Model Place Value Relationships

Transcription

1 Lesson 1.1 Reteach Model Place Value Relationships A hundred grid can help you understand place-value relationships. One small square has been shaded to represent 1. Shade the rest of the first column. Count the number of small squares. There are 10 small squares. The model for 10 has 10 times as many squares as the model for 1. Shade the remaining 9 columns. Count the number of small squares. There are 100 small squares. The model for 100 has 10 times as many squares as the model for 10. If you shade ten hundred grids, you will have shaded 1,000 squares. So, the model for 1,000 has 10 times as many squares as the model for 100. A place-value chart helps you find the value of each digit in a number. THOUSANDS Hundreds Tens Ones 8, ONES Hundreds Tens 1 Ones 6 In the number 8,16: The value of the digit 8 8 thousands, or 8,000. The value of the digit hundreds, or 00. The value of the digit 1 1 ten, or 10. The value of the digit 6 6 ones, or 6. Find the value of the underlined digit ,0.,79., Compare the values of the underlined digits.,000 0, and 70 The value of 7 in times the value of 7 in. 6.,000 and The value of in, times the value of in Reteach

2 Lesson 1.1 Enrich Comparing Values Compare the values of the underlined digits. 1.,9 and 70 The value of in times the value of in..,81 and,07 The value of in times the value of in.. 9,1 and 6,19 The value of 9 in times the value of 9 in ,16 and,08 The value of 8 in 100 1,000 10, ,000 times,9 70,81,07 9,1 6,19 87,16,08 the value of 8 in.. 8,96 and 98 The value of 8 in times the value of 8 in..,18 and 71, The value of in times the value of in ,71 and,89 The value of in times the value of in ,8 and 68 The value of 6 in ,000 1,000 06,71,89 61,8 times 8,96 98,18 71, 68 the value of 6 in. 9. Stretch Your Thinking Write a pair of numbers such that the value of the 7 in the first number 1,000 times the value of the 7 in the second number, and the value of the in the first number 100 times the value of the in the second number. Possible answer: 67,1 and 1,7 1- Enrich

3 Lesson 1. Reteach Read and Write Numbers Look at the digit 6 in the place-value chart below. It in the hundred thousands place. So, its value 6 hundred thousands. In word form, the value of th digit six hundred thousand. In standard form, the value of the digit 6 600,000. PERIOD THOUSANDS ONES Hundreds Tens Ones Hundreds Tens Ones 6 9, 0 8 Read the number shown in the place-value chart. In word form, th number written as six hundred fifty-nine thousand, fifty-eight. You can also write the number in expanded form: 600, , , Note that when writing a number in words, a comma separates periods. Read and write each number in two other forms. 1. 0, , ,78; forty-one thousand, three hundred seventy-eight. twenty-one thousand, four hundred 1,00; 0, , ,0 three hundred ninety-one thousand, thirty-two; 00, , , Reteach

4 Lesson 1. Enrich Period Posers Solve each riddle. Possible answers are given. 1. Fred: My number has two periods. One period contains the digits, 0, and 6 in that order. The other contains the digits 0, 9, and in that order. Ned: My number has two periods also. One contains the digits, 8, and 6 in that order. The other period contains the digits 1,, and 7 in that order. Fred: Yes, but my number greater than your number. What are Fred s and Ned s numbers? Fred: 06,09 Ned: 17,86. Ann: My number has two periods. One contains the digits, 1, and 8 in that order. The other contains the digit 9. Jan: My number has two periods. One period contains only 0s. The other has the digits 1 and 0 in that order. Ann: Too bad, my number must be greater than your number. Jan: Nope my number greater! What are Ann s and Jan s numbers? Ann: 9,18 Jan: 10,000. Mo: My number has two periods. One period has a 7 in the hundreds place. The other has an 8 in the tens place. Bo: My number also has two periods. One has a 1 in the hundreds place. The other has a in the tens place. Mo: All other digits in our numbers are zeros. So how can it be that your number greater than my number? What are Mo s and Bo s numbers? Mo: 80,700; Bo: 100,00. Stretch Your Thinking Write your own period poser. Then exchange it with a classmate and solve each other s posers. Check students work. 1- Enrich

5 Lesson 1. Reteach Compare and Order Numbers Compare 1,07 and,18. Write,,., or. Step 1 Align the numbers by place value using grid paper. Step Compare the digits in each place value. Start at the greatest place. Are the digits in the ten thousands place the same? Yes. Move to the thousands place. Are the digits in the thousands place the same? No. 1 thousand less than thousands. start here = < Step Use the symbols,,., or to compare the numbers., means less than.. means greater than. means equal to. There are two ways to write the comparon. 1,07,,18 or,18. 1,07 1. Use the grid paper to compare 1,09 and 0,891. Write,,., or. 1,09 0,891. Compare. Write,,., or.,. $,61 $,760 Order from greatest to least... 8,0 80, ,1; 16,0; 17,01 17,01; 16,1; 16,0. 61,08; 8,07; 9,006 8,07; 61,08; 9, Reteach

6 Lesson 1. Enrich Place-Value Puzzle Fill in each blank with a digit that will make the number sentence true. The digits to choose from are lted in the box under each number sentence. Use each digit only once. 1. 1,10. 1, 0. 1,1 0 1,, 1 9.,900,,900, 00,,900 1,,, 9. 7,010, 8,010, 9,010 7, 8, 9 6.,788.,7 8, 88., 88, 6, 7, , ,9, 6,70,, ,07. 6,91 6, 1. 86,,,, 7, ,. 1 1, , , 7 0,,, Possible answers are given. 8. If you know A greater than B and B greater than C, do you have to compare A to C to know which greater? Use an example to explain. No; possible answer:,1.,688 and,688. 1,999; so,,1 greater than 1, Enrich

7 Lesson 1. Reteach Round Numbers When you round a number, you replace it with a number that easier to work with but not as exact. You can round numbers to different place values. Round 78,6 to the place value of the underlined digit. Step 1 Identify the underlined digit. The underlined digit,, in the hundred thousands place. Step Look at the number to the right of the underlined digit. If that number 0, the underlined digit stays the same. If that number 9, the underlined digit increased by 1. The number to the right of the underlined digit 7, so the underlined digit,, will be increased by one; 1 1. Step Change all the digits to the right of the hundred thousands place to zeros. So, 78,6 rounded to the nearest hundred thousand 00, In 010, the population of North Dakota was 67,91 people. Use the number line to round th number to the nearest hundred thousand. 67,91 600,000 60, , , ,000 67,91 closer to than, so it rounds to. Round to the place value of the underlined digit. 600,000., $7,71. 7,000,00 00 $70, , ,9 8. 8, ,6 1,000 6,000 80,000 96, Reteach

8 Lesson 1. Enrich Rounding Ranges Solve each riddle. Give your answer as a range of numbers. 1. When rounded to the nearest hundred, I become 00. What numbers could I be? 0 to 9. When rounded to the nearest ten, I become 00. What numbers could I be? 9 to 0. When rounded to the nearest thousand, I become,000. What numbers could I be?,00 to,99. When rounded to the nearest hundred, I become,000. What numbers could I be?,90 to,09. When rounded to the nearest hundred thousand, I become 600,000. What numbers could I be? 0,000 to 69, When rounded to the nearest ten thousand, I become 600,000. What numbers could I be? 9,000 to 60, Compare the ranges of your answers to Exerces,, and 6 to the ranges in Exerces 1,, and. What do you notice? Give a reason for your observation. Possible answer: the ranges in,, and 6 are all narrower than the ranges in 1,, and. Th because in,, and 6, the place rounded to less than the place rounded to in 1,, and. 1-8 Enrich

9 Lesson 1. Reteach Rename Numbers You can use place value to rename whole numbers. Here are different ways to name the number 1,00. As thousands and hundreds Think: 1,00 1 thousand hundreds. You can draw a quick picture to help. T As hundreds Think: 1,00 1 hundreds. You can draw a quick picture to help. As tens Think: 1,00 10 tens. As ones Think: 1,00 1,00 ones. Rename the number. Draw a quick picture to help. 18 Check students drawings tens. 1,600 hundreds 6. 6,000 thousands., hundreds 6 tens tens thousands hundreds 71, Reteach

10 Lesson 1. Enrich Number Comparons Compare the numbers. Write,,., or., tens 8 hundreds. 7 thousands, 8 hundreds,00 tens. 71 thousands, tens 71,0. 10 thousands, hundreds 1,00 tens. ten thousands, 8 hundreds 8, hundred thousands, 7 tens 60 ten thousands, hundreds 7. ten thousands, hundreds 08 hundreds 8. thousands, 6 ones ten thousands, 17 hundreds.,,.., thousands hundred thousands, 76 hundreds 10. ten thousands, 8 hundreds hundred thousands 0 thousands, 80 tens 11. Look back at Exerce. Explain how you found the answer. Possible answer: I renamed ten thousands, 8 hundreds as hundred thousands ten thousands 8 thousands, hundreds and wrote that number in standard form: 8,00. It the same as the number on the right. 1-0 Enrich

11 Lesson 1.6 Reteach Add Whole Numbers Find the sum. 6,81 1,76 Step 1 Round each addend to estimate. 60, ,000 90,000 Step Use a place-value chart to line up the digits by place value. Step Start with the ones place. Add from right to left. Regroup as needed. Hundred Thousands Ten + Thousands 1 Thousands Hundreds Tens Ones 6, 8 1, , ,86 The sum. Since 98,86 close to the estimate 90,000, the answer reasonable. Estimate. Then find the sum. 1. Find 8,0 + 1,978. Use the grid to help , 0 + 1, , 8 1 Estimates may vary. Estimate: 00,000. Estimate:,81 1 6,601. Estimate: 10, , 00,000. Estimate:,980 1, Estimate: 70,000 79,91 700,000. Estimate: 60, 1 87, ,68 900, Estimate: 690,000 17, ,79,818 78,09 1,18 700,91 0,71 1 7, , Reteach

12 Lesson 1.6 Enrich -Foot Path Find the path with the addends that correctly leads from the START box to the FIRST SUM box, and from there to the sum in the FINISH box. Then write the letters of the boxes on your path in order to answer the riddle. START A 0, N 1,9 M 1,7 Y 1,9 FIRST SUM A, T 116,8 R 18,61 S 11,90 D 16,07 FINISH Where can you buy a ruler that feet long? AT A Y A R D SALE 1- Enrich

13 Lesson 1.7 Reteach Subtract Whole Numbers Find the difference.,18,96 Estimate first. Think:,18 close to,000.,96 close to,000. So, an estimate,000,000 1,000. Write the problem vertically. Use grid paper to align digits by place value. Step 1 Subtract the ones., 1 8, Step Subtract the tens. 0 1, 1 8, There are not enough tens to subtract. Regroup 1 hundred as 10 tens. 1 tens tens 7 tens Step Subtract the hundreds , 1 8, There are not enough hundreds to subtract. Regroup 1 thousand as 10 hundreds. 10 hundreds 9 hundreds 1 hundred Step Subtract the thousands , 1 8, 9 6 1, 1 7 thousands thousands 1 thousand 1,17 The difference. Since 1,17 close to the estimate of 1,000, the answer reasonable. Estimate. Then find the difference. 1. Estimate:,000. Estimate: 0,000. Estimate: 100,000 6,,718, 7,9 8, 6,076,18 16,70 10,61 1- Reteach

14 Lesson 1.7 Enrich Unknown Digits Complete each subtraction problem by finding the unknown digits. 1., 7, ,, , 0 6 6, , , 7 1, , 7, 6, , , , 7 9 8, , , Describe what strategy you used to complete the unknown-digit subtraction problems. Use an example to explain. Possible answer: Use the inverse relationship between subtraction and addition. In Exerce 1, in the ones place, 6 1 ; , so 7. In the tens place, 1; subtract the regrouped ten: So, the unknown tens digit 0. In the hundreds place, ; 1, so. In the thousands place, 1 ; 1 7 1, so 7. In the ten thousands place,. Subtract the regrouped ten thousand: 1 1. Add to check the answer: 1,06 1 7,7,. 1- Enrich

15 Lesson 1.8 Reteach Problem Solving Comparon Problems with Addition and Subtraction For a community recycling project, a school collects aluminum cans and plastic containers. Th year the fourth grade collected,9 cans and,18 containers. Th 10 more cans and more containers than the fourth grade collected last year. How many cans did the fourth grade collect last year? What do I need to find? I need to find the number of cans the fourth grade collected last year. Read the Problem What information do I need to use? The fourth grade students collected,9 cans th year. They collected 10 more cans th year than the fourth grade collected last year. Solve the Problem I can draw a bar model and write an equation to represent the problem. How will I use the information? I can draw a bar model to find the number of cans the fourth grade collected last year.,9 10,1,9 10,1 So, the fourth grade collected,1 aluminum cans last year. Use the information above for 1 and. 1. Altogether, how many aluminum cans and plastic containers did the fourth grade collect th year? 10,10 aluminum cans and plastic containers. Th year the fifth grade collected 16 fewer plastic containers than the fourth grade. How many plastic containers did the fifth grade collect?,966 plastic containers 1- Reteach

16 Lesson 1.8 Enrich Take a Seat! Use the table for Last night s game at the arena in Cleveland was 1 seats short of being filled to capacity. How many people attended the game? 0,6 1 0,11 Basketball Arena Seating Capacities City Capacity Cleveland 0,6 Boston 18,6 Atlanta 0,00 New Orleans 18,00 Los Angeles 18,997. How many more people can be seated in the largest arena than can be seated in the smallest arena? 0,6 18,00,06. Estimate the difference in the seating capacities of the Atlanta and Los Angeles arenas. Explain how you made your estimate. Possible answer: 1,00; I rounded 18,997 to 19,000; 0,00 19,000 1,00.. There are two sold-out basketball games tonight. One at the arena in Boston, and the other at the arena in New Orleans. How many people are attending the two games? 18,6 1 18,00 7,1. The biggest college basketball arena seats,000. Is the combined capacity of the Cleveland and Boston arenas greater than or less than the capacity of the biggest college arena? How much greater or less? Explain. greater than; 6,186; Possible answer: I subtracted,000 from the sum of the Cleveland and Boston capacities; 0,6 1 18,6 9,186; 9,186,000 6, Enrich