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

#### Biblical Worldview Shaping

**God**—Recalling that math teaches that God is great and God is good**Creation**—Describing how math testifies to a creator**Serving**—Summarizing how math equips people to serve God and others

#### Numeration

- Identifying numbers 0–100
- Writing numbers 0–100

#### Number Sense

- Composing and decomposing numbers up to 10
- Comparing numbers and the number of objects in a group
- Ordering numbers: before, after, and between
- Identifying dot patterns
- Identifying number patterns
- Using place value: ones and tens
- Identifying teen numbers as 10 and some more

#### Counting and Cardinality

- Counting and making sets to 20
- Counting by 1s and 10s to 100
- Counting on from any given number to 100
- Representing the quantity of a number—Using manipulatives; Drawing a picture
- Using ordinals: first–tenth; first, next, and last

#### Addition

- Describing addition as putting together or adding to
- Adding within 10—Joining sets; Counting on; Part-whole model
- Fluently adding within 5
- Representing addition sentences visually—Pictures; Manipulatives; Drawing or coloring; Acting out
- Telling a story for a number sentence
- Explaining the sum
- Writing number sentences (equations)
- Using vertical form
- Renaming 10 ones as 1 ten

#### Subtraction

- Describing subtraction as taking apart or taking from
- Subtracting within 10—Separating sets; Counting back differences
- Fluently subtracting within 5
- Finding the unknown part
- Representing subtraction sentences visually—Pictures; Manipulatives; Drawing or coloring; Acting out
- Telling a story for a number sentence
- Explaining the difference
- Writing number sentences (equations)
- Using vertical form

#### Fractions

- Counting equal parts in a whole
- Explaining equal parts and unequal parts
- Partitioning a whole into equal parts—Halves; Thirds; Fourths (quarters)
- Identifying fractions as part of a set of objects
- Relating fractions and fair share

#### Algebra

- Part-whole relationship
- Writing addition and subtraction sentences (equations)
- Relationship between addition and subtraction
- Using addition properties—Commutative (order principle); Identity (zero principle)

#### Geometry

- Identifying and describing plane shapes (2-D)—Circle; Square; Triangle; Rectangle; Hexagon
- Identifying and describing solid shapes (3-D)—Ball shape (sphere); Can shape (cylinder); Box shape (rectangular solid, cube); Cone shape (cone)
- Identifying shapes by their properties: corners, faces, and curved sides
- Constructing shapes with manipulatives
- Drawing shapes
- Combining shapes to form larger shapes
- Describing and comparing shapes—Similarities; Differences; Parts (sides, vertices, and corners)
- Identifying spatial relationships—Top, middle, and bottom; Beside, next to, left, and right; Above, over, below, and under; Inside, outside; On, off; Front, in front of, back, and behind
- Identifying shape patterns (color, shape, and size)

#### Estimation

- Estimating the number of objects
- Estimating measurements—Length: longer, shorter; Weight: weighs more, weighs less; Volume (capacity): holds more, holds less; Time: more time, less time

#### Measurement

- Sorting and classifying objects by attributes (number, color, size, and shape)
- Describing and comparing measurable attributes—Length: longer, shorter; Height: taller, shorter; Weight: heavier, lighter; Volume (capacity): more, less
- Measuring—Nonstandard units, inch, and centimeter; Rulers and scales; More than one attribute; Comparing measurements; Temperature: hot, cold
- Telling and writing time—To the hour; Using analog and digital clocks; Daytime and nighttime; Sequencing events; More time, less time
- Using a calendar—Days of the week; Months of the year; Yesterday, today, and tomorrow; Seasons
- Identifying and using money—Identifying pennies, nickels, dimes, and quarters; Identifying dollars; Adding and subtracting with pennies

#### Problem- Solving

- Solving addition and subtraction word problems—Using manipulatives; Drawing pictures; Acting out situations
- Explaining problem-solving strategies
- Writing and solving number sentences (equations)

#### Statistics and Graphs

- Making and interpreting graphs—Picture graphs; Bar Graphs
- Probability

#### STEM

- Following the Engineering Design Process to solve a problem—Building a tower; Building an animal enclosure; Building a snowman; Building a bridge

#### 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

#### Biblical Worldview Shaping

**Caring**—Using math to care for others**Exploring**—Using measuring to better understand God’s world**Working**—Evaluating the idea that people should avoid difficult math

#### Numeration

- Reading and writing 0–9,999
- Reading and writing number words: zero to nine hundred ninety-nine

#### Number Sense

- Ordering numbers: before, after, and between
- Identifying number patterns
- Using a number line
- Explaining and using place value: ones to thousands
- Calculating 10 more or 10 less and 100 more or 100 less
- Reading and writing numbers to 1,000 in expanded form
- Rounding to the nearest ten and hundred
- Comparing 2- and 3-digit numbers using <, =, and >
- Identifying even and odd numbers

#### Counting and Cardinality

- Counting to 1,000
- Counting by 1s, 5s, 10s, and 100s
- Counting by 2s to 60, by 3s to 30, and by 4s to 40
- Using ordinals: first–twentieth

#### Addition

- Using 100 basic facts (using fact families and other strategies)
- Adding up to four 2-digit numbers within 1,000
- Representing addition sentences visually—Drawings; Equations with symbols for the unknown number
- Fluently adding within 100
- Adding 4-digit addends
- Using vertical form
- Renaming 10 ones as 1 ten, 10 tens as 1 hundred, and 10 hundreds as 1 thousand

#### Subtraction

- Using 100 basic facts (using fact families and other strategies)
- Subtracting within 1,000—Counting back; Subtracting all; Subtracting nearly all
- Representing subtraction sentences visually—Drawings; Equations with symbols for the unknown number
- Fluently subtracting within 100
- Subtracting with 3- and 4-digit minuend and subtrahend—Take-away; Comparison; Missing addend
- Renaming 1 ten as 10 ones, 1 hundred as 10 tens, and 1 thousand as 10 hundreds

#### Multiplication

- Relating repeated addition to multiplication
- Multiplying using arrays
- Multiplying using the number line
- Writing equations
- Using vertical form
- Multiplying with factors 0–5 and 10

#### Division

- Making equal sets
- Writing equations
- Finding the missing factor
- Dividing with divisors 1–5

#### Fractions

- Partitioning circles and rectangles into equal parts—Halves; Thirds; Fourths
- Identifying fractions as part of a set
- Relating fractions and fair share
- Comparing fractions with common denominators
- Comparing fractions with 1 as the numerator

#### Decimals

- Using money

#### Algebra

- Using the relationship between addition and subtraction
- Solving equations
- Finding missing addends and factors
- Explaining and using addition, subtraction, and multiplication properties—Commutative (order principle); Associative (grouping principle); Identity: Zero Principle of Addition, Zero Principle of Subtraction, Zero Principle of Multiplication; Identity Property of Multiplication

#### Geometry

- Identifying and composing plane shapes (2-D)—Circle; Square; Triangle; Rectangle; Quadrilateral; Pentagon; Hexagon; Oval; Sides; Vertices; Slides, flips, and turns
- Identifying and composing solid shapes (3-D)—Sphere; Cylinder; Rectangular prism; Cube; Cone; Pyramid
- Identifying shapes by their properties: angles, faces, edges, vertices, and curves
- Lines—Horizontal and vertical lines; Parallel and intersecting lines; Calculating geometric measurement; Area; Perimeter
- Identifying symmetry
- Identifying shape patterns

#### Estimation

- Rounding to nearest ten and hundred
- Estimating measurements—Length: inch, foot, and yard; centimeter, meter; Weight: more than or less than 1 pound, 1 ounce; Mass: more than or less than 1 kilogram; about 1 gram or more than 1 gram; Volume (capacity): more than or less than 1 cup, 1 pint, 1 quart, and 1 gallon; more than or less than 1 liter

#### Measurement

- Measuring attributes—Length: inch, foot, and yard; centimeter, meter; Weight: ounce, pound; Volume (capacity): cup, pint, quart, and gallon; liter; Mass: gram, kilogram; Temperature: Fahrenheit, Celsius
- Using measuring tools—Length: ruler, yardstick, meter stick, and measuring tape; Scale, thermometer, cup, and liter
- Relating two measurements using different units
- Relating the measurements of different objects
- Telling and writing time—To 5-minute interval; Using analog and digital clocks; a.m. and p.m.; Elapsed time
- Using a calendar: day, week, month, and year
- Using money—Using pennies, nickels, dimes, quarters, and half-dollars; Using dollars; Adding and subtracting; Using dollar and cent symbols

#### Problem-Solving

- Solving addition, subtraction, multiplication, and division word problems—One step; Two steps; With measurements; With money
- Using a problem-solving plan—Graphs; Tables; Map skills

#### Statistics and Graphs

- Representing and interpreting data—Graphs—Picture graph, Bar graph, Coordinate graph, Line graph, Circle graph; Tables; Tallies; Venn diagram
- Probability

#### STEM

- Following the Engineering Design Process to solve a problem—Coding: locating the queen’s treasure; Coding: tidying the queen’s treasure; Coding: creating an origami crew; Coding: claiming the continent for the queen; Coding: programming a pal; Coding: cracking a binary code; Coding: artful algorithms; Coding: a puzzling condition

#### 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