s e s s i o n 5 A. 2 Stickers: How Many,, and? Math Focus Points Reading and writing 3-digit numbers Adding 10 to and subtracting 10 from a given number and describing what part of the number changes Using a place-value model to represent and compare 3-digit numbers as 100s, 10s, and 1s Representing 2- and 3-digit numbers using expanded form Today s Plan Activity Writing Numbers Above 200 Activity How Many Stickers:,,? Activity How Many Stickers? SESSION FOLLOW-UP Daily Practice and Homework 20 Min Class Individuals 20 Min Class pairs 20 Min Individuals Materials C60 C64, 1 1,000 Packet (from Session 5A.1) Student Math Handbook, pp. 27 and 31 Transparent Stickers (from Investigation 1) Student Activity Book, pp. 72 73 or C67 C68, How Many Stickers? Make copies. (as needed) C69, How Many Stickers? Make copies. (as needed) Transparent Stickers and paper-sticker sets (from Investigation 1, as needed) Student Activity Book, p. 74 or C70, Comparing Stickers Make copies. (as needed) C60 C64, 1 1,000 Packet (from Session 5A.1) Student Math Handbook, pp. 27 32 Classroom Routines Today s Number: 200 Ask students to predict whether or not they will land exactly on the number 200 if they count around the class by 10s. As students count around the class by 10s, make a vertical list of the numbers they say. Compare the final number said to 200. Is it more or less? Ask the class to generate expressions for the number 200 using only two multiples of 10 (two numbers from the list). For example: 100 1 100; 10 1 190; 150 1 50. Session 5A.2 Stickers: How Many,, and? CC53
1 Activity 2 Activity 3 Activity 4 Session Follow-Up A C T I V I T Y Writing Numbers Above 200 20 Min class individuals Display a copy of the 201 400 chart (C61). Students should refer to their set of 200 charts that they used in Session 5A.1. They will begin to fill in this chart during this session. We have talked about numbers from 1 to 200. Today we are going to look at numbers that are greater than 200. Let s start counting on from 190. We ll stop when we get to 210. As students count, record the numbers in a vertical list starting with 190 and ending with 210. Take a look at these numbers. What patterns do you notice? What part of the number stays the same, and what part changes? Focus specifically on the pairs of numbers 199 to 200; 200 to 201; and 209 to 210. Students are likely to notice that the numbers occur in a regular pattern with the counting numbers repeating from 0 to 9 in the ones place and from 90 to 00 to 10 in the tens place. You have already worked with the chart of numbers from 1 to 200. Today, you are going to complete your own number charts. Begin with 201 and fill in your chart one row at a time. After each row, check your numbers with a partner. Students spend the next few minutes filling in their 201 400 charts. Remind them to stop after each row and check their work with a partner. As they did for the numbers 100 and 200, students should highlight with a light-colored marker or crayon the other multiples of 100 on this chart (300 and 400). Ongoing Assessment: Observing Students at Work Students practice reading and writing 3-digit numbers and using patterns in the sequence of numbers, as they fill in a 201 400 chart. How fluent are students as they fill in their charts? Do they say the rote counting sequence as they fill in numbers? CC54 INVESTIGATION 5A Working with 3-Digit Numbers
1 Activity 2 Activity 3 Activity 4 Session Follow-Up How accurate and legible are students written numerals? Do students notice and use any patterns in the counting sequence? differentiation: Supporting the Range of Learners Point out to students how they can use the numbers on the chart as cues to fill in each row. Encourage students to say each number before they write it. Some students might benefit from working on two or three rows at a time help them cover the bottom part of their chart with a sheet of blank paper so that they can focus only on a limited set of numbers at one time. Teaching Note 1 Completing 1 1,000 Charts Since students will need these charts for the next session, it is important that they bring their charts back to school. You may choose to have students complete their charts in class rather than at home for homework. Students who finish quickly can play a round of Guess My Number 1 400 with a partner. Remind them to keep track of their clues using numbers and notation. When most students have finished, briefly discuss any patterns they notice. Point out that many of the patterns that they noticed in the numbers from 201 400 are similar to or the same as the patterns they noticed when they were discussing patterns on the 1 to 200 chart in the previous session. Before moving on to the next activity, ask students to find numbers that are 10 more or 10 less than a given number. Pose a few of the following problems: 232 + 10 = 259 10 = 295 + 10 = 306 10 = 351 + 10 = 400 10 = Tell students that they will complete the rest of their charts for homework. 1 A C T I V I T Y How Many Stickers:,,? 20 Min Class pairs Students will revisit Sticker Station as they work with 3-digit numbers. Remind students of their previous work with stickers specifically that at Sticker Station, stickers are sold in sheets of 100, strips of 10, and singles. Use Student Math Handbook page 27. Session 5A.2 Stickers: How Many,, and? CC55
1 Activity 2 Activity 3 Activity 4 Session Follow-Up Math Note 2 Expanded Form Expanded form is a way to show how much each digit in a multi-digit number represents. It is the sum of the values of each place. In this example, 124 has 1 hundred, 2 tens, and 4 ones. This can be recorded as 100 + 20 + 4 = 124. Sticker problems are one of the many opportunities in grade 2 to record numbers in expanded form. Expanded form is sometimes referred to as expanded notation. Teaching Note 3 Place Value Representation Students were introduced to sticker notation earlier in this unit. Sticker notation is a quick way of representing 2- and 3-digit numbers and is useful for representing the hundreds, tens, and ones structure of numbers. This structure is not as easily seen on the 100 or 1,000 charts or the number line. Using transparencies of stickers, display several problems for students to consider. First show students 6 strips of ten and 2 single stickers and ask them to determine the number of stickers. Sally went shopping at Sticker Station. She bought 6 strips of ten stickers and 2 singles. How many stickers did Sally buy? How could we record this using an equation? Record 60 + 2 = 62 and ask students to explain what each number represents using the stickers. Next, pose a problem that involves a sheet of 100 stickers. Sally also bought some moon stickers. She bought one sheet of 100 stickers, 2 strips of 10 stickers, and 4 singles. Ask a student volunteer to display Sally s moon stickers. Talk with a partner about what equation we could write that would represent the number of moon stickers Sally bought. Give students a few minutes to discuss their ideas and then ask one student to give the equation and another student to explain what each number represents using the stickers. Show students how you can use sticker notation to record this set of stickers. Record the following on the board: 2 3 100 + 20 + 4 =124 [Nina] said that Sally bought 124 stickers. She bought one sheet of 100. I m going to use a square to represent this. [Draw a square under the 100.] She bought two strips of 10, or 20. I m going to draw two lines to show these. [Draw 2 lines under the 20.] Sally also bought 4 singles which I am going to show with small dots. [Draw 4 dots under the four.] Altogether, Sally bought one hundred twenty-four stickers. Use Student Math Handbook page 31 and talk through each number and what it represents. Pose another problem for students. This time use only sticker notation. CC56 INVESTIGATION 5A Working with 3-Digit Numbers
1 Activity 2 Activity 3 Activity 4 Session Follow-Up This is what James bought when he went to Sticker Station. Record the following on the board to represent 146 stickers: Talk with a partner about how many stickers James bought. Then, on a piece of paper, show the stickers using sticker notation and write an equation that represents these stickers. Walk around the class to get a sense of how students are working with these ideas and to see if they are able to record the notation and an equation. This square shows that James bought one sheet of 100 stickers. How should I show that with a number? What about these 4 lines? How many strips of 10 did James buy? How many stickers is that? What about these 6 dots? As students share, record the following numbers and equation under the sticker notation. 100 + 40 + 6 = 146 So, James bought 146 stickers, and Sally bought 124 stickers. Who bought more stickers? How do you know? Students might say: James bought more because 146 is more than 124. It comes after 124 on the 200 chart. It s bigger. 146 stickers are more than 124 stickers. You can tell because they both have a sheet of 100, but James has 4 strips of ten and Sally only has 2 strips of ten. The singles don t really matter. As students offer their ideas, find a way to illustrate each idea. For example, point out the number on the 200 chart or highlight the parts of each number using stickers or sticker notation. [Jai] said that you can compare the numbers by comparing each part of the number. First you look at the hundreds. Since both numbers have 1 hundred, you look at the tens next. Four tens is more than two tens. So, 146 is more than 124. Session 5A.2 Stickers: How Many,, and? CC57
1 Activity 2 Activity 3 Activity Name 4 Session Follow-Up Write 146 > 124 on the board, and say: 146 is greater than 124. How Many? How Many? 72 Suppose Sally bought another sheet of 100 stickers and added them to the 124. How many stickers would Sally now have? (224) What equation could represent this amount? Sticker Notation,, How Many Stickers? (page 1 of 2),, Equation Explain to students that you could also look at which number is less than the other. Write 124 < 146 on the board, and say: 124 is less than 146. Unit 6 Pearson Education 2 318 300 241 135 Number Record the following equation on the board and ask a student volunteer to use sticker notation below the equation. 124 + 100 =224 Session 5A.2 Student Activity Book, Unit 6, p. 72; Resource Masters, C67 INV12_SE02_U6.indd 72 5/19/11 7:43 PM Name Now who has more stickers, Sally or James? How can we show this information using the greater than or less than sign?,, What part of 124 changed when you added another 100? Right, the 1 changed to a 2 because now Sally has 2 sheets or 2 groups of 100 plus 24 stickers. She has 224 stickers. 224 > 146 146 < 224 Session 5A.2 909 750 500 407 Sticker Notation Number Pearson Education 2 How Many Stickers? (page 2 of 2),, Equation How Many? How Many? Ac tivit y Unit 6 73 Student Activity Book, Unit 6, p. 73; Resource Masters, C68 INV12_SE02_U6.indd 73 5/19/11 7:43 PM How Many Stickers? 20 Min individuals For the remainder of the session, students work on representing numbers using sticker notation and recording equations in expanded notation on Student Activity Book pages 72 73 or C67 C68. Explain to students that they should represent each number using sticker notation, record the number of stickers, the number of hundreds, tens, and ones, and then write an equation. Do the first number, 135, together so that students understand what information they need to include for each number. CC58 INVESTIGATION 5A INV12_TE02_U06_S5A.2.indd 58 Working with 3-Digit Numbers 6/9/11 2:32 PM
1 Activity 2 Activity 3 Activity 4 Session Follow-Up Teaching Note If students are having difficulty with Student Activity Book pages 72 and 73, try to identify what aspect of the work they do not understand. Are they able to read the number in the first column? Use sticker notation? If not, can they show you with paper stickers how to represent the number? Once they represent the number, can they make a connection between the picture and the number of sheets/hundreds, strips/tens, and dots/singles? 4 Unit 6 Session 5A.2 C69 INV12_BLM02_U6.indd 69 4/28/11 2:24 PM How Many? How Many? Comparing Stickers Daily Practice and Homework Pearson Education, Inc., or its affiliates. All Rights Reserved. 2 Resource Masters, C69 Name Session Follow-Up,, Equation How Many? How Many? How Many Stickers? If students are comfortable and seem to understand all aspects of this chart, you can use C69, How Many Stickers? to provide them with additional numbers. When making a chart, vary the information that you provide for each number sometimes giving only the sticker notation, or the number of hundreds, tens, and ones. Students may use a copy of C69 to fill in their own numbers and complete the chart. Name differentiation: Supporting the Range of Learners the notation and the value of each number? Do students accurately record an equation that represents use sticker notation to represent the number of hundreds, tens, and ones in each number?,, Do students correctly read each number? Are they able to Adjusting the Numbers If the numbers on Student Activity Book pp. 72 73 seem too large for some students, replace the numbers with more accessible ones. Are students able to work only with tens and ones? Can they read numbers in the 100s but not beyond? If so, give them numbers that they can be successful with so that they build their understanding and use of sticker notation, identifying tens and ones, and representing numbers with an equation. A blank chart, Resource Masters C69, is provided to adapt this activity to meet the needs of students. Sticker Notation Students represent 3-digit numbers using place-value notation and note the number of hundreds, tens, and ones. They record an equation in expanded form for each number. 4 Number Ongoing Assessment: Observing Students at Work Look at the sets of stickers. Circle the set that has more, and tell how you know. Daily Practice note Students identify the larger number by comparing the number of hundreds, tens, and ones. 1. Homework: Students fill in the remaining 200 charts if they have not already done so. Remind students to bring in their completed charts for use in the next sessions. Student Math Handbook: Students and families may use Student Math Handbook page 27 32 for reference and review. See pages 189 197 in the back of this unit. How do you know? 2. How do you know? 3. How do you know? Pearson Education 2 Daily Practice: For reinforcement of this unit s content, have students complete Student Activity Book page 74 or C70. 74 Unit 6 Session 5A.2 Student Activity Book, Unit 6, p. 74; Resource Masters, C70 INV12_SE02_U6.indd 74 Session 5A.2 Stickers: How Many,, and? INV12_TE02_U06_S5A.2.indd 59 5/19/11 7:52 PM CC59 6/16/11 9:31 AM
Teacher Note Assessment: 3-Digit Numbers Benchmarks Using a place value model to represent 3-digit numbers as 100s, 10s, and 1s Representing 3-digit numbers using expanded form Adding 10 or 100 to and subtracting 10 or 100 from a given number In order to meet the benchmark, students work should show that they can: identify an amount represented by a place value representation (groups of stickers) represent a 3-digit number as groups of 100s, 10s, and 1s write an equation for a number by adding groups of 100s, 10s, and 1s accurately add 10 and 100 to and subtract 10 and 100 from any 3-digit number Meeting the Benchmark Problems 1 and 2 Students who meet the benchmark can interpret and use place value notation to determine a total amount and represent a given quantity. These students correctly represent numbers as 100s, 10s, and 1s using sticker notation and equations. They can also represent a number as the sum of hundreds, tens, and ones. Problem 3 Students who meet the benchmark can easily add and subtract 10 and 100 to and from any 3-digit number. These students know that when adding or subtracting 10, the number in the tens place increases/decreases by 1 but the quantity increases/decreases by 10. Likewise, they know that when adding or subtracting 100, the number in the hundreds place increases/decreases by 1 but the quantity increases/decreases by 100. Partially Meeting the Benchmark Problems 1 and 2 Students who partially meet the benchmark may accurately complete some but not all parts of these problems. When representing a number using sticker notation, they may make a minor error in representation such as not including the correct amount of 100s, 10s, or 1s. Likewise, they may make a counting error when determining what quantity is represented by sticker notation. Students who partially meet the benchmark may make an error in recording an equation if their sticker representation is not accurate or if they were not accurate in counting the number of groups of hundreds, tens, or ones. Problem 3 Students who partially meet the benchmark may be able to successfully add 10 to or subtract 10 from any number, but they may not yet be fluent with adding/ subtracting 100. These students may need to consult their 1 1,000 charts. Not Meeting the Benchmark Problems 1 and 2 Students who do not meet the benchmark have difficulty accurately completing the assessment problems because they may not understand the quantities represented by the sticker notation nor be able to use it to represent a 3-digit number. These students will need more exposure to place value concepts such as grouping by tens and ones, working with 2-digit numbers, and thinking about 100 as ten groups of ten. They should continue to work with representing quantities with stickers and also with cubes grouped into sticks of 10. These students may not yet be able to express a number as the sum of hundreds, tens, and ones. They should work on expressing two-digit numbers as the sum of tens and ones. Problem 3 Students who do not meet this benchmark may understand that when adding or subtracting 10 the number increases/decreases by 10, but they may rely on counting forward/back by ones to determine the answer. These students should practice adding and subtracting 10 from 2-digit numbers and think about how the number in the tens place changes. Session 5A.5 Assessment:,, and CC75
Name How Many? How Many? How Many Stickers? (page 1 of 2) Number Sticker Notation,, 135 241 300 318,, Equation Unit 6 Session 5A.2 C67 Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
Name How Many? How Many? How Many Stickers? (page 2 of 2) Number Sticker Notation,, 407 500 750 909,, Equation Unit 6 Session 5A.2 C68 Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
Name How Many? How Many? How Many Stickers? Number Sticker Notation,,,, Equation Unit 6 Session 5A.2 C69 Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
Name How Many? How Many? Daily Practice Comparing Stickers Look at the sets of stickers. Circle the set that has more, and tell how you know. note Students identify the larger number by comparing the number of hundreds, tens, and ones. 1. How do you know? 2. How do you know? 3. How do you know? Unit 6 Session 5A.2 C70 Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
Nombre Cuántas decenas? Cuántas unidades? Fecha Evaluación: Números de 3 dígitos (página 2 de 2) Problema 3 Resuelve los siguientes problemas. 176 + 10 = 176 + 100 = 176 10 = 176 100 = 425 + 10 = 425 + 100 = 425 10 = 425 100 = Unidad 6 Sesión 5A.5 C78 Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
Nombre Cuántas decenas? Cuántas unidades? Fecha Práctica diaria Cuántas pegatinas? James compró las cantidades siguientes de pegatinas en Sticker Station. Halla la cantidad total de pegatinas que Jake compró. nota Los niños combinan cuatro números para determinar la cantidad total de pegatinas. 32 Escribe una ecuación y muestra cómo lo averiguaste. Cuántas pegatinas compró Jake en total? Unidad 6 Sesión 5A.5 C79 Pearson Education, Inc., or its affiliates. All Rights Reserved. 2