The Academy of the Most Blessed Sacrament ALGEBRA I CURRICULUM OUTLINE
(last updated August 9, 2019) (177 days)
Unit 
Topic 
Dolciani 
Carter 
Larson 





I 
REAL NUMBERS AND ALGEBRAIC EXPRESSIONS 




first trimester – 15 days 



AI1d1 
Variables and Grouping Symbols (parentheses,
brackets and fraction bars; easy oops with substitution) 
1.1, 1.2 
1.2 
1.1, 1.2 
AI1d2 
Translate Words into Symbols (also,
complete word phrase when given additional information) 
1.4 
1.1 
1.3 
AI1d3 
Classifying, Ordering, and Rewriting Real Numbers (integer,
real number, whole number defined; graphing and ordering real numbers on a
number line;
rewriting repeating decimals as fractions) 
1.8 
0.2 part 1 
2.1 
AI1d4 
Simplifying and Estimating Square Roots (rounding
square roots to nearest integer) 
1.8 
0.2 part 2 
2.7 
AI1d5 
Opposites and Absolute Values (simple
sums, differences, comparisons, simple absolute value equations) 
1.9 


AI1d5 
Adding and Subtracting Real Numbers (no
algebraic expressions yet) 

0.3, 0.4 
2.2, 2.3 
AI1d5 
Multiplying and Dividing Real Numbers (no
algebraic expressions yet; find a number between any two rational numbers) 

0.3, 0.5 
2.4, 2.6 
AI2d1 
Basic Assumptions (3
properties of addition and multiplication, including closure; simple addition
of whole numbers, decimals, and mixed numbers; simple simplification of algebraic
expressions, addition and multiplication only, no combining like terms) 
2.1 


AI2d2 
Adding and Subtracting Algebraic Expressions (addition
and subtraction of positive and negative integers, decimals and fractions,
simplification of algebraic expressions, evaluation with substitution of
integers, algebraic expressions that contain opposite of sum and difference;
no combining like terms) 
2.2, 2.3, 2.4 


AI2d3 
Properties of Numbers (The RuST properties, substitution property, four addition
properties, five multiplication properties; use properties to justify each
step when simplifying or evaluating an expression) 

1.3 

AI2d4 
Distributive Property (use
as short cut; simplifying algebraic expressions) 
2.5 
1.4 
2.5 
AI2d5 
Rules for Multiplication (includes
algebraic expressions with combining like terms; integers only) 
2.6 
1.4 

AI2d6 
Reciprocal of a Real Number (simplify
algebraic expressions, including fractions and distributive property) 
2.8 


AI2d6 
Dividing Real Numbers (simplify
algebraic expressions;
all involve integers   no fractions or decimals) 
2.9 




















































Unit 
Topic 
Dolciani 
Carter 
Larson 





II 
EQUATIONS 




first
trimester – 18 days 



AI1d1 
Equations (solve
simple equations and word problems over given domain. Introduce “is element of” symbol) 
1.3 
1.5 

AI1d2 
Transforming Equations: Addition and Subtraction (integers; opposite) 
3.1 
2.2 
3.1 
AI1d3 
Transforming Equations: Multiplication and Division (includes simple fractions and mixed numbers) 
3.2 
2.2 
3.1 
AI1d4 
Using Several Transformations (simple twostep problems; fractional expressions; distributive property) 
3.3 
2.3 
3.2, 3.3 
AI1d5 
Translate Sentences and Problems Into Equations (includes
quantities grouped in parentheses, formulas, defining variable with “let”;
include twostep translations with sketch) 
1.5, 1.6 
2.1 
1.4 
AI1d6 
A Problem Solving Plan (5
step Polyatype plan; answers given as choice of 3;
solving problems involving geometry) 
1.7, 3.4 

1.5 
AI1d7 
Problem Solving: Consecutive Integers and Diagrams (word
problems) 
2.7 
2.3 

AI2d1 
Equations with Variable on Both Sides (includes
fractional expressions and distributive property; identity; no solution) 
3.5 
2.4 
3.4 
AI2d2 
Absolute Value Equations (includes realworld distance problems and tolerance problems) 

2.5 

AI2d3 
The Fraction Destroyer (solving linear equations more efficiently by removing fractions) 
supplement 


AI2d4 
Transforming Formulas (solving
literal equations; stating restrictions; Be careful, some problems may require
factoring) (Carter includes
dimensional analysis, but we will postpone this to the unit on rates and
ratios) 
4.7 
2.8 
3.8 
AI2d5 
Problem Solving Using Charts (rate
problems – calories per fruit, rides per ticket, etc.) 
3.6 


AI2d6 
Cost, Income, and Value Problems  Introductory (using
charts; includes dimes and nickels, profit as selling price minus buying
price) 
3.7 


AI2d7 
Cost, Income, and Value Problems  Challenging (also,
more challenging consecutive integer problems) 
3.7 








































































Unit 
Topic 
Dolciani 
Carter 
Larson 





III 
RATES, RATIOS AND PERCENTS 




first trimester – 14 days 



AI1d1 
Ratios (convert
simple measurements (days and weeks, etc) to reduce
ratio to simplest form;
ratios of perimeters and areas of rectangles; realworld
problems; ratio of x to y) 
7.1 
2.6 
3.5 
AI1d2 
Proportions (Solve
with crossmultiplication;
some numerators and denominators are binomials; some have
variables on both sides) 
7.2 part 1 
2.6 
3.5, 3.6 
AI1d3 
Realworld Problems with Proportions (Include
classic forestry ratio problems; also, more challenging “find ratio
of x to y” problems; confirming that a
pair of ratios are proportional) 
7.2 part 2 
2.6 

AI1d4 
The Mean Proportional (also,
using the mean proportional to find the missing number in a geometric
sequence) 
7.2 part 3 
2.6 

AI1d5 
Percents (convert
among fractions, percents, and decimals; solve
basic percentage word problems;; Dolciani omits
the percent proportion; Carter covers the percent proportion.) 
7.5 part 1 
0.6 

AI1d6 
Realworld Problems with Percents (solve
percentage realworld problems with the percent proportion: solve equations
using the decimal destroyer) 
7.5 part 2 
0.6 
3.7 
AI2d1 
Percent Change Problems 
7.6 
2.7 
post 3.7 
AI2d2 
Compound Proportions 
supplement 


AI2d3 
Dimensional Analysis (include
unit rates;
conversions between customary and metric units of measure) 
7.3 extra 
2.8 

AI2d4 
Mixture Problems (“raisins,
nuts and mixture”, “dilute 70% acid to 40% acid”, with charts) 
7.7 
2.9 
































































































Unit 
Topic 
Dolciani 
Carter 
Larson 





IV 
GRAPHING LINEAR EQUATIONS 




second trimester – 19 days 



AI1d1 
Equations in Two Variables (determine
whether an ordered pair is a solution of an equation in two variables;
isolate a given variable;
use guessandcheck to find a list of orderedpair solutions) 
8.1 


AI1d2 
Points, Lines, and Their Graphs (plot
points on coordinate plane; graph a line by finding its x and y intercepts) 
8.2 
3.1 
4.1 
AI1d3 
Slope of a Line (use
slope formula when given coordinates of two points; find any two coordinates
when given equation;
draw line on coordinate plane when given point and slope, using
“rise over run”; identify “no slope” and “slope equals zero”. Carter
also has exercises in finding a missing coordinate.) 
8.3 part 1 
3.3 
4.4 
AI1d4 
Linear Equations (recognizing
linear equations, converting equations to standard form, finding a missing
coordinate, determining whether three points are collinear) 
8.3 part 2 
3.3 
4.2 
AI2d1 
The SlopeIntercept Form of a Linear Equation (graph
equations written in slopeintercept form; transform equation to
slopeintercept form and graph; determine whether pair of lines whose
equations are given are parallel or perpendicular.) 
8.4 
4.1. 4.4 
4.5 
AI2d2 
Determining the Equation of a Line (find
equation of line when given slope and yintercept; when given slope and coordinates of
one point; when given two points; when given other descriptions) 
8.5 part 1 
4.2 
5.1, 5.2 
AI2d3 
PointSlope Form (Write
equation in pointslope form when given slope and coordinates of one point,
and convert to slopeintercept form or standard form.) 

4.3 
5.3, 5.4 
AI2d4 
Determining Equation of a Line from
a Mix of Information 
8.5 part 2 


AI3d1 
Relations (four
ways to represent a relation) 
8.6 
1.6 

AI3d2 
Functions (determining
whether a relation is a function; equations as functions; simple function notation) 
8.7 
1.7 part 1 
1.6, 1.7 
AI3d3 
Composite Functions (function
notation with simple expressions within function, composite functions;
finding the zero of a function) 
8.7 
1.7 part 2 

AI3d4 
Inverse Functions (finding
the inverse of a relation;
finding and graphing the inverse of a linear function) 

4.7 

AI3d5 
Direct Variation (finding
the constant of variation;
include realworld problems) 
8.9 
3.4 
4.6 


















































Unit 
Topic 
Dolciani 
Carter 
Larson 





V 
EXPONENTS AND POLYNOMIALS 




second trimester – 23 days 



AI1d1 
Exponents (write
multiplication expressions with variables in exponential form; evaluate
exponential expressions by substituting, including negative bases; find area
of rectangle with variable expressions as lengths, evaluate exponential
expressions with and without parentheses, evaluate with substitution) 
4.1 
7.1 

AI1d2 
Adding and Subtracting Polynomials (horizontal
and vertical; expressions with multiple variables and variety of powers;
vocabulary: degree of variable, of monomial, and of polynomial) 
4.2 
8.1 
9.1 
AI1d3 
RealWorld Problems Adding and Subtracting Polynomials (solve
equations with polynomials, where 2^{nd} degree terms drop out; solve
realworld problems involving geometry and consecutive integers) 
4.2 


AI1d4 
Multiplying Monomials (product
of power rule; all fractions simplify to integers; also, sums of products of monomials;
advanced problems: exponents are
polynomials) 
4.3 
7.1 
8.1 
AI1d5 
RealWorld Problems Multiplying Monomials (find
perimeters and surface areas of geometric figures by multiplying and adding monomials; simplify
expressions that include exponents with variables) 
4.3 


AI2d1 
Powers of Monomials (power
of product rule; power of power rule; evaluation of expressions using substitution; advanced
problems: exponents contain variables)

4.4 
7.1 

AI2d2 
Multiplying Polynomials by Monomials (distributive
property; distribute, then combine like terms; solve equations in which the
powers greater than one conveniently drop out) 
4.5 
8.2 
9.2 
AI2d3 
Multiplying Polynomials by Polynomials (horizontally
and vertically; FOIL; product of binomials and trinomials;
rewrite product in standard form;
advanced problems: solve
equations) 
4.6, 5.4 
8.3 
9.2 
AI2d4 
Special Products (recognize
patterns: binomials squared; product of sum and difference) 

8.4 
9.3 
AI3d1 
Division Properties of Exponents: Quotient of Powers (include
products of fractions containing variables with exponents; include problems that involve
finding the missing factor) 
5.2, 6.2 part 1 
7.2 pt 1a 
8.2 
AI3d2 
Division Properties of Exponents: Powers of Quotients (postpone
Dolciani “level B” factoring problems to later
unit) 
6.2 part 2 
7.2 pt 1b 
8.2 
AI3d3 
Negative Exponents (evaluate
expressions with negative exponents and exponents of zero, rewrite
expressions with positive exponents) 
7.9 
7.2 pt 2 
8.3 
AI3d4 
Scientific Notation (convert
between standard form and scientific notation; rewrite numbers in expanded notation
with powers of ten; multiply and
divide numbers written in scientific notation) 
7.10 
7.4 
8.4 
AI4d1 
RateTimeDistance Problems (motion
in opposite directions; motion in same direction; use a chart.) 
4.8 
2.9 

AI4d2 
Area Problems (flower
garden surrounded by walkway, for example.
Use Polya’s method; quadratic portions of equation
usually cancel each other out.) 
4.9 
































Unit 
Topic 
Dolciani 
Carter 
Larson 





VI 
FACTORING POLYNOMIALS 




second trimester – 22 days 



AI1d1 
GCF, and Monomial Factors of Polynomials (Review
GCF of algebraic expressions; then, factor a polynomial by finding
the GCF of the terms, and divide polynomial by monomial by finding the GCF of
the polynomial and factoring the numerator.) 
5.1 and 5.3 
8.5 part 1 

AI1d2 
Differences of Two Perfect Squares (factoring
D2PS; also,
factoring with a combination of GCF and D2PS) 
5.5 part 1 
8.8 part 1 
9.7 
AI1d3 
The Zero Product Property – Basic Problems (solving
equations when the polynomial has already been factored; multiple roots; isolating the zero) 
5.12 part 1 
8.5 part 2 
9.4 
AI1d4 
The Zero Product Property – Factoring First (solving
equations by factoring a polynomial and then applying the zero
product property) 
5.12 part 2 
8.8 part 2 

AI1d4 
Advanced Cases of D2PS (expressions
within parentheses;
exponents with variables) 
5.5 part 2 


AI2d1 
Perfect Square Trinomials (factoring
PST) 
5.6 part 1 
8.9 
9.7 
AI2d2 
Advanced Cases of PST (expressions
within parentheses, and combos with GCF or D2PS) 
5.6 part 2 


AI2d3 
Factoring Trinomials with Leading
Coefficient of One (“reverse
FOIL”; both
“c positive” and “c negative”) 
5.7 and 5.8 
8.6 part 1 
9.5 
AI2d4 
Solving Equations by Factoring
Trinomials (Use
“reverse FOIL” to factor, then use zero product property to solve.) 

8.6 part 2 
9.5 
AI2d5 
Special Problems Related to Factoring (Problems
with geometry;
finding all possible coefficients that make a trinomial
factorable) 
5.7 and 5.8 advanced 


AI3d1 
Factoring with the Box Method (factoring
trinomials with a leading coefficient other than one with the “box” method) 
5.9 
8.7 
9.6 
AI3d2 
Factoring by Grouping (factoring
trinomials with a leading coefficient other than one by grouping) 
5.10 part 1 
8.5 part 2 

AI3d3 
Solving Equations Using Several Methods of Factoring (factor
polynomials with a variety of characteristics, then use the zero product property to solve the equation) 
supplemental 


AI3d4 
Advanced Factoring by Grouping (factoring
fourterm polynomials by grouping) 
5.10 part 2 


AI3d5 
Using Several Methods of Factoring (factoring
polynomials with a variety of characteristics) 
5.11 


AI3d6 
Advanced Factoring of Trinomials (factoring
when “variable” is a binomial instead) 
5.8 and 5.9 advanced 


AI3d7 
Using Factoring to Solve RealWorld Problems (number
puzzle problems and geometry problems) 
5.13 

















Unit 
Topic 
Dolciani 
Carter 
Larson 





VII 
ALGEBRAIC FRACTIONS 




third trimester – 14 days 



AI1d1 
Simplify Algebraic Fractions by Factoring (simplify
algebraic fraction by factoring numerator and denominator; includes factoring out a negative
one to eliminate opposites. Advanced
problems involving equation solving.) 
6.1 
11.3 
12.4 
AI1d2 
Simplify Products of Fractions by
Factoring 
6.2 part 2+ 
11.4 
12.5 
AI1d3 
Simplify Algebraic Quotients by Factoring (advanced
problems involve combinations of multiplication and division) 
6.3 
11.4 

AI1d4 
Adding and Subtracting Algebraic Fractions (add
and subtract algebraic fractions, including those with numerators or
denominators with products of binomials and monomials, by factoring the
polynomials and finding the least common denominator) 
6.4 and 6.5 
11.6 
12.6 
AI2d1 
Adding and Subtracting Mixed Expressions (rewriting
sums and differences of fractions and monomials as one algebraic fraction) 
6.6 
11.7 

AI2d2 
Polynomial Long Division (supplement
with determining whether a binomial is a factor of a fourterm polynomial,
and solving factoring problems with partial solutions) 
6.7 
11.5 
12.3 
AI2d3 
Simplify Complex Fractions by
Factoring 
6.7 extra 
11.7 
post 12.5 
AI2d4 
Equations with Fractional Coefficients (using
fraction destroyer;
include realworld problems) 
7.3 


AI2d5 
Fractional Equations (using
fraction destroyer with variables in denominator) 
7.4 
11.8 
12.7 
AI2d6 
Work Problems (using work rate and tables) 
7.8 
11.8 











VIII 
SYSTEMS OF LINEAR EQUATIONS 




third trimester – 7 days 



AI1d1 
The Graphing Method (include
“no solution” and “infinitely many solutions”) 
9.1 
6.1 
7.1, 7.5 
AI1d2 
The Substitution Method (include
“no solution” and “infinitely many solutions”) 
9.2 
6.2 
7.2, 7.5 
AI1d3 
The AdditionorSubtraction Method 
9.4 
6.3 
7.3 
AI1d4 
Multiplication with the AdditionorSubtraction Method 
9.5 
6.4 
7.4 
AI1d5 
Solving Problems with Two Variables (real
world problems) 
9.3 
6.5 














































Unit 
Topic 
Dolciani 
Carter 
Larson 





IX 
INEQUALITIES 




third trimester – 10 days 



AI1d1 
Solving Inequalities (reversing
inequality symbol; graphing solution set; solving realworld problems
involving “no more than”, “at least”.) 
10.2 
5.1 and 5.2 
6.1, 6.2 
AI1d2 
Solving MultiStep Inequalities 
10.2 
5.3 
6.3 
AI1d3 
Solving Combined Inequalities (conjunctions,
disjunctions, and graphing) 
10.4 
5.4 
6.4 
AI1d4 
Absolute Value Equations (“absolute
value” as “distance”; graphing solution sets; review of topic in unit 2) 
10.5 part 1 
2.5 
6.5 
AI1d5 
Absolute Value with “Less Than” Symbol (“absolute
value” as “distance”; graphing solution sets) 
10.5, 10.6 
5.5 
6.6 
AI1d6 
Absolute Value with “Greater Than”
Symbol 
10.5, 10.6 
5.5 
6.6 
AI1d7 
Graphing Linear Inequalities in Two Variables (on
coordinate plane;
include situations with one variable only) 
10.7 
5.6 
6.7 
AI1d8 
Graphing Systems of Linear Inequalities (on
coordinate plane;
shading and double shading) 
10.8 
6.6 
7.6 










X 
RADICAL EXPRESSIONS AND EQUATIONS 




third trimester – 10 days 



AI1d1 
Properties of Rational Numbers (density
property of rational numbers; find number half way between two fractions; state
whether fraction increases or decreases as variable increases) 
11.1 
0.2 

AI1d1 
Decimal Forms of Rational Numbers (converting
between fractions and terminating or repeating decimals) 
11.2 


AI1d2 
Rational Square Roots 
11.3 
10.2 
11.2 
AI1d2 
Irrational Square Roots (simplify
by finding hidden squares through prime factorization; using calculator or
estimating from table of square root values) 
11.4 
10.2 
11.2 
AI1d3 
Square Roots of Algebraic Expressions (simplify
by finding even powers of variables; when to use absolute value symbol;
factoring a polynomial under a radical; solving an equation by isolating a
variable squared and using the definition of square root) 
11.5 
10.2 
11.2 
AI1d4 
Multiplying, Dividing, and Simplifying Radicals (attributes
of “simplest form”; rationalizing the denominator; using distributive property with
radicals) 
11.7 
10.3 
11.2 
AI1d5 
Adding and Subtracting Radicals (“like”
and “unlike” radicals; simplifying to create “like” radicals) 
11.8 
10.3 
11.2 
AI1d6 
Multiplication of Binomials Containing Radicals (FOIL
binomials containing radicals; use conjugates to rationalize the
denominator) 
11.9 
10.3 

AI1d7 
Simple Radical Equations (isolate
the radical, square both sides, and check the solution) 
11.10 
10.4 
11.3 
AI1d8 
Rational Exponents and nth Roots (converting
between radicals with indexes other than two, and fractions as exponents; solving
exponential equations; not in Academy curriculum) 
11.10 extra 
7.3 
post 8.3 
Unit 
Topic 
Dolciani 
Carter 
Larson 





XI 
QUADRATIC FUNCTIONS 




third trimester – 10 days 



AI1d1 
Quadratic Equations with Perfect Squares (express
solution in simplest radical form) 
12.1 

10.4 
AI1d2 
Completing the Square (express solution in simplest radical form) 
12.2 
9.4 
10.5 
AI1d3 
The Quadratic Formula (express
solution in simplest radical form; estimate solution) 
12.3 
9.5 
10.6 
AI1d4 
Graphing a Quadratic Equation (find
line of symmetry;
find vertex; use symmetry for short cut) 
8.8 
9.1 
10.1, 10.2 
AI1d5 
Solve the Quadratic Equation by Graphing (find
the companion function;
find the roots of the function)


9.1 
10.3 
AI1d6 
Quadratic Equations: The Discriminant (use
discriminant to count roots; does vertex lie above, on, or below
xaxis) 
12.4 

10.7 
AI1d7 
Method of Solution (solve
variety of quadratic equations by selecting the best method) 
12.5 
9.5 part 2 

AI1d8 
Solving Problems Involving Quadratic Equation (realworld
problems, mostly involving geometry) 
12.6 







XII 
SPECIAL FUNCTIONS AND OTHER TOPICS 




third
trimester – 15 days 



AI1d1 
Factor Sums and Differences of Perfect Cubes (hide
topic in intro, and reveal as a surprise) 
5.13 extra 


AI1d2 
Graphing Quadratic Inequalities in
Two Variables 

9.2 extend 

AI1d3 
Interpreting Graphs of Functions (intercepts;
symmetry; extrema; end behavior; they don’t include domain and range,
but these should be included) 

1.8 

AI1d4 
Solve a Quadratic Inequality in One Variable (intercepts;
symmetry; extrema; end behavior; they don’t include domain and range,
but these should be included) 
12.6 extra 


AI1d5 
Attributes of Graphs of Quadratic Functions (group
quadratic functions into families; predict shape of graph of quadratic
function) 

9.3 explore 
10.8 
AI1d6 
Transformations of Graphs of Quadratic Functions (translations, dilations, and reflections) 

9.3 

AI1d7 
Exponential Functions (graph exponential functions; identify data that display exponential behavior) 

7.5 
8.5 
AI1d8 
Growth and Decay (realworld problems) 

7.6 
8.6 
AI1d9 
Special Functions (absolute
value functions; piecewise functions; step functions) 

9.7 

AI1d10 
Writing Equations To Model Data (linear,
quadratic, and exponential functions) 

9.6 

AI1d11 
Square Root Functions 

10.1 
11.1 
AI1d12 
Inverse Variation 
8.10 
11.1 
12.1 
AI1d13 
Rational Functions 

11.2 
12.2 














