The BJU Press middle and high school math program enables students to use mathematics to better fulfill the dominion mandate. The math courses examine many mathematical concepts to ensure mastery, foster readiness, and encourage careful thinking. The program also incorporates various technology tools to enhance student learning and empower students to take their computational skills to the next level. All mathematical concepts are examined through the lens of a biblical worldview to lead students to formulate their own positions based on the truth of God’s Word. In short, the program serves to equip students with advanced mathematical skills to solve real-world problems within the context of a biblical worldview.

## Vision

To equip students with advanced mathematical skills and strategies for analyzing and solving real-world problems through the application of abstract reasoning within the context of a biblical worldview.

## Goals

- To ensure mastery of foundational mathematical concepts including number systems, operations, algebra, functions, geometry, probability, and statistics
- To support procedural fluency for college and career readiness through consistent, strategic practice and review
- To develop analytical thinking, reasoning skills, and perseverance in real-world problem solving through the creation and use of models
- To encourage the use of technology to enhance learning, to incorporate multiple representations of concepts, and to remove computational constraints
- To equip students to formulate a biblical view of mathematics

## Program Approach for Math

### How We Ensure Conceptual Mastery

The BJU Press middle and high school math courses ensure conceptual mastery using a variety of teaching techniques. Teachers use essential questions to flesh out the significant concepts in each lesson. They will also help students recognize and correct ineffective solutions to problems. Modeling helps students progress from simply viewing numerical equations on a page to recognizing and understanding mathematical problems in everyday life. Teachers also facilitate abstract reasoning and foster collaborative learning and classroom discussion. Students are encouraged to assert their own positions and examine the reasons behind those positions. Each course includes exercises that use a spiral review to develop understanding of the newest concept and to review previous concepts. Our Pre-Algebra course also provides QR codes that link students to additional instruction and practice.

### How We Support Procedural Fluency

The middle and high school math courses also foster procedural fluency in students. Students are able to select and execute mathematical procedures relevant to individual problems. The courses use mathematical models to teach students the relationships between quantities and structure within the numerical system. By using modeling, students learn how to lay out mathematical equations, analyze them, and predict an outcome based on previous experience so they can come to a reasonable conclusion and contribute to solving real-world problems. Working through problems and equations in this way helps them to understand the procedures necessary for using mathematical practices effectively. The spiral review exercises not only contribute to conceptual mastery but also enhance fluency by helping students develop more understanding and refresh prior knowledge. The courses enable students to use abstract reasoning and analyze incorrect solutions to problems. Teaching material includes discussion prompts and reminders to direct students’ attention to key ideas and step-by-step reasoning to ensure they understand concepts beyond simple rote memory.

### How We Develop Real-World Problem Solving

The middle and high school math courses encourage real-world problem solving through STEM activities. These projects promote greater understanding and appreciation for the role math plays in science, engineering, and design. STEM projects use a variety of disciplines to nurture holistic problem solving and student collaboration. For example, Fundamentals of Math includes a project requiring students to create five common weather observation instruments. Students will use the constructed instruments to record weather observations for several consecutive days. Course teaching material provides suggested questions that encourage students to think about their processes, how they can improve their instruments, and how they might use their instruments best. Once each STEM project is complete, students will report their results to show what they’ve learned and what they can accomplish by using STEM processes. These STEM projects present multifaceted problems and guide students through crafting optimal solutions for the best results. Multiple courses also feature a “then and now” series that demonstrates how problems have previously been solved using mathematical skills. Students also engage in strategic questioning to focus on key concepts and apply those concepts to real-world problems.

### How We Use Technology

The BJU Press middle and high school math courses introduce students to multiple technological resources to make resolving math problems simpler and more accessible. Students are taught to handle advanced calculators, and they also have access to After School Help with additional math problems and videos explaining challenging mathematical concepts.

### How We Nurture a Biblical Worldview

In a world of complicated and involved issues, students can learn to use mathematics to simplify or solve problems. Throughout BJU Press math courses, we direct students to determine the root issues of real-world problems according to a biblical worldview and solve them using mathematical processes. As students break down and define problems and make assumptions about the causes and contributions to those problems, they do so with an understanding of what the Bible says and expects. Ultimately, we encourage students to develop solutions that are appropriate and ethical. Additional features prompt worldview development as well. Fundamentals of Math uses engaging cartoons to discuss biblical worldview shaping objectives. Pre-Algebra also provides thorough explanations of why mathematical principles consistently work effectively. Students will verify that mathematical principles based on the timeless truths in God’s Word provide effective solutions for problems in our world.

## Materials

### Student Edition (eTextbook available)

Our math textbooks have clear presentations of concepts with practice exercises that promote student success and prepare students for standardized testing and college-level math courses.

### Teacher Edition

The teacher editions contain presentation suggestions, motivational ideas, and tips to address common student errors. The teacher editions also suggest easy adaptations for scheduling and assignments for minimum, standard, and extended tracks.

### Student Activities (eActivities Available)

The activity manuals (available for Grades 7–9) provide resources for extra practice, remediation and enrichment activities, calculator skills, exercises, and chapter and cumulative reviews.

### Assessments & Assessments Answer Keys

Assessments packets include section quizzes and one age-appropriate test per chapter.

## Scope & Sequence

#### Number Sense

Recognize and write 0–100,000,000,000 as numerals and words; Roman numerals I–C; Place value: ten thousandths to hundred billions; comparing; expanded form; even/odd, positive/negative, prime/composite numbers; number line; expressions and equations; Part-whole relationships; inverse operations

#### Addition & Subtraction

Basic facts (fact families and other strategies); nine-digit column addition; Mental compensation; Properties: commutative, associative, identity; zero principle

#### Multiplication

Basic facts (fact families and other strategies); multiples; repeated addition; vertical form; one to three digits times two to four digits; renaming; factor trees; prime/composite numbers; GCF; LCM; Properties: commutative, associative, identity, zero, distributive

#### Division

Basic facts (fact families and other strategies); equal sets; measurement/partition; fraction form; equations; mental division by 10; two to four digits by one or two digits; remainders; mixed number and decimal quotients; decimal equivalent for a fraction

#### Equations

Inverse operations; compensation; simplify expressions; evaluate expressions; if-then statements; solve for an unknown

#### Pre-Algebra

Missing addend/subtrahend/minuend/factor; add, subtract, multiply, and divide integers; positive/negative numbers; Variables in expressions and equations; solve for a variable in an equation

#### Fractions

Part of a whole; part of a set; equivalent fractions; comparing; ordering; lowest terms; renaming improper fractions and mixed numbers; Add, subtract, multiply, and divide like and unlike fractions; cross-products; cancellation; pictorial representations or journal entries to express understanding of operations

#### Decimals

Read and write tenths, hundredths, thousandths; write as fractions and mixed numbers; comparing; ordering; renaming to thousandths; word forms; Add and subtract; Multiply a decimal by a whole number, by a decimal, and by a power of 10; Divide a decimal by a one-digit whole number; divide a whole number by a whole number with a decimal quotient; divide to rename a fraction as a decimal; divide a decimal by a power of 10

#### Geometry

Points; lines: parallel, intersecting, perpendicular; line segments; rays; symmetry; similar/congruent; constructions; angles: right, acute, obtuse; measure angles; sum of angles in a triangle = 180°; Plane figures: regular/irregular; polygons; triangles: scalene, isosceles, equilateral; quadrilaterals; parallelograms; transformations: translation, reflection, rotation; perimeter; area; Solid figures: sphere, cone, cylinder, polyhedron, cube, prism, pyramid; face, edge, vertex, curved surface; nets; surface area; volume; Circle: center point, radius, diameter, chord, central angles, circumference

#### Estimating

Round whole numbers and decimals to a given place; round fractions to the nearest half or whole; front-end estimation; Round to estimate a sum, difference, product, and quotient

#### Measurement

Length; capacity; weight; mass; Temperature: Fahrenheit; Celsius; Time: elapsed time; time zones; timeline; 24-hour clock; wages; Rename within the metric and customary systems to add, subtract, multiply, and divide

#### Problem Solving

Graphs; tables; charts; schedule; map skills; probability; money; Venn diagram; Using a problem-solving plan; multistep problems; problems with too little or too much information; group planning; Strategies: patterns; logic; guess and check; diagram/model; simpler problem; formulas; working backwards; writing an equation

#### Statistics & Graphs

Pictograph; bar/double bar graph; line/double line graph; histogram; circle graph; coordinate graph; Tables; charts; tallies; frequency table; line plot; stem-and-leaf plot; box-and-whisker plot; Mean, median, mode; range; frequency; scale; interval

#### Ratios, Proportions, Percents

Equivalent ratios; unit rate; scale drawings; map scale; Percents as fractions and decimals; writing fractions and decimals as percents; comparing percents to decimals and fractions; finding the percent of a number; determining the sales price given a discount as a percent; Proportionate geometric figures

#### Additional content

Introduction of speed, distance, and time; unit multipliers; comparing types of graphs, independent and dependent events; patterns; squares and square roots; Roman numerals through M (1,000); additional multistep problems

**Whole numbers and decimals:** ordering, rounding and comparing; operations and estimating; exponents; roots of perfect squares; approximating square roots; order of operations

**Integers:** numbers sets and subsets; opposite numbers and absolute value; ordering and rounding; operations; order of operations involving integers

**Numerical and Algebraic Expressions:** variables and expressions; properties of addition and multiplication; factoring common factors; combining like terms; adding linear expressions; properties of exponents; scientific notation

**Fraction theory:** divisibility; factors; prime and composite numbers; GCF and LCM; renaming fractions; rational numbers; comparing and ordering rational numbers

**Fractions:** operations; order of operations involving rational numbers; evaluating algebraic expressions involving rational numbers

**Algebra:** Writing equations; solving one- and two-step equations; solving equations with grouping symbols; solving one- and twostep inequalities

**Ratios and proportion:** ratios and rates; simplifying complex ratios; solving proportions; scale models; proportional relationships

**Percents:** proportions and percent; percent equations; enlargements and reductions; percent change; sales tax; discounts; sale price; simple interest

**Measures:** customary units of length, capacity, and weight; SI (metric) units of length, capacity, and mass; relating metric and customary units; converting rates

**Introduction to Geometry:** basic terms; measuring angles; pairs of angles; perpendicular and parallel lines; characteristics and area of triangles and quadrilaterals; exploring triangle theorems

**Exploring area and volume:** circles; areas of similar polygons; surface area of prisms, cylinders, and pyramids; volume of prisms and cylinders

**Probability:** simple events; theoretical and experimental probabilities; compound events: simulations

**Statistics:** populations and samples; descriptive measures (mean, median and mode); mean absolute deviation; comparing populations using line graphs, histograms, box-and-whisker plots, stem-and-leaf plot; visualizing data

**Relations and functions:** coordinate plane; functions and function rules; graphing linear functions; slope; sequences

**Integers**: absolute value; operations, exponents, roots, and their properties; order of operations

**Expressions**: evaluating and simplifying expressions; translating word phrases; scientific notation; estimating

**Equations**: solving one- and two-step equations; simplifying; solving linear inequalities; applying equations and inequalities

**Rational expressions**: prime factorization; GCF and LCM; rational numbers; decimal equivalents; converting repeating decimals to fractions; ratios and proportions; the real number system

**Operations with rational numbers**: evaluating and simplifying expressions; solving equations involving rational numbers; operations with scientific notation

**Percents**: solving percent equations; applying percents; discount, markup, tips, commission, simple and compound interest; percent change; scales

**Applying equations**: equations with variables on both sides; identities and contradictions; writing and solving equations and inequalities to solve problems; equations with powers, radical equations

**Functions**: illustrating relations; defining and graphing functions; slope; writing linear equations; proportional relationships; graphing linear inequalities

**Systems of linear equations**: solving linear systems by graphing, substitution, and elimination; special cases of linear systems

**Geometry**: angles; polygons; the Pythagorean Theorem; distance and midpoint formulas; congruence and similarity; translation, reflection, rotation, and dilation transformations

**Perimeter, area, and volume**: perimeter and circumference; areas of quadrilaterals, triangles, circles, and composite regions; ratios of lengths and areas of similar regions; surface areas and volumes of prisms, cylinders, pyramids, cones, spheres, and composite solids

**Statistics and probability**: measures of central tendency and variation; representing data; distribution tables; scatterplots and trend lines; two-way tables; probabilities of simple and compound events

**Expressions**: review of real numbers, number lines, absolute value, arithmetic operations of integers and rational numbers, exponents, using variables, algebraic expressions, and formulas, and order of operations

**Solving equations**: writing and solving linear equations, solving literal equations and proportions; real-world applications involving similar figures, percentages, money, motion, and mixtures

**Solving inequalities**: linear inequalities, including conjunctions and disjunctions; absolute-value equations and inequalities

**Functions**: representing relationships between data, using graphs, equations, and tables; direct and inverse variations; arithmetic sequences; graphing absolute value functions

**Linear functions**: graphs, slopes, and intercepts of linear equations; determining the equation of a line; parallel and perpendicular lines; correlation and lines of fit

**Linear Systems**: solving systems graphically, by substitution, and by elimination; applications of systems, graphing linear inequalities and systems of inequalities

**Exponents**: products, quotients, and powers of exponential expressions; scientific notation; graphing exponential functions; exponential growth and decay; geometric sequences

**Polynomial Operations**: classification, evaluation, operations, special patterns

**Factoring Polynomials**: common monomials, trinomials, special patterns

**Radicals**: simplification and operations with radicals; Pythagorean theorem, distance and midpoint formulas; solving radical equations and graphing radical functions; applications

**Quadratic equations and functions**: solving by factoring, taking roots, completing the square, and the quadratic formula; graphing parabolas and finding zeros; applications

**Rational expressions and equations**: simplification and operations with rational expressions; solving rational equations; applications (Each chapter includes a feature on sequences and graphing calculator tips.)

#### Biblical Worldview Shaping

**Design**—Evaluating conclusions about design in the world based on geometric patterns**Ethics**—Applying geometric relationships to help others**Foundations**—Evaluating competing approaches to defining knowledge**Modeling**—Formulating a biblical view of geometrical modeling**Reasoning**—Applying reasoning to form true statements

#### Number and Quantity

- Vector and matrix quantities—Representing the magnitude and direction of vectors; Multiplying a vector by a matrix to produce another vector; Using matrices as transformations of the plane

#### Algebra

- Equations and inequalities—Rearranging formulas to emphasize different unknowns

#### Functions

- Linear, quadratic, and exponential models—Constructing linear and exponential functions
- Trigonometric functions—Relating radians and arcs on the unit circle; Relating trigonometric functions and the unit circle; Determining the values of sine, cosine, and tangent; Explaining the symmetry and periodicity of trigonometric functions by using the unit circle

#### Geometry

- Congruence—Defining foundational geometric terms; Representing and comparing transformations in the plane; Describing transformations that carry a polygon onto itself; Defining transformations; Graphing transformations; Determining and proving the congruence of figures; Relating triangle congruence and rigid motions; Proving theorems about lines and angles; Proving theorems about triangles; Proving theorems about parallelograms; Making geometric constructions
- Similarity, right triangles, and trigonometry—Verifying the properties of dilations; Determining the similarity of figures; Proving theorems involving similarity; Defining trigonometric ratios for acute angles; Solving right triangles by using the Pythagorean Theorem; Deriving the formula for the area of a triangle; Using the Law of Sines and Cosines
- Circles—Proving the similarity of all circles; Relating inscribed angles, radii, and chords; Constructing inscribed and circumscribed circles of a triangle; Proving properties of angles for a quadrilateral inscribed in a circle; Constructing tangent lines to the circle; Relating the length of an arc to the radius
- Expressing geometric properties with equations—Deriving the equation of a circle; Using coordinates to prove simple geometric theorems algebraically; Proving and using the slope criteria for parallel and perpendicular lines; Partitioning line segments; Using coordinates to compute perimeters and areas of polygons
- Using geometric measurement and dimension—Explaining circumference, area, and volume formulas; Using volume formulas to solve problems; Relating two-dimensional and three-dimensional objects
- Modeling with geometry—Using geometric shapes, their measures, and their properties to describe objects; Applying concepts of density in modeling situations; Applying geometric methods to solve design problems

#### Statistics and Probability

- Interpreting categorical and quantitative data—Using the mean and standard deviation to estimate population percentages

#### STEM

- Following the Engineering Design Process to solve a problem—Building and exploring Euclidean and non-Euclidean surfaces; Designing and building packaging to protect waffle cones in shipment

#### Operations

Real and complex numbers; Polynomial; Matrix; Function

#### Linear equations

Solving equations and inequalities; Absolute value equations and inequalities; Distance on number lines; Word problems; Compound inequalities

#### Linear relations

Graphs of linear functions; Slopes; Special functions; Linear inequalities; Distances and midpoints; Modeling with linear regressions

#### Systems

Solved graphically and algebraically; Systems of inequalities; Systems of three variables; Problem solving; Linear programming

#### Matrices

Organizing data; Operations; Determinants; Solving systems using Cramer's Rule and inverse matrices; Transformations

#### Quadratic equations

Solving by factoring, taking roots, completing the square, and the quadratic formula; Using the discrimiant; Complex roots; Quadratic inequalities

#### Polynomial functions

Roots, graphing, and modeling with quadratic and polynomial functions; Problem solving; Rational root, remainder, and factor theorems; Fundamental theorem of algebra

#### Radicals, Exponents, and Logarithms

Rational exponents; Inverse functions; Simplifying expressions; Solving equations, graphing and modeling with radical, exponential, and logarithmic functions; Natural and common logarithms

#### Rational Expressions

Simplifying; Solving equations; Graphing; Variations

#### Trigonometry

Right triangle and coordinate plane trigonometry; Special triangles and the unit circle; Radians; Graphs of trigonometric functions; Inverse functions

#### Trigonometric Identities

Law of Siens; Law of Cosines; Problem solving; Proving identities; Trigonometric equations

#### Sequences and Series

Explicit and recursive formulas; Arithmetic and geometric sequences and series; Summation notataion

#### Probability and Statistics

Counting principles; Theoretical and experimental probabilities; Independent, dependent, and mutually exclusive events; Binomial distribution, descriptive statistics, representing data; Normal distributions; Making inferences

#### Analytic Geometry

Circles; Parabolas; Ellipses; Hyperbolas; Systems of quadratic relations

#### Analyzing functions

Relations; linear, quadratic, power, and piecewise functions; continuity, transformations, and operations of functions, parametric representations and modeling with functions

#### Radical, polynomial, and rational functions

Describing zeros, asymptotes, and end behavior of radical, polynomial, and rational functions and solving related equations and inequalities

#### Exponential and logarithmic functions

Graphing, applying properties, solving equations, and modeling

#### Trigonometric functions

Angle and arc measures; trigonometric functions in a right triangle, for other angles, and of real numbers; graphs of trig functions; inverse trig functions

#### Trigonometric identities and equations

Derive and verify identities; use identities to solve equations; derive and apply the law of sines and law of cosines

#### Vectors, polar graphs, and complex numbers

Describe and perform operations on 2-D and 3-D vectors; graph polar coordinates and equations; represent and perform operations on complex numbers in polar form

#### Systems and matrices

Using Gaussian elimination; determinants, and inverse matrices to solve systems of equations and inequalities; decomposing into partial fractions

#### Analytic geometry

Analyzing parabolas, ellipses, circles, and hyperbolas; rotated conics; parametric and polar representations

#### Sequences and series

Recursive and explicit formulas; arithmetic and geometric sequences; summations; the binomial theorem; mathematical induction

#### Descriptive statistics

Counting principles and basic probability; graphic representations; measures of central tendency and variability; normal distributions

#### Inferential statistics

Probability distributions; the central limit theorem; confidence intervals; hypothesis testing; research studies

#### Limits, derivatives, and integrals

Limit theorems; tangents to the curve; derivative theorems including product, quotient, and chain rules; area under a curve and integration; the fundamental theorem of calculus

#### Math skills

Fractions, decimals, integers; problem solving using proportions and percent; solving linear equations; negative exponents to prepare for finance formulas

#### Measurement

Customary and SI (metric) units; conversion within and between systems using dimensional analysis; perimeter, circumference, area, volume, and capacity

#### Income

Calculating hours worked from clock times, gross pay including overtime; payroll deductions, including FICA and federal withholding; buying and selling stocks and bonds, including brokerage fees

#### Budgeting

A standardized budget; an annual budget; reducing annual budget to monthly or weekly; emergency adjustments; revising the annual budget

#### Banking

Checking accounts and deposits; overdraft penalties and protection; service charges; reconciling a bank statement; simple interest; compounding interest; interest on savings using the minimum balance or daily interest methods; effective interest rate; savings programs with regular deposits

#### Borrowing

Simple interest loans; add-on loans and annual percentage rate; discount loans; amortized loans; how credit cards work; how interest is calculated and payments are applied to credit accounts

#### Transportation

Calculating the finance charge and monthly payment for a new car; depreciation; leasing costs including residual value, mileage penalty; car insurance; cost of gas, oil, and tires; scheduled maintenance and repair costs

#### Food

Store specials and coupons; unit prices; calculating freezer payback periods; consumer price index; calorie counting; finding the calories expended in activities

#### Clothing

Planning for seasonal buying; calculating discounts including multiple ones; online shopping; internet buying tips; savings from making clothing; retail marketing of clothing, returns, net profit and gross profit margin; markup rate and breakeven point for retailer

#### Housing

Renting; buying a house, including down payments, closing costs, points, and monthly payments; owner’s equity; building a house, including converting dimensions to scale for a set of plans; finding the area of rectangular lots in acres; calculating the amount of shingles needed from a house plan, allowing for pitched roofs

#### Maintaining a home

Real-estate tax based on millage rates; homeowner’s insurance; calculating utility charges for electricity, gas, water, and sewer; communications; calculating house repairs, maintenance, and home improvements

#### Life and health insurance

Mortality tables; term, whole-life, and universal life insurance; health insurance, including payout of benefits; Social-Security retirement benefits

#### Income taxes

General principles of calculating federal income taxes; 1040EZ, 1040A, and 1040, including extra schedules A and B and Form 2441 for childcare benefits

#### Vacations

Costs of food and lodging; cost of transportation; getting around at the site; travel times across time zones; economizing admissions