parent guide to mathematics at the scholars academy · revolves around several key number‐sense...

Parent Guide to Mathematics at the Scholars Academy

This guide is meant to inform parents about the curriculum and pathways for mathematics at the Scholars Academy.

Differentiation in mathematics occurs within each classroom to meet the needs of all students. Math placement is reviewed

each year for all students to ensure that the student placement remains appropriate. Students who demonstrate a need for

instruction below their traditional grade level will be referred to intervention.

Elementary School Mathematics

The Scholars Academy adopted Singapore Math as the elementary school mathematics curriculum in 2016.

What Is Singapore Math? You may be wondering what Singapore Math is all about, and with good reason. This is a totally new kind of math for you and your child. What you may not know is that Singapore has led the world in math mastery for over a decade; its students become competent and proficient mathematicians at very early ages. Even better, they grow to be capable problem solvers who think mathematically with ease. First, you need to know that Singapore Math takes a slightly different mathematical approach than what you may be used to. It revolves around several key number‐sense strategies: (1) building number sense through part‐whole thinking, (2) understanding place value, and (3) breaking numbers into decomposed parts or friendlier numbers, ones that are easier to work with in the four operations of (addition, subtraction, multiplication and division). Second, Singapore Math does something dramatically different when it comes to word problems. It relies on model drawing, which uses units to visually represent a word problem. Students learn to visualize what a word problem is saying so they we can understand the meaning and thus how to solve the problem. Third, we have mental math, which teaches students to calculate in their heads without using paper and pencil. Sure, your child will still need to commit some facts of memory, but mental math will teach him or her to do calculations using proven strategies that don’t require pencil and paper. Fourth, the strategies taught in Singapore are layered upon one another. One strategy is the foundation for another one. Last, Singapore Math teaches students to understand math in stages, beginning with concrete (using manipulatives such as counters, number disks, dice, and so on), then moving to pictorial (solving problems where pictures are involved), and finally working in the abstract (where numbers represent symbolic values). Through the process, students learn numerous strategies to work with numbers and build conceptual understanding. With time and practice, they eventually master the traditional methods and algorithms. Middle School Mathematics In grades 5 through 8 students progress through middle school and some high school curriculum. The Scholars Academy uses a variety of instructional resources for these courses. In middle school, instruction is based on the standards issued by the National Council of Teachers of Mathematics (NCTM). There are two categories of standards. TheContent Standards cover what students should know. Content Standards are organized by level andseparated into five mathematical areas: Numbers & Operations, Algebra, Geometry, Measurement, andData Analysis& Probability.The Process Standards describe mathematical processes that all students must engage in to gain meaningful understanding of the content. There are five process standards: Problem Solving, Reasoning and Proof, Communications, Connections, and Representation.

K-2 Mathematics

Students in grades K-2 will remain in their homeroom for math. Differentiation occurs through flexible ability grouping and

curricular compacting.

Kindergarten 1st Grade 2nd Grade

Primary Resource

Standards

Singapore Math KA, KB Engage New York

All K

Select 1st grade

Singapore Math 1A, 1B Engage New York

Remainder of 1st grade

Select 2nd grade

Singapore Math 2A, 2B Engage New York

Remainder of 2nd grade

Select 3rd grade

3-4 Mathematics

Beginning in 3rd grade, students will be placed into two ability groups for math instruction based on test data, teacher

recommendations, and information processing speed. Standards listed in the table reflect the median pace for each class.

Differentiation in each class will be provided for students who need either content review or acceleration.

3rd Grade 4th Grade

Primary Resource Standards Course Title

Singapore Math 3A, 3B

Remainder of 3rd grade, select 4th grade

Math 3A

Singapore Math 4A, 4B, 5A

Remainder of 4th grade and all 5th grade

Math 4A

Primary Resource Standards Course Title

Singapore Math 3A, 3B, 4A

Remainder of 3rd and all 4th grade

Math 3B

Singapore Math 4B, 5A, 5B Progress in Mathematics

All 5th grade and some 6th grade

Math 4B

5th – 8th Grade Mathematics

In middle school, the pathway broadens to provide three paths for students. The pathway taken by a student will determine

the number of high school math courses taken at the Scholars Academy. High schools require four mathematics courses for

graduation. Students who leave the Scholars Academy with three courses completed run out of math classes before

graduating from high schools. Colleges would like to see students take math every year in high school and not all schools will

have four courses beyond Math 3 available.

5th Grade 6th Grade 7th Grade 8th Grade

Leve

l 1

Primary Resource

Grade Level

Course Title

Progress in Math

All of Grade 6

Middle School Math 1

Fundamentals of Algebra

All of Grade 7


Foundations of Algebra

All of Grade 8

Pre-Algebra

Algebra 1

High School

High School Math 1

Leve

l 2

Primary Resource

Grade Level

Progress in Math & Fundamentals of Algebra

All of Grades 6th /7th

Foundations of Algebra

All of Grade 8

Algebra 1

High School

Geometry/Algebra 2

High School

Middle School Math 1: This course will review some 5th grade standards and cover all 6th grade standards. Students who

complete this course will be ready to take Middle School Math 2.

Middle School Math 2: In this course, 7th grade standards will be addressed. Students who complete this course will be ready

to take Pre-Algebra.

Middle School Math 3: Preparation for high school level mathematics will be the focus of this course. 7th and 8th grade

standards will be compacted for 5th grade students taking this course. Pre-Algebra for 6th and 7th grade students will focus on

8th grade standards.

High School Math 1: Students enrolled in this course have shown mastery of at least 75% of the 7th grade standards. This

course is an integrated course with a primary focus on Introductory Algebra topics. This course will review 8th grade math

standards covered in Pre-Algebra. Students completing this course will be prepared to enter High School Math 2 or Geometry.

This course has a required state End of Course Exam.

High School Math 2: Students enrolled in this course have received a grade of C or higher in Math 1 or have been granted

credit for Math 1 through the Credit by Demonstrated Mastery process. This course is an integrated course with a primary

focus on High School Level Geometry. Students completing this course will be prepared to enter High School Math 3 or

Algebra II.

High School Math 3: Students enrolled in this course have received a grade of C or higher in Math 2 or have been granted

credit for Math 2 through the Credit by Demonstrated Mastery process. This course is an integrated course with a primary

focus on Advanced Algebra and Introductory Trigonometry topics. Students completing this course will be prepared to enter

High School Pre-Calculus.

Course Title Middle School Math 2 Pre-Algebra High School Math 1 High School Math 2

5th Grade 6th Grade 7th Grade 8th Grade

Leve

l 3

Primary Resource

Grade Level

Course Title

Fundamentals & Foundations of Algebra

All of Grades 7th/8th

Pre-Algebra

Algebra 1

High School

High School Math 1

Geometry/Algebra 2

High School

High School Math 2

Geometry/Algebra 2

High School

High School Math 3

Discoverers I (Kindergarten) Through learning in Counting and Cardinality, Operations and Algebraic Thinking and Number, and Operations in Base Ten Discoverers I students focus on understanding the meaning of numbers and place value up to three-digit numbers. They model numbers in concrete, pictorial and abstract formats. Use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, and eventually with equations. Choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away. Through Learning in Geometry student: Describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. identify, name, and describe two-dimensional shapes and three-dimensional shapes presented in a variety of ways. Use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes. Students identify and extend patterns and sort objects and shapes using attributes. Students will also explore measurement through comparing heights, weights, and lengths. Matching and Sorting

•Classify Objects According to Attributes Numbers to 20 •Determine the Number in a Set Without Counting •Find all Numbers that Make 10 •Write the Digits Through 20 •Use Various Strategies for Counting •Solve Unknown Story Problems •Identify Numbers in Various Formats •Compare and Order Numbers in Ascending and Descending Order •Compare Groups of Different Amounts Using Greater Than and Less Than •Understand Place Value Using Various Strategies •Use Ordinal Numbers

Numbers To 100

•Model and Write Numbers as Number Bonds •Model Ten Numbers Using Place Value Strategies •Represent Teen Numbers Compositions and Decompositions as Addition Sentences

•Count By 1s, 5s, and 10s to 100 •Count in Ascending or Descending Order from Any Given Number Within 100

Addition andSubtraction Within 10

•Equal •Count on From Numbers Other Than One •Use Number Bonds, Number Lines, Number Stories, Objects, Sets, 5 Groups and Arrays to Model Composition and Decomposition of Numbers •Identify the Connection Between Equations and Concrete and Pictorial Representations of Addition and Subtraction •Solve Result Unknown and Addend Unknown Problems •Plus and Minus Sign •Solve Take from Result Unknown Equations •Relate Addition and Subtraction •Represent and Solve Story Problems Using Objects, Drawings, Expressions and Equations •Identify Fact Families

Geometry

•Use Positional Terms •Name and Identify Solid And Flat Shapes •Build Flat Shapes with Varying Lengths •Compose and Decompose Solid Shapes from Flat Shapes

Patterns •Identify and Extend Patterns Using Attributes Measurement andData

•Compare Lengths, Heights, and Weights of Different Object

Use Different Strategies for Measuring •Use A Pictograph to Answer Questions •Use A Ruler to Measure

Discoverers II (First Grade) Students in Discoverers II Scholars will learn to tell time and solve word problems involving coins and dollar bills. Data analysis will include students generating measurement data, creating tables and graphs, and interpreting results. Finally, students investigate, describe, and compare two and three dimensional shapes.

Ordinal Numbers

Naming position

Position problems Numbers to 150

Count by tens to 100

Read and write numerals and number words for tens

Read and write numbers words within 100

Interpret 2-digit numbers as tens and ones

Count to 150

Represent up to 150 objects with a written numeral

Estimate quantities within 100 by comparing to a known quantity

Estimate a quantity within 100 by making a reasonable guess

Understand that numbers have order

Compare numbers within 100 using a hundred chart

Count on or back

Use symbols >, <, =

Add and subtract multiples of 10 from multiples of 10 to 100

Add a multiple of 10 to any 2-digit number within 100

Add ones with renaming

Add a pair of 2-digit numbers when the ones digit has a sum greater than 10 using decomposition

Add tens to a 2-digit number

Add 2-digit numbers Common Shapes

Closed shapes, corners, sides and flat surfaces

Sort shapes according to attributes

Identify patterns based on shapes

Find and name 2D and 3D shapes based on defining attributes

Create composite shapes from 2D shapes

Combine shapes and solids

Name and count shapes as parts of a whole

Partition shapes and identify halves and quarters of circles and rectangles

Length

Compare lengths

Measuring length

Order 3 lengths using indirect comparison

Express length with centimeter cubes

Measure with consistent units Graphs

Picture graphs

Tally marks

Bar graphs

Word problems about a data set with 3 categories Word Problems

Solve unknown problems using model drawings Time

Tell time to the hour and half hour from analog and digital clock

Estimate time

Patterns

Measurement

Investigate Length

Compare Lengths Directly and Indirectly

Compare Lengths with non-standard units Multiplication

Put the same number in each group

Make groups with the same number

Write multiplication equations

Multiply within 40 Division

Divide by sharing

Divide by grouping Subtraction to 150

Subtract ones, no renaming

Subtract ones, with renaming

Subtract tens from a 2-digit number

Subtract two 2-digit numbers Money

Recognize and name coins and bills up to $20

Change a coin or bill for an equivalent set of coins or bills

Understand the cent and $ symbols

Compare the price of two items in cents or dollars

Add or subtract money in cents or dollars

Solve problems involving money

Discoverers III (Second Grade) Students in Discoverers III will extend their understanding of base-ten notation while working with numbers up to 1,000. This will include counting in multiples, hundreds, tens, and ones. Students will also explore the place value relationship in working with these units and comparing multi-digit numbers. They will continue to develop fluency and mental strategies for addition and subtraction up to 100, apply various models of addition and subtraction up to 1,000, and examine word problems and equations. Within the study of length, students will look at various standard units of measure and use rulers and tools appropriately. In second grade, the meaning of multiplication and division is learned through activities and problems involving equal groups, arrays, and area models. Students will then use properties of operations with single digit factors toa extend this critical area. Unit fractions with a numerator of 1, parts of a whole, and comparing and ordering fractions are explored with visual fraction models and equal numerators and denominators. Scholars will continue to tell and write time and solve word problems involving coins and dollar bills. Data analysis will include students generating measurement data, creating tables and graphs, and interpreting results. Finally, students investigate, describe, and analyze two and three-dimensional shapes.

Numbers to 1,000

Hundreds, Tens, and Ones

Number Words

Compare Numbers within 1,000 Addition and Subtraction within 1,000

Mental Math Strategies

Estimation, Addition, and Subtraction Strategies

Sum and Difference

Add Ones, Tens, and Hundreds without Renaming

Subtract Ones, Tens, and Hundreds without Renaming

Add Ones, Tens, Hundreds with Renaming

Subtract Ones, Tens, and Hundreds with Renaming

Solve for Missing Parts in Addition and Subtraction Equations

One Step and Two Step Word Problems Length

Meters o Estimate and Measure o Addition and Subtraction

o Word Problems

Centimeters o Estimate and Measure o Addition and Subtraction o Word Problems

Inches, Feet, and Yards o Estimate and Measure o Comparing Units o Addition and Subtraction o Word Problems

Multiplication and Division

Understand Concepts of Equal Groups and Sharing

Use Repeated Addition

Use rectangular arrays and pictures

Write equations

One Step and Two Step Word Problems

Multiply and Divide by 2, 3, 4, 5, 10

Relate Facts and Apply Properties of Equations

Understand Remainders

Review of Odd and Even Numbers Money

Count Bills and Coins (If needed)

Read and Write Money Amounts in Words (If needed)

Make Equivalencies (If needed)

Make Change

Addition and Subtraction of Money

Word Problems Fractions

Identify and Write Fractions of a Whole

Recognize and Write Halves, Thirds, and Fourths

Compare and Order Fractions Time

Tell Time to 5-Minute Interval

Tell Time as Minutes Before or After the Hour

Understand am and pm Tables and Graphs

Read, Interpret, and Create Graphs/Plots o Picture Graphs o Bar Graphs o Line Plots

Geometry

Three Dimensional Shapes, Faces, and Edges

Composite Figures

Patterns

Angles

Investigators I (Third Grade) Investigators I students will focus on extending foundational knowledge from earlier years. Addition and subtraction will extend into the thousands place. Students will develop an understanding of multiplication and division and strategies for multiplication and division within 100. Skills acquisition for multiplication and division facts will include 0-9. Measurement will include length, mass and weight, capacity, money and time. Students will develop an understanding of fractions, especially unit fractions. Fractions will extend to include comparing, equivalents and simplest form, and word problems. Data analysis will include creating and reading picture and bar graphs as well as line plots. Students will be able to describe, analyze and compare two-dimensional shapes. Students will develop an understanding of the structure of rectangular arrays and of area.

Numbers 1 - 100,000

Thousands, Hundreds, Tens and Ones

Number Patterns

Rounding Numbers Addition and Subtraction

Mental Calculation

Estimation

Sum and Difference

Word Problems

Adding Ones, Tens, Hundreds and Thousands

Subtracting Ones, Tens, Hundreds and Thousands

Two Step Word Problems Multiplication and Division

Multiplying Ones, Tens, and Hundreds

Multiplying 0 - 12

Multiples

Factors

Quotient and Remainder

Dividing Three and Four-Digit numbers by a OneDigit Number.

Dividing Hundreds, Tens, and Ones

Estimation

Order of Operations

Word Problems Length

Meters and Centimeters

Kilometers

Other Units of Length Mass and Weight

Comparing Masses

Measuring Mass in Kilograms

Measuring Mass in Grams

Kilograms and Grams

More Word Problems

Measuring Weight in Pounds and Ounces Capacity

Comparing Capacity

Liters

Liters and Milliliters

Gallons, Quarts, Pints, and Cups Money

Dollars and Cents

Addition

Subtraction Fractions

Fractions of a Whole

Equivalent Fractions

Fractions and Measurements

Fraction of a Set Time

Hours and Minutes

Other Units of Time Geometry

Right Angles and Shapes Area and Perimeter

Area

Perimeter

Area of a Rectangle

Composite Figures

Investigators II (Fourth Grade)

Investigators II students will continue to focus on four operations of numbers up to the ten thousand place and will begin including operations with decimals to the hundredths place and operations involving whole numbers and decimals. Students will be able to use the order of operations to solve multi-step real world problems and to use estimation to check for accuracy. They will also develop fluency with addition and subtraction of fractions and begin understanding multiplication and division of fractions. They will begin learning about volume and how to find the volume of a three-dimensional space. Numbers 1 - 1,000,000 and decimals to thousandths

Ten Thousands, Hundreds, Tens and Ones, Tenths and Hundredths

Number Patterns

Rounding Numbers Addition and Subtraction

Mental Calculation

Estimation

Sum and Difference

Word Problems

Adding Ones, Tens, Hundreds and Thousands

Subtracting Ones, Tens, Hundreds and Thousands

Two Step Word Problems Multiplication and Division

Multiplying Three and Four-Digit by a Two-DigitNumber

Multiples

Factors

Dividing 2 and 3-digit numbers by a 1-digit number.

Division by Ones and Tens

Estimation

Order of Operations

Word problems Measurement

Length

Conversions, addition, subtraction

Meters and Centimeters

Kilometers

Miles, Yards, Feet and Inches

Mass and Weight

Comparisons

Conversions

Kilograms and Grams

Word Problems

Pounds and Ounces

Capacity

Comparisons

Conversions

Liters and Milliliters

Gallons, Quarts, Pints and Cups

Multiplying and Dividing Compound Measures

Measures and Fractions Fractions

Fractions of a Whole

Equivalent Fractions

Comparing Fractions

Add and Subtract Like and Related Fractions

Mixed Numbers, Improper Fractions

Adding and Subtracting Mixed Numbers

Multiplying a fraction by a Whole Number

Fractions and Division

Fractions and Measurements

Fraction of a set Time

Hours and Minutes

Other Units of Time Geometry

Angle Addition and Subtraction

Angle Measurement with a Protractor

Perimeter

Area of a Rectangle

Area of Composite Figures

Volume of a Rectangular Prism


This course covers topics typically presented in sixth grade.

Students will understand ratio concepts and use ratio

reasoning to solve problems. Previous understandings of

multiplication and division will be used to divide fractions

by fractions. Students will compute fluently with multi-

digit numbers and find common factors and multiples. The

system of rational numbers will be explored along with

algebraic expressions. Students will reason about and solve

one-variable equations and inequalities. Quantitative

relationships between dependent and independent

variables will be analyzed. Students will solve real-world

and mathematical problems involving area, surface area,

and volume. An understanding of statistical variability will

be developed.

Ratio and Proportions

Unit Ratios

Using Ratios to Solve Problems with Percent

Multiplicative Inverse

The Number System

Division of Fractions

Long Division

Operate with Decimals

Distributive Property

Additive Inverse

Prime Factorization

Greatest Common Factor

Least Common Multiple

Rational Numbers on a Number Line

Absolute Value

The Coordinate Plane

Ordered Pairs

Negative Integers

Expressions and Equations

Write, Read, and Evaluate Algebraic

Expressions

Solve One Step Algebraic Equations

Writeand Compare Inequalities

Solve One Step Inequalities

Geometry

Area of Triangles

Area of Special Quadrilaterals

Draw Polygons in The Coordinate Plane

Use Nets to Find Surface Area of Right Prisms

and Right Pyramids

Statistics and Probability

Determine Mean, Median, and Mode of a

Data Set

Use Dot Plots, Histograms and Box Plots

Compare Data Plots

Analyze Patterns in Data


This course covers topics typically presented in seventh

grade. Topics from Middle School Math 1 will be

incorporated for those who did not take that course as

needed. Students will analyze proportional relationships

and use them to solve real-world and mathematical

problems. Operations with fractions to add, subtract,

multiply, and divide rational numbers will be practiced.

Students will use properties of operations to generate

equivalent expressions and will solve real-world and

mathematical problems using numerical and algebraic

expressions, equations, and inequalities. Geometry topics

include drawing, constructing, and describing geometrical

figures. Students will also solve real-world and

mathematical problems involving angle measure, area,

surface area, and volume. Random sampling to draw

inferences about a population and informal inferences to

compare two populations will be discussed. Students will

investigate chance processes and develop, use, and

evaluate probability models.

Ratio and Proportions

Unit Ratio Comparisons

Proportional Reasoning

Scale Factors

The Number System

Add and Subtract Fractions and Decimals

Multiply and Divide Fractions and Decimals

Convert Between Decimals and Fractions


Factor Linear Expressions

Add and Subtract Linear Expressions

Solve Multi-Step Problems with Rational Numbers

Solve Multi-Step Algebraic Equations

Solve Multi-Step Inequalities

Geometry

Scale Drawings of Geometric Figures

Characteristics of Triangles and Angles

Area and Circumference of a Circle

Area and Perimeter of Quadrilaterals and

Polygons

Volume of Pyramids, Prisms, and Cubes

Surface Area of Pyramids, Prisms, And Cubes


Sample Size and Inferencing

Random and Simulated Sampling

Mean Absolute Deviation

Range and Interquartile Range

Compare Samples Using Measures of Variability

Theoretical and Experimental Probability

Probability of Compound Events

Middle School Math III

This course covers topics typically presented in eighth

grade. Topics from Middle School Math 1 and 2 will be

incorporated for those who did not take those courses as

needed. Students use linear equations and systems of

linear equations to represent, analyze, and solve a variety

of problems. Students strategically choose and efficiently

implement procedures to solve linear equations in one

variable, understanding that when they use the properties

of equality and the concept of logical equivalence, they

maintain the solutions of the original equation. Students

solve systems of two linear equations in two variables and

relate the systems to pairs of lines in the plane; these

intersect, are parallel, or are the same line. Students use

functions to describe quantitative relationships and grasp

the concept of a function as a rule that assigns to each

input exactly one output. Student analyze two- and three-

dimensional space and figures using distance, angle,

similarity, and congruence, and understanding and

applying the Pythagorean Theorem.

The Number System

Irrational Numbers

Square Roots

Cube Roots

π


Integer Exponents

Write a Number in Scientific Notation

Multiply and Divide Numbers in Scientific

Notation

Solve Multi-Step Algebraic Equations with

Variables on Both Sides of the Equation

Solve Multi-Step Algebraic Inequalities with

Variables on Both Sides of the Inequality

Understand the Solution to a System of Equations

Graphically

Functions

Evaluate a Function

Identify Linear Functions from Tables, Equations,

and Graphs

Slope as a Rate of Change

X and Y Intercepts of a Linear Graph

Write an Equation in Slope Intercept Form

Interpret Linear Graphs

Geometry

Congruence

Rotations, Reflections, and Translations

Dilations

Similarity in Two Dimensional Figures

Interior and Exterior Angles of a Triangle

Parallel Lines and Transversals

Angle-angle Similarity in Triangles

Pythagorean Theorem

Distance Formula

Volume of Cones, Cylinders, and Spheres


Create scatter plots

Linear Correlation

Line of Best Fit

Frequency Tables

High School Math 1

The purpose of this course is to formalize and extend the

mathematics that students learned in the middle grades.

This course deepens and extends understanding of

linear relationships, in part by contrasting them with

exponential and quadratic phenomena, and in part by

applying linear models to data that exhibit a linear trend.

In addition to studying bivariate data, students also

summarize, represent, and interpret data on a single count

or measurement variable. The Geometry standards that

appear in this course formalize and extend students’

geometric experiences to explore more complex geometric

situations and deepen their explanations of geometric

relationships, moving towards formal mathematical

arguments. This course fulfills the North Carolina high

school graduation requirement for Common Core Math I.

The final exam is the North Carolina End -of-Course Test.


The Language of Algebra

Order of Operations

Properties of Numbers

Equations, Relations, & Functions

Ratios, Proportions, & Percentages

Linear Equations & Functions

Linear Equations

Absolute Value Equations

Literal Equations

The Slope of a Line

Arithmetic Sequences

Linear Functions

Forms of the Equation of a Line

Parallel & Perpendicular Lines

Scatter Plots & Lines of Best Fit

Inverse Functions

Inequalities

Systems of Equations

Piecewise-Linear Functions

Quadratic Equations & Functions

Working with Polynomials

Special Products

Quadratic Equations

Quadratic Functions

Transformations

Curve Fitting

Geometry

Coordinate Geometry

Triangles & Congruence

Parallelograms

Rectangles

Rhombi & Squares

Circles

Exponentials & Exponential Functions

Multiplying & Dividing Exponentials

Rational Exponents

Scientific Notation

Exponential Functions

Growth & Decay

Geometric Sequences

Probability and Statistics

Samples & Studies

Statistics & Parameters

Distributions

Simulation

Permutations & Combinations

Perpendicular Bisectors

Radical Functions

The Square Root Function

Radical Expressions and Equations

The Pythagorean Theorem

Trigonometric Ratios

Rational Functions & Equations

Inverse Variation

Solving Rational Equations

Graphing Rational Functions

Operations on Rational Expressions

High School Math 2

In Math II, students continue to deepen their study of

quadratic expressions, equations, and functions;

comparing their characteristics and behavior to those of

linearand exponential relationships from Math I. The

concept of quadratics is generalized with the introduction

of higher degree polynomials. New methods for

solvingquadratic and exponential equations are developed.

The characteristics of advanced types of functions are

investigated (including power, inverse variation, radical,

absolute value, piecewise-defined, and simple

trigonometric functions). The link between probability and

data is explored through conditional probability and

countingmethods. Students explore more complex

geometric situations and deepen their explanations of

geometric relationships, moving towards formal

mathematicalarguments. Important differences exist

between Math II and the historical approach taken in

Geometry classes. For example, transformations are

explored early in thecourse and provide the framework for

studying geometric concepts such as similarity and

congruence. The study of similarity leads to an

understanding of right triangletrigonometry and connects

to quadratics through Pythagorean relationships. This

course fulfills the North Carolina high school graduation

requirement for Math II.

Intro to Geometry

Points, Lines, & Planes

Distance & Midpoint

Plane Figures & Solids

Geometric Proof

Parallel Lines & Transversal

Triangles

Classifying

Triangle Congruence

Isosceles & Equilateral Triangles

Coordinate Geometry

Concurrent Segments

Triangle Inequality

Similarity

Trigonometry

Pythagorean Theorem

Special Right Triangles

Trigonometric Ratios

Angles of Elevation & Depression

Verifying Trigonometric Identities

Circles

Circumference

Arcs & Chords

Inscribed Angles

Tangents & Secants

Chord Ratios

Equations of Circles

Transformations & Symmetry

Reflections

Translations

Rotations

Dilations

Quadrilaterals

Angles of Polygons

Parallelograms

Rectangles

Rhombi & Squares

Trapezoids & Kites

Area & Volume

Parallelograms & Triangles

Trapezoids, Rhombi, and Kites

Circles & Sectors

Surface Area

Volume

Probability & Measurement

Combinatorics

Applications of Geometric Probability

Independent & Dependent Events

Mutually Exclusive Events

Factors & Roots

Operations on Polynomials

Graphs of Polynomials

The Remainder & Factor Theorem

Rational Zero Theorem


Graphing Rational Functions

Solving Rational Inequalities

Functions

Parent Functions & Transformations

Quadratic Functions

Domain & Range

Linear Functions

Piecewise Functions

Absolute Value Functions

High School Math 3

This course is designed so that students can pull together and apply the accumulation of mathematics concepts learned previously. They apply methods from probability and statistics to draw inferences and conclusions from data. Students expand their repertoire of functions to include polynomial, rational, and radical functions, including an intense study of families of functions and the relationships therein. They expand their study of right triangle trigonometry to include general triangles and in the study of trigonometric functions to model simple periodic phenomena. Finally, students bring together all their experience with functionsand geometry to create models and solve contextual problems. Appropriate technology and tools, including manipulatives and calculators, will be used regularly for instruction and assessment. This course fulfills the North Carolina high school graduation requirement for Math III. Theory of Functions

The Language of Mathematics

Properties of Real Numbers

Equations, Relations, & Functions

The Algebra of Functions

Transformations

Inverse Functions

Review of Linear Functions

Slope

Lines of Best Fit

Piecewise Functions

Absolute Value Functions

Linear Forms Quadratic Functions

Solving Quadratic Equations

Graphing

Factoring

Completing the Square

Quadratic Formula

Complex Numbers Polynomial Functions

Operations on Polynomials

Synthetic Division

Zeroes of Polynomials

End Behavior

Graphing Polynomial Functions Radical Functions

The Square Root Function

Radical Expressions

Rational Exponents

Solving Radical Equations

Solving Radical Inequalities

Graphing Radical Functions

Exponential & Logarithmic Functions

Graphing

Multiplying & Dividing Exponentials

Solving Exponential Equations

Properties of Logarithms

Solving Logarithmic Equations

Applications Rational Functions


Solving Rational Inequalities

Asymptotes

End Behavior

Zeroes of Rational Functions

Graphing Rational Functions Trigonometric Functions

Radians

Law of Sines & Law of Cosines

Graphing Trig Functions

Translations

Verifying Trig Identities

Using Trig Angle Identities Statistics & Probability

Studies

Distributions

The Normal Distribution

Confidence Intervals

Hypothesis Testing Systems (Optional)

Solving Systems of Equations

Solving Systems of Inequalities

Linear Programming

Systems in Three Variables

Matrices

Cramer’s Rule Sequences & Series (Optional)

Sequences as Functions

Arithmetic Sequences

Geometric Sequences

Recursion

The Binomial Theorem

Mathematical Induction Conic Sections (Optional)

Midpoint & Distance Formula

Parabolas

Circles

Ellipses

Hyperbolas

parent guide to mathematics at the scholars academy · revolves around several key number‐sense...

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