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

4 Write a number such as 5,607,481 in the place-value chart. Have students write this number in the place-value chart on page 32 in their journals. Ask questions such as the following: How do you say this number? Five million, six hundred seven thousand, four hundred eighty-one What is the value of the digit 6? 6 hundred thousand What is the value of the digit in the millions place? 5 million Write additional numbers such as the following in the place-value chart, and pose questions similar to the ones above: , , ,964 2,371, ,729, ,457, ,291,370 Informing Instruction Watch for students who insert the word and when reading a whole number. A number such as 4,009 should be read as four thousand nine, not four thousand and nine. Proper use of the word and is especially important in reading decimals. Adjusting the Activity Remind students that numbers are divided into groups of digits separated by commas. Each group of digits is read as though it is a separate number; then the name of the group is read (with the exception of the ones group). Illustrate this with a diagram like the one below.,, million thousand ELL A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Writing Numbers as Sums of Ones, Tens, and Hundreds (Student Reference Book, p. 4) WHOLE-CLASS Write a number, such as 853, on the board. Ask what each digit in the number is worth, and record the values as a vertical sum. For 853, you would write: is worth is worth is worth Recording numbers in this way is an example of expanded notation. Repeat this process using up to six digits in a number if students are ready. Then write vertical sums, such as those shown in the margin, and ask students to add them mentally. Students will discover the pattern that the sum is the number obtained by reading the individual addends from largest to smallest. For example, equals seven hundred sixty-five, or 765. See Student Reference Book, page 4 for another example of expanded notation. NOTE There are various ways to write a number in expanded notation. For example, 853 may be written as 8 * * * 1 or as 8[100s] + 5[10s] + 3[1s] , ,692 50, , , ,000 50, ,020 Lesson

5 Date Complete. Taking Apart, Putting Together 1. In 574, 2. In 9,027, 5 is worth is worth 7 is worth 70 0 is worth 4 is worth 4 2 is worth 3. In 280,743, 4. In 56,010,837, 8 is worth 80,000 6 is worth 2 is worth 200,000 1 is worth 4 is worth 40 5 is worth 5. In 705,622,463, 6. In 123,456,789, 5,000,000 5 is worth 4 is worth 6 is worth 600,000 3 is worth 7 is worth 700,000,000 2 is worth 9, ,000,000 10,000 50,000, ,000 3,000,000 20,000,000 Add , ,000, ,000, ,000 9,000,000 9,000, , , ,000 70, , ,062, ,270,031 4 Expressing Values of Digits (Math Journal 1, p. 33) PARTNER Ask students to complete Problems 1 4 independently before completing the rest of journal page 33 with a partner. Have them share their responses to Problem 11. Recognizing Student Achievement Journal page 33 Problems 1 4 Use journal page 33, Problems 1 4 to assess students ability to identify the values of digits in whole numbers. Students are making adequate progress if they correctly identify the values of digits through hundred-thousands. Some students may be able to identify the values of digits in whole numbers up to 1,000,000,000. [Number and Numeration Goal 1] 11. Think about why we need zeros when writing numbers. What would happen if you did not write the zero in the number 5,074? The number would read five hundred seventy-four. The value would be about 1 10 the value of 5,074. Math Journal 1, p Ongoing Learning & Practice Identifying Polygon Properties (Math Journal 1, p. 34) Students check all statements that apply to a given polygon and write an additional true statement for each. Ask students to explain why they did not check some of the statements. Math Boxes 2 3 (Math Journal 1, p. 35) Date Polygon Checklist Place a check mark next to all of the statements that are true about each figure. Write an additional true statement for each figure pair of parallel sides 4 sides of equal length at least 1 right angle kite quadrangle square polygon parallelogram concave convex parallelogram opposite sides parallel Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 2-1. The skills in Problems 5 and 6 preview Unit 3 content. Writing/Reasoning Have students write a response to the following: Explain how you know that the circles you drew for Problem 3 are concentric. Sample answer: The circles have the same center but different radii. Study Link 2 3 (Math Masters, p. 45) all sides of equal length all angles of equal measure one right angle polygon equilateral triangle regular polygon all sides of equal length all angles of equal measure pentagon octagon Home Connection Students review place-value skills. They use place value to compare numbers and to transform given numbers by changing a single digit. 1 pair of parallel sides all angles smaller than right angles Math Journal 1, p Unit 2 Using Numbers and Organizing Data

6 3 Differentiation Options ENRICHMENT Solving Number-Grid Puzzles (Math Masters, p. 46) 5 15 Min Date 1. Add mentally. a. 4 5 b Math Boxes c , d. 5 8 e f What is the value of the digit 8 in the numbers below? a. 584 b. 38,067 c. 49,841 d. 820, , ,000 e. 8,391,467 8,000, To apply students understanding of the base-ten place-value system, have them solve number-grid puzzles. Ask students to share patterns and compare features of the grid puzzle pieces. SMALL-GROUP EXTRA PRACTICE 5-Minute Math 5 15 Min To offer students more experience with place value, see 5-Minute Math, pages 12 and Use your compass to draw a pair of concentric circles. Sample answer: 5. A sailfish can swim at a speed of 110 kilometers per hour. A tiger shark can swim at a speed of 53 kilometers per hour. How much faster can a sailfish swim than a tiger shark? 57 kilometers per hour Math Journal 1, p I am a 2-dimensional figure. I have two pairs of parallel sides. None of my angles is a right angle. All of my sides are the same length. What am I? rhombus Use your Geometry Template to draw me. 6. Multiply mentally. a. 8 1 or 8 b c d e ELL SUPPORT Building a Math Word Bank (Differentiation Handbook, p. 140) SMALL-GROUP 5 15 Min To provide language support for numbers, have students use the Word Bank Template found on Differentiation Handbook, page 140. Ask students to write the terms counting numbers and whole numbers, draw pictures representing the terms, and write other related words that describe them. See the Differentiation Handbook for more information. Teaching Master Name Date Study Link Master Name Date Number-Grid Puzzles STUDY LINK Place Value in Whole Numbers 1. Find the missing numbers. 9,961 9,962 9,972 9,973 9,981 9,992 10,010 a. b. Explain how you found. Sample answer: I started with 9,962 and counted down 4 rows by tens to get 10,002. Then I counted across by ones to get 10, Below is a number-grid puzzle cut from a different number grid. Figure out the pattern, and use it to fill in the missing numbers. 1,750 1,850 1,950 2,040 1,640 9,984 a. b. Explain how you found. Sample answer: I started with 1,900 and counted back by 100s while going upward in the column to get to 1,700. Then, I counted back across the row by 10s to get to 1,640. c. Describe how this number grid is different from number grids you have used before. Sample answer: The pattern in this number grid shows multiples of 10, while the pattern in the other number grids shows multiples of 1. Math Masters, p. 46 9,997 9,998 10,003 10,004 10,005 10,006 1,670 1,680 1,760 1,790 1,870 1,980 1,990 1,900 2,100 9,979 9,989 10, Write the number that has 2. Write the number that has 4 6 in the millions place, 7 in the ten-thousands place, 4 in the thousands place, 3 in the millions place, 7 in the ten-millions place, 1 in the hundred-thousands place, 5 in the hundred-thousands place, 8 in the tens place, 8 in the hundred-millions place, and 2 in the ten-millions place, and 0 in the remaining places. 0 in the remaining places , 5 0 4, , 1 7 0, Compare the two numbers you wrote in Problems 1 and 2. Which is greater? 876,504,000 million 6,000, The 6 in 46,711,304 stands for 6, or. a. The 4 in 508,433,529 stands for thousand 400, , or. million 80,000,000 b. The 8 in 182,945,777 stands for 80, or. million 500,000,000 c. The 5 in 509,822,119 stands for 500, or. thousand 30,000 d. The 3 in 450,037,111 stands for 30, or. Try This 5. Write the number that is 1 hundred thousand more. a. 210, ,366 b. 496, ,708 c. 321, ,589 d. 945,620 1,045, Write the number that is 1 million more. a. 3,499,702 4,499,702 b. 12,877,000 13,877,000 c. 29,457,300 30,457,300 d. 149,691, ,691,688 Practice 71, 84, 97 11, 37, , 45, 58, 8., 89, 115, 141 Rule: 13 Rule: 26 Math Masters, p. 45 Lesson

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