The Academy of the Most Blessed Sacrament ALGEBRA I CURRICULUM OUTLINE
(last updated August 9, 2019) (177 days)
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Unit |
Topic |
Dolciani |
Carter |
Larson |
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I |
REAL NUMBERS AND ALGEBRAIC EXPRESSIONS |
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first trimester – 15 days |
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AI1d1 |
Variables and Grouping Symbols (parentheses,
brackets and fraction bars; easy oops with substitution) |
1.1, 1.2 |
1.2 |
1.1, 1.2 |
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AI1d2 |
Translate Words into Symbols (also,
complete word phrase when given additional information) |
1.4 |
1.1 |
1.3 |
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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 |
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AI1d4 |
Simplifying and Estimating Square Roots (rounding
square roots to nearest integer) |
1.8 |
0.2 part 2 |
2.7 |
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AI1d5 |
Opposites and Absolute Values (simple
sums, differences, comparisons, simple absolute value equations) |
1.9 |
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AI1d5 |
Adding and Subtracting Real Numbers (no
algebraic expressions yet) |
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0.3, 0.4 |
2.2, 2.3 |
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AI1d5 |
Multiplying and Dividing Real Numbers (no
algebraic expressions yet; find a number between any two rational numbers) |
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0.3, 0.5 |
2.4, 2.6 |
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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 |
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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 |
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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) |
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1.3 |
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AI2d4 |
Distributive Property (use
as short cut; simplifying algebraic expressions) |
2.5 |
1.4 |
2.5 |
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AI2d5 |
Rules for Multiplication (includes
algebraic expressions with combining like terms; integers only) |
2.6 |
1.4 |
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AI2d6 |
Reciprocal of a Real Number (simplify
algebraic expressions, including fractions and distributive property) |
2.8 |
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AI2d6 |
Dividing Real Numbers (simplify
algebraic expressions;
all involve integers - - no fractions or decimals) |
2.9 |
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Unit |
Topic |
Dolciani |
Carter |
Larson |
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II |
EQUATIONS |
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first
trimester – 18 days |
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AI1d1 |
Equations (solve
simple equations and word problems over given domain. Introduce “is element of” symbol) |
1.3 |
1.5 |
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AI1d2 |
Transforming Equations: Addition and Subtraction (integers; opposite) |
3.1 |
2.2 |
3.1 |
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AI1d3 |
Transforming Equations: Multiplication and Division (includes simple fractions and mixed numbers) |
3.2 |
2.2 |
3.1 |
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AI1d4 |
Using Several Transformations (simple two-step problems; fractional expressions; distributive property) |
3.3 |
2.3 |
3.2, 3.3 |
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AI1d5 |
Translate Sentences and Problems Into Equations (includes
quantities grouped in parentheses, formulas, defining variable with “let”;
include two-step translations with sketch) |
1.5, 1.6 |
2.1 |
1.4 |
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AI1d6 |
A Problem Solving Plan (5
step Polya-type plan; answers given as choice of 3;
solving problems involving geometry) |
1.7, 3.4 |
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1.5 |
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AI1d7 |
Problem Solving: Consecutive Integers and Diagrams (word
problems) |
2.7 |
2.3 |
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AI2d1 |
Equations with Variable on Both Sides (includes
fractional expressions and distributive property; identity; no solution) |
3.5 |
2.4 |
3.4 |
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AI2d2 |
Absolute Value Equations (includes real-world distance problems and tolerance problems) |
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2.5 |
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AI2d3 |
The Fraction Destroyer (solving linear equations more efficiently by removing fractions) |
supplement |
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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 |
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AI2d5 |
Problem Solving Using Charts (rate
problems – calories per fruit, rides per ticket, etc.) |
3.6 |
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AI2d6 |
Cost, Income, and Value Problems - Introductory (using
charts; includes dimes and nickels, profit as selling price minus buying
price) |
3.7 |
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AI2d7 |
Cost, Income, and Value Problems - Challenging (also,
more challenging consecutive integer problems) |
3.7 |
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Unit |
Topic |
Dolciani |
Carter |
Larson |
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III |
RATES, RATIOS AND PERCENTS |
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first trimester – 14 days |
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AI1d1 |
Ratios (convert
simple measurements (days and weeks, etc) to reduce
ratio to simplest form;
ratios of perimeters and areas of rectangles; real-world
problems; ratio of x to y) |
7.1 |
2.6 |
3.5 |
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AI1d2 |
Proportions (Solve
with cross-multiplication;
some numerators and denominators are binomials; some have
variables on both sides) |
7.2 part 1 |
2.6 |
3.5, 3.6 |
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AI1d3 |
Real-world 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 |
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AI1d4 |
The Mean Proportional (also,
using the mean proportional to find the missing number in a geometric
sequence) |
7.2 part 3 |
2.6 |
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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 |
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AI1d6 |
Real-world Problems with Percents (solve
percentage real-world problems with the percent proportion: solve equations
using the decimal destroyer) |
7.5 part 2 |
0.6 |
3.7 |
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AI2d1 |
Percent Change Problems |
7.6 |
2.7 |
post 3.7 |
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AI2d2 |
Compound Proportions |
supplement |
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AI2d3 |
Dimensional Analysis (include
unit rates;
conversions between customary and metric units of measure) |
7.3 extra |
2.8 |
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AI2d4 |
Mixture Problems (“raisins,
nuts and mixture”, “dilute 70% acid to 40% acid”, with charts) |
7.7 |
2.9 |
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Unit |
Topic |
Dolciani |
Carter |
Larson |
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IV |
GRAPHING LINEAR EQUATIONS |
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second trimester – 19 days |
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AI1d1 |
Equations in Two Variables (determine
whether an ordered pair is a solution of an equation in two variables;
isolate a given variable;
use guess-and-check to find a list of ordered-pair solutions) |
8.1 |
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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 |
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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 |
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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 |
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AI2d1 |
The Slope-Intercept Form of a Linear Equation (graph
equations written in slope-intercept form; transform equation to
slope-intercept form and graph; determine whether pair of lines whose
equations are given are parallel or perpendicular.) |
8.4 |
4.1. 4.4 |
4.5 |
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AI2d2 |
Determining the Equation of a Line (find
equation of line when given slope and y-intercept; 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 |
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AI2d3 |
Point-Slope Form (Write
equation in point-slope form when given slope and coordinates of one point,
and convert to slope-intercept form or standard form.) |
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4.3 |
5.3, 5.4 |
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AI2d4 |
Determining Equation of a Line from
a Mix of Information |
8.5 part 2 |
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AI3d1 |
Relations (four
ways to represent a relation) |
8.6 |
1.6 |
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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 |
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AI3d3 |
Composite Functions (function
notation with simple expressions within function, composite functions;
finding the zero of a function) |
8.7 |
1.7 part 2 |
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AI3d4 |
Inverse Functions (finding
the inverse of a relation;
finding and graphing the inverse of a linear function) |
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4.7 |
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AI3d5 |
Direct Variation (finding
the constant of variation;
include real-world problems) |
8.9 |
3.4 |
4.6 |
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Unit |
Topic |
Dolciani |
Carter |
Larson |
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V |
EXPONENTS AND POLYNOMIALS |
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second trimester – 23 days |
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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 |
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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 |
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AI1d3 |
Real-World Problems Adding and Subtracting Polynomials (solve
equations with polynomials, where 2nd degree terms drop out; solve
real-world problems involving geometry and consecutive integers) |
4.2 |
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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 |
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AI1d5 |
Real-World 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 |
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AI2d1 |
Powers of Monomials (power
of product rule; power of power rule; evaluation of expressions using substitution; advanced
problems: exponents contain variables)
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4.4 |
7.1 |
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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 |
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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 |
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AI2d4 |
Special Products (recognize
patterns: binomials squared; product of sum and difference) |
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8.4 |
9.3 |
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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 |
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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 |
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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 |
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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 |
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AI4d1 |
Rate-Time-Distance Problems (motion
in opposite directions; motion in same direction; use a chart.) |
4.8 |
2.9 |
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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 |
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Unit |
Topic |
Dolciani |
Carter |
Larson |
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VI |
FACTORING POLYNOMIALS |
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second trimester – 22 days |
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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 |
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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 |
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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 |
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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 |
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AI1d4 |
Advanced Cases of D2PS (expressions
within parentheses;
exponents with variables) |
5.5 part 2 |
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AI2d1 |
Perfect Square Trinomials (factoring
PST) |
5.6 part 1 |
8.9 |
9.7 |
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AI2d2 |
Advanced Cases of PST (expressions
within parentheses, and combos with GCF or D2PS) |
5.6 part 2 |
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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 |
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AI2d4 |
Solving Equations by Factoring
Trinomials (Use
“reverse FOIL” to factor, then use zero product property to solve.) |
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8.6 part 2 |
9.5 |
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AI2d5 |
Special Problems Related to Factoring (Problems
with geometry;
finding all possible coefficients that make a trinomial
factorable) |
5.7 and 5.8 advanced |
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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 |
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AI3d2 |
Factoring by Grouping (factoring
trinomials with a leading coefficient other than one by grouping) |
5.10 part 1 |
8.5 part 2 |
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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 |
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AI3d4 |
Advanced Factoring by Grouping (factoring
four-term polynomials by grouping) |
5.10 part 2 |
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AI3d5 |
Using Several Methods of Factoring (factoring
polynomials with a variety of characteristics) |
5.11 |
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AI3d6 |
Advanced Factoring of Trinomials (factoring
when “variable” is a binomial instead) |
5.8 and 5.9 advanced |
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AI3d7 |
Using Factoring to Solve Real-World Problems (number
puzzle problems and geometry problems) |
5.13 |
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Unit |
Topic |
Dolciani |
Carter |
Larson |
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VII |
ALGEBRAIC FRACTIONS |
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third trimester – 14 days |
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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 |
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AI1d2 |
Simplify Products of Fractions by
Factoring |
6.2 part 2+ |
11.4 |
12.5 |
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AI1d3 |
Simplify Algebraic Quotients by Factoring (advanced
problems involve combinations of multiplication and division) |
6.3 |
11.4 |
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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 |
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AI2d1 |
Adding and Subtracting Mixed Expressions (rewriting
sums and differences of fractions and monomials as one algebraic fraction) |
6.6 |
11.7 |
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AI2d2 |
Polynomial Long Division (supplement
with determining whether a binomial is a factor of a four-term polynomial,
and solving factoring problems with partial solutions) |
6.7 |
11.5 |
12.3 |
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AI2d3 |
Simplify Complex Fractions by
Factoring |
6.7 extra |
11.7 |
post 12.5 |
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AI2d4 |
Equations with Fractional Coefficients (using
fraction destroyer;
include real-world problems) |
7.3 |
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AI2d5 |
Fractional Equations (using
fraction destroyer with variables in denominator) |
7.4 |
11.8 |
12.7 |
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AI2d6 |
Work Problems (using work rate and tables) |
7.8 |
11.8 |
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VIII |
SYSTEMS OF LINEAR EQUATIONS |
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third trimester – 7 days |
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AI1d1 |
The Graphing Method (include
“no solution” and “infinitely many solutions”) |
9.1 |
6.1 |
7.1, 7.5 |
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AI1d2 |
The Substitution Method (include
“no solution” and “infinitely many solutions”) |
9.2 |
6.2 |
7.2, 7.5 |
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AI1d3 |
The Addition-or-Subtraction Method |
9.4 |
6.3 |
7.3 |
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AI1d4 |
Multiplication with the Addition-or-Subtraction Method |
9.5 |
6.4 |
7.4 |
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AI1d5 |
Solving Problems with Two Variables (real
world problems) |
9.3 |
6.5 |
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Unit |
Topic |
Dolciani |
Carter |
Larson |
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IX |
INEQUALITIES |
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third trimester – 10 days |
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AI1d1 |
Solving Inequalities (reversing
inequality symbol; graphing solution set; solving real-world problems
involving “no more than”, “at least”.) |
10.2 |
5.1 and 5.2 |
6.1, 6.2 |
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AI1d2 |
Solving Multi-Step Inequalities |
10.2 |
5.3 |
6.3 |
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AI1d3 |
Solving Combined Inequalities (conjunctions,
disjunctions, and graphing) |
10.4 |
5.4 |
6.4 |
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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 |
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AI1d5 |
Absolute Value with “Less Than” Symbol (“absolute
value” as “distance”; graphing solution sets) |
10.5, 10.6 |
5.5 |
6.6 |
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AI1d6 |
Absolute Value with “Greater Than”
Symbol |
10.5, 10.6 |
5.5 |
6.6 |
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AI1d7 |
Graphing Linear Inequalities in Two Variables (on
coordinate plane;
include situations with one variable only) |
10.7 |
5.6 |
6.7 |
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AI1d8 |
Graphing Systems of Linear Inequalities (on
coordinate plane;
shading and double shading) |
10.8 |
6.6 |
7.6 |
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X |
RADICAL EXPRESSIONS AND EQUATIONS |
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third trimester – 10 days |
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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 |
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AI1d1 |
Decimal Forms of Rational Numbers (converting
between fractions and terminating or repeating decimals) |
11.2 |
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AI1d2 |
Rational Square Roots |
11.3 |
10.2 |
11.2 |
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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 |
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AI1d6 |
Multiplication of Binomials Containing Radicals (FOIL
binomials containing radicals; use conjugates to rationalize the
denominator) |
11.9 |
10.3 |
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AI1d7 |
Simple Radical Equations (isolate
the radical, square both sides, and check the solution) |
11.10 |
10.4 |
11.3 |
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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 |
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Unit |
Topic |
Dolciani |
Carter |
Larson |
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XI |
QUADRATIC FUNCTIONS |
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third trimester – 10 days |
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AI1d1 |
Quadratic Equations with Perfect Squares (express
solution in simplest radical form) |
12.1 |
|
10.4 |
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AI1d2 |
Completing the Square (express solution in simplest radical form) |
12.2 |
9.4 |
10.5 |
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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 |
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AI1d5 |
Solve the Quadratic Equation by Graphing (find
the companion function;
find the roots of the function)
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9.1 |
10.3 |
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AI1d6 |
Quadratic Equations: The Discriminant (use
discriminant to count roots; does vertex lie above, on, or below
x-axis) |
12.4 |
|
10.7 |
|
AI1d7 |
Method of Solution (solve
variety of quadratic equations by selecting the best method) |
12.5 |
9.5 part 2 |
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AI1d8 |
Solving Problems Involving Quadratic Equation (real-world
problems, mostly involving geometry) |
12.6 |
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XII |
SPECIAL FUNCTIONS AND OTHER TOPICS |
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third
trimester – 15 days |
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AI1d1 |
Factor Sums and Differences of Perfect Cubes (hide
topic in intro, and reveal as a surprise) |
5.13 extra |
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AI1d2 |
Graphing Quadratic Inequalities in
Two Variables |
|
9.2 extend |
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AI1d3 |
Interpreting Graphs of Functions (intercepts;
symmetry; extrema; end behavior; they don’t include domain and range,
but these should be included) |
|
1.8 |
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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 |
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AI1d5 |
Attributes of Graphs of Quadratic Functions (group
quadratic functions into families; predict shape of graph of quadratic
function) |
|
9.3 explore |
10.8 |
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AI1d6 |
Transformations of Graphs of Quadratic Functions (translations, dilations, and reflections) |
|
9.3 |
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AI1d7 |
Exponential Functions (graph exponential functions; identify data that display exponential behavior) |
|
7.5 |
8.5 |
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AI1d8 |
Growth and Decay (real-world problems) |
|
7.6 |
8.6 |
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AI1d9 |
Special Functions (absolute
value functions; piece-wise functions; step functions) |
|
9.7 |
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AI1d10 |
Writing Equations To Model Data (linear,
quadratic, and exponential functions) |
|
9.6 |
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AI1d11 |
Square Root Functions |
|
10.1 |
11.1 |
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AI1d12 |
Inverse Variation |
8.10 |
11.1 |
12.1 |
|
AI1d13 |
Rational Functions |
|
11.2 |
12.2 |
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