Student Success Adapted Program Lesson-by-lesson support for struggling students!

Student Success Adapted Program Lesson-by-lesson support for struggling students! Lesson Sampler Chapter 2: Numeration

2.1 3.3 Representing Numbers Student Book pp. 40 43 Teacher s Resource pp. 12 16 GOAL Represent numbers to one million using a place value chart, numerals, and words. Preparation and Planning Masters Key Question 2 Assessment Question Checking and Practising BLM 2.1 pp. 38 39 Learning BLM 2.1 pp. 40 41 Place Value Chart to Hundred Thousands, MB p. 43 About the Math In this lesson, students extend their understanding of the place value system up to 1 million. They represent whole numbers up to 1 million using models, symbols, and words. Place value charts and counters are used to represent numbers and to develop and extend an understanding of the place value system. Place value charts, where it is the position of the counters on the chart that determines their values, are a transition step from base ten blocks, where placement is helpful to interpreting the number but does not affect the value. Differentiating Instruction Remind students that place value is simply a way of saying that the position of a digit tells us its value; for example, the 2 in 23 means 20, but the 2 in 42 means 2. Have students concentrate on patterns within the place value system to make its extension more meaningful; that is, we don t have digits greater than 9, so, as soon as we have 10 ones, we trade them for 1 ten in the place to the left of the ones. Similarly, 10 tens make 100, and 10 hundreds make 1000, so it is logical that 10 thousands is the next place value, and 10 ten thousands the next. Some students may need practice modelling numbers to 1000, using base ten blocks or a place value chart to 1000 and counters. You may want to review the words for numbers to 100, particularly the teens. For students who need scaffolding during independent practice, provide Checking and Practising BLM 2.1. For students who need extra learning support, provide Learning BLM 2.1. Answers to Learning BLM 2.1 87 (8 tens); 18(8 ones); 851 (8 hundreds) 10; 10; 10 eight; one hundred thousand, 100 000 285 100, 92 851, 892 851 Thousands eight, ninety-two; eight, fifty-one; eight, ninety-two, eight, fifty-one Reflecting: The line that divides the thousands and ones shows the space; In standard form, the place tells the value. We need 0 to hold the place so that the other digits are in the correct places. Copyright 2009 by Nelson Education Ltd. Overview 2.1: Representing Numbers 37

C&P Name: Date: 2.1 Representing Numbers Page 1 Student Book pages 40 43 Checking 1. a) Model the number 24 640 on a place value chart. You will need a place value chart counters Look at the ones first. 24 640 The ones digit is 0, so there will be counters in the ones column. There will be counters in the tens column. There will be counters in the hundreds column. Then, look at the thousands. 24 640 There will be counters in the one thousands column. There will be counters in the ten thousands column. Will there be any counters in the hundred thousands column? Sketch your model on the chart below. Thousands b) Write 24 000 in words. Write 600 in words. Write the word for 4 tens or 40 ones. Put these together to write the number 24 640 in words. Hint: Do not use the word and between thousands, hundreds, tens, or ones. 38 Checking & Practising BLM 2.1: Representing Numbers Copyright 2009 by Nelson Education Ltd.

C&P Name: Date: 2.1 Representing Numbers Page 2 Practising 2. Model each number using counters on a place value chart. Sketch your models on the charts below. a) four hundred seventeen thousand twenty-five Thousands Step 1: Model the 417 thousands. Hint: 17 thousands is 1 ten thousand and 7 one thousands. Step 2: Model the 25 ones. Hint: There are no hundreds in this number. Step 3: Write the number in standard form. Hint: Did you remember to write a 0 in the hundreds place? b) six hundred ninety-one thousand six hundred fifty-nine Thousands Write the number in standard form. Hint: Did you remember to leave a space between the ones and the thousands? Copyright 2009 by Nelson Education Ltd. Checking & Practising BLM 2.1: Representing Numbers 39

L Name: Date: 2.1 Representing Numbers Page 1 Student Book pages 40 43 GOAL Represent numbers to one million using a place value chart, numerals, and words. You will need a place value chart counters In 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 ones 18 8 hundreds 8 tens 8 ones 851 8 hundreds 8 tens 8 ones Show how the place values are related. 1 ten ones 1 hundred tens 1 thousand hundreds Here is a model of 187 (one hundred eighty-seven). Here is a model of 187 000 (one hundred eighty-seven thousand). Thousands The 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.

L Name: Date: 2.1 Representing Numbers Page 2 Write the digits of numerals in groups of 3. space space Start at the right. Leave a space between each group of 3. 1 000 000 is 1 million. 1 000 000 3 digits 3 digits Here are some other examples: 10 000 28 510 187 000 Rewrite 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. Thousands standard form The usual way that numbers are written For example, 766 921 is in standard form. Write 892 000 in words. hundred thousand Write 851 in words. hundred Write 892 851 in words. hundred thousand hundred Reflecting How 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 Numbers 41

2.2 3.3 Using Expanded Form Student Book pp. 44 47 Teacher s Resource pp. 17 21 GOAL Represent, describe, and compare numbers to one million. Preparation and Planning Masters Key Question 2 Assessment Question Checking and Practising BLM 2.2 pp. 43 44 Learning BLM 2.2 pp. 45 46 Place Value Chart to Hundred Thousands, MB p. 43 About the Math In this lesson, students write numbers to 1 million in standard and expanded form. They connect the representation of a number on a place value chart and in expanded form. Students also compare numbers using standard and expanded form. Note that kilometres are introduced in this lesson. Differentiating Instruction Students 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 compare the highest place value first, as it has the greatest value. Demonstrate with examples the importance of lining up the 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 the same 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 in the highest place is the same, they should compare the value to the right. Have students compare 321 600 and 256 700, 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 may want to begin with 4-digit numbers and build to 6-digit numbers. As an intermediate step, you may want to have students 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 face down. On the chalkboard, draw 2 place value charts to the hundred thousands, 1 for each team. Teams take turns drawing the top card from their deck and placing the number on the place value chart. The object of the game is to make the greatest number, so students will need to be strategic about where they place each number. Once two 6-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 2.2 Step 3: 48, 84, 44 Step 4: 344 800, 348 400, 384 400 Step 5: 4, 8, 4; 40 000, 8000, 400 8, 4, 4; 300 000, 80 000, 4000, 400 384 400; 384 400; 384 400 Reflecting: 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 1 Student Book pages 44 47 Checking 1. a) It takes the planet Jupiter one hundred three thousand You will need a place value chart counters nine hundred forty-four hours to travel around the Sun. Show this number on the place value chart below. Thousands Write the number in standard form. It takes Saturn 200 000 50 000 8000 100 40 4 hours to travel around the Sun. Show this number on the place value chart below. Thousands Write the number in standard form. b) Does Jupiter or Saturn take longer to go around the Sun? How do you know? Copyright 2009 by Nelson Education Ltd. Checking & Practising BLM 2.2: Using Expanded Form 43

C&P Name: Date: 2.2 Using Expanded Form Page 2 Practising 2. 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. Thousands Write it in expanded form. Model another 6-digit number. Thousands Write it in standard form. Write it in expanded form. Model another 6-digit number. Thousands Write it in standard form. Write it in expanded form. 44 Checking & Practising BLM 2.2: Using Expanded Form Copyright 2009 by Nelson Education Ltd.

L Name: Date: 2.2 Using Expanded Form Page 1 Student Book pages 44 47 GOAL Represent, describe, and compare numbers to one million. You will need a place value chart counters The distance from Earth to the Moon, in kilometres, is the greatest number you can make with the digits shown, starting with the 3. 3 0 4 8 4 0 What 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. Thousands 3 Step 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. Thousands 3 0 0 Step 3: Write the 3 different numbers you can make with 4, 4, and 8. 4 4 8 Copyright 2009 by Nelson Education Ltd. Learning BLM 2.2: Using Expanded Form 45

L Name: Date: 2.2 Using Expanded Form Page 2 Step 4: Write the 3 possible distances. Thousands 3 4 0 0 3 4 0 0 3 8 0 0 Step 5: 344 800, 348 400, and 384 400 are possible distances. Find out which is greater. Write each number in expanded form. expanded form A way to write a number that shows the value of each digit 344 800 3 hundred thousands 4 ten thousands 4 thousands 8 hundreds 300 000 40 000 4000 800 348 400 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. 344 800 348 400 384 400 So, is the greatest number. The distance between Earth and the Moon is km. Reflecting 384 400 is a 6-digit number. Why does the expanded form of 384 400 only have 4 values added together? 46 Learning BLM 2.2: Using Expanded Form Copyright 2009 by Nelson Education Ltd.

2.3 3.3 Renaming Numbers Student Book p. 48 Teacher s Resource pp. 22 24 GOAL Rename numbers that have up to seven digits. Preparation and Planning Masters Explore BLM-A 2.3 p. 48 Explore BLM-B 2.3 p. 49 Key Assessment Question Entire exploration About the Math In this exploration, students rename a 6-digit number using a variety of strategies of their choice, which may include writing the number in expanded form and/or using a place value chart. Some students may interpret the problem as simply asking them to relate the sizes of the containers to the place values, and will generate one solution to the problem. Others may realize that there are a large number of possible ways to fill the containers with the popcorn. Encourage each student to share his or her personal strategy. Litres are introduced in this lesson. Litres and capacity are worked with in greater depth in Lesson 8.8. Differentiating Instruction If students are having difficulty getting started, ask them what they would multiply the capacity of container Z by to get the capacity of container Y (10), and so on. Ask them what the pattern is. (multiply by 10 each time) Have them 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 as representing 43 as 4 tens and 3 ones, you can represent it as 3 tens and 12 ones or 43 ones. Help students extend this 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 them to model 321 using counters and a place value chart (or base ten blocks), and then write the number in expanded form. (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 version of the central problem for the lesson. Note: The lesson goal has been changed for this BLM. Answers to Explore BLM-B 2.3 A. 1000, 900, 40, 7 1, 9, 4, 7 B. 21, 947 Copyright 2009 by Nelson Education Ltd. Overview 2.3: Renaming Numbers 47

E-A Name: Date: 2.3 Renaming Numbers Student Book page 48 A group of students broke a world record by filling a container with 221 947 L of popcorn. U 100 000 L V 10 000 L W 1000 L X 100 L Y 10 L Z 1 L Which of these containers could you use to measure 221 947 L? Write 221 947 in expanded form. Use the expanded form to show one way you could measure 221 947 L. 2 100 000 L 10 000 L 1000 L 100 L 10 L 1 L Or, you could fill the 1 L container times to measure 221 947 L. Look at the two groups of 3 digits in 221 947. 221 947 221 thousands ones You could fill the 1000 L container times and the 1 L container times. Describe other ways you could use the containers to measure 221 497 L. Idea: Represent 221 947 using counters on a place value chart. Then, regroup tens as ones, or hundreds as thousands, and so on, to find new combinations. 48 Explore BLM-A 2.3: Renaming Numbers Copyright 2009 by Nelson Education Ltd.

E-B Name: Date: 2.3 Renaming Numbers Student Book page 48 GOAL Rename numbers that have up to five digits. You will need a place value chart counters A 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 L 20 000 (ten thousands) (one thousands) (hundreds) (tens) (ones) V 10 000 L W 1000 L X 100 L Y 10 L Z 1 L 2 10 000 L 1000 L 100 L 10 L 1 L B. 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 Numbers 49

2.4 3.3 Rounding Numbers Student Book pp. 50 52 Teacher s Resource pp. 29 32 GOAL Round numbers to the nearest hundred thousand, the nearest ten thousand, and the nearest thousand. Preparation and Planning Masters Key Question 3 Assessment Question Checking and Practising BLM 2.4 pp. 51 52 Learning BLM 2.4 pp. 53 54 About the Math In this lesson, students round numbers using place values and number lines. The context of the lesson is population, a context where benchmark numbers are often used. Number lines are particularly suitable for estimating numbers by relating them to benchmark numbers. Students use number lines marked at multiples of 100 000, 10 000, and 1000 to round numbers to the nearest hundred thousand, ten thousand, and thousand. Differentiating Instruction Ask students to create number lines that can be used to locate the positions of numbers to 10, then to 100, and then 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 to locate the positions of numbers to 10 000, to 100 000, and to 1 million. Ensure that students realize that the same 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 about the difference between estimating and counting exactly; students require explicit exposure to situations where an estimate is all that is required. Other examples are animal populations, distances in astronomy, or large amounts of money. Encourage students to think of a number such as 422 536 as greater than 400 000 but less than 500 000. For those 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 explain how they know which of these numbers is greater or less than 3278. Check that they are using place values to compare 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 of the central problem for the lesson. Note: The lesson goal has been changed for this BLM. Answers to Learning BLM 2.4 A. 9192 is closer to 9000 on the number line. B. 9200 C. 9190 Reflecting: Down; It is closer to the left end of the number line; Up; There are 9 tens, which is almost another hundred; Down; There are 2 ones, and 2 is closer to 0 than 10; 9000; It gives a useful estimate of the size. It shows that not many people live in the Inuvik Region. The population will change, but it will probably stay close to 9000; 10 000 50 Overview 2.4: Rounding Numbers Copyright 2009 by Nelson Education Ltd.

C&P Name: Date: 2.4 Rounding Numbers Page 1 Student Book pages 50 52 Checking 1. a)round the populations of Kelowna and Abbotsford to the nearest hundred thousand, the nearest ten thousand, and the nearest thousand. Use number lines. Record your estimates in the table below. Population Nearest Nearest Nearest City in 2006 100 000 10 000 1000 Kelowna 162 276 Abbotsford 159 020 Use this number line to round the populations to the nearest hundred thousand. Use this number line to round the populations to the nearest ten thousand. Use this number line to round the populations to the nearest thousand. 100 000 150 000 200 000 150 000 160 000 170 000 155 000 160 000 165 000 b) 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 Numbers 51

C&P Name: Date: 2.4 Rounding Numbers Page 2 Practising 3. 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 and fresh water Nearest Nearest Nearest Province (km 2 ) 100 000 10 000 1000 British Columbia 944 735 Alberta 661 848 Saskatchewan 651 036 Manitoba 647 797 b) Which provinces have the same area, to the nearest hundred thousand? 900 000 1 000 000 940 000 950 000 944 000 945 000 c) Which provinces have the same area, to the nearest ten thousand? 600 000 700 000 640 000 650 000 660 000 645 000 650 000 655 000 660 000 52 Checking & Practising BLM 2.4: Rounding Numbers Copyright 2009 by Nelson Education Ltd.

L Name: Date: 2.4 Rounding Numbers Page 1 Student Book pages 50 52 GOAL Round numbers to the nearest thousand, the nearest hundred, and the nearest ten. The population of an area is the total number of people who live there. The Inuvik Region in the Northwest Territories had a population of 9192 in 2006. What other ways can you use to show the population of the Inuvik Region? A. The population of an area is always changing. Yukon Territory Beaufort Sea Port Radium Northwest Nunavut Territories Yellowknife Great Slave Lake Lake Athabasca Prince George Tuktoyaktuk Inuvik Great Bear Lake C A N A D A Hudson Bay You could use an estimate to show the population of the Inuvik Region. Spokane Edmonton Calgary Regina Winnipeg Lake Winnipeg 9192 9000 9500 10 000 You 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 10 000 The population of the Inuvik Region is. C. Round the population of the Inuvik Region to the nearest ten. 9100 9120 9140 9160 9180 10 000 The population of the Inuvik Region is. Copyright 2009 by Nelson Education Ltd. Learning BLM 2.4: Rounding Numbers 53

L Name: Date: 2.4 Rounding Numbers Page 2 Reflecting You 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 the population to? 54 Learning BLM 2.4: Rounding Numbers Copyright 2009 by Nelson Education Ltd.

2.5 3.3 Exploring One Million Student Book p. 53 Teacher s Resource pp. 33 35 GOAL Describe one million in various ways. Preparation and Planning Masters Explore BLM-A 2.5 p. 56 Explore BLM-B 2.5 p. 57 Key Assessment Question Entire exploration About the Math In this exploration, students are asked to describe 1 million by comparing 1 million of one thing with a smaller number of something else. Students will draw on their understanding of the metric system to create interesting facts about 1 million. They will likely need to multiply by 1 million and/or divide 1 million by another number. A calculator can be used for such calculations. This exploration will be richer if students are able to use the Internet for research, but students can also use facts found in books and magazines. Differentiating Instruction After reading the book How Much Is a Million? by David M. Schwartz, provide students with a concrete representation of 1 million. Show 1 grain of salt and then 10 grains of salt. Make a tiny pile of salt and tell students that this is about 100 grains. Show a pinch of salt (about 1000 grains); 1 teaspoon (about 4 10 000 grains; 1 tablespoon (about 100 000 grains); and 1 cup (about 1 000 000 grains). 2 Ask students what they would name the place value to the left of the hundred thousands place (they might say a thousand 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 facts involving 1 million. For example, a raisin is about 1 cm long, so 1 million raisins will be about 1 000 000 cm long. 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 the 1 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 will stretch from the school to that landmark. Or, if a student lives about 1 km from the school, he or she could say that 1 million raisins would make a row stretching from home to school 10 times. Help students see that a number can have a continuous context, such as the distance between 2 places, or a discrete context, such as a number 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 a number of interesting facts about 1 million. Answers to Explore BLM-B 2.5 10, 10; 100 000, 100 000; 1 000 000; 1 000 000, Vancouver Copyright 2009 by Nelson Education Ltd. Overview 2.5: Exploring One Million 55

E-A Name: Date: 2.5 Exploring One Million Student Book page 53 If you wrote a book about 1 million, what interesting facts would you include? You will need a calculator A 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 travel 1 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-B Name: Date: 2.5 Exploring One Million Student Book page 53 GOAL Describe one million in various ways. You will need a calculator If you wrote a book about 1 million, what interesting facts 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 1 000 000 So, 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 cats It 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 m Write the distance from Calgary to Vancouver in metres. 1000 km 1000 m m Length of 1 bobcat 1 m Length of a row of 1 million bobcats 1 000 000 1 m m A row of 1 million bobcats would stretch from Calgary to. Copyright 2009 by Nelson Education Ltd. Explore BLM-B 2.5: Exploring One Million 57

2.6 3.3 Decimal Place Value Student Book pp. 56 59 Teacher s Resource pp. 39 43 GOAL Read, write, and model decimals. Preparation and Planning Masters Key Question 2 Assessment Question Checking and Practising BLM 2.6 pp. 59 60 Learning BLM 2.6 pp. 61 62 Decimal Place Value Chart, MB p. 44 Base Ten Blocks, MB pp. 39 42 About the Math Base ten materials help students understand our base ten place value system. In this lesson, students use base ten blocks on a place value chart to model decimals to thousandths. They write decimals in standard form, expanded form, and words. They also attach a numeral to a model for decimal thousandths. Differentiating Instruction The understanding of decimals is dependent on a previous understanding of the concept of a fraction. Review with students how, in a fraction, the denominator tells the number of parts the whole is divided up into, and the numerator tells how many of those parts are under consideration. Discuss with students how the numerator and denominator of 1, 1, and 1 are represented in the base ten model. To show thousandths, a whole 10 100 1000 divided into 1000 equal parts is needed. The large cube fits this description. 1 small cube is 1 because it 1000 takes 1000 of these to make 1 whole (the large cube). Similarly, it takes 100 rods to make 1 large cube, so 1 rod is 1, and it takes 10 flats to make 1 large cube, so 1 flat is 1. 100 10 Model 393 thousandths on a place value chart and ask students to identify the value of each place. (The 3 flats are 3 tenths, the 9 rods are 9 hundredths, and the 3 small cubes are 3 thousandths.) Then, guide students to make the connection that the decimal 0.393 means 3 tenths, 9 hundredths, and 3 thousandths. Tell students that, in the model they are using, 10 large cubes would represent the whole number 10. Ask students to imagine 10 large cubes, and then 100 large cubes to help them understand just how small those values to the right of the decimal point actually are. Ask students how many small cubes you would use to represent 0.393. (3 flats is 300 small cubes, 9 rods is 90, and 3 more is 393.) Explain that when they read the decimal or write it in words, they should think of it in small cubes, so they would say 393 thousandths and write three hundred and ninety-three thousandths. For students who need scaffolding during independent practice, provide Checking and Practising BLM 2.6. For students who need extra learning support, provide Learning BLM 2.6, which provides a more structured introduction to the concepts. Answers to Learning BLM 2.6 3 25 365 10, 0.3; 100, 0.25; 1000, 0.365 1, 8, 3, 4; 2, 6, 9, 6 0.1, 0.01, 0.001 3 9 3 3, 9, 3; 10 100 1000 ; 1 0.3 0.09 0.003 393; three hundred and ninety-three Reflecting: 3 tenths; 3 thousandths; the 3 in the first place after the decimal point 58 Overview 2.6: Decimal Place Value Copyright 2009 by Nelson Education Ltd.

C&P Name: Date: 2.6 Decimal Place Value Page 1 Student Book pages 56 59 Checking 1. 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 ten blocks a decimal place value chart Tenths Hundredths Thousandths Write 1.098 in expanded form. Hint: Do not include place values that are 0. 1.098 1 whole hundredths thousandths or 1 100 1000 or 1 0. 0. Write 1.098 kg in words. one and thousandths of a kilogram b) Lauren bought a 1.401 kg package of trail mix. Model 1.401 kg using base ten blocks. Sketch your model. Tenths Hundredths Thousandths Copyright 2009 by Nelson Education Ltd. Checking & Practising BLM 2.6: Decimal Place Value 59

C&P Name: Date: 2.6 Decimal Place Value Page 2 Write 1.401 in expanded form. 1.401 whole tenths thousandth or or 0. 0. Write 1.401 kg in words. Practising 2. 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. Tenths Hundredths Thousandths b) 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.

L Name: Date: 2.6 Decimal Place Value Page 1 Student Book pages 56 59 GOAL Read, 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 ten blocks a decimal place value chart How can Mateo model the mass of the trail mix? You can write fractions as decimals. Fraction Decimal 1 tenth 1 10 0.1 1 hundredth 1 100 0.01 1 thousandth 1 1000 0.001 Complete the chart. Fraction Decimal 3 tenths 10 0. 25 hundredths 100 0. 365 thousandths 0. You can write decimals in expanded form. 1000 1.257 1 whole 2 tenths 5 hundredths 7 thousandths Write these decimals in expanded form. 1.834 whole tenths hundredths thousandths 2.696 wholes tenths hundredths thousandths You can use base ten blocks to model fractions or decimals. one 1 or 1.0 one tenth 1 or 0. 10 one hundredth 1 100 or 0. one thousandth 1 1000 or 0. 10 10 10 Copyright 2009 by Nelson Education Ltd. Learning BLM 2.6: Decimal Place Value 61

L Name: Date: 2.6 Decimal Place Value Page 2 Use base ten blocks to model 1.393 on a decimal place value chart. Make a copy of this model. Tenths Hundredths Thousandths 1 3 9 3 Write 1.393 in expanded form. 1.393 1 whole tenths hundredths thousandths or 1 10 100 1000 or 0. 0. 0. + + 300 90 3 small cubes thousandths Write 1.393 in words. one and thousandths Reflecting In 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 3.3 Renaming Decimals Student Book pp. 60 63 Teacher s Resource pp. 44 48 GOAL Represent decimals and relate them to fractions. Preparation and Planning Masters Key Question 2 Assessment Question Checking and Practising BLM 2.7 pp. 64 65 Learning BLM 2.7 pp. 66 67 Hundredths Grid, MB p. 37 Thousandths Grid, MB p. 38 Differentiating Instruction About the Math In this lesson, students use hundredths and thousandths grids to model decimals pictorially. They make connections between decimals and fractions, and learn that there are numerous names for the same decimal number. A key concept is that the whole grid is 1 whole, just as the large base ten cube was 1 whole in the model used in Lesson 2.1. It follows that, if 2 grids of the same size are used to represent 2 decimals or fractions, and the same amount of the grid is coloured for each, the 2 numbers have the same value. Although they have the same value, they are different because they cannot always be modelled on the same grid. For example, 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 use grids to represent numbers and to identify numbers represented on grids. Post a chart of these various relationships that students can refer to. Provide examples to help students better understand the concept Hundredths and Thousandths Grids of a placeholder; for instance, write 0.67 on the chalkboard and ask students to model 67 hundredths with counters on a decimal 1 tenth 1 0.1 10 place value chart. Then, write 0.670 on the board and ask students to model 1 column 10 hundredths 10 0.10 100 670 thousandths below the first model on the same chart. Ask what is different about 100 thousandths 100 0.100 1000 the models. (nothing) Ask what is different about the decimals. (One has a 0 in the 1 hundredth 1 0.01 thousandths place.) Tell students that these 1 square 100 numbers are equivalent because they 10 thousandths 10 0.010 1000 represent the same value. 1 For students who need scaffolding during 1 rectangle 1 thousandth 1000 0.001 independent practice, provide Checking and Practising BLM 2.7. For students who need extra learning support, provide Learning BLM 2.7, which presents the concepts more incrementally. Answers to Learning BLM 2.7 Step 2: 10; 10 Step 3: 0.24 Step 4: 2, 4 Step 5: 240 1000 Step 6: 100; hundredth, 1, 0.01; 10; 100 10; 100 Step 7: 0.240 Step 8: 2, 4, 0 Reflecting: 24 hundredths 2 tenths 4 hundredths, and 240 thousandths 2 tenths 4 hundredths 0 thousandths. The 0 thousandths is equal to 0, so the two decimals are the same. Copyright 2009 by Nelson Education Ltd. Overview 2.7: Renaming Decimals 63

C&P Name: Date: 2.7 Renaming Decimals Page 1 Student Book pages 60 63 Checking 1. There are 1000 students at Belle s school. 400 students play an instrument. You will need pencil crayons thousandths grids a) 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. 1000 Each 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. 100 10 64 Checking & Practising BLM 2.7: Renaming Decimals Copyright 2009 by Nelson Education Ltd.

C&P Name: Date: 2.7 Renaming Decimals Page 2 Practising 2. Emanuel coloured part of a thousandths grid. a) Write a fraction to represent the coloured part. b) Write a decimal thousandth to represent the coloured part. 5. a) 0.29 Write the decimal in expanded form. tenths hundredths 1 column is 1 tenth. 1 square is 1. Colour the decimal on the grid. Write the decimal as an equivalent decimal thousandth. 0.29 b) 0.68 Colour the decimal on the grid. Write the decimal as an equivalent decimal thousandth. 0.68 Copyright 2009 by Nelson Education Ltd. Checking & Practising BLM 2.7: Renaming Decimals 65

L Name: Date: 2.7 Renaming Decimals Page 1 Student Book pages 60 63 GOAL Represent 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. 1 10 1 100 You will need pencil crayons thousandths grids hundredths grids How can you use decimals to compare the Grade 5 students in the 2 schools? Step 1: Write a fraction for the number of Grade 5 students in Anne s school. 24 100 Step 2: Model the fraction on a hundredths grid. There are 10 columns in a hundredths grid. Each column is one tenth or 1 or 0.1. 10 There are 100 squares in a hundredths grid. Each square is one hundredth or 1 or 0.01. 100 How many squares are in 1 column? So, one tenth hundredths. Colour 24 hundredths on the grid. Step 3: Write the fraction 24 as a decimal. 0. 100 Step 4: Write the fraction 24 in expanded form. 100 24 is the same as 24 hundredths. 100 24 hundredths is tenths hundredths. 66 Learning BLM 2.7: Renaming Decimals Copyright 2009 by Nelson Education Ltd.

L Name: Date: 2.7 Renaming Decimals Page 2 Step 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. 10 There are squares in a thousandths grid. 1 10 1 100 1 1000 Each square is one or or 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. 1000 There are 100 rectangles in a column. So, 1 tenth thousandths. Colour 240 hundredths on the grid. Step 7: Write the fraction Step 8: Write the fraction 240 1000 is the same as 240 thousandths. as a decimal. 0. in expanded form. 240 thousands is tenths hundredths thousandths The amount that is coloured on both grids is the same. The decimals 0.24 and 0.240 are equivalent decimals. Reflecting 240 1000 240 1000 equivalent Having the same value For example, How did writing both decimals in expanded form show that they are equivalent? 8 10 80 100 Copyright 2009 by Nelson Education Ltd. Learning BLM 2.7: Renaming Decimals 67

2.8 3.3 Communicating about Equivalent Decimals Student Book pp. 64 65 Teacher s Resource pp. 49 52 GOAL Explain whether two decimals are equivalent. Preparation and Planning Masters Key Question 2 Assessment Question Checking and Practising BLM 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. 38 About the Math In this lesson, students communicate their understanding of equivalent fractions and decimals. Encourage a variety of strategies and have materials (place value charts, thousandths and hundredths grids, counters, base ten blocks) available for those who wish to use them. Review and post the Communication Checklist to help remind students of the expectations. Differentiating Instruction Have 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 the class, and record their answers on chart paper. (It is a decimal; There are 6 tenths; There is no whole number before the decimal.) Or, students may make a model. Next, have students describe 0.60. Again, have them share their descriptions and record their answers. (There are 60 hundredths; The 6 is in the tenths place; The number is less than 1 because there is no whole number before the decimal.) 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 are the same size, and each decimal is represented by the same amount of a grid. On a place value chart they have the same numbers 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 2.8 Stefan used math language (e.g., models, represent, decimals, tenths grid) and included a diagram. He did not include the 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 a thousandths 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 1 Student Book pages 64 65 Checking 1. 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. Communication Checklist Did you use math language? Did you include the right amount of detail? Did you include a diagram? 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. Tenths Hundredths Thousandths Copyright 2009 by Nelson Education Ltd. Checking & Practising BLM 2.8: Communicating about Equivalent Decimals 69

C&P Name: Date: 2.8 Communicating about Equivalent Decimals Page 2 Practising 2. Jeremy and Anna are driving to Peace River with their parents. Jeremy says that they have driven 0.3 of the way. 30 Anna says that they have driven of the way. 100 Explain why they are both right. Represent 0.3 and 30 100 on the hundredths grids. 0.3 30 100 Use your diagrams to help you explain why 0.3 and Use the Communication Checklist. 30 100 are equivalent. Communication Checklist Did you use math language? Did you include the right amount of detail? Did you include a diagram? 70 Checking & Practising BLM 2.8: Communicating about Equivalent Decimals Copyright 2009 by Nelson Education Ltd.

L Name: Date: 2.8 Communicating about Equivalent Decimals Page 1 Student Book pages 64 65 GOAL Explain 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 chocolate bar are the same amount. Colin wants to know why. How can Stefan explain how he knows that the decimals are equivalent? Stefan s Explanation I ll use models to represent the chocolate bar, and I ll colour the decimals. I can model 0.5 on a tenths grid. I can model 0.50 on a hundredths grid. I can model 0.500 on a thousandths grid. The decimals 0.5, 0.50, and 0.500 are equivalent because the same amount is coloured on all 3 grids. Copyright 2009 by Nelson Education Ltd. Learning BLM 2.8: Communicating about Equivalent Decimals 71

L Name: Date: 2.8 Communicating about Equivalent Decimals Page 2 What did Stefan explain well? Use the Communication Checklist. Communication Checklist Did you use math language? Did you include the right amount of detail? Did you include a diagram? 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? Reflecting How did the diagrams help Stefan explain? 72 Learning BLM 2.8: Communicating about Equivalent Decimals Copyright 2009 by Nelson Education Ltd.

2.9 3.3 Rounding Decimals Student Book pp. 66 68 Teacher s Resource pp. 53 56 GOAL Interpret rounded decimals, and round decimals to the nearest tenth or the nearest hundredth. Preparation and Planning Masters Key Question 2 Assessment Question Checking and Practising BLM 2.9 pp. 74 75 Learning BLM 2.9 pp. 76 77 Hundredths Grids, MB p. 37 Thousandths Grids, MB p. 38 About the Math In this lesson, students use decimal representations on thousandths grids to help them round decimals. The lesson provides an example of how meaningful answers can often be obtained through estimation. Before students begin rounding, review the values of the sections on a thousandths grid: columns are tenths, squares are hundredths, and rectangles are thousandths. Encourage students to draw on their experience rounding whole numbers the conventions for rounding decimals exactly parallel those used for whole numbers. Differentiating Instruction Show 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 the same, 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 the place 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 of the central problem for the lesson. Note: The lesson goal has been changed for this BLM. Answers to Learning BLM 2.9 A. less than 3; closer to 3; 3 B. 0.3; 3 C. 30; 30; 30 Reflecting: 7; 1; Since 7 full columns are shaded in and only 1 square is shaded in on the next column, the number is rounded to 7 tenths. Copyright 2009 by Nelson Education Ltd. Overview 2.9: Rounding Decimals 73

C&P Name: Date: 2.9 Rounding Decimals Page 1 Student Book pages 66 68 Checking 1. The chart on this page shows batting averages for 2 professional baseball players. Batting averages are reported in decimal thousandths. A batting average of 0.447 means the player can expect to get 447 hits in 1000 times at bat. a) Model J. McDonald s batting average of 0.447 on the thousandths grid provided here. You will need pencil crayons thousandths grids Batting Averages Player Batting average J. McDonald 0.447 R. Clayton 0.288 b) 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 2 Practising 2. 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 tenth 0.158 0.15 0.16 0.1 0.2 0.228 0.22 0.23 0.2 0.3 1.067 1.06 1.07 1.0 1.1 2.039 2.03 2.04 2.0 2.1 3. Which numbers below round to the same hundredth? 0.234 0.324 0.237 0.229 Look 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 Decimals 75