APS District Curriculum Map
8 ESSENTIAL COMPONENTS
1. Performance Standards
Algebra 1
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Month: August
Strand II
Benchmark A
1. Classifies numbers and members of the following sets (NM – IA.1):
 natural,
 whole,
 integers,
 rationals, and
 irrationals.
2. Simplifies numerical expressions using the order of operations,
including exponents (NM – IA.2).
3. Evaluates the numerical value of expressions of one or more variables
that are (NM – IA.3):
 polynomial,
 rational, and
 radical.
6. Represents and analyzes relationships using written and verbal expressions, tables, equations, and
graphs, and describes the connections among those representations to (NM – IA.6):
 translates from verbal expression to algebraic formulae
(e.g., “Set up the equations that represent the data in the
following equation: John’s father is 23 years older than John.
John is 4 years older than his sister Jane. John’s mother is
3 years younger than John’s father. John’s mother is 9 times
as old as Jane. How old are John, Jane, John’s mother, and
John’s father?”),
(e.g. twenty-four divided by the um of three and five;  24 – (3 +5) 
7. Knows, explains, and uses equivalent representations for the same real number including (NM – IA.7):
 integers,
 decimals,
 percents,
 ratios,
 scientific notation,
 numbers with integer exponents,
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APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
 inverses (reciprocal), and
 prime factoring.
8. Simplifies algebraic expressions using the distributive property
(NM – IA.8).
9.
Explains and uses the concept of absolute value (NM – IA.9).
16. Uses the four basic operations (+, -, x, ÷) with (NM – IA.17):
 linear expressions,
 polynomial expressions, and
 rational expressions.
Benchmark B
18. Describes the concept of a graph of a function (NM – IB.3).
19. Translates among tabular, symbolic, and graphical representations of functions (NM – IB.4).
Benchmark C
1. Uses a variety of computational methods (e.g., mental arithmetic, paper
and pencil, technological tools) (NM – IC.2).
34. Understands and uses (NM – IC.11):
 such operations as taking the inverse, finding the reciprocal, taking a root, and raising to a
fractional power, and
 the rules of exponents.
Strand IV
Benchmark B
1. Understands the meaning of measurement data and categorical data, and
of the term “variable” (NM – IIIB.1)
2.
Understands the meaning of “univariate” (i.e., one variable) and
“bivariate” (i.e., two variable) data (NM – IIIB.2).
5. Draws conclusions concerning the relationships among bivariate data (NM – IIIC.2):
 makes predictions from a linear pattern in data,
 determines the strength of the relationship between two sets of data by examining the
correlation, and
understands that correlation does not imply a cause-and-effect relationship.
Algebra 1
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APS District Curriculum Map
2. Essential Questions
Questions that lead students to
Big Ideas.
3. Big Ideas
Student answers to EQs that lead
them to the Big Ideas
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
(3, 7, 2, 16 ,6 ,18, 19, 20, 8) Why are algebraic rules necessary? What are the characteristics of the different
sets of Real numbers and how are they connected?
(9, 34, B1)What previous learning helps us to understand the language of Algebra?
(3, 7, 2, 16 ,6 ,18 ,19 ,20 ,8) Computational methods are used to simplify expressions with Real number
sets.
(9, 34, B1) Algebraic foundations (e.g. absolute value, reciprocal, inverse operations, variables) are the
rules and guidelines to help us understand Algebra.
4. Cognitive Level
Webb’s/Bloom’s Taxonomy Link
5. Content
What students need to know
(nouns)
Vocabulary List
Words students need to know to
understand concept
6. Skills
What students need to be able to
do (verbs)
2, 16. Order of operations
1, 3, 7. Sets of numbers
6, 18, 19. Rule of four
9. Absolute value
25. Computational methods
34, reciprocals and inverse operation
B.1. Variable
8 Distributive property
Uivariate
Bivariate
2, 16. Substitute and evaluate, simplify expressions, connect table to graph, to symbols, to situation
1,3, 7. Use equivalent representation of numbers, classifies types of numbers
6, 18, 19. Translate from word to symbol
9. Define absolute value
25. Utilizes a variety of techniques appropriately
34. Appropriately uses reciprocals and inverse operations
B.1. Understands variables
8 simplify algebraic expressions
Learning Activities / Lesson
Plan Links
Essential Experiences or Guided
Practice
Algebra 1
3
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
7. Assessments:
Formative Assessments
How will students and teacher
know what students have
learned so far? Differentiated
Rubric Links / Attached
Summative Assessments
How will students show that
they have mastered the
standard? Differentiated
Rubric Links / Attached
8. Resources
Links,
Curriculum Frameworks,
Other Websites
APS/LEI/TLS/JAN08
Algebra 1
4
APS District Curriculum Map
8 ESSENTIAL COMPONENTS
1. Performance Standards
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Month: September
Strand II
Benchmark A
8. Simplifies algebraic expressions using the distributive property
(NM – IA.8).
10. Knows, explains, and uses equivalent representations for algebraic
expressions (NM – IA.10).
12. Solves (NM – IA.13):
a. formulas for specified variables, and
b. radical equations involving one radical.
16. Uses the four basic operations (+, -, x, ÷) with (NM – IA.17):

linear expressions,

polynomial expressions, and

rational expressions.
Benchmark B
20. Explains and uses function notation (NM – IB.5).
21. Determines the domain of independent variables and the range of
dependent variables defined by a graph, a set of ordered pairs, or a
symbolic expression (NM – IB.6).
Benchmark C
24. Models real-world phenomena using linear and quadratic equations
and linear inequalities (e.g., apply algebraic techniques to solve rate
problems, work problems, and percent mixture problems; solve
problems that involve discounts, markups, commissions, and profit and
compute simple and compound interest; apply quadratic equations to
model throwing a baseball in the air) (NM – IC.1).
27. Expresses the relationship between two variables using an equation and a graph to (NM-IC.4):
a.
Graphs a linear equations and linear inequalities in two variables,
b. Solves linear inequalities and equations in one variable,
c.
Solves systems of linear equations in two variables and graph solutions, and
d. Uses the graph of a system of equations in two variables to help determine the solution.
34. Understands and uses (NM – IC.11):

such operations as taking the inverse, finding the reciprocal, taking a root, and raising to a fractional power, and

the rules of exponents.
Benchmark D
36. Calculates the percentage of increase and decrease of a quantity
(NM – ID.3).
Strand IV
Benchmark C
6. Draws conclusions concerning the relationships among bivariate data (NM – IIIC.2):

makes predictions from a linear pattern in data,

determines the strength of the relationship between two sets of data by examining the correlation, and

understands that correlation does not imply a cause-and-effect relationship.
2. Essential Questions
Questions that lead students to
Big Ideas.
Algebra 1
(27,24,36,21 ) How are linear equations and inequalities, and their representations helpful in solving problems?
(12,IVc5) Why are functions and relations useful and represented in multiple ways?
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APS District Curriculum Map
3. Big Ideas
Student answers to EQs that lead
them to the Big Ideas
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
(27, 24, 36, 21 ) Univariate equations and inequalities are used to model situations.
(12,IVc5) Relation / functions, graphing, rule of 4, formulas are different representations of algebraic functions and used in order to organize and display information.
4. Cognitive Level
Webb’s/Bloom’s Taxonomy Link
5. Content
What students need to know
(nouns)
8. Distributive property
10. Algebraic expressions
12 a. Formulas
16. linear expressions
21. Coordinate plane, ordered pairs, domain and range
24, 36. Problem solving
27. Inequalities and equations in one variable
IV. 5 Rule of 4
Vocabulary List
Words students need to know to
understand concept
6. Skills
What students need to be able to
do (verbs)
8. Makes, predicts, and see, trends with tables and graphs
10. Identifies, simplifies
12 a. Rearrange and simplify formulas
16.
21. Plot ordered pairs; Identify domain and range
24, 36. Model and solve real world problems
27. Solves and graphs one-variable equations
34. square roots
Learning Activities / Lesson
Plan Links
Essential Experiences or Guided
Practice
7. Assessments:
Formative Assessments
How will students and teacher
know what students have
learned so far? Differentiated
Rubric Links / Attached
Summative Assessments
How will students show that
they have mastered the
standard? Differentiated
Rubric Links / Attached
Algebra 1
6
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
8. Resources
Links,
Curriculum Frameworks,
Other Websites
APS/LEI/TLS/JAN08
Algebra 1
7
APS District Curriculum Map
8 ESSENTIAL COMPONENTS
1. Performance Standards
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Month: October
Strand II
Benchmark A
8. Represents and analyzes relationships using written and verbal expressions, tables, equations, and
graphs, and describes the connections among those representations to (NM – IA.6):
 translates from verbal expression to algebraic formulae
(e.g., “Set up the equations that represent the data in the
following equation: John’s father is 23 years older than John.
John is 4 years older than his sister Jane. John’s mother is
3 years younger than John’s father. John’s mother is 9 times
as old as Jane. How old are John, Jane, John’s mother, and
John’s father?”),
 given data in a table, constructs a function that represents these data (linear only), and
 given a graph, constructs a function that represents the graph (linear only).
9. Knows, explains, and uses equivalent representations for the same real number including (NM – IA.7):
 integers,
 decimals,
 percents,
 ratios,
 scientific notation,
 numbers with integer exponents,
 inverses (reciprocal), and
 prime factoring.
10. Knows, explains, and uses equivalent representations for algebraic
expressions (NM – IA.10).
12. Solves (NM – IA.13):
c. formulas for specified variables, and
d. radical equations involving one radical.
16. Uses the four basic operations (+, -, x, ÷) with (NM – IA.17):
 linear expressions,
 polynomial expressions, and
Algebra 1
8
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
 rational expressions.
Benchmark B
21. Determines the domain of independent variables and the range of
dependent variables defined by a graph, a set of ordered pairs, or a
symbolic expression (NM – IB.6).
Benchmark C
25. Uses a variety of computational methods (e.g., mental arithmetic, paper
and pencil, technological tools) (NM – IC.2).
32. Generates an algebraic sentence to model real-life situations
(NM – IC.9).
34. Understands and uses (NM – IC.11):
 such operations as taking the inverse, finding the reciprocal, taking a root, and raising to a
fractional power, and
 the rules of exponents.
Benchmark D
36. Calculates the percentage of increase and decrease of a quantity
(NM – ID.3).
.
2. Essential Questions
Questions that lead students to
Big Ideas.
3. Big Ideas
Student answers to EQs that lead
them to the Big Ideas
Algebra 1
(27,24,36,21 ) How are linear equations and inequalities, and their representations helpful in solving
problems?
(12,IVc5) Why are functions and relations useful and represented in multiple ways?
(6, 10, 21) How can the relationship between two variables be represented as a linear function or graphic
representations?
(7) How do operations with fractions and decimals compare to operations with whole numbers?
(27, 24, 36, 21) Univariate equations and inequalities are used to model situations.
(12,IVc5) Relation / functions, graphing, rule of 4, formulas are different representations of algebraic
functions and used in order to organize and display information.
(6,21,10) Graphs, tables, charts, patterns, descriptions expressions can represent the relationship between
two variables.
(7)
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APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
,
4. Cognitive Level
Webb’s/Bloom’s Taxonomy Link
5. Content
What students need to know (nouns)
Early October
10. Algebraic expressions
27. Inequalities and equations in variable
32. Rule of 4
Mid October
6. Written and verbal instruction
Equations, tables, graphs, data analysis
7. Equivalent representation i.e. ratios, percents, exponents, scientific notation
25. Computational methods
Vocabulary List
Words students need to know to
understand concept
6. Skills
What students need to be able to
do (verbs)
Early October
10. Identifies, simplifies and explains
27. Translate from words to symbols
32. Solves and graphs one-variable equations and inequalities
Mid October
6. Construct functions
Translate to algebraic formulas
7. Knows and explains and uses equivalent representations
25. Uses variety of computational methods (ongoing)
Learning Activities / Lesson
Plan Links
Essential Experiences or Guided
Practice
7. Assessments:
Formative Assessments
How will students and teacher
know what students have
learned so far? Differentiated
Rubric Links / Attached
Algebra 1
10
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Summative Assessments
How will students show that
they have mastered the
standard? Differentiated
Rubric Links / Attached
8. Resources
Links,
Curriculum Frameworks,
Other Websites
APS/LEI/TLS/JAN08
Algebra 1
11
APS District Curriculum Map
8 ESSENTIAL COMPONENTS
1. Performance Standards
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Month: November
Strand II
Benchmark A
15. Manipulates simple expressions with + and – exponents (NM – IA.16).
16. Uses the four basic operations (+, -, x, ÷) with (NM – IA.17):
 linear expressions,
 polynomial expressions, and
 rational expressions.
Benchmark B
17. Distinguishes between the concept of a relation and a function
(NM – IB.1).
Benchmark C
24. Models real-world phenomena using linear and quadratic equations
and linear inequalities (e.g., apply algebraic techniques to solve rate
problems, work problems, and percent mixture problems; solve
problems that involve discounts, markups, commissions, and profit and
compute simple and compound interest; apply quadratic equations to
model throwing a baseball in the air) (NM – IC.1).
26. Expresses the relationship between two variables using a table with a
finite set of values and graphs the relationship (NM – IC.3).
34. Understands and uses (NM – IC.11):
 such operations as taking the inverse, finding the reciprocal, taking a root, and raising to a
fractional power, and
 the rules of exponents.
Strand IV
Benchmark B
3. For univariate data, displays the distribution and describes its shape
using appropriate summary statistics, and understands the distinction
between a statistic and a parameter (NM – IIIB.3):
 constructs and interprets frequency tables, histograms, stem and leaf plots, and box and whisker
Algebra 1
12
APS District Curriculum Map
Grade Level:


_Course /Subject:
Algebra I
MONTHLY TEMPLATE
plots,
calculates and applies measures of central tendency (mean, median, and mode) and measures
of variability (range, quartiles, standard deviation), and
compares distributions of univariate data using back-to-back stem and leaf plots and parallel box
and whisker plots.
Benchmark C
4. Compares and draws conclusions between two or more sets of univariate data using basic data analysis
techniques and summary statistics
(NM – IIIC.1).
7. Draws conclusions concerning the relationships among bivariate data (NM – IIIC.2):
 makes predictions from a linear pattern in data,
 determines the strength of the relationship between two sets of data by examining the
correlation, and
 understands that correlation does not imply a cause-and-effect relationship.
2. Essential Questions
Questions that lead students to
Big Ideas.
3. Big Ideas
Student answers to EQs that lead
them to the Big Ideas
4. Cognitive Level
Webb’s/Bloom’s Taxonomy Link
5. Content
What students need to know
(nouns)
Algebra 1
II;
1. relations
4 linear inequalities
15. positive and negative exponents
17. linear functions
24. 3 linear equations
4. linear inequalities
!V;
3, Data Analysis
a. measure of central tendancy and variability
13
APS District Curriculum Map
b.
c.
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
graphs i.e. histogram, bar graphs, box-and-whisker
distributions
IV; B,
4 – data analysis
Vocabulary List
Words students need to know to
understand concept
6. Skills
What students need to be able to
do (verbs)
15. simplify expressions
17 distinguish between relations and functions
24. model linear equations
26. represent relationships
IV; B 3
Calculate and interpret mean, median, mode, range
a. construct, display and interpret frequency tables, box-and-whisker, etc.
b. compare distribution
IV; B 4
Calculate and interpret mean, median, mode, range
a. construct, display and interpret frequency tables, box-and-whisker, etc.
b. compare distribution
c. draws conclusion
Learning Activities / Lesson
Plan Links
Essential Experiences or Guided
Practice
7. Assessments:
Formative Assessments
How will students and teacher
know what students have
learned so far? Differentiated
Rubric Links / Attached
Summative Assessments
How will students show that
they have mastered the
standard? Differentiated
Rubric Links / Attached
Algebra 1
14
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
8. Resources
Links,
Curriculum Frameworks,
Other Websites
APS/LEI/TLS/JAN08
Algebra 1
15
APS District Curriculum Map
8 ESSENTIAL COMPONENTS
1. Performance Standards
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Month: December
Strand II
Benchmark A
16. Uses the four basic operations (+, -, x, ÷) with (NM – IA.17):
 linear expressions,
 polynomial expressions, and
 rational expressions.
Benchmark B
18. Describes the concept of a graph of a function (NM – IB.3).
19. Translates among tabular, symbolic, and graphical representations of functions (NM – IB.4).
Benchmark C
2. Uses a variety of computational methods (e.g., mental arithmetic, paper
and pencil, technological tools) (NM – IC.2). (+)
33. Writes an equation of the line that passes through two given points
(NM – IC.10).
34. Understands and uses (NM – IC.11):
 such operations as taking the inverse, finding the reciprocal, taking a root, and raising to a
fractional power, and
 the rules of exponents.
Benchmark D
37. Estimates the rate of change of a function or equation by finding the
slope between two points on the graph (NM – ID.5).
38. Evaluates the estimated rate of change in the context of the problem
(NM – ID.6).
Strand IV
Benchmark B
3. For univariate data, displays the distribution and describes its shape
using appropriate summary statistics, and understands the distinction
Algebra 1
16
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
between a statistic and a parameter (NM – IIIB.3):
 constructs and interprets frequency tables, histograms, stem and leaf plots, and box and whisker
plots,
 calculates and applies measures of central tendency (mean, median, and mode) and measures
of variability (range, quartiles, standard deviation), and
 compares distributions of univariate data using back-to-back stem and leaf plots and parallel box
and whisker plots.
Benchmark C
5. Compares and draws conclusions between two or more sets of univariate data using basic data analysis
techniques and summary statistics
(NM – IIIC.1).
8. Draws conclusions concerning the relationships among bivariate data (NM – IIIC.2):
 makes predictions from a linear pattern in data,
 determines the strength of the relationship between two sets of data by examining the
correlation, and
 understands that correlation does not imply a cause-and-effect relationship.
2. Essential Questions
Questions that lead students to
Big Ideas.
How do linear patterns appear in
various representations?
How do you determine if a graph
represents a linear function?
In what way do relations and
functions help us to interpret realworld problems?
3. Big Ideas
Student answers to EQs that lead
them to the Big Ideas
There are four ways to represent
functions: verbal, table, graph, and
equations/formulae
Algebra 1
17
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
The rate of change is constant
when a function is linear.
4. Cognitive Level
Webb’s/Bloom’s Taxonomy Link
5. Content
What students need to know
(nouns)
II; 18, 19,33,37,38 – Linear Functions
IV; B5 – Correlation of bivariate data
Vocabulary List
Words students need to know to
understand concept
6. Skills
What students need to be able to
do (verbs)
IV; B5 – calculate, interpret correlations
Graph a function
Calculate a slope
Write an equation
Estimate rate of change
Translate functions i.e. graphical, tabular, symbolic
Learning Activities / Lesson
Plan Links
Essential Experiences or Guided
Practice
7. Assessments:
Formative Assessments
How will students and teacher
know what students have
learned so far? Differentiated
Rubric Links / Attached
Summative Assessments
How will students show that
they have mastered the
standard? Differentiated
Rubric Links / Attached
Algebra 1
Vertical line test
Plotting data from a table to a graph
Find slope from a graph
Create an equation from a graph
Measure, put in table, plot,
Vertical line test
18
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
8. Resources
Links,
Curriculum Frameworks,
Other Websites
APS/LEI/TLS/JAN08
Algebra 1
19
APS District Curriculum Map
8 ESSENTIAL COMPONENTS
1. Performance Standards
(Power Standards are italicized)
2. Essential Questions
Questions that lead students to
Big Ideas.
3. Big Ideas
Student answers to EQs that lead
them to the Big Ideas
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Month: January
Strand IIB: Determines the domain of independent variables and the range of dependent variables defined
by a graph, a set of ordered pairs, or a symbolic expression (NM – IB.6).
Strand IIC: Uses a variety of computational methods (e.g., mental arithmetic, paper and pencil,
technological tools) (NM – IC.2).
Expresses the relationship between two variables using an equation and a graph to (NM – IC.4):
a. graphs a linear equation and linear inequality in two variables,
b. solves linear inequalities and equations in one variable,
c. solves systems of linear equations in two variables and graphs the solutions, and
d. uses the graph of a system of equations in two variables to help determine the solution.
Solves applications involving systems of equations (NM – IC.5).
Verifies that a point lies on a line, given an equation of the line, and be able to derive linear equations by
using the point-slope formula (NM – IC.12).
Strand IIIB: Given two linear equations, determines whether the lines are parallel, perpendicular, or
coincide (NM – IIB.3).
What are similarities and differences between systems of linear equations and linear inequalities?
What methods can be used to solve systems of equations and when would you use each one?
Systems of linear equations have three possible outcomes: dependent (infinite number of solutions),
independent (one solution), or inconsistent (no solution – lines are parallel)
4. Cognitive Level
Webb’s/Bloom’s Taxonomy Link
5. Content
What students need to know
(nouns)
Order of operations with exponents, polynomial expressions, degrees, graphs, domain/range, computational
methods, integers, systems of equations, linear inequalities, linear equations with one and two variables,
two points on a line, numbers, number of variables, meaning of algebraic expressions (variable), solutions,
parallel/slope, perpendicular
Vocabulary List
Words students need to know to
understand concept
6. Skills
What students need to be able to
do (verbs)
Algebra 1
Apply and implement order of operations w/exponents, determine number of variables, judge meaning of
variables, compare, order/sequence, and classify expressions by degree, graph, solve, and apply systems
of equations, linear inequalities, linear equations with one and two variables, verify (demonstrate) two points
20
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
on a line, derive linear equations, read and check domain and range, demonstrate computational methods,
determine and verify parallel, perpendicular lines/slope
Learning Activities / Lesson
Plan Links
Essential Experiences or Guided
Practice
7. Assessments:
Formative Assessments
How will students and teacher
know what students have
learned so far? Differentiated
Rubric Links / Attached
Summative Assessments
How will students show that
they have mastered the
standard? Differentiated
Rubric Links / Attached
Check for understanding – vocabulary, graphing,
Substitution, elimination, pictorial graph, equation examples (algebraically, graphically)
Given a pictorial graph or equation student classifies the system as dependent, independent, or
inconsistent.
Simple quizzes, linear combinations
8. Resources
Links,
Curriculum Frameworks,
Other Websites
APS/LEI/TLS/JAN08
Algebra 1
21
APS District Curriculum Map
8 ESSENTIAL COMPONENTS
1. Performance Standards
(Power Standards are italicized)
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Month: February
Strand IIA: Simplifies algebraic expressions using the distributive property (NM – IA.8).
Knows, explains, and uses equivalent representations for the same real number including (NM – IA.7):
d. integers,
e. decimals,
f. percents,
g. ratios,
h. scientific notation,
i. numbers with integer exponents,
j. inverses (reciprocal), and
h. prime factoring.
Strand IIB: Determines the domain of independent variables and the range of dependent variables defined
by a graph, a set of ordered pairs, or a symbolic expression (NM – IB.6). Should be put into where what a
function is, not here
Strand IIC: Uses a variety of computational methods (e.g., mental arithmetic, paper and pencil,
technological tools) (NM – IC.2).
Expresses the relationship between two variables using an equation and a graph to (NM – IC.4):
k. graphs a linear equation and linear inequality in two variables,
l. solves linear inequalities and equations in one variable,
m. solves systems of linear equations in two variables and graphs the solutions, and
d. uses the graph of a system of equations in two variables to help determine the solution.
Solves applications involving systems of equations (NM – IC.5).
Generates an algebraic sentence to model real-life situations (NM – IC.9).
WHERE DID THIS COME FROM – CHECK IIIA is it in Algebra I?
Strand IIIA: Demonstrates an understanding of inductive and deductive reasoning, explains the difference
between inductive and deductive reasoning, and identifies and provides examples of each (NM – IIA.6):
a. for inductive reasoning, demonstrates understanding that showing a statement is true for a
finite number of examples does not show it is true for all cases unless the cases verified are all
cases, and
b. for deductive reasoning, proves simple theorems.
Strand IIIB: Given two linear equations, determines whether the lines are parallel, perpendicular, or
coincide (NM – IIB.3).
Algebra 1
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APS District Curriculum Map
2. Essential Questions
Questions that lead students to
Big Ideas.
3. Big Ideas
Student answers to EQs that lead
them to the Big Ideas
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
What methods can be used to solve systems of equations and when would you use each one?
Solutions for equations move from simple to complex.
Systems of equations can be applied to a wide variety of real world situations.
4. Cognitive Level
Webb’s/Bloom’s Taxonomy Link
5. Content
What students need to know
(nouns)
Inductive and deductive reasoning, distributive property, equivalent representations (integers), laws of
exponents, computational methods, systems of equations, linear inequalities, linear equations with one and
two variables, reasonableness of algebraic sentences, real life problems with domain and range, symbolic
expressions, graphs, parallel/slope, perpendicular
Vocabulary List
Words students need to know to
understand concept
6. Skills
What students need to be able to
do (verbs)
Identify, explain and demonstrate inductive and deductive reasoning, recognize-identify-compute distributive
property, identify, explain, manipulate and use/implement equivalent representations (integers) and laws of
exponents, create, analyze and extrapolate graphs, graph real-life problems with domain and range,
demonstrate computational methods, graph, solve and apply systems of equations, linear inequalities, linear
equations with one and two variables, generate and justify reasonableness of algebraic sentences,
determine and verify parallel/perpendicular lines and slope,
Learning Activities / Lesson
Plan Links
Essential Experiences or Guided
Practice
7. Assessments:
Formative Assessments
How will students and teacher
know what students have
learned so far? Differentiated
Rubric Links / Attached
Algebra 1
Application to real world problems
Peer generated problems shared with classmates
Problems of the day
Warm-ups
Check for understanding
Activity lab (graphing calculator)
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APS District Curriculum Map
Summative Assessments
How will students show that
they have mastered the
standard? Differentiated
Rubric Links / Attached
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Application to real world problems
Written assessment and problem solving
8. Resources
Links,
Curriculum Frameworks,
Other Websites
APS/LEI/TLS/JAN08
Algebra 1
24
APS District Curriculum Map
8 ESSENTIAL COMPONENTS
1. Performance Standards
(Power Standards are italicized)
2. Essential Questions
Questions that lead students to
Big Ideas.
3. Big Ideas
Student answers to EQs that lead
them to the Big Ideas
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Month: March
Strand IIA: Evaluates the numerical value of expressions of one or more variables that are (NM – IA.3):
n. polynomial,
o. rational, and
c. radical.
Simplifies algebraic monomial expressions raised to a power [e.g., (5xy2 )3] and algebraic binomial [e.g.,
(5x2 + y)2] expressions raised to a power (NM – IA.4).
Factors polynomials, difference of squares and perfect square trinomials, and the sum and difference of
cubes (NM – IA.14).
Strand IIA: Simplifies numerical expressions using the order of operations, including exponents (NM – IA.2).
Compares and orders polynomial expressions by degree (NM – IA.5).
Strand IIB: Describes the concept of a graph of a function (NM – IB.3).
Translates among tabular, symbolic, and graphical representations of functions (NM – IB.4).
Uses the quadratic formula and factoring techniques to determine whether the graph of a quadratic function
will intersect the x-axis in zero, one, or two points (NM – IB.12).
Applies quadratic equations to physical phenomena (e.g., the motion of an object under the force of gravity)
(NM – IB.13).
Strand IIC: Uses a variety of computational methods (e.g., mental arithmetic, paper and pencil,
technological tools) (NM – IC.2).
Evaluates numerical and algebraic absolute value expressions (NM – IC.6).
Understands and uses (NM – IC.11):
a. such operations as taking the inverse, finding the reciprocal, taking a root, and raising to a
fractional power, and
b. the rules of exponents.
How do quadratic functions model real-world problems and their solutions?
The characteristics of quadratic functions and their representations are useful in modeling and solving realworld problems.
4. Cognitive Level
Webb’s/Bloom’s Taxonomy Link
Algebra 1
25
APS District Curriculum Map
5. Content
What students need to know
(nouns)
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Quadratics, parabolas, quadratic formula, monomials, polynomials, polynomial multiplication, representation
of a function, factoring, absolute values
Vocabulary List
Words students need to know to
understand concept
6. Skills
What students need to be able to
do (verbs)
Graph, solves and factor quadratics and parabolas, correlate quadratics, quadratic formula and
representations of a function, solve and evaluate absolute values, add, subtract, multiply, divide, simplify,
evaluate and apply monomials and polynomials, find degrees
Learning Activities / Lesson
Plan Links
Essential Experiences or Guided
Practice
7. Assessments:
Battleship with graphing calculator (Susan Kennedy; Monroe)
Formative Assessments
How will students and teacher
know what students have
learned so far? Differentiated
Rubric Links / Attached
Summative Assessments
How will students show that
they have mastered the
standard? Differentiated
Rubric Links / Attached
Unit test: Solving quadratic equation using a graph, factors or the quadratic formula.
Unit test: Solve a real-world problem involving a quadratic function (APS Task Bank problems).
Rubrics (ACE)
Project (bouncing ball LeeAnn Moores, Freedom)
8. Resources
Links,
Curriculum Frameworks,
Other Websites
APS/LEI/TLS/JAN08
Algebra 1
26
APS District Curriculum Map
8 ESSENTIAL COMPONENTS
1. Performance Standards
2. Essential Questions
Questions that lead students to
Big Ideas.
3. Big Ideas
Student answers to EQs that lead
them to the Big Ideas
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Month: April
2
Strand IIA: Solves (NM – IA.13):
p. formulas for specified variables, and
b. radical equations involving one radical.
Simplifies fractions with polynomials in the numerator and denominator by factoring both and reducing them
to the lowest terms (NM – IA.15).
Strand IIB: Explains and uses function notation (NM – IB.5).
Determines the domain of independent variables and the range of dependent variables defined by a graph,
a set of ordered pairs, or a symbolic expression (NM – IB.6).
Strand IIC: Models real-world phenomena using linear and quadratic equations and linear inequalities
(e.g., apply algebraic techniques to solve rate problems, work problems, and percent mixture problems;
solve problems that involve discounts, markups, commissions, and profit and compute simple and
compound interest; apply quadratic equations to model throwing a baseball in the air) (NM – IC.1).
Uses a variety of computational methods (e.g., mental arithmetic, paper and pencil, technological tools) (NM
– IC.2).
Verifies that a point lies on a line, given an equation of the line, and be able to derive linear equations by
using the point-slope formula (NM – IC.12).
Strand IID: Evaluates the estimated rate of change in the context of the problem (NM – ID.6).
Strand IVB#2: Understands the meaning of “univariate”(i.e. one variable) and bivariate (i.e. two variable)
data (NM-IIIB.2)
How do linear and non-linear functions compare?
How do you know whether a relationship is linear or quadratic?
How do we choose the appropriate relation or function to model given data or information?
Linear functions have constant rates of change and non-linear functions have non-constant rates of change.
4. Cognitive Level
Webb’s/Bloom’s Taxonomy Link
5. Content
What students need to know
(nouns)
Algebra 1
Discriminants, quadratics, radicals, rate of change (slope), polynomial/rational expressions
27
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Vocabulary List
Words students need to know to
understand concept
6. Skills
What students need to be able to
do (verbs)
Identify discriminants, compare linear and quadratics equations, solve formulas, graph, simplify by factoring
and reducing
Learning Activities / Lesson
Plan Links
Essential Experiences or Guided
Practice
7. Assessments:
Formative Assessments
How will students and teacher
know what students have
learned so far? Differentiated
Rubric Links / Attached
Summative Assessments
How will students show that
they have mastered the
standard? Differentiated
Rubric Links / Attached
Collaborative problem solving
Quiz: discriminants, graphing, factoring, simplifying
Unit test: Comparison of linear and quadratic functions.
8. Resources
Links,
Curriculum Frameworks,
Other Websites
APS/LEI/TLS/JAN08
Algebra 1
28
APS District Curriculum Map
8 ESSENTIAL COMPONENTS
1. Performance Standards
(Power Standards are italicized)
2. Essential Questions
Questions that lead students to
Big Ideas.
3. Big Ideas
Student answers to EQs that lead
them to the Big Ideas
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Month: May
Strand IIA: Simplifies square roots and cube roots with monomial radicands that are perfect squares or
perfect cubes (e.g., 9a2x4) (NM – IA.11).
Strand IIC: Uses a variety of computational methods (e.g., mental arithmetic, paper and pencil,
technological tools) (NM – IC.2).
Strand IIIB: Uses basic geometric ideas (e.g., the Pythagorean Theorem, area, and perimeter of objects) in
the context of the Euclidean Plane and calculates the perimeter of a rectangle with integer coordinates and
sides parallel to the coordinate axes and with sides not parallel (NM – IIB.4).
Strand IIIC: Solves problems using the Pythagorean Theorem (e.g., “Given the length of a ladder and the
distance of the base of the ladder from a wall, determine the distance up the wall to the top of the ladder.”)
(NM – IID.4).
Strand IVC: Explains the concept of a random variable (NM – IIID.1).
Understands the concept of probability as relative frequency (NM – IIID.2).
Uses simulations to compute the expected value and probabilities of random variables in simple cases (NM
– IIID.3).
How are the Pythagorean Theorem and the distance formula related?
Why do we use probability?
The Pythagorean Theorem describes the relationship between the sides of a right triangle.
The distance formula is an application of the Pythagorean Theorem when used on a coordinate plane.
Probability is used to figure out when a risk is less risky.
4. Cognitive Level
Webb’s/Bloom’s Taxonomy Link
5. Content
What students need to know
(nouns)
Pythagorean Theorem, right triangles, probability (simple), radicals
Vocabulary List
Words students need to know to
understand concept
6. Skills
What students need to be able to
do (verbs)
Algebra 1
Find area and perimeter, solve right triangle, find and calculate simple probability, solve formulas
29
APS District Curriculum Map
Grade Level:
_Course /Subject:
Algebra I
MONTHLY TEMPLATE
Learning Activities / Lesson
Plan Links
Essential Experiences or Guided
Practice
7. Assessments:
Formative Assessments
How will students and teacher
know what students have
learned so far? Differentiated
Rubric Links / Attached
Summative Assessments
How will students show that
they have mastered the
standard? Differentiated
Rubric Links / Attached
Experiments (coin tosses, dot cubes, number cubes, M & Ms)
Quiz: difference between experimental and theoretical probability
Unit test: Pythagorean Theorem; theoretical probabilities
Project: Marilyn Burns—Pythagoream Theorem (Barbara Bachechi, Manzano)
8. Resources
Links,
Curriculum Frameworks,
Other Websites
APS/LEI/TLS/JAN08
Algebra 1
30