The Academy of the Most Blessed Sacrament PREALGEBRA MATH CURRICULUM OUTLINE
(last updated August 9, 2019) (170 days)
Unit 
Topic 
Glencoe PreAlg 
Larson CC 




I 
THE TOOLS OF ALGEBRA & OPERATIONS
WITH INTEGERS 



first trimester – 18 days 


AI1d1 
Order of Operations 
1.1 
1.3 
AI1d2 
The Pesky “Dash” Symbol (three uses of the “dash” symbol) 
supplemental 

AI1d3 
Numerical and Algebraic Expressions (defining
a variable) 
1.1, 1.2 

AI1d4 
Substitution and Evaluation (includes
twopart word problems: write
algebraic expression, then substitute and evaluate when given additional
information) 
1.2 
1.1 
AI1d5 
Simplifying Algebraic Expressions (using
properties of addition and multiplication) 
1.3 

AI2d1 
Integers and Absolute Value (compare,
order, evaluate with substitution) 
2.1 
1.4 
AI2d2 
Add and Subtract Integers 
2.2, 2.3 
1.5, 1.6 
AI2d2 
Multiply and Divide Integers (also,
simplifying algebraic multiplication expressions; finding mean) 
2.4, 2.5 
1.7 
AI2d3 
Add, Subtract, Multiply, Divide Decimal Numbers (supplemental
material for negative numbers; also, modular arithmetic) 
0.3 

AI3d1 
Ordered Pairs and Relations (relations
as ordered pairs, tables, and graphs.
Coordinate plane.) 
1.4 

AI3d2 
Functions (mapping; algebraic
function rule) 
1.5 

AI3d3 
Graphing in Four Quadrants (new
topic: graphing algebraic
relationship) 
2.6 
1.8 
AI3d4 
Adding and Subtracting Matrices (include
definition of dimensions) 
Extend 2.3 









































































Unit 
Topic 
Glencoe PreAlg 
Larson CC 




II 
OPERATIONS WITH RATIONAL NUMBERS, AND
SIMPLIFYING ALGEBRAIC EXPRESSIONS 



first trimester – 14 days 


AI1d1 
Writing Fractions as Decimals (compare fractions with decimals; ordering fractions and decimals, including negatives) 
3.1 
5.1 
AI1d2 
Writing Decimals as Fractions (converting both terminating and repeating decimals to fractions) 
3.2 
5.1 
AI1d3 
Classification of Numbers (definition of natural number, whole number, integers) 
3.2 
5.1 
AI1d4 
Multiplying Rational Numbers (products
of positive and negative fractions and mixed numbers; substitute and
evaluate; supplemented with
multiplication of algebraic expressions) 
3.3 
5.4 
AI1d5 
Dividing Rational Numbers (quotients
of positive and negative fractions and mixed numbers; substitute and
evaluate; simple division of algebraic fractions) 
3.4 
5.5 
AI1d6 
Adding and Subtracting Like Fractions (sums
and differences of positive and negative fractions and mixed numbers; Note: Section 3.5 Example 6 and
Page 153 Part C should be postponed until after section 4.1 below.) 
3.5 
5.2 
AI1d7 
Adding and Subtracting Unlike Fractions (sums
and differences of positive and negative fractions and mixed numbers) 
3.6 
5.3 
AI2d1 
Simplifying Expressions using Distributive Property (Supplement with discussion of the
three uses of the “long dash”: negative sign, subtraction operation, and
opposite symbol) (√ AL – multiply mixed number by whole number) (√ AL – find the obscured numbers) (√ AL – factoring a linear expression) 
4.1 
2.2 
AI2d2 
Simplifying Expressions by
Combining Like Terms 
4.2 

AI2d3 
Simplifying Expressions with Multiple Steps (Twostep
problems: use distributive property, then combine like terms; Supplement with 3.5 Example 6 and Page 153 Part C) 
4.2 
2.3 








































































Unit 
Topic 
Glencoe PreAlg 
Larson CC 




III 
EQUATIONS 



first trimester – 15 days 


AI1d1 
Solving OneStep Equations by
Adding and Subtracting Integers 
4.3 
2.5 
AI1d2 
Solving OneStep Equations by
Adding and Subtracting Fractions, Mixed Numbers, and Decimals 
4.3 
2.7, 5.7 
AI1d3 
Solving One and TwoStep Equations by Dividing (include fractions, decimals, and negatives; twostep with simplification first) 
4.4 
2.6, 5.7 
AI1d4 
Solving OneStep Equations by Multiplying (onestep, with fractions, decimals, and negatives; include use of reciprocals) 
4.4 
2.6, 5.6 
AI1d5 
Solving TwoStep and MultiStep Equations (write
the justification for each step) 
4.5 
3.1 
AI1d6 
MultiStep Challenging Equations (including fractions and decimals; simplifying
expressions first) 
supplemental 
3.2 
AI2d1 
More MultiStep Challenging Equations (including distributive property; negative
and positive mixed numbers) 
supplemental 

AI2d2 
Real World Problems (introduce Polya’s
4step method) (√ AL – match situation with equation) 
4.6 

AI2d3 
Solving Equations with Variable on Each Side (includes
decimals and fractions) 
5.2 
3.3 
AI2d4 
Solving Challenging Equations with
Variable on Each Side 
supplemental 

AI2d5 
Solving RealWorld Problems with Equations with Variable on Each Side (√ AL – “How many times smaller” problems) 
5.2 









IV 
INEQUALITIES, AND SPECIAL EQUATIONS 



second trimester – 12 days 


AI1d1 
Writing and Graphing Inequalities (graph inequality on number line; examine graph and write corresponding inequality) 
5.3 

AI1d2 
Solving Inequalities with Addition and Subtraction (fractions and decimals; realworld problems) 
5.4 
3.4 
AI1d3 
Solving Inequalities with Multiplication and Division (including reversal of inequality symbol; fractions and decimals; realworld problems) 
5.4 
3.5 
AI1d4 
MultiStep Inequalities (includes
realworld problems with phrases “no more than”, “at most”, etc) 
5.5 
3.6 
AI2d1 
Solving Literal Equations (isolating
a variable) 
supplemental 
post 3.3 
AI2d2 
Perimeter and Area of Rectangles and Triangles (Use
of formulas;
isolating a variable in a formula) 
5.1 

AI2d3 
Solving Equations with the Fraction
Destroyer 
supplemental 

AI2d4 
Recognizing Identities, and Equations with No Solution (Also,
absolute value equations, and equations with a choice of missing values) (√ AL – problems in “properties of addition and
subtraction”) 
5.5 part 2 













Unit 
Topic 
Glencoe PreAlg 
Larson CC 




V 
RATIO, PROPORTION, SIMILAR FIGURES, AND
PERCENTS 



second
trimester – 19 days 


AI1d1 
Ratios and Unit Rates (ratios
as fractions only; simplify by converting measurements; simple unit rates) 
6.1, 6.2 
6.1 
AI1d2 
Dimensional Analysis (dimensional
analysis requires supplemental material; conversions between metric and
customary units of measure) 
6.3 

AI1d3 
Solving Proportions with Cross Products (include
use of distributive property, and decimal numbers) 
6.5 
6.2, 6.3 
AI1d4 
Confirming Proportional Relationships, and RealWorld Problems with Proportions (identify
proportional relationship from data in table or from graph; solve for
constant of proportion;
solve realworld problems with proportions) (√ AL – challenging problems in identifying
proportional relationships) (√ AL – challenging realworld problems with ratios and
proportions) 
6.4, 6.5 

AI2d1 
Real World Applications of Ratios: Scale Drawings (finding
a length or distance when given the scale; finding the scale when given
information on lengths and distances; scale vs scale factor) 
6.6 
6.6 
AI2d2 
Real World Applications of Ratios: Similar Figures (geometry:
includes symbols for similar and congruent; identify corresponding sides) 
6.7 
6.4, 6.5 
AI2d3 
Real World Applications of Ratios: Indirect Measurement (includes
surveying methods) (√ AL – challenging problems with scale drawings) 
6.9 

AI2d4 
Converting Among Fractions, Percents, and Decimals (this
is all review) 
7.1, 7.2 
7.1, 7.3 
AI3d1 
Solving RealWorld Problems Using the Percent Formula (√ AL – real world “flight” problem, “pay raise” problem, and others) 
7.3, 7.5 
7.2, 7.4 
AI3d2 
Percents and Mental Math 
7.4 

AI3d3 
Percent of Change 
7.6 
7.5 
AI3d4 
RealWorld Percent Problems: Simple Interest (Larson
includes compound interest) 
7.7 
7.7 
AI3d5 
RealWorld Percent Problems: Circle Graphs 
7.8 
post 11.1 
































































Unit 
Topic 
Glencoe PreAlg 
Larson CC 




VI 
STATISTICS AND PROBABILITY 



second trimester – 23 days 






AI1d1 
Theoretical and Experimental Probability (postpone
finding odds to later lesson) 
Carter 13.6 pt 1 

AI1d2 
Probability Tables (vocabulary: experiment, event, sample space) 
Holt 101 

AI1d3 
Experimental Probability (estimate
probability by examining results of an experiment) 
Holt 102 

AI2d1 
Ideal Sample Space (theoretical
probability of an event in an ideal sample space) 
Holt 104 part 1 

AI2d2 
Probability of Mutually Exclusive Events (also,
complement of an event) 
Holt 104 part 2 
11.8 
AI2d3 
Probability of Compound Events: Independent Events (determine
whether a pair of events are independent or dependent; find probability if they are
independent) 
Hot 105 part 1 Carter 13.10 pt 1 
11.9 
AI2d4 
Probability of Compound Events: Dependent Events (find
probability using multiplication or with a tree diagram) 
Holt 105 part 2 Carter 13.10 pt 1 
11.9 
AI2d5 
Making Predictions (using
experimental probability and proportions) 
Holt 106 Carter 13.6 pt 2 

AI3d1 
Odds (finding
the odds of an event;
converting between probability and odds) 
Holt 107 Carter 13.6 pt 1+ 
6.7 
AI3d2 
Fundamental Counting Principle (find
number of possible outcomes and number of successful outcomes of an
experiment, and use this to find probability of an event) 
Holt 108 Carter 13.8 
6.8 
AI3d3 
Counting Outcomes Involving Combinations (distinguish
between permutations and combinations; use factorial notation to count
possible outcomes involving combinations) 
Holt 109 part 1 Carter 13.9 
11.7 
AI3d4 
Counting Outcomes Involving Permutations (use
factorial notation to count possible outcomes involving permutations; solve probability problems involving
combinations and permutations) 
Holt 109 part 2 
11.6 
AI3d5 
Geometric and Continuous Probability 
Carter Page 820 

AI3d6 
Random Sampling Techniques 
Carter 13.7 

AI3d7 
Comparing Populations (double
boxandwhisker plots, and mean absolute deviation) 
Carter Pages 924925 

ER1d1/2 
Design a Simulation to Find Probability (Performance
assessment) 
Holt 103 













































Unit 
Topic 
Glencoe PreAlg 
Larson CC 




VII 
LINEAR FUNCTIONS AND GRAPHING 



third
trimester – 24 days 


AI1d1 
Relations and Functions (domain
and range; independent and dependent variable; determining whether a relation is a
function; four ways to portray a
function) 
8.1 part 1 
8.1 
AI1d2 
Function Notation (function
rule; compound functions) 
8.1 part 2 
8.7 
AI1d3 
Write Equation from a Given Sequence (find
nth term in an arithmetic sequence; includes illustrated problems) 
8.2 

AI1d4 
Graph Linear Equation by Finding x and y Intercepts (discrete
vs continuous data; graphing realworld situation) 
8.3 
8.3 
AI1d5 
Rate of Change (find
rate of change from graph or table) 
8.4 

AI1d6 
Direct Variation (determine
whether rate of change is constant; find constant of variation) 
8.5 
post 8.5 
AI2d1 
Slope (two
ways: rise over run, and the slope
formula) 
8.6 
8.4 
AI2d2 
Graph an Equation from SlopeIntercept Form (equation
already in slopeintercept form) 
8.7 part 1 
8.5 
AI2d3 
Transform Equation to SlopeIntercept Form, and Graph (includes
transforming equation to slopeintercept form) 
8.7 part 2 

AI2d4 
Find Equation of Line (Basic) (when given slope and yintercept, or when shown a graph) 
8.8 part 1 
8.6 
AI2d5 
Find Equation of Line (Intermediate) (when given two points when given a table of values, using pointslope form; transforming to slopeintercept form ) 
8.8 part 2 

AI3d1 
Solving Systems of Equations by Graphing (include
cases of no solution and infinitely many solutions) 
8.10 part 1 
8.8 
AI3d2 
Solving Systems of Equations by Substitution (simple
cases only –
one variable already isolated) 
8.10 part 2 
post 8.8 
AI3d3 
Graphing Linear Inequalities 
post 8.3 
8.9 
AI3d4 
Translations and Reflections (on
the coordinate plane;
introduce “prime” notation for coordinates) 
2.7 
12.4, 12.5 
AI3d5 
Dilations (on
the coordinate plane; scale factors greater than one, less than one) (Larson
12.6 covers rotations) 
6.8 
12.7 
ER1d1,2 
Drawing Line of Best Fit; Making Predictions (use
special twoday lab) 
8.9 
post 8.5 
















































Unit 
Topic 
Glencoe PreAlg 
Larson CC 




VIII 
POWERS, ROOTS, AND CLASSIFICATION OF
NUMBERS 



third trimester – 22 days 


AI1d1 
Powers and Exponents (write
expressions using exponents, including simple cases with variables and
multiplication; no power rules yet; nonnegative exponents only; base
with positive and negative fractions and decimal numbers) 
9.1 
1.2 
AI1d2 
Rules of Divisibility (supplemented
to include divisibility by 4, 7, 8, 9, and 11) 
pre 9.1 

AI1d3 
Prime Factorization (review
“prime” and “composite”, introduce “monomial”, review “factor tree” and
“birthday cake”; prime factorization of simple cases with variables) 
9.2 
4.1 
AI1d4 
Product of Powers and Quotient of Powers Properties (positive
exponents only) 
9.3 
4.5 
AI1d5 
Greatest Common Factor Using Prime Factorization (GCF
of a pair of algebraic expressions) 
post 9.2 part 1 
4.2 
AI2d1 
Least Common Multiple Using Prime Factorization (LCM
of a pair of algebraic expressions) 
post 9.2 part 2 
4.4 
AI2d2 
Addition and Subtraction of Algebraic Fractions (with
unlike denominators) 
supplemental 

AI2d3 
Negative Exponents – Rewrite Expressions (convert
algebraic expressions to positive exponents; rewrite fractions as expressions
containing negative exponents) 
9.4 
4.6 
AI2d4 
Negative Exponents – Evaluate
Expressions 
9.4 

AI2d5 
Scientific Notation  Conversions (convert
to and from standard form; sequencing; comparing) 
9.5 
4.7 
AI2d6 
Scientific Notation – Add, Subtract, Multiply,
and Divide 
post 9.5 
4.7 
AI2d7 
Power of Power and Power of Product Properties (simplify
algebraic expressions) 
9.6 

AI3d1 
Square Roots (radical
symbol, plusorminus symbol, estimating square roots, decimal numbers and
fractions as radicands) 
10.1 
9.1 
AI3d2 
Set Theory, and Classification of Numbers (intersection
and unions symbols, Venn diagrams; subset; empty set; classification of real numbers as
natural numbers, whole numbers, integers, rational numbers, and irrational
numbers) 
pre 10.2 10.2 part 1 

AI3d3 
The Real Number System, and Square Root Equations (classification
of real numbers, comparing and ordering with number line, solving simple
quadratic equations with the definition of square root. 
10.2 part 2 
9.4 
AI3d4 
Cube Roots and Higher Roots (cube
root symbol, negative radicand, higher roots) 
post 10.1, supplemental 









































Unit 
Topic 
Glencoe PreAlg 
Larson CC 




IX 
RIGHT TRIANGLES AND ANGLES 



third
trimester – 23 days 


AI1d1 
Classifying Triangles, Finding Missing Angle Measurement (supplemental: using algebra to find missing measurement) 
10.3, supplemental 

AI1d2 
Triangle Inequality Theorem (use
lab in class) 
post 10.3 

AI1d3 
Pythagorean Theorem and its Converse (use
lab on Page 581; include problems in finding missing leg length) 
10.4 
9.3 
AI1d4 
Distance Between Two Coordinates (two
methods: distance formula and
coordinate plane) 
10.5 
9.5 
AI2d1 
Special Right Triangles (Solve
for distances in 454590 and 306090 triangles) 
10.6 
9.6 
AI2d2 
Using a Table of Trigonometric Ratios (use
lab to introduce the tangent ratio) 
supplemental 

AI2d3 
Using the Tangent Ratio (Use both trig tables and calculators) 
supplemental 
9.7 
AI2d4 
Using the Sine and Cosine Ratios (Use
both trig tables and calculators) 
supplemental 
9.8 
AI2d5 
Using a Mix of Trigonometric Ratios (Use
both trig tables and calculators) 
supplemental 

AI3d1 
Angle Pairs (vertical
angles, adjacent angles, supplementary angles, complementary angles) 
11.1 part 1 
12.1 
AI3d2 
Parallel Lines and Transversals (alternate
interior angles, alternate exterior angles, corresponding angles) 
11.1 part 2 
12.2 
AI3d3 
Congruent Parts of Congruent Triangles (alternate
interior angles, alternate exterior angles, corresponding angles) 
11.2 

AI3d4 
Quadrilaterals and Their Angles 
11.4 
10.2 
AI3d5 
Interior Angles of a Polygon 
11.5 
12.3 
AI3d6 
Perimeters and Areas of Similar
Polygons 
11.6 extend 

AI4d1 
Area and Circumference of Circles 
11.7 – 11.8 
10.4 
AI4d2 
Cross Sections of 3Dimensional Figures 
12.1 
post 10.6 