<p>Students will round numbers to the nearest 10 in this lesson. They are going to:&nbsp;<br>- recognize that a value is approximated while rounding.&nbsp;<br>- round two-digit numbers to the nearest ten.&nbsp;<br>- round three-digit numbers to the nearest hundred.&nbsp;</p>

<p>- What are the mathematical representations for relationships?&nbsp;<br>- How does effective communication benefit from mathematics?&nbsp;<br>- How can relationships in mathematical situations be described by patterns?&nbsp;<br>- How do we represent, compare, quantify, and model numbers using mathematics?&nbsp;<br>- What does it mean to analyze and estimate numerical quantities?&nbsp;<br>- What makes a tool and/or strategy suitable for a certain task?&nbsp;<br>- When is it appropriate to estimate versus calculate?&nbsp;</p>

<p>- Estimate: Use strategies to quickly find a number that is close to the exact answer.&nbsp;<br>- Round: Find an approximate number that has fewer nonzero digits, so that it will be easier for further estimation calculation(s). Usually, numbers are rounded to the nearest ones, tens, hundreds, etc.</p>

<p>- base-ten blocks<br>- Aunts, Uncles, and Many Cousins practice worksheet (M-3-6-1_Aunts, Uncles, and Many Cousins Practice Worksheet and KEY)<br>- Round and Round and Round practice worksheet (M-3-6-1_Round and Round Practice Worksheet and KEY)<br>- Round to the Nearest Ten practice worksheet (M-3-6-1_Round to Nearest Ten Practice Worksheet and KEY)<br>- Round to the Nearest Hundred practice worksheet (M-3-6-1_Round to Nearest Hundred Practice Worksheet and KEY)<br>- Lesson 1 Exit Ticket (M-3-6-1_Lesson 1 Exit Ticket and KEY)</p>

<p>- Students' ability to round two-digit numbers to the nearest ten and three-digit numbers to the nearest hundred can be assessed using the Round and Round and Round practice worksheet (M-3-6-1_Round and Round Practice Worksheet with KEY).&nbsp;<br>- Evaluate the students' level of understanding of rounding using the Lesson 1 Exit Ticket (M-3-6-1_Lesson 1 Exit Ticket with KEY).</p>

<p>Explicit instruction, Modeling, Scaffolding, and Active Engagement&nbsp;<br>W: Student will learn to round two-digit figures to the nearest ten and three-digit numbers to the nearest hundred. They will discover that rounding, as opposed to providing the exact figure, is often sufficient information when indicating how many.<br>H: Start a conversation by introducing questions like, "How many people attended the party?" Engage students by explaining to them how rounding is frequently used in the real world to determine how many when an exact answer is not required.<br>E: Instruct students to use base-ten blocks to represent numbers. Students will investigate the relative closeness of values to multiples of 10 or 100 using base-ten blocks. They will have a chance to practice rounding using particular experiences. In order to determine whether a rule for rounding halfway numbers is necessary, students will also examine numbers such as 45 in the interval 40 to 50, or 450 in the interval 400 to 500.<br>R: As they discuss each real-world example, students will be forced to rethink and update their understanding of rounding during the lesson. We will use the practice worksheets Rounding to the Nearest Ten and Rounding to the Nearest Hundred in class. Students can then use The Round and Round and Round practice worksheet to review the nearest ten and nearest hundred rounding concepts.<br>E: The accuracy of the practice worksheet Round and Round and Round will be used to assess students. Lesson 1 Exit Ticket will also be used to evaluate students.<br>T: By using the ideas in the Extension section, the lesson can be modified to fit the needs of the students. For those who are having trouble learning to round, specific recommendations are given, and for those who have mastered the skill, the Extension section offers more challenges.&nbsp;<br>O: The lesson is scaffolded in that students first use base-ten blocks to identify which multiple-of-ten numbers are closer to. Through this exercise, students can practice rounding to the nearest ten. After then, the procedure is repeated with regard to rounding to the nearest hundred. To develop their understanding of these ideas, students will practice rounding to both the nearest ten and hundred.</p>

<p>The main topic of this lesson is rounding numbers to the nearest ten and hundred.<br>Before beginning this lesson, assist students in reviewing base-ten block counting by 10s and 100s. To do so, give base-ten blocks to groups of two or three students. At least 10 hundreds, 10 tens, and 30 ones should be distributed to each group. Here's how to introduce the lesson.<br><br><strong>“How much did the groceries cost? How many people came to the party? How many marbles are in the pail? People often answer these questions by saying about how many. The groceries cost about $40. About 20 guests came to the party. There are about 100 marbles in the pail. Today we will learn to round numbers, a useful technique to answer questions about how many. But first, we will go over counting by 10s and counting by 100s using base-ten blocks. This will help us in preparing to learn how to round numbers.”</strong><br><br><strong>Review – Counting by Tens and Hundreds</strong><br><br>Hold up one of the tens, the long, narrow base-ten block representing ten units. Write 10 on the board. Now hold up a second of the tens, then write the number 20 on the board. Hold up additional tens to help students learn counting by tens and using base-ten blocks to visualize each multiple of ten. As students say the multiple of 10, make sure to write them on the board. Then, keep counting by tens until at least 100.<br><br><strong>10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, . . .</strong><br><br>Present one of the hundreds, which is a square, flat base-ten block representing one hundred units. Write the number 100 on the board. Hold up another one of the hundreds then write the number 200 on the board. Hold up additional hundreds to help students count by hundreds and using base-ten blocks to illustrate each multiple of one hundred. As students say the multiples of 100, make sure to write them on the board. Then, keep counting by hundreds until at least 1000.<br><br><strong>100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, . . .</strong><br><br><strong>Aunts, Uncles, and Many Cousins! Practice Worksheet</strong><br><br>Give each student a copy of the practice worksheet, Aunts, Uncles, and Many Cousins! (M-3-6-1_Aunts, Uncles, and Many Cousins Practice Worksheet with KEY).&nbsp;<br><br>Help students in finishing the first example. Ask, <strong>"Will someone please volunteer to read the Ryan sentence aloud?”</strong>. Once a student has finished reading the sentence, ask students to use base-ten blocks to build number 32. <strong>"Please build the number 32, which is the number of cousins Ryan has, using base-ten blocks."</strong><br><br>Ask a student to show the class how s/he built 32 using base-ten blocks. Make sure all of the students in the class can easily see your base-ten blocks. This can be done using large magnetic demonstrative base-ten blocks combined with a whiteboard, virtual base-ten blocks combined with an interactive whiteboard, base-ten blocks combined with a document camera, or over-head base-ten blocks combined with an overhead projector. It is important for students to be able to model their thinking for their classmates.<br><br>Next, ask students to draw 32. <strong>“Draw the number 32 on the hundred grid.”</strong> While students are drawing 32, present 3 tens and 2 ones altogether. This will model the portion of the hundred grid that represents 32. Use this to help students verify that they correctly drew 32.<br><br>Refer to the multiples of ten that were written on the board at the beginning of the class. Ask students: <strong>"Which two multiples of ten is 32 between on a number line?"</strong> Students will probably mention 30 and 40. Ask students to explain how they know this to be true.<br><br>Explain to students, <strong>“The last step is to decide whether 32 is closer to 30 or 40. Please work with your group to decide this, then finish the rest of the practice worksheet.”</strong> Do not ask students to help you answer this question. The purpose of the Aunts, Uncles, and Many Cousins! practice worksheet is for students to collaborate to determine which numbers between 30 and 40 are closer to 30 and which are closer to 40. This will support students’ understanding of the rule for rounding numbers to the nearest ten.<br><br>While the students are working in groups, keep an eye on them. If students are having trouble determining if a certain number is closer to 30 or 40, help them make a comparison between the number of units that must be added to reach 40 and the number of units that must be removed to have only 30. For example, 32 is closer to 30 than it is to 40 since only 2 units must be subtracted to get 30, whereas 8 must be added to get 40.<br><br>Listen very carefully when groups are discussing whether 35 is closer to 30 and 40. 35 is not closer to either 30 and 40 since the distance on the number line between the two is the same. This is an important point; it required mathematicians to write a special rule for how to round numbers ending in 5 to the nearest ten.<br><br>After the groups of students are finished with the Aunts, Uncles, and Many Cousins! practice worksheet, draw the portion of the number line between 30 and 40 on the board.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/pic 1.png" width="429" height="61"><br><br>Work through the last example on the practice worksheet as a class. Most groups will already have completed this, but here is an opportunity to talk about the discussion that students made.<br><br>As shown below, students should have drawn a circle around the numbers 31, 32, 33, and 34, to represent that they are all closer to 30 than to 40. In order to show that they are closer to 40 than 30, students should have drawn a square around 36, 37, 38, and 39.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/pic 2.png" width="428" height="65"><br><br>Ask a student or pair of students to volunteer to build the number 36 for the class. (When working in pairs, students can support each other in recording, showing, and explaining the procedures to the class, and students also feel less scared when sharing their work.) Give students a means to use the demonstration options we talked about earlier to show how they are using base-ten blocks in a way that all students can see. To find out if 36 is more like 30 or 40, have a different student or pair of students use the model for 36. Continue to ask students to explain their reasoning for other numbers between 30 and 40.<br><br>Make sure you talk about 35 last. Make sure every student understands that there is no right or wrong answer for question about 35 on the practice worksheet because 35 is the same distance from both 30 and 40. There is no greater difference between the two numbers.<br><br><strong>Round to the Nearest Ten</strong><br><br>Give each student a copy of the practice worksheet for Round to the Nearest Ten (M-3-6-1_Round to Nearest Ten Practice Worksheet with KEY). Students should work in groups to finish the first two number line examples. These examples use the same directions as the number line example on the Aunts, Uncles, and Many Cousins! practice worksheet.&nbsp;<br><br>While the groups are working, keep an eye on them. Be sure every student knows how to identify which numbers are closer to each multiple of ten. When all groups are finished with these two examples, draw both number lines on the board. Have a student or pair of students to circle and square the relevant numbers for each example, as shown here.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/pic 3.png" width="422" height="122"><br><br>Explain the concept of rounding. <strong>“Ryan has 32 cousins. Although this is true, we might instead state that Ryan has about or approximately 30 cousins. We often round numbers rather than providing an exact number when describing how many. First, we will learn how to round to the nearest multiple of 10, more often referred to as rounding to the nearest ten.”</strong><br><br>Write the example on the board.<br><br>Ryan has 32 cousins. About how many cousins does Ryan have?<br><br>Take the students through these steps to round to the nearest ten. On the board, write each step. Ask students to help you fill in the blanks.<br><br>Ask, <strong>“If we count by tens, what two multiples of ten is 32 between?”</strong><br><br>Step 1: 32 is between 30 and 40<br><br>Ask, <strong>“Is the number 32 closer to 30 and 40?”</strong><br><br>Step 2: 32 is closer to 30<br><br>Ask,<strong> “Since the number 32 is closer to 30, we say 32 rounds to 30 or 32 rounds down to 30.”</strong><br><br>Step 3: 32 rounds to 30<br><br>Write the example on the board.<br><br>Juanita has 36 cousins. About how many cousins does Juanita have?<br><br>Take the students through these steps to round to the nearest ten. On the board, write each step. Ask students to help you fill in the blanks.<br><br>Example: Round 36 to the nearest ten.<br><br>Ask, <strong>“If we count by tens, what two multiples of ten is 36 between?”</strong><br><br>36 is between 30 and 40<br><br>Ask, <strong>“Is the number 36 closer to 30 and 40?”</strong><br><br>36 is closer to 40<br><br>Ask, <strong>“Since the number 36 is closer to 40, what number does 36 round to? About how many cousins does Juanita have?”</strong><br><br>36 rounds to 40<br><br>Write the example on the board.<br><br>Miriam has 85 cousins. About how many cousins does Miriam have?<br><br>Take the students through these steps to round to the nearest ten. On the board, write each step. Ask students to help you fill in the blanks.<br><br>Example: Round 85 to the nearest ten.<br><br>Ask, <strong>“If we count by tens, what two multiples of ten is 85 between?”</strong><br><br>85 is between 80 and 90<br><br>Ask, <strong>“Is the number 85 closer to 80 and 90?”</strong><br><br>85 is closer to neither 80 or 90<br><br>Explain <strong>"Mathematicians had to decide how to round 85 to the nearest ten because it is the same distance from 80 and 90. They decided to round 85 ends in 5, they would round 85 up to 90. Miriam has about 90 cousins.”</strong><br><br>85 rounds to 90<br><br>Now ask: <strong>"If rounding to the nearest multiple of ten, which of the numbers between 70 and 80 would round to 70? Which would round to 80?”</strong> Help students in drawing the links between rounding and the relative distances from the multiples of 10. Students will probably say that numbers with a circle round to 70 as they are closer to 70, and numbers with a square round to 80 as they are closer to 80.<br><br>Now ask the question, <strong>"Will 75 round to 70 or 80?"</strong> Help students understand that mathematicians agreed that 75 rounds to 80. They established a rule to round up to 80 because 75 is not closer to 70 or 80.<br><br>Have a similar discussion with the 40–50 number line. Again make sure that students understand that 45 is the same distance from 40 and 50. However, 45 rounds to 50 because that is the rule mathematicians decided upon.<br><br>Request that students finish the remaining Round to the Nearest Ten practice worksheet examples in their groups. As a class, review these examples to make sure everyone knows how to round to the nearest ten.<br><br><strong>Round to the Nearest Hundred</strong><br><br>Give each student a copy of the practice worksheet for Round to the Nearest Hundred (M-3-6-1_Round to Nearest Hundred Practice Worksheet with KEY). Students should finish the first two number line examples in groups. These examples use the same directions as the number line example on the Aunts, Uncles, and Many Cousins! And Round to the Nearest Ten practice worksheet.<br><br>When most students are finished with the two number line examples, write this example on the board.&nbsp;<br><br>Taya has $362. About how many dollars does Taya have?<br><br>Use this example to explain the concept of rounding to the nearest hundred. <strong>“Taya has $362. Although this is true, we might instead state that Taya has about or approximately $360 or $400. We often round numbers rather than providing an exact number when describing how many. Now, we will learn how to round to the nearest multiple of 100, more often referred to as rounding to the nearest hundred.”</strong><br><br>Each group should still have at least 10 hundreds, 10 tens, and 30 ones from the previous work on rounding to the nearest ten. Ask the groups of students to build 362 with base-ten blocks and to draw 362 using the hundred grids. Ask them to build and draw 347 as well. Also, encourage them to try to complete the statements in each of these examples.<br><br>Review both examples as a class. Help students understand how to round to the nearest hundred. Write each step on the board. Ask students to help you fill in the blanks.<br><br>Example: Taya has $362. About how many dollars does Taya have? Round 362 to the nearest hundred.<br><br>Ask,<strong> “If we count by hundreds, what two multiples of one hundred is 362 between?”</strong><br><br>Step 1: 362 is between 300 and 400<br><br>Ask, <strong>“Is the number 362 closer to 300 or 400?”</strong><br><br>Step 2: 362 is closer to 400<br><br>Make sure to ask how they know 362 is closer to 400. This needs students to follow the other steps provided. First, recognize that 350 is the halfway point between 300 and 400. Next, recognize that 362 is greater than the halfway point of 350.<br><br>Explain, <strong>“Since the number 362 is closer to 400, we say 362 rounds to 400.”</strong><br><br>Step 3: 362 rounds to 400<br><br>Example: Jamal has $347. About how many dollars does Jamal have? Round 347 to the nearest hundred.<br><br>Ask a student to volunteer to describe each step in rounding 347 to the nearest hundred. (The steps are presented here, but a student may be able to explain them without you providing them.) Peer-to-peer instruction is really valuable. It empowers students to collaborate and encourages them to take responsibility for their own learning.<br><br>Ask, <strong>“If we count by hundreds, what two multiples of one hundred is 347 between?”</strong><br><br>Step 1: 347 is between 300 and 400<br><br>Ask, <strong>“Is the number 347 closer to 300 or 400?”</strong><br><br>Step 2: 347 is closer to 300<br><br>Make sure to ask how they know 347 is closer to 300. First, students have to understand that 350 is the halfway point between 300 and 400. Next, recognize that 347 is less than the halfway point of 350.<br><br>Explain, <strong>“Since the number 347 is closer to 300, we say 347 rounds to 300.”</strong><br><br>Step 3: 347 rounds to 300<br><br>Ask students to work in groups to finish the remaining examples on the Round to the Nearest Hundred practice worksheet. Review these examples with the class to make sure that all students understand how to round to the nearest hundred.&nbsp;<br><br>Make sure that students ask questions about anything they don't understand. Before beginning the practice task, students should have all of their questions answered.&nbsp;<br><br>Students can now complete the Round and Round practice worksheet (M-3-6-1_Round and Round Practice Worksheet with KEY) in class or as homework. This practice worksheet can be used to check students’ understanding of rounding to the nearest ten or hundred.<br><br><strong>Extension:</strong><br><br>Return to the use of base-ten blocks to help students who have yet to mastered the concept of rounding. Ask students to calculate how many units would be added to the next multiple and subtracted to make the previous multiple. For example, if you want to round 36 to the nearest ten, you must add four units to reach 40 and subtract six units to get 30. This should help them determine which multiple the value is closer to. Additional materials are available in the Small Group area for students who may benefit from additional instruction or practice.<br><br>Students who are ready for an additional challenge should be introduced to round four-digit numbers to the nearest ten and hundred. These students can also be taught to round to the nearest thousand. The Expansion section includes specific tools for students who are ready to go above and beyond the standard's requirements.<br><br><strong>Routine:</strong> As real-life scenarios happen during the school year, instruct students to practice rounding numbers to the nearest ten or hundred. For example, the daily temperature and the cost of technological equipment can often be rounded to the nearest ten and hundred, respectively. Students can also use rounding to estimate answers to a wide range of problems in the mathematics curriculum.<br><strong>Small Group:</strong> Students that require further practice might be divided into small groups to do the following task.&nbsp;<br>One student from the group should roll two 10-sided number cubes. The first number rolled is in the tens place, while the second number is in the ones place. All students should write down the number rolled. Students should then be encouraged to round their numbers to the nearest ten. It will be important to listen carefully in order to discover and correct mistakes in their thinking. The method should be performed with three 10-sided number cubes and rounded to the nearest hundred.<br><br>If students struggle with rounding, they should be encouraged to study the topic using base-ten blocks. For example, if you want to round 36 to the nearest ten, you must add four units to reach 40 and subtract six units to get 30. This should help students in determining which multiple the value is closer to, allowing them to round the number appropriately. Avoid focusing on a certain rounding rule. Instead, focusing on the number's relative distance from multiples of 10 or 100 will develop a better conceptual understanding of rounding.&nbsp;<br><br>These two websites can be used for more practice. The first is an interactive game that focuses on rounding to the nearest ten and the second is similar but focuses on rounding to the nearest hundred.<br><br><strong>Expansion:</strong> The following Web sites are recommended for students who are ready for a more difficult challenge. The first two sites round four-digit numbers to the closest ten and hundred. This requires students to go beyond dealing with only two and three digit numbers. The third site specializes in rounding four-digit numbers to the nearest thousand. This requires students to go beyond rounding to the nearest ten or hundred.</p>