Objectives To provide practice with place-value skills using a calculator routine; and to review reading and writing large numbers. 1 materials Teaching the Lesson Key Activities Students enter a number in their calculators and then change one or more digits in the display by adding or subtracting one or more numbers. Key Concepts and Skills • Read and write large numbers. [Number and Numeration Goal 1] • Identify places in whole numbers and the values of the digits in those places. [Number and Numeration Goal 1] • Add and subtract multidigit whole numbers. [Operations and Computation Goal 2] • Solve open sentences. [Patterns, Functions, and Algebra Goal 2] ⵧ Math Journal 1, p. 36 ⵧ Study Link 2 3 䉬 ⵧ Teaching Aid Master (Math Masters, p. 388 or 389; optional) ⵧ Transparency (Math Masters, p. 47; optional) ⵧ calculator ⵧ slate Ongoing Assessment: Recognizing Student Achievement Use a Math Log or Exit Slip. [Number and Numeration Goal 1] 2 Ongoing Learning & Practice Students play Fishing for Digits to practice identifying digits in whole numbers and expressing their value. Students practice and maintain skills through Math Boxes and Study Link activities. materials ⵧ Math Journal 1, p. 37 ⵧ Student Reference Book, p. 242 ⵧ Study Link Master (Math Masters, p. 48) ⵧ Game Master (Math Masters, p. 472; optional) ⵧ calculator ⵧ overhead calculator (optional) 3 materials Differentiation Options READINESS Students use a place-value tool to practice finding numbers that are 10 more or less, 100 more or less, or 1,000 more or less than a given number. ENRICHMENT Students decipher a place-value code. ⵧ Teaching Masters (Math Masters, pp. 49 and 50) ⵧ Teaching Aid Masters (Math Masters, pp. 399–402) ⵧ scissors; stapler See Advance Preparation Additional Information Advance Preparation For the optional Readiness activity in Part 3, decide whether you will prepare Compact Place-Value Flip Books (Math Masters, pp.399–402) ahead of time or have students make them. 100 Unit 2 Using Numbers and Organizing Data Technology Assessment Management System Math Log or Exit Slip See the iTLG. Getting Started Mental Math and Reflexes Students display a number on their calculators for their partners to read. They also take turns dictating numbers for their partners to display on their calculators. Math Message (Write 56,385 and 7,490,613 on the board.) Be prepared to read the numbers aloud. Study Link 2 3 Follow-Up 䉬 Have partners compare answers. Ask students to draw a star next to any problems they wish to discuss with the whole class. 1 Teaching the Lesson 䉴 Math Message Follow-Up WHOLE-CLASS ACTIVITY Have pairs of students read the numbers to each other. Then ask someone to read the number 56,385 aloud. Students indicate thumbs-up if they agree with the reading. Ask students to respond to the following questions on their slates and refer to a place-value chart if necessary. ● Which digit is in the tens place? 8 How much is that digit worth? 80 ● Which digit is in the hundreds place? 3 How much is that digit worth? 300 ● Which digit is in the ones place? 5 How much is that digit worth? 5 Ask someone to read 7,490,613 to the class and pose questions similar to the ones above. ● Which digit is in the ten-thousandths place? 9 How much is that digit worth? 90,000 ● Which digit is in the millions place? 7 How much is that digit worth? 7,000,000 ● Which digit is worth 200 times as much as the 3 in the ones place? The 6 in the hundreds place is worth 600. Tell students that in this lesson they will solve calculator problems that require them to focus on the digits and values of digits in numbers. Lesson 2 4 䉬 101 䉴 Practicing Place-Value Skills WHOLE-CLASS ACTIVITY with a Calculator (Math Journal 1, p. 36; Math Masters, p. 47) Make a chart on the board or use a transparency of Math Masters, page 47. (See below.) For each problem, provide the “Change to” digit and the “Operation” sign for students to record on journal page 36 as you guide the class through the examples. Students solve each problem on their calculators. Only the given digit may be changed. All of the other digits in the starting number must remain the same. Discuss students’ solutions. ELL Adjusting the Activity Have students build the starting number with base-10 blocks and take away or add the necessary blocks to show the new number. Ask students to take note of how many blocks they added or subtracted and translate that into what they would do on the calculator. AUDITORY 䉬 KINESTHETIC 䉬 TACTILE 䉬 VISUAL Start with Place of Digit Change to Operation New Number a. 570 Tens 0 ⴚ 500 b. 409 Hundreds 8 ⴙ 809 c. 54,463 Thousands 9 ⴙ 59,463 d. 760,837 Tens 0 ⴚ 760,807 e. 52,036,458 Ones 9 ⴙ 52,036,459 f. Ten Thousands 5 ⴙ 52,056,459 g. Millions 1 ⴚ 51,056,459 Say: Problem 1 ● Enter 570 in your calculator. ● Underline the digit in the tens place on your chart. 7 ● Change the digit in the tens place to 0. Use the key. Write “0” in the “Change to” column and “” in the “Operation” column. ● (Give students time to carry out the operation on the calculator.) How did you do that? Press ● 70 . What is the new number? 500 (Students record the new number on their chart.) Problem 2 Links to the Future Solving these problems requires students to informally identify solutions to open sentences and explain the strategies they used. The solutions, for example, to Problems 1 and 3 can be more formally expressed as 570 x 500; x 70 and 54,463 x 59,463; x 5,000. Lesson 3-11, Open Sentences, will provide students with further instruction regarding Patterns, Functions, and Algebra Goal 2. 102 Unit 2 Using Numbers and Organizing Data ● Enter 409. ● Use the ● How did you do that? Press ● What is the new number? 809 key to change the digit in the hundreds place to 8. 400 . Problem 3 ● Enter 54,463. ● Use the to 9. ● How did you do that? Press ● What is the new number? 59,463 key to change the digit in the thousands place 5,000 . Adjusting the Activity Problem 4 ● Pose similar problems, but do not Enter 760,837. indicate which operation key ( ● Use the should be used. Remind students that only ● How did you do that? Press ● What is the new number? 760,807 key to change the digit in the tens place to 0. 30 or ) the given digit may change. . AUDITORY 䉬 KINESTHETIC 䉬 TACTILE 䉬 VISUAL Problem 5 ● Enter 52,036,458. ● Use the Press ● Use the to 5. Press ● Use the Press ● key to change the digit in the ones place to 9. 1 . key to change the digit in the ten-thousands place 20,000 . key to change the digit in the millions place to 1. 1,000,000 . What is the new number? 51,056,459 䉴 Solving Change Problems INDEPENDENT ACTIVITY (Math Journal 1, p. 36) Students solve the calculator “change” problems in Problem 2 on journal page 36. Ongoing Assessment: Recognizing Student Achievement Math Log or Exit Slip Use a Math Log or an Exit Slip (Math Masters, page 388 or 389) to assess students’ ability to identify places in whole numbers and the values of the digits in those places. Have students explain how they solved Problem 2f on journal page 36. Students are making adequate progress if their responses include that the digit in the ten-millions place in 873,562,003 is 7. The value of the 7 is 70,000,000. To change the digit in the ten-millions place to a 1, subtract 60,000,000. Some students may respond that another way to solve the problem is to add –60,000,000. Student Page Date Time LESSON 2 4 䉬 Calculator “Change” Problems 1. Follow your teacher’s directions to complete the “change” problems below. Use your calculator. 4 Place of [Number and Numeration Goal 1] Start with Digit a. 570 Tens b. 409 Hundreds c. 54,463 d. 760,837 Tens e. 52,036,458 Ones New Change to Operation 0 8 9 0 9 5 1 Thousands f. Ten Thousands g. Millions Number 500 809 59,463 760,807 52,036,459 52,056,459 51,056,459 2. Complete these calculator “change” problems on your own. Start with 夹 a. 893 b. 5,489 c. 94,732 d. 218,149 e. 65,307,000 Place of Digit Change to Tens 3 Hundreds 7 Thousands 6 Ten Thousands 0 Millions 9 f. 873,562,003 Ten Millions 1 g. 103,070,651 Hundred Millions 8 New Number Operation 833 5,789 96,732 208,149 69,307,000 813,562,003 803,070,651 36 Math Journal 1, p. 36 Lesson 2 4 䉬 103 Game Master Name Date Time 1 2 4 3 Fishing for Digits Record Sheet Beginning Number 1 2 Ongoing Learning & Practice X New Number New Number 2 䉴 Playing Fishing for Digits New Number New Number 3 New Number (Student Reference Book, p. 242; Math Masters, p. 472; optional) New Number 4 PARTNER ACTIVITY New Number New Number 5 Fishing for Digits combines place-value and calculator skills. The steps in the game are similar to the calculator practice done in this lesson. Go over the game directions on page 242 in the Student Reference Book. Play a sample round as a class using an overhead calculator, if available. If you want students to use the Fishing for Digits Record Sheet (Math Masters, page 472), model its use first. New Number Final Number Name Date Time 1 2 4 3 Fishing for Digits Record Sheet Beginning Number 1 X New Number New Number 2 New Number New Number 3 New Number 䉴 Math Boxes 2 4 New Number 4 5 INDEPENDENT ACTIVITY 䉬 New Number New Number New Number (Math Journal 1, p. 37) Final Number Math Masters, p. 472 Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 2-2. The skill in Problem 6 previews Unit 3 content. 䉴 Study Link 2 4 INDEPENDENT ACTIVITY 䉬 (Math Masters, p. 48) Home Connection Students practice place-value skills and reading, writing, and ordering numbers up to one billion. Student Page Date Study Link Master Time LESSON 2 4 䉬 Name 䉬 with the digits 3, 0, 3, 8, and 0? Fill in the circle next to the best answer. algorithm. a. 83,003 B 83,030 C 83,300 D 80,033 b. 145 34 3. About 5 centimeters 3 b. c. 24 21 128 a. 16 2 in. 2 ft b. 20 10 ft 7 yd c. 48 in. 137 yd 2 8 ft e. 9 8 2 6. 40 5 d. 60 10 a. 80,007,941 c. 8,714,366 80,000,000 8,000,000 835,099,714 d. 860,490 800,000,000 800,000 487,000,063 15,000,297 a. four hundred eighty-seven million, sixty-three b. fifteen million, two hundred ninety-seven I am an 8-digit number. • The digit in the thousands place is the result of dividing 64 by 8. • The digit in the millions place is the result of dividing 63 by 9. • The digit in the ten-millions place is the result of dividing 54 by 6. • The digit in the tens place is the result of dividing 40 by 5. • The digit in the hundred-thousands place is the result of dividing 33 by 11. • All the other digits are the result of subtracting any number from itself. 6 45 5 9 7, 3 0 8, 0 8 0 20 37 Math Journal 1, p. 37 104 b. Write each number using digits. What number am I? 129 97,654,320 Try This 6. Divide mentally. in. d. 1 yd 1 ft e. 413 ft 5. centimeters 97 2 5 8 1, 9 7 0, 0 0 0 Write the value of the digit 8 in each numeral below. b. ft the hundred-millions place, the ten-thousands place, the millions place, the hundred-thousands place, the ten-millions place, and all other places. Write the largest number you can. Use each digit just once. 3 5 0 7 9 2 6 4 4. a. About 1 4 in in in in in in 10 11 nearest centimeter. a. 14 in. Write the number that has 5 7 1 9 8 0 15,964 1,400,960 1,509,460 15,094,600 150,094,400 4. Measure these line segments to the 5. Complete. 2. 15,964 1,509,460 150,094,400 1,400,960 15,094,600 297 136 4 Sample answer: Write the numbers in order from smallest to largest. 433 179 3. Draw a concave pentagon. 1. 2. Add mentally or with a paper-and-pencil Time Place Values in Whole Numbers 24 1. What is the largest number you can make A Date STUDY LINK Math Boxes Unit 2 Using Numbers and Organizing Data Math Masters, p. 48 Teaching Master Name 3 Differentiation Options Date LESSON 䉬 Display each number below in your place-value flip book. Then display, read, and record the numbers that are 10 more, 100 more, and 1,000 more. Circle the digit that changed. Number PARTNER ACTIVITY READINESS 䉴 Using a Place-Value Tool Use a Place-Value Tool 24 1. 146 2,368 15–30 Min 4,571 (Math Masters, pp. 49 and 399–402) 15,682 2. 100 more 156 2 46 6 08 2, 4 68 4, 6 71 15, 7 82 4 1,000 more 1 ,146 1 ,508 3 ,368 5 ,571 16 ,682 Display each number below in your place-value flip book. Then display, read, and record the numbers that are 10 less, 100 less, and 1,000 less. Circle the digit that changed. Number 10 less 100 less 1,000 less 2,345 2,3 3 5 2, 2 45 1 ,345 3,491 3,4 8 1 6,8 2 9 12,3 5 7 45,1 2 0 3, 3 91 6, 7 39 12, 2 67 45, 0 30 2 ,491 5 ,839 1 1 ,367 4 4 ,130 6,839 12,367 45,130 3. 10 more 518 2,3 7 8 4,5 8 1 15,6 9 2 508 To provide experience identifying the place value of digits in large numbers, have students use a Compact Place-Value Flip Book to solve problems. The flipping of the digits in the place-value tool provides a hands-on way for students to see the operation that occurs when the digit within a number changes. Have students describe how they would change the original number to make the new number for each prompt. Time Use your place-value flip book to help you answer the following questions. a. What number is 50 more than 329? b. What number is 300 more than 517? c. What number is 60 less than 685? d. What number is 400 less than 932? 379 817 625 532 Math Masters, p. 49 The Compact Place-Value Flip Book can be used to display numbers from 99,999 to 0.0001. When students have completed the activity, collect and save the books for use in Unit 4—Decimals and Their Uses. ENRICHMENT 䉴 Deciphering a Place-Value Code PARTNER ACTIVITY 15–30 Min (Math Masters, p. 50) To apply students’ understanding of place value, have them decipher the packing-system code used at a bakery. Encourage students to use a visual organizer such as the following to help them solve the problem. Students might begin by asking “How many boxes of x muffins?” beginning with 27, then 9, and so on. Teaching Master Name LESSON 24 䉬 Date Time Crack the Muffin Code Daniel takes orders at the Marvelous Muffin Bakery. The muffins are packed into boxes that hold 1, 3, 9, or 27 muffins. When a customer asks for muffins, Daniel fills out an order slip. 4 175 • If a customer orders 5 muffins, Daniel writes CODE 12 on the order slip. • If a customer orders 19 muffins, Daniel writes CODE 201 on the order slip. • If a customer orders 34 muffins, Daniel writes CODE 1021 on the order slip. 1. Total Muffins Boxes of 27 Boxes of 9 Boxes of 3 What would Daniel write on the order slip if a customer asked for 47 muffins? Explain. 1202 Sample answer: Daniel needs 1 box of 27 muffins (the “1” in the code), 2 boxes of 9 muffins (18 muffins; the first “2” in the code); zero boxes of 3 muffins (the “0” in the code), and 2 boxes of 1 muffin (2 muffins; the last “2” in the code). Boxes of 1 CODE 2. If the Marvelous Muffin Bakery always packs its muffins into the fewest number of boxes possible, what is a code Daniel would never write on an order slip? Explain. CODE Have students describe how the chart they used to solve the problem is different from and similar to a base-ten place-value chart. In this problem, you multiply by 3 to get the next column. In the base-ten place-value chart, you multiply by 10. In both charts, each time you have enough in one column, that column becomes 0 and the next column becomes 1. Sample answer: 300 CODE 300 means that the bakery would be using 3 boxes of 9 to pack 27 muffins instead of using 1 box of 27 to pack 27 muffins (CODE 1000). 3. The largest box used by the bakery holds 27 muffins. Daniel thinks the bakery should have a box one size larger. How many muffins would the new box hold? Explain. 81 muffins Sample answer: There is a pattern in the numbers 1, 3, 9, 27. The rule is 3. So, the next number in the pattern is 27 3 81. Math Masters, p. 50 Lesson 2 4 䉬 105

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