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LName:Date:2.1 Representing Numbers Page 1Student Book pages 40–43GOALRepresent numbers to one million using a placevalue chart, numerals, and words.You will need• a place value chart• countersIn 1997, David Huxley pulled an airplane with a mass of about 187 000 kg.In 1999, Juraj Barbaric pulled a train with a mass of about 892 851 kg.How can you model, read, and write these masses?Circle the value of 8 in each number.87 8 hundreds 8 tens 8 ones18 8 hundreds 8 tens 8 ones851 8 hundreds 8 tens 8 onesShow how the place values are related.1 ten ____ ones 1 hundred ____ tens 1 thousand ____ hundredsHere is a model of 187 (one hundred eighty-seven).HundredsTensOnesHere is a model of 187 000 (one hundred eighty-seven thousand).HundredsThousandsTensOnesHundredsOnesTensOnesThe three 0s in 187 000 show that there are no hundreds, tens, or ones.The 0s fill those places so that the 1, 8, and 7 have the correct values.The value of the 7 is seven thousands or 7000.The value of the 8 is _________ ten thousands or 80 000.The value of the 1 is ________________________ or ____________________.40 Learning BLM 2.1: Representing Numbers Copyright © 2009 by Nelson Education Ltd.

LName:Date:2.1 Representing Numbers Page 2Write the digits of numerals in groups of 3.spacespaceStart at the right.Leave a space between each group of 3.1 000 000 is 1 million.1 000 0003 digits3 digitsHere are some other examples: 10 000 28 510 187 000Rewrite the numerals below with the correct space between groups of 3.285100 ____________ 92851 ____________ 892851 ____________This way of writing numbers is called standard form.Model 892 851 on a place value chart.Sketch your model.ThousandsOnesHundreds Tens Ones Hundreds Tens Onesstandard formThe usual way thatnumbers are writtenFor example, 766 921is in standard form.Write 892 000 in words. _______ hundred _______–_______ thousandWrite 851 in words. _______ hundred _______–_______Write 892 851 in words._______ hundred _______–_______ thousand _______ hundred _______–_______ReflectingHow is the space in 187 000 shown on the place value chart?Why do we need 0 to represent some numbers in standard form?Copyright © 2009 by Nelson Education Ltd.Learning BLM 2.1: Representing Numbers41

2.2 3.3Using Expanded FormStudent Book pp. 44–47Teacher’s Resource pp. 17–21GOALRepresent, describe, and compare numbers to one million.Preparation and PlanningMastersKey Question 2AssessmentQuestion• Checking and PractisingBLM 2.2 pp. 43–44• Learning BLM 2.2 pp. 45–46• Place Value Chart to HundredThousands, MB p. 43About the MathIn this lesson, students write numbers to 1 million in standardand expanded form. They connect the representation of anumber on a place value chart and in expanded form. Studentsalso compare numbers using standard and expanded form. Notethat kilometres are introduced in this lesson.Differentiating InstructionStudents have learned that a number with more digits is greater than a number with fewer digits, up to 10 000.Explain that this also applies to greater whole numbers. Ensure that students understand that they should comparethe highest place value first, as it has the greatest value. Demonstrate with examples the importance of lining upthe digits correctly when comparing numbers; for example, have students compare 256 700 and 32 160.Students will also know that a number with more tens is greater than a number with fewer tens. Explain that thesame is true when comparing numbers in the thousands. For example, to compare 267 000 km with 389 000 km,say, “3 hundred thousands 2 hundred thousands, so 389 000 267 000.” Explain that if the value inthe highest place is the same, they should compare the value to the right. Have students compare 321 600 and256 700, then 256 700 and 239 100, and then 256 700 and 257 700.Help students connect the representation of a number on a place value chart and in expanded form. You maywant to begin with 4-digit numbers and build to 6-digit numbers. As an intermediate step, you may want to havestudents place number cards (0–9) on a place value chart to represent the number.Provide practice by having students play this game in 2 teams. Place 2 shuffled sets of 0–9 number cards facedown. On the chalkboard, draw 2 place value charts to the hundred thousands, 1 for each team. Teams take turnsdrawing the top card from their deck and placing the number on the place value chart. The object of the game isto make the greatest number, so students will need to be strategic about where they place each number. Once two6-digit numbers are formed, have students compare the numbers to determine which is greater.For students who need scaffolding during independent practice, provide Checking and Practising BLM 2.2.For students who need extra learning support, provide Learning BLM 2.2.Answers to Learning BLM 2.2Step 3: 48, 84, 44Step 4: 344 800, 348 400, 384 400Step 5: 4, 8, 4; 40 000, 8000, 4008, 4, 4; 300 000, 80 000, 4000, 400384 400; 384 400; 384 400Reflecting: You don’t need to include the 0s in expanded form because they don’t have any value.42 Overview 2.2: Using Expanded Form Copyright © 2009 by Nelson Education Ltd.

C&P Name: Date:2.2 Using Expanded Form Page 2Practising2. Use 8 counters to model 3 different 6-digit numbers.Draw your models in the place value charts below.Model a 6-digit number.Write it in standard form.ThousandsHundreds TensOnesHundredsOnesTensOnes______________Write it in expanded form._________ _________ _________ _________ _________ _________Model another 6-digitnumber.ThousandsHundreds TensOnesHundredsOnesTensOnesWrite it in standard form.______________Write it in expanded form._____________________________________________________________________________Model another 6-digitnumber.ThousandsHundreds TensOnesHundredsOnesTensOnesWrite it in standard form.______________Write it in expanded form._____________________________________________________________________________44 Checking & Practising BLM 2.2: Using Expanded Form Copyright © 2009 by Nelson Education Ltd.

LName:Date:2.2 Using Expanded Form Page 1Student Book pages 44–47GOALRepresent, describe, and compare numbers toone million.You will need• a place value chart• countersThe distance from Earth to the Moon, inkilometres, is the greatest number you can makewith the digits shown, starting with the 3.30484 0What is the distance from Earth to the Moon?There are 6 number cards, so the distance is a 6-digit number.Step 1: The problem says that the first digit is 3.Write the first digit in the first column.HundredsThousandsTensOnesHundredsOnesTensOnes3Step 2: To make the greatest number, put the 0s in the places with the least value.Note: 0 is smaller than all the other numbers.Write the two 0s in the tens and ones places.HundredsThousandsTensOnesHundredsOnesTensOnes3 0 0Step 3: Write the 3 different numbersyou can make with 4, 4, and 8.448Copyright © 2009 by Nelson Education Ltd.Learning BLM 2.2: Using Expanded Form45

LName:Date:2.2 Using Expanded Form Page 2Step 4: Write the 3 possible distances.ThousandsHundreds Tens Ones HundredsOnesTensOnes3 4 0 03 4 0 03 8 0 0Step 5: 344 800, 348 400, and 384 400 are possible distances.Find out which is greater. Write each number in expanded form.expanded formA way to write anumber that showsthe value of each digit344 800 3 hundred thousands 4 ten thousands 4 thousands 8 hundreds 300 000 40 000 4000 800348 400 3 hundred thousands ___ ten thousands ___ thousands ___ hundreds 300 000 __________ _______ __ __________384 400 3 hundred thousands ___ ten thousands ___ thousands ___ hundreds __________ __________ _______ __ __________The number of hundred thousands (3) is the same in each number.Compare the ten thousands. Circle the number that has the most ten thousands.344 800 348 400 384 400So, _______________________________ is the greatest number.The distance between Earth and the Moon is ___________ km.Reflecting384 400 is a 6-digit number. Why does the expanded form of 384 400 only have 4 valuesadded together?46 Learning BLM 2.2: Using Expanded Form Copyright © 2009 by Nelson Education Ltd.

2.3 3.3Renaming NumbersStudent Book p. 48Teacher’s Resource pp. 22–24GOALRename numbers that have up to seven digits.Preparation and PlanningMasters • Explore BLM-A 2.3 p. 48• Explore BLM-B 2.3 p. 49KeyAssessmentQuestionEntire explorationAbout the MathIn this exploration, students rename a 6-digit number using avariety of strategies of their choice, which may include writingthe number in expanded form and/or using a place value chart.Some students may interpret the problem as simply asking themto relate the sizes of the containers to the place values, and willgenerate one solution to the problem. Others may realize thatthere are a large number of possible ways to fill the containerswith the popcorn. Encourage each student to share his or herpersonal strategy.Litres are introduced in this lesson. Litres and capacity areworked with in greater depth in Lesson 8.8.Differentiating InstructionIf students are having difficulty getting started, ask them what they would multiply the capacity of container Z byto get the capacity of container Y (10), and so on. Ask them what the pattern is. (multiply by 10 each time) Havethem compare this pattern to the pattern in the place values.As students represent numbers, encourage them to model the numbers in a variety of ways; for example, as well asrepresenting 43 as 4 tens and 3 ones, you can represent it as 3 tens and 12 ones or 43 ones. Help students extendthis understanding; for example, 120 000 is 120 thousands as well as 1 hundred thousand and 2 ten thousands.If students focus on using the standard expansion of the number and do not consider alternate forms, ask themto model 321 using counters and a place value chart (or base ten blocks), and then write the number in expandedform. (3 hundreds 2 tens 1 one) Then, ask students to trade some of the blocks to rename 321. ( for example,32 tens 1 one, or 3 hundreds 21 ones) Discuss why all the models represent 321.For students who need scaffolding of the exploration, provide Explore BLM-A 2.3.For students working in a lower number range, provide Explore BLM-B 2.3, which presents an adapted versionof the central problem for the lesson. Note: The lesson goal has been changed for this BLM.Answers to Explore BLM-B 2.3A. 1000, 900, 40, 71, 9, 4, 7B. 21, 947Copyright © 2009 by Nelson Education Ltd.Overview 2.3: Renaming Numbers47

E-BName:Date:2.3 Renaming NumbersStudent Book page 48GOALRename numbers that have up to five digits.You will need• a place value chart• countersA litre (L) is a unit used to measure capacity.Capacity is the amount that a container can hold.A group of students broke a school record by filling a container with 21 947 L of popcorn.Which containers could you fill if you had 21 947 L of popcorn?A. Decide how many of each container you need to make 21 947 L.Fill in the number of each container in the place value chart below.Measuring 21 947 L20 000 _________ _________ _________ _________(ten thousands) (one thousands) (hundreds) (tens) (ones)V10 000 LW1000 LX100 LY10 LZ1 L2 ____ ____ ____ ____ 10 000 L 1000 L 100 L 10 L 1 LB. Here is another way to measure 21 947 L.21 947 is 21 thousands and 947 ones. You could fill the 1000 L container__________ times and the 1 L container __________ times.Copyright © 2009 by Nelson Education Ltd.Explore BLM-B 2.3: Renaming Numbers49

2.4 3.3Rounding NumbersStudent Book pp. 50–52Teacher’s Resource pp. 29–32GOALRound numbers to the nearest hundred thousand, thenearest ten thousand, and the nearest thousand.Preparation and PlanningMastersKey Question 3AssessmentQuestion• Checking and PractisingBLM 2.4 pp. 51–52• Learning BLM 2.4 pp. 53–54About the MathIn this lesson, students round numbers using place values andnumber lines. The context of the lesson is population, a contextwhere benchmark numbers are often used. Number lines areparticularly suitable for estimating numbers by relating themto benchmark numbers. Students use number lines marked atmultiples of 100 000, 10 000, and 1000 to round numbers tothe nearest hundred thousand, ten thousand, and thousand.Differentiating InstructionAsk students to create number lines that can be used to locate the positions of numbers to 10, then to 100, andthen to 1000. Engage students in a conversation about how the benchmarks they used are similar in each case,so that they can extend those notions beyond 1000. Then ask students to create number lines that can be used tolocate the positions of numbers to 10 000, to 100 000, and to 1 million. Ensure that students realize that thesame benchmark number can be used to estimate different numbers.Discuss with students why, when a population is given, it is usually not an exact number. Speak deliberately aboutthe difference between estimating and counting exactly; students require explicit exposure to situations where anestimate is all that is required. Other examples are animal populations, distances in astronomy, or large amountsof money.Encourage students to think of a number such as 422 536 as greater than 400 000 but less than 500 000. Forthose students who need it, provide practice rounding 4-digit numbers to the nearest hundred and thousand;for example, ask students to compare 3278 to 3000 and 4000, and then to 3200 and 3300. Ask them to explainhow they know which of these numbers is greater or less than 3278. Check that they are using place values tocompare numbers.For students who need scaffolding during independent practice, provide Checking and Practising BLM 2.4.For students who need extra learning support, provide Learning BLM 2.4, which presents an adapted version ofthe central problem for the lesson. Note: The lesson goal has been changed for this BLM.Answers to Learning BLM 2.4A. 9192 is closer to 9000 on the number line.B. 9200C. 9190Reflecting: Down; It is closer to the left end of the number line; Up; There are 9 tens, which is almost anotherhundred; Down; There are 2 ones, and 2 is closer to 0 than 10; 9000; It gives a useful estimate of the size. It shows thatnot many people live in the Inuvik Region. The population will change, but it will probably stay close to 9000; 10 00050 Overview 2.4: Rounding Numbers Copyright © 2009 by Nelson Education Ltd.

C&P Name: Date:2.4 Rounding Numbers Page 1Student Book pages 50–52Checking1. a)Round the populations of Kelowna and Abbotsford to the nearest hundredthousand, the nearest ten thousand, and the nearest thousand.Use number lines. Record your estimates in the table below.Population Nearest Nearest NearestCity in 2006 100 000 10 000 1000Kelowna 162 276Abbotsford 159 020Use this number line to roundthe populations to the nearesthundred thousand.Use this number line to roundthe populations to the nearestten thousand.Use this number line to roundthe populations to the nearestthousand.100 000 150 000 200 000150 000 160 000 170 000155 000 160 000 165 000b) Do the 2 populations round to the same hundred thousand? __________Do the 2 populations round to the same ten thousand? __________Do the 2 populations round to the same thousand? __________Copyright © 2009 by Nelson Education Ltd.Checking & Practising BLM 2.4: Rounding Numbers51

C&P Name: Date:2.4 Rounding Numbers Page 2Practising3. Vasco looked up the total land and fresh water area of each Western province.a) Round each area to the nearest hundred thousand, ten thousand, and thousand.Use the number lines on this page to help you estimate.Land andfresh water Nearest Nearest NearestProvince (km 2 ) 100 000 10 000 1000British Columbia 944 735Alberta 661 848Saskatchewan 651 036Manitoba 647 797b) Which provinces have the same area,to the nearest hundred thousand?900 000 1 000 000940 000 950 000944 000 945 000c) Which provinces have thesame area, to the nearestten thousand?600 000 700 000640 000 650 000 660 000645 000 650 000 655 000 660 00052 Checking & Practising BLM 2.4: Rounding Numbers Copyright © 2009 by Nelson Education Ltd.

LName: ____________________________________________Date: ________________________2.4 Rounding Numbers Page 1Student Book pages 50–52GOALRound numbers to the nearest thousand, the nearesthundred, and the nearest ten.The population of an area is the total number ofpeople who live there.The Inuvik Region in the Northwest Territories hada population of 9192 in 2006.What other ways can you use to showthe population of the Inuvik Region?A. The population of an area is always changing.YukonTerritoryBeaufort SeaPort RadiumNorthwestNunavutTerritoriesYellowknife Great SlaveLakeLakeAthabascaPrince GeorgeTuktoyaktukInuvikGreat BearLakeC A N A D AHudsonBayYou could use an estimate to show thepopulation of the Inuvik Region.SpokaneEdmontonCalgaryReginaWinnipegLakeWinnipeg91929000 9500 10 000You could round 9192 to the nearest thousand.How do you know that 9000 is the nearest thousand?B. Round the population of the Inuvik Region to the nearest hundred.Hint: Is 9192 closest to 9100, 9200, 9300, . . . ?9000 9200 9400 9600 9800 10 000The population of the Inuvik Region is ________________.C. Round the population of the Inuvik Region to the nearest ten.9100 9120 9140 9160 9180 10 000The population of the Inuvik Region is ________________.Copyright © 2009 by Nelson Education Ltd.Learning BLM 2.4: Rounding Numbers53

LName:Date:2.4 Rounding Numbers Page 2ReflectingYou rounded 9192 to the nearest thousand.Was the number rounded up or down? __________ Why?You rounded 9192 to the nearest hundred.Was the number rounded up or down? __________ Why?You rounded 9192 to the nearest ten.Was the number rounded up or down? __________ Why?Which rounded number would you use to describe the population of the Inuvik Region?__________ Why?If the population of the Inuvik Region increased by 900, what number would you round thepopulation to? __________54 Learning BLM 2.4: Rounding Numbers Copyright © 2009 by Nelson Education Ltd.

2.5 3.3Exploring One MillionStudent Book p. 53Teacher’s Resource pp. 33–35GOALDescribe one million in various ways.Preparation and PlanningMasters • Explore BLM-A 2.5 p. 56• Explore BLM-B 2.5 p. 57KeyAssessmentQuestionEntire explorationAbout the MathIn this exploration, students are asked to describe 1 million bycomparing 1 million of one thing with a smaller number ofsomething else. Students will draw on their understanding of themetric system to create interesting facts about 1 million. They willlikely need to multiply by 1 million and/or divide 1 million byanother number. A calculator can be used for such calculations.This exploration will be richer if students are able to use theInternet for research, but students can also use facts found inbooks and magazines.Differentiating InstructionAfter reading the book How Much Is a Million? by David M. Schwartz, provide students with a concreterepresentation of 1 million. Show 1 grain of salt and then 10 grains of salt. Make a tiny pile of salt and tellstudents that this is about 100 grains. Show a pinch of salt (about 1000 grains); 1 teaspoon (about410 000 grains; 1 tablespoon (about 100 000 grains); and 1 cup (about 1 000 000 grains).2Ask students what they would name the place value to the left of the hundred thousands place (they might say athousand thousands, which is an excellent response). Tell them that 1 million is 1000 thousands.Work through a couple of examples with students to demonstrate how to manipulate numbers to create factsinvolving 1 million. For example, a raisin is about 1 cm long, so 1 million raisins will be about 1 000 000 cmlong. Then, students can convert this length into one that is easier for them to visualize. There are 100 cm in 1 m,so 1 million cm 1 000 000 100 10 000 m. (Have students count to check that there are six 0s after the1 when they key 1 million into their calculators.) There are 1000 m in 1 km, so 10 000 m 10 000 1000 10 km. Suppose 10 km is the distance from the school to some landmark. Then, a row of 1 million raisins willstretch from the school to that landmark. Or, if a student lives about 1 km from the school, he or she could saythat 1 million raisins would make a row stretching from home to school 10 times. Help students see that anumber can have a continuous context, such as the distance between 2 places, or a discrete context, such as anumber of raisins. Encourage students to research topics they are interested in.For students who need assistance in getting started on the exploration, provide Explore BLM-A 2.5.For students who need extra learning support, provide Explore BLM-B 2.5, which guides students to create anumber of interesting facts about 1 million.Answers to Explore BLM-B 2.510, 10; 100 000, 100 000; 1 000 000; 1 000 000, VancouverCopyright © 2009 by Nelson Education Ltd.Overview 2.5: Exploring One Million55

E-AName: ____________________________________________Date: ________________________2.5 Exploring One MillionStudent Book page 53If you wrote a book about 1 million,what interesting facts would you include?You will need• a calculatorA humpback whale has a mass of 40 000 kg.40 000 25 ____________________________ humpback whales have a mass of 1 million kg.A Pacific walrus has a mass of 4000 kg._________ Pacific walruses have a mass of 1 million kg.A bottlenosed dolphin has a mass of 400 kg._________ bottlenosed dolphins have a mass of 1 million kg.Research another animal mass.Use the mass to write an interesting fact about 1 million.The distance between Vancouver and Winnipeg is about 2000 km.Divide 1 million km by the distance. Use a calculator.1 000 000 km _________ km _________You would need to travel between Vancouver and Winnipeg _________ times to travel1 million km.Research the distance between 2 other cities in Canada.Use the distance to write an interesting fact about 1 million.56 Explore BLM-A 2.5: Exploring One Million Copyright © 2009 by Nelson Education Ltd.

E-BName: ____________________________________________Date: ________________________2.5 Exploring One MillionStudent Book page 53GOALDescribe one million in various ways.You will need• a calculatorIf you wrote a book about 1 million, what interestingfacts would you include?The mass of a blue whale is about 100 000 kg.What number can you multiply 100 000 by to get 1 million?100 000 _________ 1 000 000So, _________ blue whales have a total mass of 1 million kg.Cats sleep about 10 hours a day.How many cats will it take to sleep 1 million hours in 1 day?1 000 000 10 about _________ catsIt will take about _________ cats to sleep 1 million hours in 1 day.The distance from Calgary to Vancouver is about 1000 km.1 km 1000 mWrite the distance from Calgary to Vancouver in metres.1000 km 1000 m _______ __ mLength of 1 bobcat 1 mLength of a row of 1 million bobcats 1 000 000 1 m _______ __ mA row of 1 million bobcats would stretch from Calgary to _______ ________________________.Copyright © 2009 by Nelson Education Ltd.Explore BLM-B 2.5: Exploring One Million57

C&P Name: ____________________________________________ Date: ________________________2.6 Decimal Place Value Page 1Student Book pages 56–59Checking1. a)Rachel bought a 1.098 kg package of trail mix.Model 1.098 kg using base ten blocks.Hint: Leave the column empty when the place value is 0.Sketch your model.You will need• base tenblocks• a decimalplace value chartHundredsTensOnesTenthsHundredthsThousandthsWrite 1.098 in expanded form.Hint: Do not include place values that are 0.1.098 1 whole __ hundredths __ thousandthsor 1 100 1000or 1 0. 0.Write 1.098 kg in words.one and ___________________________ thousandths of a kilogramb) Lauren bought a 1.401 kg package of trail mix.Model 1.401 kg using base ten blocks.Sketch your model.HundredsTensOnesTenthsHundredthsThousandthsCopyright © 2009 by Nelson Education Ltd.Checking & Practising BLM 2.6: Decimal Place Value59

C&P Name: ____________________________________________ Date: ________________________2.6 Decimal Place Value Page 2Write 1.401 in expanded form.1.401 ___ whole __ tenths __ thousandthor ________ or ________ 0. 0.Write 1.401 kg in words.Practising2. A Canadian penny costs 0.008 cents to make.a) Model 0.008 on a place value chart.Hint: Leave the column empty when the place value is 0.Sketch your model.HundredsTensOnesTenthsHundredthsThousandthsb) Write the cost in expanded form.Hint: Only include place values that are not 0.The expanded form of 0.008 is just ________________ or or 0. .c) Write the cost in words.3. a) Write 6 0.5 0.02 0.006 in standard form. .b) Write 1 0.2 0.005 in standard form. .60 Checking & Practising BLM 2.6: Decimal Place Value Copyright © 2009 by Nelson Education Ltd.

LName: ____________________________________________Date: ________________________2.6 Decimal Place Value Page 1Student Book pages 56–59GOALRead, write, and model decimals.Mateo bought a package of trail mix to take on a hike.The mass of the trail mix is 1.393 kg.You will need• base tenblocks• a decimalplace value chartHow can Mateo model the mass of the trail mix?You can write fractions as decimals.FractionDecimal1 tenth 1100.11 hundredth 11000.011 thousandth 110000.001Complete the chart.FractionDecimal3 tenths100.25 hundredths1000.365 thousandths 0.You can write decimals in expanded form.10001.257 1 whole 2 tenths 5 hundredths 7 thousandthsWrite these decimals in expanded form.1.834 __ whole __ tenths __ hundredths __ thousandths2.696 __ wholes __ tenths __ hundredths __ thousandthsYou can use base ten blocks to model fractions or decimals.one1 or 1.0one tenth1or 0.____10one hundredth1100or 0.____ ____one thousandth11000or 0.____ ____ ____÷10 ÷10 ÷10Copyright © 2009 by Nelson Education Ltd.Learning BLM 2.6: Decimal Place Value61

LName: ____________________________________________Date: ________________________2.6 Decimal Place Value Page 2Use base ten blocks to model 1.393 on a decimal place value chart.Make a copy of this model.HundredsTensOnes Tenths Hundredths Thousandths1 3 9 3Write 1.393 in expanded form.1.393 1 whole __ tenths __ hundredths __ thousandthsor 1 10 100 1000or ___ 0. 0. 0.+ + 300 90 3 small cubes _________ thousandthsWrite 1.393 in words.one and ____________________________ thousandthsReflectingIn 1.393, the 3 in the 1st place after the decimal point represents ____________.The 3 in the 3rd place after the decimal point represents ____________.Which of these 3s represents a greater mass?62 Learning BLM 2.6: Decimal Place Value Copyright © 2009 by Nelson Education Ltd.

2.7 3.3Renaming DecimalsStudent Book pp. 60–63Teacher’s Resource pp. 44–48GOALRepresent decimals and relate them to fractions.Preparation and PlanningMastersKey Question 2AssessmentQuestion• Checking and PractisingBLM 2.7 pp. 64–65• Learning BLM 2.7 pp. 66–67• Hundredths Grid, MB p. 37• Thousandths Grid, MB p. 38Differentiating InstructionAbout the MathIn this lesson, students use hundredths and thousandths gridsto model decimals pictorially. They make connections betweendecimals and fractions, and learn that there are numerous namesfor the same decimal number. A key concept is that the wholegrid is 1 whole, just as the large base ten cube was 1 whole in themodel used in Lesson 2.1. It follows that, if 2 grids of the samesize are used to represent 2 decimals or fractions, and the sameamount of the grid is coloured for each, the 2 numbers have thesame value. Although they have the same value, they are differentbecause they cannot always be modelled on the same grid. Forexample, you can model 0.4 but not 0.40 on a tenths grid.Students need a solid understanding of the relationships between the units on the grids to be able to efficiently usegrids to represent numbers and to identify numbers represented on grids. Post a chart of these various relationshipsthat students can refer to. Provide examples tohelp students better understand the conceptHundredths and Thousandths Gridsof a placeholder; for instance, write 0.67 onthe chalkboard and ask students to model67 hundredths with counters on a decimal1 tenth10.110place value chart. Then, write 0.670 onthe board and ask students to model 1 column 10 hundredths10 0.10100670 thousandths below the first model onthe same chart. Ask what is different about100 thousandths100 0.1001000the models. (nothing) Ask what is differentabout the decimals. (One has a 0 in the1 hundredth 1 0.01thousandths place.) Tell students that these 1 square100numbers are equivalent because they10 thousandths 10 0.0101000represent the same value.1For students who need scaffolding during 1 rectangle 1 thousandth10000.001independent practice, provide Checkingand Practising BLM 2.7.For students who need extra learning support, provide Learning BLM 2.7, which presents the concepts moreincrementally.⎬ ⎫ ⎭⎬ ⎫ ⎭Answers to Learning BLM 2.7Step 2: 10; 10Step 3: 0.24Step 4: 2, 4Step 5:2401000Step 6: 100; hundredth, 1 , 0.01; 10;10010; 100Step 7: 0.240Step 8: 2, 4, 0Reflecting: 24 hundredths 2 tenths 4 hundredths, and 240 thousandths 2 tenths 4 hundredths 0thousandths. The 0 thousandths is equal to 0, so the two decimals are the same.Copyright © 2009 by Nelson Education Ltd.Overview 2.7: Renaming Decimals63

C&P Name: ____________________________________________ Date: ________________________2.7 Renaming Decimals Page 1Student Book pages 60–63Checking1. There are 1000 students at Belle’s school.400 students play an instrument.You will need• pencilcrayons• thousandths gridsa) Colour a thousandths grid to show 400 out of 1000 students.Hint: Each column is 1 tenth. 1000 10 _________,so each column is _________ thousandths.b) Write a fraction to represent the coloured part of the grid.Write this fraction as a decimal. _________1000Each square on the grid is 1 _________.Count the number of squares you coloured.Write another fraction to represent the coloured part of the grid.Each column on the grid is 1 _________.Count the number of columns you coloured.Write another fraction to represent the coloured part of the grid.Write this fraction as a decimal. _________1001064 Checking & Practising BLM 2.7: Renaming Decimals Copyright © 2009 by Nelson Education Ltd.

C&P Name: ____________________________________________ Date: ________________________2.7 Renaming Decimals Page 2Practising2. Emanuel coloured part of a thousandths grid.a) Write a fraction to represent the colouredpart. _________b) Write a decimal thousandth to representthe coloured part. _________5. a) 0.29Write the decimal in expanded form._________ tenths _________ hundredths1 column is 1 tenth.1 square is 1 _________.Colour the decimal on the grid.Write the decimal as an equivalent decimalthousandth.0.29 _________b) 0.68Colour the decimal on the grid.Write the decimal as an equivalent decimalthousandth.0.68 _________Copyright © 2009 by Nelson Education Ltd.Checking & Practising BLM 2.7: Renaming Decimals65

LName: ____________________________________________Date: ________________________2.7 Renaming Decimals Page 1Student Book pages 60–63GOALRepresent decimals and relate them to fractions.Anne goes to a school with 100 students.Belle goes to a school with 1000 students.There are 24 Grade 5 students in Anne’s school.There are 240 Grade 5 students in Belle’s school.1101100You will need• pencilcrayons• thousandths grids• hundredths gridsHow can you use decimals to comparethe Grade 5 students in the 2 schools?Step 1: Write a fraction for the number ofGrade 5 students in Anne’s school.24100Step 2: Model the fraction on a hundredths grid.There are 10 columns in a hundredths grid.Each column is one tenth or1or 0.1.10There are 100 squares in a hundredths grid.Each square is one hundredth or1or 0.01.100How many squares are in 1 column? _________So, one tenth _________ hundredths.Colour 24 hundredths on the grid.Step 3: Write the fraction24as a decimal. 0._________100Step 4: Write the fraction24in expanded form.10024is the same as 24 hundredths.10024 hundredths is _________ tenths _________ hundredths.66 Learning BLM 2.7: Renaming Decimals Copyright © 2009 by Nelson Education Ltd.

LName: ____________________________________________Date: ________________________2.7 Renaming Decimals Page 2Step 5: Write a fraction for the number of Grade 5 students in Belle’s school.Step 6: Model the fraction on a thousandths grid.There are 10 columns in a thousandths grid.Each column is one tenth or 1 or 0.1.10There are _________ squares in a thousandths grid.110110011000Each square is one _________ oror 0._________.How many squares are in a column? _________So, 1 tenth _________ hundredths.There are 1000 rectangles in a thousandths grid.Each rectangle is one thousandth or 1 or 0.001.1000There are 100 rectangles in a column.So, 1 tenth _________ thousandths.Colour 240 hundredths on the grid.Step 7: Write the fractionStep 8: Write the fraction2401000is the same as 240 thousandths.as a decimal. 0._________in expanded form.240 thousands is _________ tenths _________ hundredths _________ thousandthsThe amount that is coloured on both grids is the same.The decimals 0.24 and 0.240 are equivalent decimals.Reflecting24010002401000equivalentHaving the samevalueFor example,How did writing both decimals in expanded form show that they are equivalent?81080100Copyright © 2009 by Nelson Education Ltd.Learning BLM 2.7: Renaming Decimals67

2.8 3.3Communicating aboutEquivalent DecimalsStudent Book pp. 64–65Teacher’s Resource pp. 49–52GOALExplain whether two decimals are equivalent.Preparation and PlanningMastersKey Question 2AssessmentQuestion• Checking and PractisingBLM 2.8 pp. 69–70• Learning BLM 2.8 pp. 71–72• Tenths Grid, MB p. 36• Hundredths Grid, MB p. 37• Thousandths Grid, MB p. 38About the MathIn this lesson, students communicate their understandingof equivalent fractions and decimals. Encourage a variety ofstrategies and have materials (place value charts, thousandthsand hundredths grids, counters, base ten blocks) availablefor those who wish to use them. Review and post theCommunication Checklist to help remind students ofthe expectations.Differentiating InstructionHave students brainstorm math words to use in their explanations. Post a chart of these words: decimal, fraction,expanded form, equivalent, tenth, hundredth, thousandth, place value chart, hundredths grid, thousandths grid,model, represent, column, square, rectangle, regroup, rename, and so on.Have students in pairs describe the decimal 0.6. Then, ask students to share their description with the rest of theclass, and record their answers on chart paper. (It is a decimal; There are 6 tenths; There is no whole number beforethe decimal.) Or, students may make a model.Next, have students describe 0.60. Again, have them share their descriptions and record their answers. (There are60 hundredths; The 6 is in the tenths place; The number is less than 1 because there is no whole number before thedecimal.) Or, students may make a model.Ask students if the following statement is true: “0.6 and 0.60 are equivalent decimals.” (Yes, because the 2 grids arethe same size, and each decimal is represented by the same amount of a grid. On a place value chart they have the samenumbers of counters in the same places, etc.)For students who need scaffolding during independent practice, provide Checking and Practising BLM 2.8.For students who need extra learning support, provide Learning BLM 2.8.Answers to Learning BLM 2.8Stefan used math language (e.g., models, represent, decimals, tenths grid) and included a diagram. He did not includethe right amount of detail.He modelled 0.5 on a tenths grid because it is tenths; 0.50 on a hundredths grid because it is hundredths; 0.500 on athousandths grid because it is thousandths.The 3 grids are all the same size, so equal amounts coloured have the same value.Reflecting: It was easy to see and compare the values of the decimals.68 Overview 2.8: Communicating about Equivalent Decimals Copyright © 2009 by Nelson Education Ltd.

C&P Name: ____________________________________________ Date: ________________________2.8 Communicating about Equivalent Decimals Page 1Student Book pages 64–65Checking1. Emily explained why 0.2 and 0.20 are equivalent.I can model 0.2 and 0.20 on a place value chart.They are equivalent.CommunicationChecklist✔ Did you use mathlanguage?✔ Did you include theright amount ofdetail?✔ Did you include adiagram?Use the Communication Checklist to improve Emily’s explanation.Did Emily use math language?Underline the math language Emily used in her explanation.Did Emily include the right amount of detail?Rewrite Emily’s explanation using more detail.I can model 0.2 and 0.20 on a place value chart.0.2 is _______ tenths and 0.20 is _______ hundredths.I can regroup 20 hundredths as 2 _______.So, 0.2 and 0.20 are _______ decimals.Did Emily include a diagram?Show 0.2 and 0.20 on the place value chart below.HundredsTensOnesTenthsHundredthsThousandthsCopyright © 2009 by Nelson Education Ltd.Checking & Practising BLM 2.8: Communicating about Equivalent Decimals69

C&P Name: ____________________________________________ Date: ________________________2.8 Communicating about Equivalent Decimals Page 2Practising2. Jeremy and Anna are driving to Peace River with their parents.Jeremy says that they have driven 0.3 of the way.30Anna says that they have driven of the way.100Explain why they are both right.Represent 0.3 and30100on the hundredths grids.0.330100Use your diagrams to help you explain why 0.3 andUse the Communication Checklist.30100are equivalent.CommunicationChecklist✔ Did you use mathlanguage?✔ Did you include theright amount ofdetail?✔ Did you include adiagram?70 Checking & Practising BLM 2.8: Communicating about Equivalent Decimals Copyright © 2009 by Nelson Education Ltd.

LName: ____________________________________________Date: ________________________2.8 Communicating about Equivalent Decimals Page 1Student Book pages 64–65GOALExplain whether two decimals are equivalent.Stefan has a chocolate bar.His brother, Colin, wants him to share it.Stefan tells Colin that 0.5, 0.50, and 0.500 of the chocolatebar are the same amount.Colin wants to know why.How can Stefan explain how he knows that the decimals are equivalent?Stefan’s ExplanationI’ll use models to represent the chocolate bar, and I’ll colour the decimals.I can model 0.5 ona tenths grid.I can model 0.50 on ahundredths grid.I can model 0.500 on athousandths grid.The decimals 0.5, 0.50, and 0.500 are equivalent because the same amountis coloured on all 3 grids.Copyright © 2009 by Nelson Education Ltd.Learning BLM 2.8: Communicating about Equivalent Decimals71

LName: ____________________________________________Date: ________________________2.8 Communicating about Equivalent Decimals Page 2What did Stefan explain well? Use the Communication Checklist.CommunicationChecklist✔ Did you use mathlanguage?✔ Did you include theright amount ofdetail?✔ Did you include adiagram?Improve Stefan’s explanation.Explain why Stefan modelled 0.5 on a tenths grid, 0.50 on a hundredths grid,and 0.500 on a thousandths grid.Explain why Stefan could compare the coloured amounts on the 3 different grids.Hint: How are the grids alike? How are they different?ReflectingHow did the diagrams help Stefan explain?72 Learning BLM 2.8: Communicating about Equivalent Decimals Copyright © 2009 by Nelson Education Ltd.

2.9 3.3Rounding DecimalsStudent Book pp. 66–68Teacher’s Resource pp. 53–56GOALInterpret rounded decimals, and round decimals to thenearest tenth or the nearest hundredth.Preparation and PlanningMastersKey Question 2AssessmentQuestion• Checking and PractisingBLM 2.9 pp. 74–75• Learning BLM 2.9 pp. 76–77• Hundredths Grids, MB p. 37• Thousandths Grids, MB p. 38About the MathIn this lesson, students use decimal representations onthousandths grids to help them round decimals. The lessonprovides an example of how meaningful answers can often beobtained through estimation. Before students begin rounding,review the values of the sections on a thousandths grid:columns are tenths, squares are hundredths, and rectangles arethousandths. Encourage students to draw on their experiencerounding whole numbers—the conventions for roundingdecimals exactly parallel those used for whole numbers.Differentiating InstructionShow students 0.152 represented on a thousandths grid. Ask them to round 0.152 to the nearest hundredth:“How many full squares are coloured?” (15)“How many rectangles are coloured?” (2)“Are 2 rectangles close to 1 full square?” (no)“So, will you add another square to 15 when you round, or will you round 0.152 to 0.15?” (Round to 0.15)Ask students to round 152 to the nearest tenth (150) and compare this to the way they rounded 0.152. (It’s thesame, we dropped the 2.) Ask students to round 0.152 to the nearest tenth:“How many full columns are coloured?” (1)“What does 1 column represent?” (one tenth)“Besides the 10 squares in the column, how many full squares are coloured?” (5)“Will you count this half of a column as another tenth or not? Explain.” (Yes, because when the number in theplace you’re rounding off at is 5 or more, you count it as 1 in the next place.)“Do you need to consider the thousandths when you’re rounding to the nearest tenth?” (no)For students who need scaffolding during independent practice, provide Checking and Practising BLM 2.9.For students who need extra learning support, provide Learning BLM 2.9, which presents an adapted version ofthe central problem for the lesson. Note: The lesson goal has been changed for this BLM.Answers to Learning BLM 2.9A. less than 3; closer to 3; 3B. 0.3; 3C. 30; 30; 30Reflecting: 7; 1; Since 7 full columns are shaded in and only 1 square is shaded in on the next column, the number isrounded to 7 tenths.Copyright © 2009 by Nelson Education Ltd.Overview 2.9: Rounding Decimals73

C&P Name: ____________________________________________ Date: ________________________2.9 Rounding Decimals Page 1Student Book pages 66–68Checking1. The chart on this page shows batting averagesfor 2 professional baseball players.Batting averages are reported in decimal thousandths.A batting average of 0.447 means the player can expect toget 447 hits in 1000 times at bat.a) Model J. McDonald’s batting average of0.447 on the thousandths grid provided here.You will need• pencilcrayons• thousandths gridsBatting AveragesPlayerBattingaverageJ. McDonald 0.447R. Clayton 0.288b) Round 0.447 to the nearest hundredth.0.447 is about _________c) J. McDonald will probably get about_________ hits in 100 times at bat.d) Round 0.447 to the nearest tenth.0.447 is about _________e) J. McDonald will probably get about _________ hits in 10 times at bat.f) Round R. Clayton’s batting average of 0.288 without using a grid.Think of 288 as a whole number.You can round 288 to 290. You can round 0.288 to 0.__ __.You can round 288 to 300. You can round 0.288 to 0.__.74 Checking & Practising BLM 2.9: Rounding Decimals Copyright © 2009 by Nelson Education Ltd.

C&P Name: ____________________________________________ Date: ________________________2.9 Rounding Decimals Page 2Practising2. Round each decimal to the nearest hundredth and the nearest tenth.Circle the nearest hundredth and nearest tenth for each decimal in the chart below.a)b)c)d)Decimal Nearest hundredth Nearest tenth0.158 0.15 0.16 0.1 0.20.228 0.22 0.23 0.2 0.31.067 1.06 1.07 1.0 1.12.039 2.03 2.04 2.0 2.13. Which numbers below round to the same hundredth?0.234 0.324 0.237 0.229Look at the digits in the tenths place in each number.Could 0.324 round to the same hundredth as the other 3 numbers? _________Explain why or why not.Look at 0.234 and 0.237.Would you round 0.234 to 0.23 or 0.24? _________Would you round 0.237 to 0.23 or 0.24? _________Do these 2 numbers round to the same hundredth? _________Look at 0.229. Would you round 0.229 to 0.22 or 0.23? _________Which of the other numbers rounds to the same hundredth? _________Copyright © 2009 by Nelson Education Ltd.Checking & Practising BLM 2.9: Rounding Decimals75

LName:Date:2.9 Rounding Decimals Page 1Student Book pages 66–68GOALInterpret rounded decimals, and round decimals tothe nearest tenth.You will need• pencilcrayons• hundredths gridsRachel has a Little League batting average of 0.28.This means she can expect to get 28 hits in 100 times at bat.About how many hits would you expect Rachelto get in 10 times at bat?Rachel modelled 0.28 on a hundredths grid.A. Did Rachel colour more or less than 3 full columns? _________Is the part Rachel coloured closer to 2 full columns or 3 full columns?__________________________3 columns are _________ tenths.B. Round Rachel’s batting average to the nearest tenth. 0.__Rachel will probably get about _________ hits in 10 times at bat.76 Learning BLM 2.9: Rounding Decimals Copyright © 2009 by Nelson Education Ltd.

LName: ____________________________________________Date: ________________________2.9 Rounding Decimals Page 2C. Rachel’s batting average is 0.28.This means that she can expect to get 28 hits in 100 times at bat.How many hits would Rachel need to get a batting average of 0.30? _________How many squares would need to be coloured in on a hundredths grid? _________0.30 _________ hundredthsReflectingRound 0.71 to the nearest tenth. _________How many full columns would you colour in on a hundredths grid? _________How many squares in the next column would be coloured in? _________What does this tell you about rounding 0.71 to the nearest tenth?Copyright © 2009 by Nelson Education Ltd.Learning BLM 2.9: Rounding Decimals77

2.10 3.3Comparing andOrdering DecimalsStudent Book pp. 70–72Teacher’s Resource pp. 59–62GOALCompare and order decimals up to decimal thousandths.Preparation and PlanningMastersKey Question 2AssessmentQuestion• Checking and PractisingBLM 2.10 pp. 79–80• Learning BLM 2.10 pp. 81–82About the MathStudents use number lines marked with decimal benchmarksand place value charts to compare and order decimals up tothousandths. Students can compare decimals using normal placevalue rules. For example, to compare 0.24 and 0.57, comparethe tenths: 2 tenths 5 tenths, so 0.24 0.57.Differentiating InstructionDraw a number line showing 0 and 100 on the chalkboard. Add the benchmark 50 to the line. Ask students todescribe how they would use the number line to compare 36 and 82. Check that they understand that they onlyneed to look at the tens digits of the numbers. Write 82 36 on the chalkboard.Then, ask students to create a number line to compare 0.82 and 0.36. Provide 2 students with cards showing 0.00and 1.00, and ask them to stand on opposite sides of the classroom. Ask why 0.00 and 1.00 are used rather thanjust 0 and 1. (We will be comparing hundredths.) Ask whether 0.82 and 0.36 will be between these 2 numbers, andhow they know. (Yes, both numbers are 0.00 and 1.00, because they have nothing in the ones place, but morethan nothing in the other places.) Ask students what benchmark they might add to the number line (0.50). Haveanother student stand between the first 2 students with a card showing 0.50. Choose 2 more students to represent0.82 and 0.36. Have the class decide where to place them on the number line and explain how they decided.Write 0.82 0.36 on the chalkboard.Then, ask students whether and how they could use this number line to compare 0.419 with 0.82. (Yes, justcompare the tenths, 4 tenths is less than 8 tenths, so 0.419 0.82.)For students who need scaffolding during independent practice, provide Checking and Practising BLM 2.10.For students who need extra learning support, provide Learning BLM 2.10.Answers to Learning BLM 2.10 0.50; 0.50; Conor’s distanceErica0.45Travis’s DistanceTravis0.92 Hundreds Tens Ones Tenths Hundredths0.00 0.501.009 2 0.50; 0.50; ; Travis’s distance7 tenths; Conor, Erica0.92, 0.77; Travis’s distanceConor’s DistanceHundreds Tens OnesTenths Hundredths7 7Reflecting: Ali; Ali’s is the only distance that is greater than 1 m.78 Overview 2.10: Comparing and Ordering Decimals Copyright © 2009 by Nelson Education Ltd.

C&P Name: ____________________________________________ Date: ________________________2.10 Comparing and Ordering Decimals Page 1Student Book pages 70–72Checking1. Here are the distances for the penny-flicking eventon Olympics Day.a) Place each distance on the number line below.Travis’s distance has been done for you.Travis0.991.00 1.50 2.00Penny-FlickingStudentDistance(m)Ali 1.02Erica 1.20Travis 0.99Conor 1.15Write the distances in order from least to greatest.b) Which student flicked the penny the farthest? _________________________________Practising2. For a craft, Jacqui needed1.6 m of string1.2 m of wool0.9 m of wire0.1 m of ribbonPlace these materials on the number line below.0.00 0.50 1.00 1.50 2.00Order the lengths from least to greatest.Copyright © 2009 by Nelson Education Ltd.Checking & Practising BLM 2.10: Comparing and Ordering Decimals79

C&P Name: ____________________________________________ Date: ________________________2.10 Comparing and Ordering Decimals Page 23. The masses of 3 salmon are0.548 kg, 0.521 kg, and0.621 kg.Use either a number line orplace value charts tocompare the masses.0.500 0.550 0.600 0.650HundredsTensOnesTenthsHundredthsHundredsTensOnesTenthsHundredthsHundredsTensOnesTenthsHundredthsWhich salmon has the greatest mass? __________________Explain your strategy.80 Checking & Practising BLM 2.10: Comparing and Ordering Decimals Copyright © 2009 by Nelson Education Ltd.

LName: ____________________________________________Date: ________________________2.10 Comparing and Ordering Decimals Page 1Student Book pages 70–72GOALCompare and order decimals up to decimalthousandths.A Grade 5 class organized a cotton-ball toss for Olympics Day attheir school. The results are in the chart.How can you compare the tosses?You can use benchmarks to compare numbers.A benchmark is a familiar number, like 0 or 1.Benchmarks often have a digit that is 1 or 5, and 0s forthe other digits.Some examples are 10, 50, 100, 0.1, 0.5, 0.10, and 0.50.Compare Erica’s distance with Conor’s distance using abenchmark of 0.50.Cotton-Ball TossStudentDistance(m)Ali 1.15Erica 0.45Travis 0.92Conor 0.77benchmarkA familiar value thatcan be used tocompare onenumber with anothernumberErica0.45Conor0.770.00 0.501.00Was Erica’s distance less than () 0.50 or greater than () 0.50? __________________Was Conor’s distance less than 0.50 or greater than 0.50? __________________0.77 0.45Whose distance was greater? __________________0.00 0.501.00Compare Erica’s distance of 0.45 m with Travis’s distance of 0.92 m.Was Erica’s distance less than () 0.50 or greater than () 0.50? __________________Was Travis’s distance less than 0.50 or greater than 0.50? __________________0.92 _________ 0.45Whose distance was greater? __________________Copyright © 2009 by Nelson Education Ltd.Learning BLM 2.10: Comparing and Ordering Decimals81

LName: ____________________________________________Date: ________________________2.10 Comparing and Ordering Decimals Page 2You can use place value charts to compare numbers.Erica’s DistanceHundreds TensConor’s DistanceHundreds TensOnesOnesTenths Hundredths4 5Tenths Hundredths7 7Which is greater, 7 tenths or 4 tenths? __________________0.77 > 0.45So, _________’s distance is greater than _________’s distance.Travis tossed the cotton ball _________ m. Conor tossed it _________ m.Represent these distances on the place value charts below.Travis’s DistanceHundredsTensOnesTenthsHundredthsConor’s DistanceHundredsTensOnesTenthsHundredthsCompare the distances. 0.92 _________ 0.77Whose distance is greater? __________________ReflectingWhich of the 4 students tossed the cotton ball the farthest? __________________How do you know?82 Learning BLM 2.10: Comparing and Ordering Decimals Copyright © 2009 by Nelson Education Ltd.

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