# Place Value in Whole Numbers

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1 Place Value in Whole Numbers Objectives To provide practice identifying values of digits in numbers up to one billion; and to provide practice reading and writing numbers up to one billion. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Read and write numbers up to 1,000,000,000; identify the values of digits. [Number and Numeration Goal 1] Write numbers in expanded notation. [Number and Numeration Goal 4] Find the sum of numbers written in expanded notation. [Operations and Computation Goal 2] Use and describe patterns to find sums. [Patterns, Functions, and Algebra Goal 1] Key Activities Students review basic place-value concepts for whole numbers. They express whole numbers as sums of ones, tens, hundreds, and so on, and observe the relationship between such sums and the way numbers are read. Informing Instruction See page 97. Recognizing Student Achievement Use journal page 33. [Number and Numeration Goal 1] Key Vocabulary counting number whole number digit place expanded notation Materials Math Journal 1, pp. 32 and 33 Student Reference Book, p. 4 Study Link 2 2 transparency of Math Masters, p. 398 (optional) calculator slate Identifying Polygon Properties Math Journal 1, p. 34 Students identify properties of polygons. Math Boxes 2 3 Math Journal 1, p. 35 Students practice and maintain skills through Math Box problems. Study Link 2 3 Math Masters, p. 45 Students practice and maintain skills through Study Link activities. ENRICHMENT Solving Number-Grid Puzzles Math Masters, p. 46 Students apply their understanding of the base-ten place-value system to solve number-grid puzzles. EXTRA PRACTICE 5-Minute Math 5-Minute Math, pp. 12 and 18 Students practice place-value skills. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 140 Students add the terms counting numbers and whole numbers to their Math Word Banks. Advance Preparation For Part 1, make an overhead transparency of Math Masters, page 398, or copy the place-value chart on the board. Teacher s Reference Manual, Grades 4 6 pp. 59, 60, 259, Unit 2 Using Numbers and Organizing Data

2 Getting Started Mathematical Practices SMP2, SMP6, SMP7, SMP8 Content Standards 4.OA.5, 4.NBT.1, 4.NBT.2, 4.G.1, 4.G.2 Mental Math and Reflexes Have students skip count by 10s, 100s, 1,000s, and 10,000s on their calculators, counting both up and down starting with different numbers. For example, ask students to count up by 10s beginning with 40 and to count down by 10s beginning with 293. Pay special attention to transitions. For example, point out what happens when you go from 95 to 105 or from 203 to 193. Math Message Write the largest number you can using the digits 0, 3, 9, and 7. Use each digit only once. Study Link 2 2 Follow-Up Ask students to draw a star next to their most inventive solutions to the broken-calculator problems and share them with a partner. 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS Have partners compare answers. 9,730 Ask students to respond to the following questions on their slates: Which digit is in the ones place? 0 Adjusting the Activity Have students use the digits 9, 7, 3, and 0 to write decimal numbers less than one. Remind them to use zero in the ones place ; 0.397; 0.739; 0.793; 0.937; Ask students to identify the value of each digit. AUDITORY KINESTHETIC TACTILE VISUAL Which digit is in the tens place? 3 How much is that digit worth? 30 How much is the digit 7 worth? 700 What is the smallest whole number you can write using the digits 9, 7, 3, and 0? Do not use 0 in the thousands place. 3,079 Tell students that in this lesson they will look at the digits and the values of digits in numbers through hundred-millions. Reviewing Place Value for Whole Numbers (Math Journal 1, p. 32; Math Masters, p. 398) ELL WHOLE-CLASS Ask someone to describe the counting numbers. The numbers 1, 2, 3, and so on Remind students that zero is usually not considered a counting number. Explain that all of the counting numbers as well as the number zero are called whole numbers; that is, the whole numbers are the numbers 0, 1, 2, 3, and so on. Is every counting number also a whole number? yes Lesson

3 Date Place-Value Chart Math Journal 1, p. 32 Math Masters, page 398 is identical to journal page M 10M M 100K 10K K H T O 4 Hundred Ten Hundred Ten Number Millions Millions Millions Thousands Thousands Thousands Hundreds Tens Ones Remind students that any number in our base-ten numeration system can be written by using one or more of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. What makes this possible is that digits take on different values, depending on their positions or places in a number. To support English language learners, discuss the different meanings of the homonyms whole and hole. Discuss the everyday and mathematical uses of the word place. Display the place-value chart (Math Masters, page 398) on the overhead projector or draw it on the board, and write the numbers as shown below. Number Hundred Ten Thousands Hundreds Tens Ones Thousands Thousands 100K 10K K H T O , , , To support English language learners, explain the meaning of the symbols. For example, 100K means one hundred-thousand. The symbol K for thousand is derived from the prefix kilo-, as in kilometer in the metric system. The symbol M for million is derived from the prefix mega-. Continue to use the full name of a place in oral work. Remind students that the value of a digit in a numeral depends on its position in the place-value chart. For example: A 2 in the ones column stands for 2 ones. It is worth 2. A 2 in the tens column stands for 2 tens. It is worth 20. A 2 in the hundreds column stands for 2 hundreds. It is worth 200 (and so on). When you get to the hundred-thousands place, ask students to name the three places to the left. Millions, ten-millions, and hundred-millions Point out that each number in the table is 10 times the number in the line before it. You can illustrate this relationship using both multiplication and division. For example, 2, = 20,000 and = Unit 2 Using Numbers and Organizing Data

### Multiplication Arrays

Multiplication Arrays Objective To provide opportunities to use arrays, multiplication/ division diagrams, and number models to represent multiplication number stories. www.everydaymathonline.com epresentations

### Objective To introduce the concept of square roots and the use of the square-root key on a calculator. Assessment Management

Unsquaring Numbers Objective To introduce the concept of square roots and the use of the square-root key on a calculator. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts

### Subtraction of Multidigit Numbers

Subtraction of Multidigit Numbers Objectives To review the trade-first and counting-up methods, and to introduce the partial-differences method of solving multidigit subtraction problems; and to provide

### Objective To guide exploration of the connection between reflections and line symmetry. Assessment Management

Line Symmetry Objective To guide exploration of the connection between reflections and line symmetry. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

### Formula for the Area of a Triangle Objective To guide the development and use of a formula for the area of a triangle.

Formula for the rea of a Triangle Objective To guide the development and use of a formula for the area of a triangle. www.everydaymathonline.com epresentations etoolkit lgorithms Practice EM Facts Workshop

### Properties of Polygons Objective To explore the geometric properties of polygons.

Properties of Polygons Objective To explore the geometric properties of polygons. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

### Multiplication Fact Power and Shortcuts

Multiplication Fact Power and Shortcuts Objectives To discuss multiplication facts and the importance of fact power; and to review fact shortcuts. www.everydaymathonline.com epresentations etoolkit Algorithms

### Review: Comparing Fractions Objectives To review the use of equivalent fractions

Review: Comparing Fractions Objectives To review the use of equivalent fractions in comparisons. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters

### Family Letters. Assessment Management. Playing Fraction Of

Formula for the Area of a Parallelogram Objectives To review the properties of parallelograms; and to guide the development and use of a formula for the area of a parallelogram. www.everydaymathonline.com

### Subtracting Mixed Numbers

Subtracting Mixed Numbers Objective To develop subtraction concepts related to mixed numbers. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters

### Calculator Practice: Computation with Fractions

Calculator Practice: Computation with Fractions Objectives To provide practice adding fractions with unlike denominators and using a calculator to solve fraction problems. www.everydaymathonline.com epresentations

### Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

### Review: Addition and Subtraction of Positive and Negative Numbers

Review: Addition and Subtraction of Positive and Negative Numbers Objective To practice adding and subtracting positive and negative numbers. www.everydaymathonline.com epresentations etoolkit Algorithms

### Objective To guide the development and use of a rule for generating equivalent fractions. Family Letters. Assessment Management

Equivalent Fractions Objective To guide the development and use of a rule for generating equivalent fractions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

### Multiplication and Division Fact Families

Multiplication and Division Fact Families Objectives To review fact families and the Multiplication/Division Facts Table; and to guide children as they practice multiplication and division facts. www.everydaymathonline.com

### Simplifying Expressions: Combining Like Terms Objective To simplify algebraic expressions by combining like terms.

Simplifying Expressions: Combining Like Terms Objective To simplify algebraic expressions by combining like terms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop

### Change Number Stories Objective To guide children as they use change diagrams to help solve change number stories.

Number Stories Objective To guide children as they use change diagrams to help solve change number stories. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

Subtraction from Addition Objectives To review the and 1 shortcuts; and to guide children to identify the subtraction facts related to given addition facts. www.everydaymathonline.com epresentations etoolkit

### Reading and Writing Large Numbers

Reading and Writing Large Numbers Objective To read and write large numbers in standard, expanded, and number-and-word notations. www.everydaymathonline.com epresentations etoolkit Algorithms Practice

### Family Letters. Assessment Management. Playing Target: 50

The Partial-Sums Algorithm Objectives To guide children as they make ballpark estimates; and to provide opportunities to model and practice the partialsums algorithm for - and -digit numbers. www.everydaymathonline.com

### The Partial-Quotients Division Algorithm, Part 1

The Partial-Quotients Division Algorithm, Part 1 Objectives To introduce and provide practice with a low-stress division algorithm for 1-digit divisors. www.everydaymathonline.com epresentations etoolkit

### Exponential Notation for Powers of 10

Expntial Notation for Objective To introduce number-and-word notation for large numbers and expntial notation for powers of 10. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM

### The Lattice Method of Multiplication

The Lattice Method of Multiplication Objective To review and provide practice with the lattice method for multiplication of whole numbers and decimals. www.everydaymathonline.com epresentations etoolkit

### Multiplication Facts Survey

Multiplication Facts Survey Objective To guide children as they determine which multiplication facts they still need to learn. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM

### Baseball Multiplication Objective To practice multiplication facts.

Baseball Multiplication Objective To practice multiplication facts. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common

### Fractions and Decimals

Fractions and Decimals Objectives To provide experience with renaming fractions as decimals and decimals as fractions; and to develop an understanding of the relationship between fractions and division.

### Sunrise-Sunset Line Graphs

Sunrise-Sunset Line Graphs Objectives To guide children as they analyze data from the sunrise-sunset routine; and to demonstrate how to make and read a line graph. www.everydaymathonline.com epresentations

### Comparing and Ordering Fractions

Comparing and Ordering Fractions Objectives To review equivalent fractions; and to provide experience with comparing and ordering fractions. www.everydaymathonline.com epresentations etoolkit Algorithms

### A Coin-Toss Experiment

A Coin-Toss Experiment Objective To guide children as they develop intuition equally likely events. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

### Subtraction Strategies

Subtraction Strategies Objective To review solution strategies for subtraction of multidigit numbers. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

### The Distributive Property

The Distributive Property Objectives To recognize the general patterns used to write the distributive property; and to mentally compute products using distributive strategies. www.everydaymathonline.com

Addition Number Stories Objective To guide children as they make up, represent, and solve addition number stories. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop

### Factor Trees. Objective To provide experiences with finding the greatest common factor and the least common multiple of two numbers.

Factor Trees Objective To provide experiences with finding the greatest common factor and the least common multiple of two numbers. www.everydaymathonline.com epresentations etoolkit Algorithms Practice

### Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms.

Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts

### Constructing Geometric Solids

Constructing Geometric Solids www.everydaymathonline.com Objectives To provide practice identifying geometric solids given their properties; and to guide the construction of polyhedrons. epresentations

### materials materials materials Technology Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Objectives To guide children as they make ballpark estimates; and to provide opportunities to model and practice the partialsums algorithm for - and -digit numbers. Teaching the Lesson Key Activities Children

The Addition/Subtraction Facts Table Objectives To provide experience exploring patterns in sums of two dice; and to introduce the Addition/Subtraction Facts Table. www.everydaymathonline.com epresentations

### Reading and Writing Small Numbers

Reading Writing Small Numbers Objective To read write small numbers in stard exped notations wwweverydaymathonlinecom epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

### Exploring Length, Area, and Attributes

Explorations Exploring Length, Area, and Attributes Objectives To guide children as they measure lengths and distances to the nearest inch and centimeter, explore area by tiling surfaces, and sort attribute

### Assessment Management

Area Objectives To provide experiences with the concept of area, distinguishing between area and perimeter, and finding areas of rectangular figures by partitioning and counting squares. www.everydaymathonline.com

### Math Message and Number Sequences

Math Message and Number Sequences Objectives To introduce the Math Message routine; and to review number sequences and number lines. www.everydaymathonline.com epresentations etoolkit Algorithms Practice

### Measuring with Yards and Meters

Measuring with Yards and Meters Objectives To provide review for the concept of nonstandard units of measure; and to introduce yard and meter. www.everydaymathonline.com epresentations etoolkit Algorithms

### Multiplication and Division of Positive and Negative Numbers

Multiplication and Division of Positive Objective o develop and apply rules for multiplying and dividing positive and www.everydaymathonline.com epresentations eoolkit Algorithms Practice EM Facts Workshop

### Solving Simple Equations Objective To use trial and error and a cover-up method to

Solving Simple Equations Objective To use trial and error and a cover-up method to solve equations. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

### The Median. Objectives To review how to display a set of data with a line plot; and to review how to find the median of a set of data.

The Median Objectives To review how to display a set of data with a line plot; and to review how to find the median of a set of data. www.everydaymathonline.com epresentations etoolkit Algorithms Practice

### Comparing Fractions Objective To provide practice ordering sets of fractions.

Comparing Fractions Objective To provide practice ordering sets of fractions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management

### Hidden Treasure: A Coordinate Game. Assessment Management. Matching Number Stories to Graphs

Hidden Treasure: A Coordinate Game Objective To reinforce students understanding of coordinate grid structures and vocabulary. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM

### Review of Basic Fraction Concepts

Review of asic Fraction Concepts Objective To review fractions as parts of a whole (ONE), fractions on number lines, and uses of fractions. www.everydaymathonline.com epresentations etoolkit lgorithms

### Number Models for Area

Number Models for Area Objectives To guide children as they develop the concept of area by measuring with identical squares; and to demonstrate how to calculate the area of rectangles using number models.

### Multiplying Fractions by Whole Numbers

Multiplying Fractions by Whole Numbers Objective To apply and extend previous understandings of multiplication to multiply a fraction by a whole number. www.everydaymathonline.com epresentations etoolkit

### Assessment Management

Areas of Rectangles Objective To reinforce students understanding of area concepts and units of area. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

### Objective To review the partial-quotients division algorithm with whole numbers.

Objective To review the partial-quotients division algorithm with whole numbers. 1 Teaching the Lesson materials Key Activities Students review and practice the use of a friendly number paper-and-pencil

### Multiplication Facts Practice

Multiplication Facts Practice Objectives To introduce the 5-facts test; and to provide practice with multiplication facts. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts

### Frames and Arrows Having Two Rules

Frames and Arrows Having Two s Objective To guide children as they solve Frames-and-Arrows problems having two rules. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop

### Objectives To review making ballpark estimates; and to review the counting-up and trade-first subtraction algorithms. materials. materials.

Objectives To review making ballpark estimates; and to review the counting-up and trade-first subtraction algorithms. Teaching the Lesson materials Key Activities Children make ballpark estimates for -digit

### Objective To introduce and practice the partial-sums addition algorithm.

Objective To introduce and practice the partial-sums addition algorithm. 1 Teaching the Lesson Key Activities Children are introduced to the partial-sums algorithm using base-1 blocks and paper-and-pencil

### The Length-of-Day Project

The Length-of-Day Project Objectives To review telling time and finding elapsed time; and to introduce the Length-of-Day project. www.everydaymathonline.com epresentations etoolkit Algorithms Practice

### Addition and Subtraction of Decimals Objective To add, subtract, and round decimals.

Addition and Subtraction of Decimals Objective To add, subtract, and round decimals. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

### The Half-Circle Protractor

The Half-ircle Protractor Objectives To guide students as they classify angles as acute, right, obtuse, straight, and reflex; and to provide practice using a half-circle protractor to measure and draw

### Inequalities. Assessment Management. Dividing Decimals by Decimals: Part 1

Inequalities Objectives To find and represent all the values that make an inequality in one variable true; and to represent real-world situations with inequalities. www.everydaymathonline.com epresentations

### Volume of Pyramids and Cones

Volume of Pyramids and Cones Objective To provide experiences with investigating the relationships between the volumes of geometric solids. www.everydaymathonline.com epresentations etoolkit Algorithms

### Parentheses in Number Sentences

Parentheses in Number Sentences Objective To review the use of parentheses. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management

### Objective To introduce a formula to calculate the area. Family Letters. Assessment Management

Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

### Measuring with a Ruler

Measuring with a Ruler Objective To guide children as they measure line segments to the nearest inch, _ inch, _ inch, centimeter, _ centimeter, and millimeter. www.everydaymathonline.com epresentations

### Objectives To review and provide practice with the lattice method for multiplication.

Objectives To review and provide practice with the lattice method for multiplication. Teaching the Lesson materials Key Activities Students review the lattice method for multiplication with - and -digit

### The Mean and the Median

The Mean and the Median Objectives To introduce the mean of a set of data; and to review the median of a set of data. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop

### Middle Value (Median) of a Set of Data

Middle Value (Median) of a Set of Data Objectives To guide children as they sort numerical data and arrange data in ascending or descending order, and as they find the middle value (median) for a set of

### Pattern-Block Fractions

Pattern-lock Fractions Objective To guide students as they find fractional parts of polygonal regions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

### Surface Area. Assessment Management

Surface Area Objective To introduce finding the surface area of prisms, cylinders, and pyramids. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters

### Using Tree Diagrams to Calculate Probabilities

Using Tree Diagrams to Calculate Probabilities Objective To use tree diagrams to help calculate probabilities. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

### Assessment Management

Facts Using Doubles Objective To provide opportunities for children to explore and practice doubles-plus-1 and doubles-plus-2 facts, as well as review strategies for solving other addition facts. www.everydaymathonline.com

### Common Core State Standards. Mathematical Practices SMP1, SMP5, SMP6, SMP8. Content Standards 3.OA.5, 3.OA.8

Project Objective To introduce the rules for order of operations. www.everydaymathonline.com etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards

### Capacity. Assessment Management

Capacity Objective To review units of capacity. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards

### Family Letters. Assessment Management. Math Boxes 1 4

Objective To calculate and compare the median and mean of a data set. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management

### Topic: 1 - Understanding Addition and Subtraction

8 days / September Topic: 1 - Understanding Addition and Subtraction Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step

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### 1 Teaching the Lesson

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