use ratios for the sine, cosine and
tangent to solve right triangle problems
IM1. Recognize graphs and everyday
relationships that represent functions
IM1. Explore area formulas using
manipulatives
IM1. Find and compare corresponding
lengths, areas, and volumes of similar
figures using ratios
IM2. Find the surface area and volume of
spheres, and use the fact that all spheres
are similar to solve problems
IM2. Model real world situations in which
one quantity is proportional to the square
or cube of another quantity
IM3. Convert polar coordinates to
rectangular coordinates and vise verse,
and find the sin,cos and tan of any angle
IM3. Solve real-world problems using
graphic representations of vectors
IM3. Solve real-world problems using
vectors in rectangular form
IM3. Solve real-world problems by using
pairs of equations in parametric form
IM3. Locate points in a plane using polar
coordinates and bearing
IM3. Convert polar coordinates to
rectangular coordinates and vise verse,
and find the sin, cos and tan of any angle
IM3. Solve real-world problems using
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
9-12.
5.10
Compare, describe, and analyze two-and
three-dimensional figures and their
intersections with a plane. [Geometry,
Pre-Calculus]
graphic representations of vectors
IM3. Solve real-world problems using
vectors in rectangular form
IM3. Solve real-world problems by using
pairs of equations in parametric form
IM3. Investigate properties of 3-D figures
Standard 6: Understand and apply basic and advanced concepts of statistics and data analysis
ITP Indicator
CODE
K.6.1
D1.Read amounts on scales of
bar and line graphs
D2.Locate amounts in specific
cells of a table
D3.Compate quantities
D4.Use tables and graphs to
generalize and draw
conclusions
D1.Read amounts on scales of
bar and line graphs
D2.Locate amounts in specific
cells of a table
D3.Compate quantities
D4.Use tables and graphs to
generalize and draw
conclusions
K.6.2
Page 33 of 51
1.6.1
BENCHMARK
Collects and displays data using charts
and graphs.
Interprets graphs (bar and pictograph).
Local Indicator
Demonstrate the use of graphing; line, bar,
tally, picture
Demonstrate the use of graphing; line, bar,
tally, picture
Collect, organize, interpret data, and
make predictions using simple charts,
tables, and graphs.
Chapter test
ILS
Performance task
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
D2.Locate amounts in specific
cells of a table
D3.Compare quantities to
determine ranks, sums, or
differences
D1.Read amounts on scales of
bar and line graphs
D4.Use tables and graphs to
determine rates or identify
trends, understand underlying
or functional relationships, and
generalize or draw conclusions
D1.Read amounts on scales of
bar and line graphs
2.6.1
Collects and organizes data on tables,
graphs, and charts.
Class graphs
2.6.2
Reads and interprets tables, graphs, and
charts.
Class graphs
3.6.1
D1.Read amounts on scales of
bar and line graphs
D2.Locate amounts in specific
cells of a table
D3.Compate quantities to
determine ranks, sums, or
differences
D4.Use tables and graphs to
determine rates or identify
trends, understand underlying
or functional relationships, and
generalize or draw conclusions
D1.Read amounts on scales of
bar and line graphs
D2.Locate amounts in specific
cells of a table
D1.Read amounts on scales of
bar and line graphs
D3.Compate quantities to
3.6.2
Collect and organize data into graphs
Graph temperature in journals (daily)
(bar, line, pictographs, circle), tables, and
charts.
Read and make simple inferences from
Make decisions about temperature using the
data displayed in diagrams, charts, bar
temperature graph from the journal
graphs, and tables (e.g., generalize or
draw simple conclusions).
Page 34 of 51
4.6.1
Read and interpret simple tables, graphs
(e.g., simple bar, line, and charts (e.g.
pie)
Constructs or interprets simple bar, line and
picto graphs
4.6.2
Use line, circle, and bar graphs with
various scale increments to display
information.
Recognize that data represents specific
pieces of information, may have different
scale increments to display this information
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
determine ranks, sums, or
differences
D4.Use tables and graphs to
determine rates or identify
trends, understand underlying
or functional relationships, and
generalize or draw conclusions
Halloween and birthday graphs
4.6.3
D1.Read amounts on scales of
bar and line graphs
D2.Locate amounts in specific
cells of a table
D3.Compate quantities to
determine ranks, sums, or
differences and to find ratios
5.6.1
5.6.2
A17.Understand and apply
measures of central tendency
and variability
D1.Read amounts on scales of
bar and line graphs
D2.Locate amounts in specific
cells of a table
D3.Compate quantities to
determine ranks, sums, or
differences and to find ratios
D4.Use tables and graphs to
determine rates or identify
trends, understand underlying
or functional relationships, and
generalize or draw conclusions
A17.Understand and apply
Page 35 of 51
6.6.1
7.6.1
Understands appropriate measures of
central tendency
Use graphs and plots to display
information
Find mean, median and mode
Find range
Draw conclusions and make predictions from
information on a graph
Use a bar graph to compare information
Use coordinates to make a line graph
Read a pictograph for information
Understands appropriate measures of
central tendency (mean, median, mode)
Read and interpret tables, graphs, and
charts
Can find mean, median and mode
Reads graphs of four types: bar, pictograph,
line and circle
Uses appropriate scales and intervals in
making bar graphs
Understand appropriate measures of
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
measures of central tendency
and variability
D1.Read amounts on scales of
bar and line graphs
D2.Locate amounts in specific
cells of a table
D3.Compate quantities to
determine ranks, sums, or
differences and to find ratios
D4.Use tables and graphs to
determine rates or identify
trends, understand underlying
or functional relationships, and
generalize or draw conclusions
A17.Understand and apply
measures of central tendency
and variability
D1.Read amounts on scales of
bar and line graphs
D2.Locate amounts in specific
cells of a table
D3.Compate quantities to
determine ranks, sums, or
differences and to find ratios
D4.Use tables and graphs to
determine rates or identify
trends, understand underlying
or functional relationships, and
generalize or draw conclusions
d.2. Interpret data from a
variety of sources
Page 36 of 51
statistics, (e.g. mean, median, mode, and
range)
7.6.2
Make comparisons, predictions and
inferences from data in a variety of
formats
Solves real world problems by making a
table
Solves real world problems by finding a
pattern
Solves real world problems by using a
“guess and test” strategy
8.6.1
8.6.2
9-12.6.1
Use appropriate format for organizing
and displaying statistical data
Understand faulty arguments, common
errors, and misleading presentations of
data
9-12.6.1.a Understands and applies basic
concepts of data collection, data analysis,
and distribution. [Pre-Calculus and
Algebra II]
9-12.6.1b Understands and applies
advanced concepts of data collection,
data analysis, and distribution (PreCalculus and Algebra II)
Organizes and displays data graphically
Determines central tendency values from a
set of data (mean, median and mode)
Displays data in a variety of plots and graphs
Determines appropriate ways to display
information from real world data
Finds solutions to real world questions by
reading and analyzing graphs
IM1. Makes appropriate predictions based on
tendencies indicated by real world data
displayed in scatter plots, circle and bar
graphs
IM1. Determines appropriate way to display
information from real world data
IM1. Recognize when data displays give
misleading impressions
APM. Apply logical reasoning to
interpreting graphs and tables
in reasoning
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
IM2. Use a survey of part of a population to
predict results for the entire population
IM2. Recognize different ways to select a
sample
IM2. Recognize factors that influence
statistics and survey results
IM2. Model real life situations with
equations
IM2. Classify expressions
IM2. Use rules of exponents to simplify
expressions
d.1. Make inferences based on
data presented in a variety of
ways
9-12.6.2
Understands appropriate methods for
using data to make predictions (trends,
surveys, samples). [Algebra I, II, and
Pre-Calculus]
a.4. Understand and apply
concepts in probability and
9-12.6.3
Selects and uses the best method of
representing and describing a set of data
Page 37 of 51
IM3. Explore and analyze types of frequency
distributions
IM3. Explore the effect of adding a constant
to a data set
IM3. Explore the effect of multiplying each
data value by a constant
IM3. Find the expected average gain or less
in a real-world situation
IM3. Find the expected average gain or loss
in a real-world situation
IM3. Use standardized values and the normal
distribution of compare real-world data
IM1. Collect real world data and analyze it
IM1. Investigate and model sampling
techniques
Pass. Use tables and graphs to organize data
Pass. Use tables and graphs to solve
problems
APM. Be able to make conjectures and form
conclusions given a set of data
IM1. Display and interpret data using
histograms, frequency tables and stem and
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
statistics
(e.g., scatter plot, line graph, two-way
table). [Algebra I, II, Geometry, General
Math, and Pre-Calculus]
9-12.6.4
Page 38 of 51
Understands measures of central
tendency and variability (e.g., standard
deviation, range, quartile deviation) and
their applications to specific situations.
[Pre-Calculus, Algebra II, General
Math]
leaf plots
IM1. Model situations and solve simple
equations spreadsheets, tables, graphs,
equations and technology
Pass. Apply the distributive property
Pass. Simplify expressions by adding like
terms
Pass. Check that a number is a solution of an
equation
Pass. Use addition or subtractions to solve an
equation
Pass. Use multiplication or division to solve
an equation
Pass. Translate verbal phrase into algebraic
expressions
Pass. Use a table of values to sketch and
graph of a linear equation
IM3. Use systematic lists to organize data
IM3. Use statistics to reach conclusions via
line graphs, scatter plots, etc.
IM3. Use statistics to reach conclusions via
line graphs, scatter plots, etc.
APM. Know the parts of a right triangle
IM3. Use technology and compute the mean
and standard deviation of a data set
IM3. Explore and apply properties of normal
distributions
IM3. Use technology to find least-squares
line and median-median lines
IM3. Use standardized values and the normal
distribution to compare real-world data and
find percentiles
IM3. Use technology to compute the mean
and standard deviation of a data set
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
IM3. Use technology to find least-squares
line and median-median lines
APM. Calculate mean, median and mode
from a set of data
Standard 7: Understand and apply basic and advanced concepts of probability.
ITP Indicators
A16.Apply probability
concepts and counting rules
A14.Estimate measurements
with appropriate precision
A16.Apply probability
concepts and counting rules
A17.Understand and apply
measure of central tendency
and variability
CODE
1.7.1
2.7.1
2.7.2
3.7.1
A1.Represent, compare and
order numbers
A16.Apply probability
concepts and counting rules
A16.Apply probability
concepts and counting rules
Page 39 of 51
3.7.2
4.7.1
BENCHMARK
Understands that some events are certain
and others are impossible.
Understands the basic concepts of likely
and unlikely outcomes.
Local Indicators
Teacher Observaiton
Understands that some events can be
predicted fairly well, but others cannot
because we do not always know
everything that may affect an event.
Understands that some events are sure to
happen, some events are sure not to
happen, and some events may or may not
happen.
Understands that the word “chance” refers
to the likelihood of an event.
Predicts outcome of simple experiments
Determine the probability of simple
events using basic experiments or
Make predictions based on situations
presented
Can estimate
Every Day counts exploration of patterns
Make a table of likely and unlikely events
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
4.7.2
A16.Apply probability
concepts and counting rules
D4.Use tables and graphs to
determine rates or identify
trends, understand underlying
or functional relationships,
and generalize or draw
conclusions
A16.Apply probability
concepts and counting rules
5.7.1
6.7.1
6.7.2
A16.Apply probability
concepts and counting rules
Page 40 of 51
7.7.1
simulations (e.g., using coins, spinners,
and dice).
Use basic sample groups (e.g., all possible
outcomes) to describe events.
Use a variety of simple models (tree
diagrams, sample spaces, grids, tables) to
represent the possible outcomes for
probability situations.
Draw conclusions and make predictions
from simple probability situations
Determine probability using simulations
or experiments
Determine probability using
math/theoretical models
7.7.2
Understand the concepts of combinations
and permutations
7.7.3
Understand how predictions are based on
data and probabilities
Predicts results of probability situations
Uses simulations to find experimental
probability
Solves real world problems by using
simulations
Solves to find the theoretical probability of
an event
Uses a sample space to list the set of all
possible outcomes
Uses the counting principle to find the
number of outcomes
Solves to find the probability of
independent and dependent events
Uses permutations to find all the
arrangements of items in a group
Uses combinations to find the number of
arrangements when order does not matter
Estimates the size of a population using the
capture/recapture method
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
A16.Apply probability
concepts and counting rules
8.7.1
A16.Apply probability
concepts and counting rules
8.7.2
a.4. Understand and apply
concepts of probability and
statistics
9-12.7.1
Understands the basic concepts of
probability and applies them to real-world
situations. [Algebra II, I, Pre-Calculus,
General Math]
9-12.7.2
Understands the differences among
experimental, simulation, and theoretical
probability techniques and uses the
appropriate method to determine
probabilities. [Pre-Calculus, Algebra I, II,
General Math]
9-12.7.3
Determines the probability and
understands the concepts of independent
Page 41 of 51
Understand that the measure of certainty
in a given situation depends on a number
of factors (sample size, method of data
collection, what is known about the
situation, how current data are)
Understand the difference between
theoretical and experimental probability
Makes appropriate assessments of surveys
using real world sampling situations
Evaluates and assesses real world situations
to determine if there is too much or too little
information
IM1. Theoretically and experimentally
explore probability
IM2. Find the probability of an event and/or
of mutually exclusive events
IM2. Relate probability to odds
IMJ3. Perform experiments using random
numbers
IM3. Perform experiments using random
numbers
Understands the differences between
experimental and theoretical probability
techniques and uses the appropriate method
to determine probabilities.
IM1. Recognize direct variation graphs
IM2. Use an experiment to simulate the
results of a survey and to estimate
probabilities
IM2. Calculate the odds of winning one of
the Iowa lottery games and make a decision
as to the intelligence of playing the game
IM3. Find the probability of either of two
events happening
IM3. Find the probability of either of two
events happening
IM2. Find the probability of independent
and/or dependent events
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
and dependent events. [Algebra I, II, PreCalculus, General Math]
Counting techniques
9-12.7.4
Page 42 of 51
IM3. Draw a tree diagram to find the
probability under restricted conditions
APM. Find the probability of a single event,
mutually exclusive events, dependent and
independent events
IM3. Explore probabilities in a binomial
experiment
IM2. Use tree diagrams, tables or systematic
lists to count outcomes, choices and
possibilities
IM2. Use the multiplication counting
principle to find the number of different
arrangements of a group of items
IM2. Find the number of ways to select
some items from a group
IM2. Use a calculator to calculate
combinations, permutations and factorials
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
Standard 8: Understand and apply basic and advanced properties of functions and algebra.
ITP Indicators
C1.Solve single-step and
multiple-step math problems
CODE
K.8.1
BENCHMARK
Extend and create simple repeating
patterns (e.g., with physical objects,
geometric shapes).
Local Indicators
Identify, extend and create patterns
A7.Solve equations and
inequalities
1.8.1
Understand simple repeating and growing
patterns.
Performance task
Teacher observation
1.8.2
Solve simple open sentences involving
addition and subtraction to 12.
1.8.3
Understand that regularities exist in a
variety of contexts (e.g., events, designs,
shapes, sets of numbers).
Understand and extend a wide variety of
patterns (linear and non-linear).
Chapter test
ILS
Independent practice
Independent practice
Teacher observation
A9.Explore numerical patterns
2.8.1
C1.Solve single-step and
multiple-step math problems
C2.Identify extraneous or
insufficient information in
problems
C3.Chose a method for solving
a problem
2.8.2
Understand basic number patterns (skip
counting).
Skip counts
2.8.3
Use variables (e.g., letters, boxes, or other
symbols) and number sentences to
represent solutions to problems (e.g.
7+N=23).
Solve simple number sentences involving
addition and subtraction (e.g., sentences
involving one or both operations).
Solve number sentences involving basic
Solves story problems
A7.Solve equations and
inequalities
2.8.4
A3.Classify numbers by
3.8.1
Page 43 of 51
Every Day counts
Solves number sentences
Use manipulatives to create multiplication
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
divisibility
C1.Solve single-step and
multiple-step math problems
A9.Explore numerical patterns
A8.Use variable expressions to
model situations
A7.Solve equations and
inequalities
3.8.2
3.8.3
3.8.4
4.8.1
4.8.2
A8.Use variable expressions to
model situations
A9.Explore numerical patterns
4.8.3
4.8.4
multiplication and division facts.
and divisions sentences
Understand the concepts “elements” and
“repetitions” in a pattern (e.g. ABB, ABB
has three elements and two repetitions).
Use a variety of methods and tools to
represent patterns and relationships.
Understand the concept of an equation
(e.g., a number sentence that shows two
quantities that are equal).
Solve open sentences involving
multiplication and division (N+17=23).
Use symbols of equality (=) and
inequality (<, >).
Every Day counts calendar
Understand that the same pattern can be
represented in different ways (e.g., using
words, pictures, and numbers).
Understand the characteristics and
features of coordinates and the coordinate
plane (e.g. the horizontal axis and vertical
axis).
Identify patterns and explain the rule that
the pattern is generated from.
A9.Explore numerical patterns
5.8.1
A7.Solve equations and
inequalities
A8.Use variable expressions to
model situations
A7.Solve equations and
inequalities
6.8.1
Solve simple (addition, subtraction)
equations with one variable using
informal or formal methods.
7.8.1
Understands basic algebraic terms and
symbols (e.g. equation, inequality,
Page 44 of 51
Every Day counts calendar
Math 4 Today activities
Demonstrate knowledge of fact families and
inverse properties
Demonstrate ways to interpret operational
and relational symbolism problems with <,
>, or +
Show that patterns can be displayed
differently (draw a picture, explain in
words)
Show location of specific coordinates on
horizontal and vertical axis
Use division patterns to find quotients
Use patterns in multiplying decimals
Create a pattern and present the pattern to a
group
Writes and solves equations
Evaluates and writes variable expressions
Correctly writes equations
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
variable, exponent)
D4.Use tables and graphs to
determine rates or identify
trends, understand underlying
or functional relationships, and
generalize or draw conclusions
A7.Solve equations and
inequalities
A7.Solve equations and
inequalities
A8.Use variable expressions to
model situations
C1.Solve single-step and
multiple-step math problems
Page 45 of 51
7.8.2
8.8.1
Solves expressions using variables
Use a coordinate grid for a variety of
representations (e.g., number, figures,
points, lines)
8.8.2
Solve simple inequalities with rational
number solutions, using concrete and
informal methods.
8.8.3
Solve two-step equations of one variable
using informal and formal methods.
Accurately solves expressions with
exponents
Evaluates and writes variable expressions
Graphs points in a coordinate plane
Solves one and two step equations and
inequalities using basic arithmetic
operations including combining like terms
Writes and graphically displays inequalities
on number lines
Uses a variety of strategies to plot solutions
to linear equations (plotting ordered pairs,
using slope-intercept)
Solves one and two step equations and
inequalities using basic arithmetic
operations including combining like terms
Solves real world problems by writing and
solving equations
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
a.2. Understand and apply
concepts and procedures of
algebra
Page 46 of 51
9-12.8.1
9-12.8.1bUnderstand properties of linear
graphs and the relationships between a
graph and its corresponding expression
(e.g., maximum and minimum points,
slopes, intercepts). [Algebra I, II,
Geometry, Pre-Calculus]
9-12.8.1b Understand properties of
nonlinear graphs and the relationships
between a graph and its corresponding
expression (e.g., maximum and minimum
points, slopes, intercepts). (Algebra I,II,
Geometry, Pre-Calculus)
IM1. Explore and apply direct variation,
slope and tangent
IM1. Use direct variation models to make
predictions and find the slope of a line
IM1. Find circumference of circles and arc
lengths
IM1. Recognize direct variation graphs
Pass. Recognize graphs of horizontal and
vertical lines
Pass. Find slope of a line from a graph
Pass. Find the slope and y-intercept form to
sketch a quick graph
IM2. Recognize and interpret graphs of
functions, including growth and decay of
graphs
IM2. Find the domain and range of a
function
IM2. Review linear functions, slope of a
line, and direct variation
IM2, Solve systems of linear equations by
graphing and graph systems of linear
inequalities
IM3. Locate the maximum and/or minimum
using formulas, graphs and network
diagrams
IM3. Model and solve real-world problems
using linear programming
IM3. Graph equations used to model realworld problems
IM3. Solve systems of linear and real-world
problems using algebra, graphs, and
matrices
IM3. Model and solve real-world problems
using linear programming
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
9-12.8.2
Page 47 of 51
Understand the general properties and
characteristics of many types of basic
functions and their corresponding graphs
(e.g., notation and terminology of linear,
quadratic, step, absolute value). [Algebra
I, II]
Pass. Find intercepts of lines
Pass. Find the distance between two points
Pass. Find the midpoint of a line segment
IM1. Investigate, write and graph equations
for horizontal and vertical lines
IM2. Explore hyperbolas and model real
world situations involving constant products
IM2. Graph quadratic functions using
technology
IM2. Find the vertex, line of symmetry and
intercepts of a parabola
IM2. Explore translations of parabolas
IM2. Solve simple quadratic equations by
graphing and undoing
IM2. Solve the assigned homework
problems relating graph analysis to a career
IM2. Use a graphing calculator to graph
functions
IM2. Graph quadratic functions using
graphing calculators
IM2. Use graphing calculators to observe
how changes in an equation affect the graph
of a parabola
APM. Find the slope of a graphed line
APM. Find the intercepts of a graphed line
IM1. Explore ways to represent functions
IM1. Explore, multiply and simplify square
roots
IM2. Model exponential growth and decay
using tables, graphs and equations
IM3. Represent functions using graphs,
tables and equations
IM3. Find the domain, range and equation
of a linear function
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
IM3. Write, graph and apply piecewise and
absolute value functions
IM3. Graph quadratic functions involving
real-world problems
IM3. Write, evaluate and apply direct
variation functions and polynomials
IM3. Explore, solve and apply functions
involving radicals
IM3. Evaluate, graph and apply rational
functions
IM3. Explore and apply functions formed
by combining two functions
IM3. Graph quadratic functions involving
real-world problems
IM3. Write, evaluate and apply direct
variation functions and polynomials
IM3 Explore, solve and apply functions
involving radicals
IM3. Evaluate, graph and apply rational
functions
IM3. Use technology and matrices to find
quadratic models for data
IM3. Use technology and matrices to find
quadratic models for data
9-12.8.3
9-12.8.4
Page 48 of 51
Understand the general properties and
characteristics of many types of
trigonometric functions and their
corresponding graphs (e.g., sine, cosine).
[Pre-Calculus
Understand the general properties and
characteristics of many types of advanced
functions and their corresponding graphs
(e.g., exponential, logarithmic). [PreCalculus]
IM2. Model exponential growth and decay
using tables, graphs and equations
IM3. Model real-world situations using
exponential functions with base “e”
IM3. Recognize when a function has an
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
inverse, and if it does, fin and graph it
IM3. Explore the relationship between
exponential functions and log functions
IM3. Simplify and evaluate log expressions
IM3. Recognize when a function has an
inverse, and if it does, find and graph it
Page 49 of 51
Mathematics Alignment Results – November 5, 2003
Humboldt Community Schools Mathematics Core Curriculum
9-12.8.5
Page 50 of 51
IM1. Simplify variable expressions and
solve simple equations
IM1. Use algebra tiles to solve equations
with the variable on both sides
IM1. Rewrite algebraic and geometric
equations in simplest form
IM1. Solve equations using reciprocals
Pass. Find solutions of a linear equation
with two variables
IM2. Solve systems of linear equations by
graphing and graph systems of linear
inequalities
IM2. Solve systems of linear equations by
substitution
IM2. Solve systems of equations by
addition and choose a method for solving a
specific system of inequalities
IM2. Solve simple quadratic equations by
graphing and undoing
IM2. Solve quadratic equations by factoring
IM2. Use the quadratic formula to solve
quadratic equations and real world problems
IM2. Use the discriminant to find the
number of real solutions of a quadratic
equation
IM2. Apply systems to solve real world
problems to decide the best economic plan
IM2. Use a graphic calculator to find the
inverse of a matrix and use this to solve a
system
IM3. Graph equations used to model realworld equations
IM3. Solve systems of linear and real-world
problems using algebra, graphs and matrices
IM3. Graph equations used to model realworld problems
APM. Solve linear systems by graphing
Mathematics Alignment Results – November 5, 2003
Use a variety of methods (e.g. with
graphs, algebraic methods, and matrices)
to solve linear and quadratic equations
[Algebra I, II, Pre-Calculus
Uses a variety of methods(e.g., with
graphs, algebraic methods, and matrices)
to solve linear inequalities (Algebra I, II,
Pre-Calculus)
Uses a variety of methods (e.g., with
graphs, algebraic methods, and matrices)
to solve systems of equations and
inequalities (Algebra I, II, Pre-Calculus)
Humboldt Community Schools Mathematics Core Curriculum
9-12.8.6
9-12.8.7
Page 51 of 51
Understand the basic concept of complex
numbers (e.g. conjugate) [Algebra II, PreCalculus]
Understand various applications
(compound interest) of formal notation
(e.g., sigma notation, factorial
representation). [Pre-Calculus]
IM1. Rewrite and solve simple inequalities
IM1. Find area of circles and sectors
Pass. Graph an inequality
Pass. Write equivalent inequalities
Pass. Use multiplication and division to
solve inequalities
Pass. Solve multi-step inequalities
IM1. Solve pairs of two-variable equations
using substitution
IM1. Use dimensional analysis to solve
everyday problems
IM2. Add, subtract, and multiply complex
numbers
IM3. Write and apply formulas for
sequences in which each term is found by
using the preceding term(s)
IM3. Write and apply explicit and recursive
formulas for sequences
IM3. Find the sum of a finite arithmetic
series
IM3. Find the sum of a finite geometric
series
IM3. Recognize when an infinite series has
a sum and if it does, find it
IM3. Write and apply formulas for
sequences related to algebraic, geometric,
and everyday situations
IM3. Write and apply explicit and recursive
formulas for sequences
IM3. Recognize when an infinite series has
a sum and it if does, find it
Mathematics Alignment Results – November 5, 2003