Model Place Value Relationships

Lesson 1.1ReteachNameModel Place Value RelationshipsA 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 ofsmall squares. There are 10 small squares. The model for10 has 10 times as many squares as the model for 1 . Shade the remaining 9 columns. Count the number ofsmall squares. There are 100 small squares. The model for100 has 10 times as many squares as the model for 10. If you shade ten hundred grids, you will have shaded1,000 squares. So, the model for 1,000 has 10 timesas many squares as the model for 100.A place-value chart helps you find the value of each digit in a es8,516In the number 8,516:The value of the digit 8 is 8 thousands, or 8,000.The value of the digit 5 is 5 hundreds, or 500 .10 .The value of the digit 6 is 6 ones, or 6 .The value of the digit 1 is 1 ten, orFind the value of the underlined digit.1.7562.3.1,0254,2794.35,703Compare the values of the underlined digits.5.6.700 and 70The value of 7 intimes the value of 7 inChapter Resources Houghton Mifflin Harcourt Publishing Companyis5,000 and 500The value of 5 in.times the value of 5 in1-21is.Reteach

Lesson 1.1EnrichNameComparing ValuesCompare the values of the underlined digits.1.2.3,492 and 704The value of 4 inThe value of 8 inisistimesthe value of 4 in3.the value of 8 in4.isistimes6.495,123 and 63,129timesthe value of 3 in.The value of 5 inisis8.837,164 and 4,508timesthe value of 5 in.The value of 6 inisistimesthe value of 6 in.631,485 and 682The value of 8 intimes.506,712 and 324,859The value of 9 intimes.43,158 and 71,435The value of 3 inthe value of 8 in9.timesThe value of 2 inthe value of 9 in7.2,481 and 5,072the value of 2 in5.8,596 and 985.Stretch Your Thinking Write a pair of numbers such thatthe value of the 7 in the first number is 1,000 times the valueof the 7 in the second number, and the value of the 3 in the firstnumber is 100 times the value of the 3 in the second number.Chapter Resources Houghton Mifflin Harcourt Publishing Company1-22Enrich

Lesson 1.2ReteachNameRead and Write NumbersLook at the digit 6 in the place-value chart below. It is in the hundredthousands place. So, its value is 6 hundred thousands .In word form, the value of this digit is six hundred thousand.In standard form, the value of the digit 6 is sTensOnes659,058Read the number shown in the place-value chart.In word form, this number is written as six hundredfifty-nine thousand, fifty-eight.You can also write the number in expanded form:600,000 1 50,000 1 9,000 1 50 1 8Note that whenwriting a numberin words, a commaseparates periods.Read and write each number in two other forms.1.40,000 1 1,000 1 300 1 70 1 82.twenty-one thousand, four hundred3.391,032Chapter Resources Houghton Mifflin Harcourt Publishing Company1-23Reteach

Lesson 1.2EnrichNamePeriod PosersSolve each riddle.1.Fred: My number has two periods.One period contains the digits 3, 0,and 6 in that order. The other containsthe digits 0, 9, and 5 in that order.2.Jan: My number has two periods. Oneperiod contains only 0s. The other hasthe digits 1 and 0 in that order.Ned: My number has two periods also.One contains the digits 4, 8, and 6 inthat order. The other period containsthe digits 1, 2, and 7 in that order.3.Ann: My number has two periods. Onecontains the digits 4, 1, and 8 in thatorder. The other contains the digit 9.Ann: Too bad, my number must begreater than your number.Fred: Yes, but my number is greaterthan your number.Jan: Nope—my number is greater!What are Fred’s and Ned’s numbers?What are Ann’s and Jan’s numbers?Mo: My number has two periods. One period has a 7 inthe hundreds place. The other has an 8 in the tens place.Bo: My number also has two periods. One has a 1 in thehundreds place. The other has a 2 in the tens place.Mo: All other digits in our numbers are zeros. So how canit be that your number is greater than my number?What are Mo’s and Bo’s numbers?4.Stretch Your Thinking Write your own period poser.Then exchange it with a classmate and solve each other’s posers.Chapter Resources Houghton Mifflin Harcourt Publishing Company1-24Enrich

Lesson 1.3ReteachNameCompare and Order NumbersCompare 31,072 and 34,318. Write ,, ., or 5.Step 1 Align the numbers by place value using grid paper.Step 2 Compare the digits in each place value. Start at thegreatest 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 is less than 4 thousands.start here331403712833140371281 43 3Step 3 Use the symbols ,, ., or 5 to compare the numbers., means is less than. means is greater than.5 means is equal to.There are two ways to write the comparison.31,072 , 34,3181.or34,318 . 31,072Use the grid paper to compare 21,409 and 20,891.Write ,, ., or 5.21,40920,891Compare. Write ,, ., or 5.2. 53,621 53,7603.82,5505.561,028; 582,073; 549,00680,711Order from greatest to least.4.16,451; 16,250; 17,014Chapter Resources Houghton Mifflin Harcourt Publishing Company1-25Reteach

Lesson 1.3EnrichNamePlace-Value PuzzleFill in each blank with a digit that will make the number sentencetrue. The digits to choose from are listed in the box under eachnumber sentence. Use each digit only once.1.15,120 . 125,20 . 125,101, 2, 32.43,900 , 42,900 5 423,00 , 42,9001, 3, 4, 93.,010 , 2278,010 , 29,0108 5 35,88 . 35,7,294 , 63,7057, 8, 94.3,788 . 35,7885, 6, 7, 85.68,138 . 63, 4, 96.46,047 .63,941 5 463,41 .86,423, 4, 5, 7, 97.101,52.11,508 . 101,62 . 101,370, 3, 5, 88.If you know A is greater than B and B isgreater than C, do you have to compare A to C to knowwhich is greater? Use an example to explain.Chapter Resources Houghton Mifflin Harcourt Publishing Company1-26Enrich

Lesson 1.4ReteachNameRound NumbersWhen you round a number, you replace it with a number that iseasier to work with but not as exact. You can round numbers todifferent place values.Round 478,456 to the place value of the underlined digit.Step 1 Identify the underlined digit.The underlined digit, 4, is in the hundred thousands place.Step 2 Look at the number to the right of the underlined digit.If that number is 0– 4, the underlined digit stays the same.If that number is 5–9, the underlined digit is increased by 1.The number to the right of the underlined digit is 7 , so theunderlined digit, 4, will be increased by one; 4 1 1 5 5 .Step 3 Change all the digits to the right of thehundred thousands place to zeros.So, 478,456 rounded to the nearest hundred thousand is 500,000 .1.In 2010, the population of North Dakota was 672,591 people.Use the number line to round this number to the nearesthundred thousand.600,000650,000672,591 is closer to700,000than,.so it rounds toRound to the place value of the underlined digit.2.3,4523.1804. r Resources Houghton Mifflin Harcourt Publishing Company1-27Reteach

Lesson 1.4EnrichNameRounding RangesSolve each riddle. Give your answer as a range of numbers.1.When rounded to the nearesthundred, I become 500. Whatnumbers could I be?2.When rounded to the nearest ten,I become 500. What numbers couldI be?3.When rounded to the nearestthousand, I become 3,000. Whatnumbers could I be?4.When rounded to the nearesthundred, I become 3,000. Whatnumbers could I be?5.When rounded to the nearesthundred thousand, I become600,000. What numbers could I be?6.When rounded to the nearest tenthousand, I become 600,000. Whatnumbers could I be?7.Compare the ranges of your answers toExercises 2, 4, and 6 to the ranges in Exercises 1, 3, and 5.What do you notice? Give a reason for your observation.Chapter Resources Houghton Mifflin Harcourt Publishing Company1-28Enrich

Lesson 1.5ReteachNameRename NumbersYou can use place value to rename whole numbers.Here are different ways to name the number 1,400. As thousands and hundredsThink: 1,400 5 1 thousand 4 hundreds.You can draw a quick picture to help.T As hundredsThink: 1,400 5 14 hundreds.You can draw a quick picture to help. As tensThink: 1,400 5 140 tens. As onesThink: 1,400 5 1,400 ones.Rename the number. Draw a quick picture to help.1.180 53.6,000 55.2 hundreds 6 tens 5tensthousandsChapter Resources Houghton Mifflin Harcourt Publishing Companytens2.1,600 54.2,700 5 276.71 thousands 51-29hundredsReteach

Lesson 1.5EnrichNameNumber ComparisonsCompare the numbers. Write ,, ., or 5.1.400 tens2.7 thousands, 8 hundreds3.715 thousands, 34 tens4.10 thousands, 5 hundreds5.34 ten thousands, 85 hundreds6.6 hundred thousands, 47 tens60 ten thousands, 4 hundreds7.2 ten thousands, 45 hundreds308 hundreds8.25 thousands, 56 ones9.476 thousands48 hundreds2,500 tens715,0341,050 tens348,5003 ten thousands, 17 hundreds4 hundred thousands, 76 hundreds10.35 ten thousands, 8 hundreds11.Look back at Exercise 5. Explain how youfound the answer.Chapter Resources Houghton Mifflin Harcourt Publishing Company3 hundred thousands50 thousands, 80 tens1-30Enrich

Lesson 1.6ReteachNameAdd Whole NumbersFind the sum. 63,821 1 34,765 13,4,8,875OnStep 3 Start with the ones place.Add from right to left.Regroup as needed.639TensHThoundreus a dndsTho Tenus andsThous andsHundredsStep 2 Use a place-value chartto line up the digits byplace value.esStep 1 Round each addend to estimate.60,000 1 30,000 5 90,000268156The sum is 98,586 . Since 98,586 is closeto the estimate 90,000, the answer is reasonable.Estimate. Then find the sum.1.Find 238,503 341,978. Use the grid to help.Estimate:2.Estimate:3.52,8511 65,6015.Estimate:147,0261 106,792Chapter Resources Houghton Mifflin Harcourt Publishing CompanyEstimate:4.54,9801 24,6116.Estimate:278,3091 422,1821-31Estimate:604,5421 87,1067.Estimate:540,7211 375,899Reteach

Lesson 1.6EnrichName3-Foot PathFind the path with the addends that correctly leads from the STARTbox to the FIRST SUM box, and from there to the sum in the FINISHbox. Then write the letters of the 5 boxes on your path in order toanswer the riddle.STARTA20,16511N13,9421Y14,292M14,57455FIRST INISHWhere can you buy a ruler that is 3 feet long?ATSALEChapter Resources1-32 Houghton Mifflin Harcourt Publishing CompanyEnrich

Lesson 1.7ReteachNameSubtract Whole NumbersFind the difference. 5,128 2 3,956Estimate first.Think: 5,128 is close to 5,000. 3,956 is close to 4,000.So, an estimate is 5,000 2 4,000 5 1,000.Write the problem vertically. Use grid paper to align digits by place value.Step 1 Subtractthe ones.Step 2 Subtractthe tens.826525, 1 2 82 3, 9 5 620 12There are not enough tens to subtract.Regroup 1 hundred as 10 tens.12 tens 2 5 tens 5 7 tens5, 1 2 83,9 5 627 210Step 3 Subtract thehundreds.Step 4 Subtract thethousands.4 0 125, 1 2 83,9 5 621 7 245,2 3,1,There are not enough hundreds tosubtract. Regroup 1 thousand as10 hundreds.10 hundreds 2 9 hundreds 5 1 hundred100 124 thousands 2 3 thousands 51 thousand1 2 89 5 61 7 21,172 . Since 1,172 is closeThe difference isto the estimate of 1,000, the answer is reasonable.Estimate. Then find the difference.1.Estimate:6,2532 3,718Chapter Resources Houghton Mifflin Harcourt Publishing Company2.Estimate:74,5292 38,4531-333.Estimate:232,3182 126,705Reteach

Lesson 1.7EnrichNameUnknown DigitsComplete each subtraction problem by finding the unknown digits.1.4 2,5 322,3 41 5, 23.027,38, 7 57,7.44.6 32,8 9 719 0, 723,9 564 1,12 1 2 8, 715.2.,9 3 6,25, 6 34 5 4, 8 0 86.6 80 0,2 2 3 8, 1 7 24,8 2 8Describe what strategy you used to complete theunknown-digit subtraction problems. Use an example to explain.Chapter Resources Houghton Mifflin Harcourt Publishing Company1-34Enrich