The Academy of the Most Blessed Sacrament PRE-ALGEBRA 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 two-part 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

(Two-step 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 One-Step Equations by Adding and Subtracting Integers

4.3

2.5

AI1d2

Solving One-Step Equations by Adding and Subtracting Fractions, Mixed Numbers, and Decimals

4.3

2.7, 5.7

AI1d3

Solving One- and Two-Step Equations by Dividing

(include fractions, decimals, and negatives;  two-step with simplification first)

4.4

2.6, 5.7

AI1d4

Solving One-Step Equations by Multiplying

(one-step, with fractions, decimals, and negatives; include use of reciprocals)

4.4

2.6, 5.6

AI1d5

Solving Two-Step and Multi-Step Equations

(write the justification for each step)

4.5

3.1

AI1d6

Multi-Step Challenging Equations

(including fractions and decimals;  simplifying expressions first)

supplemental

3.2

AI2d1

More Multi-Step Challenging Equations

(including distributive property;  negative and positive mixed numbers)

supplemental

 

AI2d2

Real World Problems

(introduce Polya’s 4-step 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 Real-World 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; real-world problems)  

5.4

3.4

AI1d3

Solving Inequalities with Multiplication and Division

(including reversal of inequality symbol; fractions and decimals; real-world problems)  

5.4

3.5

AI1d4

Multi-Step Inequalities

(includes real-world 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 Real-World Problems with Proportions

(identify proportional relationship from data in table or from graph; solve for constant of proportion;  solve real-world problems with proportions)

( AL – challenging problems in identifying proportional relationships)

( AL – challenging real-world 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 Real-World 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

Real-World Percent Problems:  Simple Interest

(Larson includes compound interest)

7.7

7.7

AI3d5

Real-World 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 10-1

 

AI1d3

Experimental Probability

(estimate probability by examining results of an experiment)

Holt 10-2

 

AI2d1

Ideal Sample Space

(theoretical probability of an event in an ideal sample space)

Holt 10-4 part 1

 

AI2d2

Probability of Mutually Exclusive Events

(also, complement of an event)

Holt 10-4 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 10-5 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 10-5 part 2

Carter 13.10 pt 1

11.9

AI2d5

Making Predictions

(using experimental probability and proportions)

Holt 10-6

Carter 13.6 pt 2

 

AI3d1

Odds

(finding the odds of an event;  converting between probability and odds)

Holt 10-7

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 10-8

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 10-9 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 10-9 part 2

11.6

AI3d5

Geometric and Continuous Probability

Carter Page 820

 

AI3d6

Random Sampling Techniques

Carter 13.7

 

AI3d7

Comparing Populations

(double box-and-whisker plots, and mean absolute deviation)

Carter

Pages 924-925

 

ER1d1/2

Design a Simulation to Find Probability

(Performance assessment)

Holt 10-3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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 real-world 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 Slope-Intercept Form

(equation already in slope-intercept form)

8.7 part 1

8.5

AI2d3

Transform Equation to Slope-Intercept Form, and Graph

(includes transforming equation to slope-intercept form)

8.7 part 2

 

AI2d4

Find Equation of Line (Basic)

(when given slope and y-intercept, 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 point-slope form;  transforming to slope-intercept 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 two-day 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;  non-negative 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, plus-or-minus 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 45-45-90 and 30-60-90 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 3-Dimensional Figures

12.1

post 10.6