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# Elementary Math

The BJU Press elementary school math program seeks to give students the solid foundation they need to use math for life. Our materials carefully progress from tangible representations to abstract concepts so that students not only understand mathematical practices but can choose the appropriate method to tackle a specific problem. Students will eventually be able to confront and solve problems using their mathematical skills, their individual life experiences, and logical reasoning. Using math is a key component of fulling the Creation Mandate. Our goal is to give students the skill sets they need to address real-world problems for the glory of God and the benefit of others.

## Vision

To enable students to master foundational math skills by applying consistent reasoning to concrete and abstract models for the purpose of solving problems within the context of a biblical worldview.

## Goals

• To develop number sense through the progression from manipulatives to abstract representations
• To promote computational fluency and automaticity through consistent, strategic practice and spiral review
• To develop a foundation in number systems, fraction theory, algebra, geometry, and statistics
• To build grit and problem-solving skills through meaningful, authentic applications, including word problems and collaborative STEM experiences
• To make sense of mathematical concepts and applications in light of biblical principles

## Program Approach for Elementary Math

The BJU Press elementary school math program seeks to give students the solid foundation they need to use math for life. Our materials carefully progress from tangible representations to abstract concepts so that students not only understand mathematical practices but can choose the appropriate method to tackle a specific problem. Students will eventually be able to confront and solve problems using their mathematical skills, their individual life experiences, and logical reasoning. Using math is a key component of fulling the Creation Mandate. Our goal is to give students the skill sets they need to address real-world problems for the glory of God and the benefit of others.

### Developing Number Sense

Teaching a new concept requires starting at the concrete level (the students use manipulatives), moving to the semi-concrete level (the student watches the teacher demonstrate or uses pictures from the book), and finally progressing to the abstract level (the student solves problems using numerals, signs, and symbols). Each new concept presented at any grade level is presented by implementing this three-stage process. Review of major concepts may also follow this format.

The key to our approach is teaching understanding by using manipulatives, ensuring that the student is not just following a procedure that gives him the correct answer. This interactive, hands-on-learning approach is critical for math success. While the use of manipulatives is easily recognized as important for K5, the strategy is equally significant for new concepts taught through grade 5. BJU Press provides packets of manipulatives for student use in K5–grade 4, making this instructional approach easy to implement. While manipulative packets are not produced for grade 5, there are many suggestions for hands-on, interactive strategies in the teacher edition to continue to reinforce understanding.

### Promoting Fluency and Automaticity

Although problem solving is the primary goal of math instruction, it is also essential to develop accurate computation. This, of course, requires practice of basic math facts and skills. Every lesson has ample opportunity for review and practice in every piece of the program, including the teacher editions, student worktexts, reviews (grades 1–3) or activities (grades 4–5) books, Teacher Tools Online, and AfterSchoolHelp.com. The goal is accurate and quick recall of facts so that students may focus their time and energy on the main task of using math to solve problems in real life. Balance is the key.

### Developing Basic Foundations

The key to success in math is a strong foundation of number sense and comprehension of concepts. Students must have a thorough understanding of the mathematical processes and know how to use the processes to determine an accurate answer. While memorization is a key element in math, a student who tries to survive on memorization alone will struggle as higher-level skills are introduced. To excite students about learning math, we have designed a program that engages interest using age-appropriate, colorful themes and hands-on involvement for developing understanding and for enhancing mastery. Our math books use a format that focuses on a single main concept in each chapter. Greater levels of difficulty are added as understanding increases. Our worktexts are filled with colorful photographs and illustrations that picture the problems students are solving as well as the themes.

### Building Grit and Skill

BJU Press elementary math for K5–grade 5 provides a framework for critical thinking through instruction in problem solving. Problem solving is the process of confronting a problem and then using one’s knowledge, reasoning abilities, and experiences to reach a solution.

Math concepts are introduced through real-life problems that are encountered at home, at school, and in the community. Word problems pose application questions that students must work through—both in class and on their own. These activities model the skills necessary for becoming adept at problem solving. Furthermore, they enable students to see that math is more than just a subject in the classroom; it is found everywhere we go in life. Most teacher edition includes a “Teach for Understanding” section that guides the teacher in helping students work through problems, showing them how and why various procedures work. Students do not all learn at the same pace or grasp concepts in the same way. The teacher editions present concepts more than one time and in more than one way to ensure that all students are given the opportunity to learn and grow. Our goal is to help all students become more proficient problem solvers.

### Making Sense of Concepts

God not only created the world but also created order that math seeks to define. Though creation has been tarnished by the Fall of man into sin, God’s original design and consistency can be found in mathematical details, such as the symmetry of the peacock, the spirals of the nautilus shell, and the orbit of the planets around the stars. The orderliness of math points to the Creator of order. The BJU Press elementary math program integrates biblical content to cultivate a Christian worldview that will help students take their place in God’s world. Each teacher edition guides the teacher in explaining math concepts through a biblical worldview, identifying Christian principles, highlighting Christian character traits, and pointing out that math is an important tool for making wise use of God’s creation. God’s world is a place that can be measured with numbers. And if we know how to use numbers, we can become very skilled at having the kind of dominion that helps others and glorifies God.

## Materials

### Student Worktext

Using age-appropriate content and colorful illustrations, each student worktext provides two pages of explanation and practice problems per lesson as well as a chapter review. Some worktexts also include STEM activities and an “Exploring Ideas” page.

### Teacher Edition

The teacher edition for each grade contains full-color, reduced-size student pages with overprint answers. Each lesson opens with a list of objectives and with materials needed for that lesson. Additionally, each lesson typically includes suggestions for teacher-directed review, strategies for teaching new concepts, and answers.

### Visuals & Manipulatives Packets

To build and reinforce understanding, new concepts are introduced in each grade with the use of manipulatives. Both the teacher visuals packet and the student manipulatives packet include items such as pocket charts, number lines, paper coins and bills, rulers, workmats, counters, and geometric shapes, giving the students hands-on practice of the concept. Items may be prepared at the beginning of the school year or as needed for each chapter.

### Reviews & Activities

Reviews provide opportunities for extra practice that teachers may use for homework, assessment, or cumulative review. As students complete practice activities on the current lesson and spiral reviews of previous concepts, they take a crucial step toward gaining automaticity with the material. Review books are available for grades 1–5, with additional reviews available online.

### Assessments

Each assessments packet includes a test for each chapter. The assessments answer key is also available for each grade.

## Scope & Sequence

#### Numeration

Identify numbers 0–100; Write numbers 0–100

#### Number Sense

Compose/decompose numbers; Identify ordinal positions: first–tenth; first, next, last; Determine order: before, after, between; Find patterns in numeration; Develop place value: tens and ones; Identify teen numbers as 10 and some more

#### Counting & Cardinality

Count and make sets to 20; Count to 100 by 1s and 10s; Count on from any given number; Represent the quantity of a number using manipulatives or by drawing a picture

#### Whole Number Operations: Addition & Subtraction

Sums to 10: join sets; count on; compose/decompose numbers; Differences to 10; take apart; unknown part; count back; Represent addition/subtraction sentences with pictures (manipulatives, draw, act out); Write addition/subtraction sentences (equations); Solve word problems; Tell a story for a number sentence; Explain the sum or difference

#### Algebra Readiness

Understand part-whole relationship; Correlate the relationship between addition and subtraction

#### Equal Parts of a Whole (Fraction Concepts)

Count equal parts in a whole; Distinguish between equal parts and unequal parts; Partition a whole into equal parts

#### Geometry

Describe attributes of flat shapes: circle, square, triangle, rectangle in various orientations; Describe attributes of solid figures: ball shape (sphere), can shape (cylinder), box shape (rectangular solid, cube), cone shape (cone); Construct shapes with manipulatives; Identify spatial relationships: top, middle, bottom; left, right; over, under; inside, outside; on, off; front, back; Extend and construct patterns (color, shape, size)

#### Estimation

Number of objects; Length: longer, shorter; Weight: weighs more, weighs less; Capacity: holds more, holds less; Time: more time, less time

#### Measurement

Sort and classify objects by attributes (number, color, size, shape); Compare measurable attributes; length (longer/shorter), height (taller/shorter), weight (heavier, lighter), capacity (more, less); Measure: nonstandard units and inches; more than one attribute; Determine temperature: hot, cold; Tell time: read and write time to the hour; daytime, nighttime; sequence events; more time, less time; Read a calendar: days of the week; months of the year; yesterday, today, tomorrow; seasons; Identify and count pennies

#### Problem Solving

Solve word problems using manipulatives, drawing pictures, or acting-out situations; Write and solve number sentences (equations)

#### Numeration

Read and identify 0-999; Write and picture 0-999; Number words: zero to twenty

#### Number Sense

Make 10; Ordinals: first-tenth; first, next, last; before, after, between; Patterns; sequencing: first, next, last; before, after, between

#### Number Line

Place Value; Hundreds/tens/ones; 1 more/1 less, 10 more/10 less, 100 more/100 less; Expanded form; Compare with < and >; Even/odd numbers

#### Counting

Find patterns in numeration; Count to 999; Count by 1s, 5s, 10s to 200; Count forward and backward

#### Addition

100 basic facts (using strategies); Number sentences (equations) and vertical form; Two- and three-digit addends; money; Rename 10 ones as 1 ten

#### Subtraction

100 basic facts (using fact families and other strategies); 2-digit minuend and subtrahend; equation; vertical form; money; Word problems: take-away, comparison, missing addend; Subtract 0 rule

#### Multiplication Readiness

Repeated addition; counting by 2s, 5s, 10s

#### Algebra Readiness

Represent a picture with a number sentence; missing addend; Understand and use Addition Properties (Commutative, Associative, Identity)

#### Fractions

Equal parts; halves; thirds; fourths (quarter); part of a set of objects; fair share; probability

#### Geometry

Plane shapes: circle, square, triangle, rectangle; sides and corners; Solid figures: sphere, cylinder, rectangular prism, cube, cone; corners, faces, curved sides; Spatial relationships; patterns; perimeter; Venn diagram

#### Estimation

Numbers of objects; Length: is longer, is shorter; Weight: weighs more, weighs less; Capacity: holds more, holds less

#### Measurement

Length/height: nonstandard units, inch, centimeter; Weight: weighs more, weighs less; pound, kilogram; Capacity: holds more, holds less; cup, pint, quart, gallon, liter; Temperature: Fahrenheit; Celsius; Measuring tools: ruler, scale, thermometer, cup; Time: hour and half-hour; elapsed time; Calendar: days, weeks, months; Money: penny, nickel, dime, quarter

#### Problem Solving

Word problems; Reasoning; Problem-Solving Plan; STEM; Graphs and Data: Pictograph, bar graph, tally chart

#### STEM

Coding activities

#### Numeration

Identify and write 0–9,999; number words: zero to nine hundred ninety-nine

#### Number Sense

Place value: thousands/hundreds/ tens/ones; 10 more/10 less; 100 more/100 less; even/odd numbers; round to the nearest ten and hundred; compare with < and >; expanded form; Ordinals: first–twentieth; Patterns; sequencing: before, after, between; number line

#### Counting

Count by 1s, 5s, 10s, and 100s; by 2s to 60; by 3s to 30; by 4s to 40

#### Addition

100 basic facts (using fact families and other strategies); 4-digit addends; vertical form addition; rename 10 ones as 1 ten, 10 tens as 1 hundred, 10 hundreds as 1 thousand; money; word problems; strategies; Order Principle, Zero Principle, Grouping Principle

#### Subtraction

100 basic facts (using fact families and other strategies); Three- and four-digit minuend and subtrahend; rename 1 ten as 10 ones, 1 hundred as 10 tens, 1 thousand as 10 hundreds; money; Word problems; take-away, comparison, missing addend; strategies; Zero Principle

#### Multiplication

Repeated addition; array; number line; equation; vertical form; factors: 0–5, 10; word problems; Order Principle, Identity Principle, Zero Principle

#### Division

Equal sets; equation; missing factor; divisor: 1–5; word problems

#### Algebra Readiness

Equation; missing addend; missing factor; Order Principle, Grouping Principle, Zero Principle

#### Fractions

Equal parts; halves to tenths; part of a set; fair share; compare with common denominators; compare with 1 as the numerator

Money

#### Geometry

Plane figures: circle, square, triangle, rectangle, pentagon, hexagon, oval; sides, vertices; similar, congruent; symmetry; slides, flips, turns; Solid figures: sphere, cylinder, rectangular prism, cube, cone, pyramid; faces, edges, vertices, curves; Lines: horizontal/vertical; parallel/intersecting; Area; perimeter; patterns

#### Estimation

Round to nearest ten and hundred; Length: inch, foot, yard; centimeter, meter; Weight: more than/less than 1 pound, 1 ounce; Mass: more than/less than 1 kilogram; about 1 gram/more than 1 gram; Capacity: more than/less than 1 cup, 1 pint, 1 quart, 1 gallon; more than/less than 1 liter

#### Measurement

Length: inch, foot, yard; centimeter, meter; Capacity: cup, pint, quart, gallon; liter; Weight: ounce, pound; Mass: gram, kilogram; Temperature: Fahrenheit; Celsius; Measuring tools: ruler, scale, thermometer, cup, liter; Time: to five-minute interval; A.M./P.M.; elapsed time; Calendar: day, week, month, year; Money: penny, nickel, dime, quarter, half-dollar, one dollar

#### Problem Solving

Word problems; graphs; tables; charts; map skills; probability; money

#### Statistics & Graphs

Pictograph; bar graph; coordinate graph; line graph; circle graph; tables; charts; tallies

#### Calculators

Addition; subtraction

#### Number Sense

Recognize and write 0–1,000,000 with numerals and words; Roman numerals I–XIII; Ordinals; first through ninety-ninth; order; number line; 10 more/10 less; place value; ones to hundred thousands; expanded form; even/odd numbers; round to the nearest ten, hundred, one thousand, compare with > and <

#### Counting

Count by 1s, 2s, 5s, 10s, 100s, 1,000s, 10,000s; count by 2s to 20, by 3s to 30, by 4s to 40, by 5s to 50, by 6s to 60, by 7s to 70, by 8s to 80, by 9s to 90

#### Addition

100 basic facts; fact families; five-digit addends; vertical form; rename 10 ones as 1 ten to 10 one thousands as 1 ten thousand; money; strategies; word problems; Commutative Property, Associative Property, Identity Property

#### Subtraction

100 basic facts; fact families; five-digit minuend and subtrahend; word problems; rename 1 ten as 10 ones to 1 ten thousand as 10 one thousands; money; word problems; strategies; take-away, comparison; missing addend; Zero Principle

#### Multiplication

110 basic facts; fact families; multiples; repeated addition; arrays; number line; equation; vertical form; 1 digit factors; 2 to 3 digits by 1 digit; renaming; strategies; word problems; Commutative Property; Associative Property; Identity Property; Zero Property

#### Division

110 basic facts; fact families; equal sets; repeated subtraction; measurement; partition/strategies; equation; division frame; word problems; 2 and 3 digits by 1 digit; 1-digit remainders

#### Algebra Readiness

Equation; missing addend; missing factor; negative numbers (temperature); Properties

#### Fractions

Part of a whole; part of a set; equivalent fractions; compare; order; mixed numbers; add and subtract like fractions

#### Decimals

Read and write tenths and hundredths; mixed numbers; compare; order; add and subtract; rename 10 tenths as 1 one and 10 hundredths as 1 tenth; word forms; money; word problems

#### Geometry

Plane figures: circle, polygons, square, triangle, rectangle, pentagon, hexagon, octagon; edge, vertex; slides, flips, turns; Solid figures: sphere, cube, cylinder, cone, rectangular prism, rectangular pyramid; faces; edges; vertices; curved surface; Lines: horizontal/vertical; parallel/ intersecting; symmetry; Area; perimeter; patterns

#### Estimation

Round to nearest ten, hundred, and one thousand; Length; distance; capacity; weight; mass

#### Measurement

Length: ½ inch, foot, yard, mile; centimeter, meter, kilometer; Capacity: cup, pint, quart, gallon; milliliter, liter; Weight: ounce, pound; Mass: gram, kilogram; Temperature: Fahrenheit; Celsius; Time: to 1-minute interval; past and future elapsed time to 5-minute interval; before/after the hour; A.M./P.M.; noon/midnight; Calendar: date, future date; schedule; Money: coins; five-dollar bill; ten-dollar bill; dollar sign; decimal point; addition, subtraction

#### Problem Solving

Word problems; graphs; tables; charts; schedule; map skills; logic; probability; money; multi-step problems; problems with too little information; Problem Solving Plan

#### Data & Graphs

Bar graph, pictograph; line plot; line graph; coordinate graph; circle graph; tables and charts; tallies

#### Calculators

Addition; Subtraction

#### Number Sense

Recognize and write 0–100,000,000 with numerals and words; Roman numeraIs I–XXXIX

#### Number Patterns

Ordinals; first through ninetyninth; order; number line; 10 more/10 less; Place value: ones to hundred millions; expanded form; even/ odd numbers; round to the nearest ten, hundred, one thousand; compare with >, <, and =

#### Counting

Count by 1s, 2s, 5s, 10s, 100s, 1,000s, 10,000s; count by 2s to 20, by 3s to 30, by 4s to 40, by 5s to 50, by 6s to 60, by 7s to 70, by 8s to 80, by 9s to 90

#### Addition

100 basic facts; fact families; six-digit addends; vertical form; rename 10 ones as 1 ten to 10 one thousands as 1 ten thousand; Strategies; word problems; money; Commutative property, associative property, identity property

#### Subtraction

100 basic facts (using strategies); fact families; six-digit minuend and subtrahend; rename 1 ten as 10 ones to 1 ten thousand as 10 one thousands; Strategies; word problems; money; take-away, comparison; missing addend; unknown part; Zero principle

#### Multiplication

110 basic facts; fact families; multiples; repeated addition; arrays; number line; equations; vertical form; one-digit factors; one digit times two to four digits; two digits times two or three digits; renaming; strategies; word problems; Commutative property, associative property, identity property, zero property, multiplication, addition principle

#### Division

110 basic facts (using strategies); fact families; equal sets; repeated subtraction; measurement; partition/ strategies; equation; round the division; adjust the quotient; division frame; word problems; finding averages; computation: two to four digits by one digit; two to three digits by two digits; one to two digit remainders; divisibility rules

#### Algebra Readiness

Equations; missing addend; missing factor; negative numbers; function tables; variables

#### Fractions

Part of a whole; part of a set; add and subtract like fractions and mixed numbers with like fractions; rename improper fractions; Equivalent fractions; compare; order

#### Decimals

Read and write tenths and hundredths; mixed numbers; compare; order; add and subtract; rename 10 tenths as 1 one and 10 hundredths as 1 tenth; word forms; money; word problems; round to nearest whole

#### Geometry

Plane figures: circle, polygon, square, triangle, rectangle, pentagon, parallelogram, rhombus, hexagon, octagon; edge, vertex; slides, flips, turns; Solid figures: sphere, cube, cylinder, cone, rectangular prism, square prism, triangular prism, rectangular pyramid, square pyramid, triangular pyramid; face, edge, vertex, curved surface; Lines: horizontal/vertical, parallel/ intersecting, segments; points; rays; angles: right, acute, obtuse; Symmetry; similar; congruent; Circle: radius, diameter; Perimeter; area; complex area; volume; patterns

#### Estimation

Round to nearest ten, hundred, and one thousand, one million; Round for addition, subtraction, multiplication, and division; Length; distance; capacity; weight; mass

#### Measurement

Length: ¼ and ½ inch, foot, yard, mile; centimeter, meter, kilometer, millimeter; Capacity: cup, pint, quart, gallon; milliliter, liter; Weight: ounce, pound, ton; Mass: gram, kilogram; Temperature: Fahrenheit; Celsius; Time: to one-minute interval; past and future elapsed time to five-minute interval; before/ after the hour; a.m./p.m.; noon/ midnight; Calendar: date, future date; schedule; Money: coins; one-, five-, ten-, and twenty-dollar bills; dollar sign; decimal point; addition; subtraction; multiplication; division

#### Problem Solving

Use a problem-solving plan: problems; graphs; tables; charts; write word problems; schedule; map skills; logic; probability; money; multistep problems; problems with too little information, fractions

#### Data

Pictograph; bar, line, circle, and coordinate graphs; Tables; charts; tallies; line plot; stem-and-leaf plot; Mean, median, mode, range, frequency

#### Calculators

Addition; subtraction; division

#### Number Sense

Recognizing and writing 0–100,000,000,000 as numerals and words; Roman numerals I–C; Place value: ones to hundred billions; comparing; expanded form; even/odd numbers; positive/negative numbers; number line; expressions and equations

#### Addition & Subtraction

Basic facts (fact families and other strategies); six-digit numbers; renaming to hundred thousands; inverse relationship; strategies; word problems; money; compensation; Properties: commutative, associative, identity, zero principle

#### Multiplication

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

#### Division

Basic facts (fact families and other strategies); equal sets; inverse of multiplication; measurement; partition; fraction form; equations; two to four digits by one or two digits; remainders; strategies; word problems; money

#### Fractions

Part of a whole; part of a set; equivalent fractions; comparing; ordering; lowest terms; renaming improper fractions and mixed numbers; Adding and subtracting like and unlike fractions; adding and subtracting mixed numbers with like and unlike fractions; Multiplying a whole number times a fraction and a fraction times a whole number; multiplying a fraction times a fraction; multiplying a whole number times a mixed number; multiplying a mixed number times a mixed number; Dividing a whole number by a fraction; dividing a fraction by a fraction; reciprocals

#### Decimals

Reading and writing tenths, hundredths, thousandths; writing as fractions and mixed numbers; comparing; ordering; renaming to thousandths; word forms; money; word problems; rounding to nearest hundredth; Multiplying a decimal by a whole number, by a decimal, and by a power of 10; Dividing a decimal by a one-digit whole number; dividing a whole number by a whole number with a decimal quotient; dividing to rename a fraction as a decimal; dividing a decimal by a power of 10

#### Geometry

Points; horizontal/vertical lines; parallel/intersecting/perpendicular lines; line segments; rays; angles: right, acute, obtuse; measuring angles; Plane figures: circle, polygon, square, triangle, rectangle, pentagon, hexagon, octagon, quadrilateral, parallelogram, rhombus, trapezoid; edge, vertex; similar, congruent, symmetrical; translation, reflection, rotation; perimeter, circumference, 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; Triangles: sum of angles = 180º; acute, obtuse, right; isosceles, scalene, equilateral

#### Estimation

Rounding to a given place; Rounding for addition, subtraction, multiplication, and division; Whole numbers; fractions; decimals; Length; distance; capacity; weight; mass

#### Measurement

Length; capacity; weight; mass; temperature; Time: past and future elapsed time; equivalent units; converting units; adding and subtracting; Calendar; writing dates

#### Problem Solving

Use a problem-solving plan: problems; graphs; tables; charts; schedule; map skills; logic; probability; money; multistep problems; problems with too little or too much information

#### Data

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

#### Ratios, Proportions, Percents

Equivalent ratios; unit rate; scale drawings; map scale; Writing percents as fractions and decimals; writing fractions as percents; comparing percents to decimals and fractions; finding the percent of a number

#### Calculators

Varied activities