<p>This unit involves having students compare and sort three-digit numbers. Students are going to:&nbsp;<br>- use the symbols &lt;, &gt;, or = to compare numbers,&nbsp;<br>- read the number sentence with the symbol aloud.&nbsp;<br>- sort the numbers from smallest to largest.&nbsp;<br>- sort the numbers in ascending order of greatest to least.</p>

<p>- What mathematical representations exist for relationships?&nbsp;<br>- How can the study of mathematics aid in clear communication?&nbsp;<br>- How can identifying regularity or repetition help with problem-solving efficiency?&nbsp;<br>- How are numbers represented, compared, quantified, and modeled using mathematics?&nbsp;<br>- What does it mean to evaluate or estimate a numerical quantity?&nbsp;<br>- What qualifies a tool or strategy as suitable for a particular task?</p>

<p>- Equal To: The same value as.&nbsp;<br>- Greater Than: Bigger.&nbsp;<br>- Less Than: Smaller.</p>

<p>- number tiles 1–9 (3–6 sets)&nbsp;<br>- jar (one jar for each set of number tiles)&nbsp;<br>- whiteboard&nbsp;<br>- whiteboard marker&nbsp;<br>- whiteboard eraser&nbsp;<br>- Comparing Numbers Group Activity sheet (M-2-1-3_Comparing Numbers Group Activity)&nbsp;<br>- Ordering and Comparing Numbers Worksheet (M-2-1-3_Ordering and Comparing Numbers Worksheet and KEY)&nbsp;<br>- Order Up game (M-2-1-3_Game Board)&nbsp;<br>- place-value number cubes (hundreds, tens, ones) for each partnership&nbsp;<br>- pencil&nbsp;<br>- base-ten blocks</p>

<p>- Watch students work through the M-2-1-3_Ordering and Comparing Numbers Worksheet and KEY to see how they are ordering and comparing numbers.&nbsp;<br>- Watch students playing the game Order Up (M-2-1-3_Game Board).&nbsp;<br>- Watch how students react as they go through instructional procedures.</p>

<p>Explicit instruction, modeling, scaffolding, and active engagement<br>W: Explain to the class that they will be sorting and comparing three-digit numbers in this lesson.&nbsp;<br>H: Students will engage in Order Up and Number Tile activities.&nbsp;<br>E: Using number tiles, students will determine which place to put the tiles to create the largest and smallest numbers—hundreds, tens, or ones.&nbsp;<br>R: Students will consider how well they understand ordering and comparing numbers as a result of the pre-, during, and post-lesson questions.&nbsp;<br>E: Use the worksheet on ordering and comparing numbers as well as the answers to the questions you answered during the lesson to gauge your level of comprehension.&nbsp;<br>T: You can modify the lesson by implementing the ideas mentioned in the Extension section.&nbsp;<br>T: The Extension section's recommendations can be used to modify the lesson.&nbsp;<br>O: The goal of the lesson is to go over and expand on the idea of comparing and ordering numbers. Students are required to use the same tiles to create multiple three-digit numbers. Students will generate the largest and smallest numbers. Students are going to go over and practice the &lt;, &gt;, and = symbols.&nbsp;</p>

<p><strong>Part 1</strong><br><br>Get students to choral count as you start the lesson.<br><br><strong>"Count forward by 10s, starting at 132."</strong>&nbsp;Make students stop at 232.&nbsp;(132, 142, 152, 162, 172, 182, 192, 202, 212, 222, 232)<br><strong>“Count forward by 5s, starting at 385.”</strong>&nbsp;Make students stop at 445.&nbsp;(385, 390, 395, 400, 405, 410, 415, 420, 425, 430, 435, 440, 445)<br><strong>“Count forward by 100s, starting at 570.” </strong>Make students stop at 1,070.&nbsp;(570, 670, 870, 970, 1070).<br><strong>“Count backward by 100s, starting at 842.”</strong>&nbsp;Make students stop at 42.&nbsp;(842, 742, 642, 542, 442, 342, 242, 142, 42)<br><strong>“Count backward by 5s, starting at 745.”&nbsp;</strong>Make students stop at 690.&nbsp;(745, 740, 735, 730, 725, 720, 715, 710, 705, 700, 695, 690)<br><strong>“Count backward by 10s, starting at 360.”</strong>&nbsp;Make students stop at 280.&nbsp;(360, 350, 340, 330, 320, 310, 300, 290, 280)<br><br><strong>Part 2</strong><br><br><strong>"Can any of you count to 1,000? What is the largest number you can count to 1,000 if you are counting?"&nbsp;</strong><i>(1000)</i> Put this in writing on the board's right side.<br><strong>"What is the smallest number?"</strong><i><strong>&nbsp;</strong>(1)</i> Put this in writing on the board's left side.<br><strong>"Choose a number from 1 to 1,000."</strong>&nbsp;When a student is called upon, write their number in the center of the board.<br><strong>"Select a smaller amount."</strong> When a student is called upon, write their number on the board between 1 and the student-choice number that is written in the center.<br><strong>"Select a larger number."</strong>&nbsp;Reach out to a student and record their number by writing it between the student's choice number that is written in the center of the board and 1,000.<br><strong>"You will be participating in a game in pairs. Building the biggest number you can is the aim of the game."</strong><br><br>Draw three horizontal lines on the board. __________ __________ _____________________<br><br><strong>"I'm going to pull three numeral tiles out of a container. You will choose which line to put each number on—line 1, line 2, or line 3—after I have drawn it. A number cannot be removed once it is recorded."</strong><br><br>Pick one tile to draw from the collection. Display the tile in front of the class. <strong>"What line ought this number to appear on?"</strong>&nbsp;Once they've written their response on the board, put the tile back in the jar and draw another one. Show the tile to the students.&nbsp;<strong>"What line should this number go on?"</strong>&nbsp;Once they've written their response on the board, put the tile back in the jar and draw another one. After displaying the last tile to the class, write the number on the blank line.<br><br>Make someone read the number voluntarily.&nbsp;<strong>"Is this the biggest number that we could have made?"</strong>&nbsp;Write and circle the greatest number that the students could have made on the board.<br><br><strong>"What is the smallest number you could have made?"&nbsp;</strong>Put the students' answers in writing on the board.<br><br><strong>"You will now play a game where the objective is to create the largest number, just like the class did. I'll pair you up, and your task will be to collaborate to generate the largest possible number."</strong><br><br>Pair up the students. Give a copy of the Comparing Numbers Group Activity sheet (M-2-1-3_Comparing Numbers Group Activity) to every student.<br><br>Make a tile. Students choose where to place the number after you read it to them in groups. In the bucket, swap out the tile. Additionally, let the students know that once they write down a number, they cannot alter it. Students' papers should bear the group's selection for the number placement.<br><br>Students should choose where to put the second tile's number after it is drawn.<br><br>Each group should write the number on the line that remains after drawing the third tile.<br><br>Ask a volunteer from every group to approach the board and write their number there. Assign the student volunteer to read the class his or her assigned number.<br><br><strong>"What is the largest number?"&nbsp;</strong>Put a circle around it.&nbsp;<strong>"What makes you believe that this is the largest number?"</strong><br><br>Ask students to fill in the first line of their paper with the largest number.&nbsp;<strong>"What is the second-largest number? Why ?"&nbsp;</strong>Ask students to fill in line two of their papers with the number that they saw on the board.<br><br>Once you have determined the next largest number, repeat this process with the remaining numbers on the board.<br><br>To play games 2 and 3, follow the same procedures as in game 1. Students should write the numbers in game 3 from least to greatest rather than greatest to least.<br><br>Next, say,<strong> "I am going to write some symbols on the board."</strong>&nbsp;Write &gt; and =. <strong>"This symbol represents greater than,"</strong> say, pointing to &gt;.&nbsp;Put 127 &gt; 120 in the marker and write,<strong> "One hundred twenty-seven is greater than one hundred twenty."</strong>&nbsp;Say, <strong>"This symbol represents less than,"</strong> while pointing to the &lt; symbol.&nbsp;Put 451 &lt; 845 and write, <strong>"Four hundred fifty-one is less than eight hundred forty-five."&nbsp;"This symbol stands for equal to or the same as," </strong>you can say, pointing to the = symbol.&nbsp;Write 53 = 53 and say, <strong>"Fifty-three equals fifty-three."&nbsp;</strong><br><br>Draw attention to the fact that the less-than and greater-than symbols resemble an open mouth.<strong> "Would you rather have 20 cookies or 80 cookies?"</strong> asked the class.<i>&nbsp;(80)</i> Write 20 &lt; 80, highlighting how the symbol resembles a mouth devouring the larger number. <strong>"Which would you prefer: two donuts or seventeen donuts?"&nbsp;</strong><i>(17) </i>Put 17 &gt; 2, highlighting the fact that the symbol resembles a mouth devouring the larger number.<br><br>Students should be asked which symbols fit in the following examples:<br><br>235&nbsp;&nbsp;&nbsp;&nbsp; 352&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&lt;)<br><br>768&nbsp;&nbsp;&nbsp;&nbsp; 712&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&gt;)<br><br>165&nbsp;&nbsp;&nbsp;&nbsp; 165&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(=)<br><br>545&nbsp;&nbsp;&nbsp;&nbsp; 554&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&lt;)<br><br>213&nbsp;&nbsp;&nbsp;&nbsp; 123&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&gt;)<br><br>As the appropriate symbols are inserted, have the students chorally read the examples.<br><br>Provide a copy of the M-2-1-3_Ordering and Comparing Numbers Worksheet and Key to every student. Let them practice ordering and comparing numbers. While the students complete the worksheet, go around the classroom observing and clarifying things for those who don't understand how to order and compare numbers and who need more attention.<br><br><strong>Extension:</strong><br><br><strong>Routine:</strong> Partners play Order Up (M-2-1-3_Game Board). A set of place-value number cubes and a game board are required for every pair of students.<br><br>First box: 1, last box: 1,000. Each player writes one in each box. The goal is to generate a three-digit number by rolling all three place-value number cubes by Player 1. Somewhere between 1 and 1,000 is the number that he or she writes on their game board. Player 2 follows suit. To create a three-digit number and write it on their game board in the proper order, players must keep taking turns rolling the number cubes. The player whose boxes are filled in the most at the end of the allotted time wins.<br><br>More activities are listed under Related Resources.<br><br><strong>Small Group: </strong>Assist students in building each number they are ordering or comparing using base-ten blocks. Permit students to arrange and compare numbers using hundreds of&nbsp;charts and/or number lines.<br><br><strong>Expansion:</strong> Students will sketch three number tiles and write the six possible combinations for the three number tiles in order of greatest to least. (1, 2, 3 would become 321, 312, 231, 213, 132, 123, for instance). After two more iterations of the procedure, students will compare their work to that of the other students who have finished the expansion.<br><br>Alternatively, students could create thousands of numbers by repeating the same exercise with four number tiles.</p>