<p>Students will use splitting to add and subtract three-digit numbers throughout this unit. Students are going to:<br>- divide each addend into ones, tens, and hundreds. Afterward, they will compute the total of the two initial addenda by adding the sums of the ones, tens, and hundreds.<br>- divide the minuend into ones, tens, and hundreds. To find the difference, they will then remove the ones, tens, and hundreds from the subtrahend.</p>

<p>- What mathematical representations exist for relationships?<br>- How does effective communication benefit from mathematics?<br>- How can numbers be represented, compared, quantified, and modeled using mathematics?<br>- What does it mean to evaluate or estimate a numerical quantity?<br>- What qualifies a tool or strategy as suitable for a particular task?</p>

<p>- Expanded Form: A way to write numbers that shows the value of each digit (e.g., 4,372 = 4,000 + 300 + 70 + 2).</p>

<p>- whiteboard for each student&nbsp;<br>- whiteboard marker for each student&nbsp;<br>- whiteboard eraser for each student&nbsp;<br>- Adding and Subtracting by Splitting Worksheet (M-2-2-2_Adding and Subtracting by Splitting Worksheet and KEY)&nbsp;<br>- Top-It directions (M-2-2-1_Top-It Directions)&nbsp;<br>- Beat the Calculator directions (M-2-2-1_Beat the Calculator Directions)&nbsp;<br>- number cards&nbsp;<br>- calculators&nbsp;<br>- paper&nbsp;<br>- pencils</p>

<p>- Utilize the M-2-2-2_Adding and Subtracting by Splitting Worksheet and KEY to assess students' ability to add and subtract three-digit numbers using splitting.</p>

<p>Direct Instruction, Modeling, Active Participation, and Scaffolding&nbsp;<br>W: Explain to the class that splitting numbers can be helpful when adding and subtracting.&nbsp;<br>H: Teach students the division of a three-digit number into ones, tens, and hundreds. Create a link with an&nbsp;extended form. (For instance, 745 and 700 + 40 + 5 are equivalent).&nbsp;<br>E: Using division, students will add and subtract three-digit numbers.&nbsp;<br>R: Students will consider their comprehension of splitting to add and subtract three-digit numbers as a result of the questions posed before, during, and following the lesson.&nbsp;<br>E: To assess students' comprehension of applying the splitting method to add and subtract three-digit numbers, use the Adding and Subtracting by Splitting Worksheet and their answers to the lesson's questions.&nbsp;<br>T: You can modify the lesson by implementing the ideas mentioned in the Extension section.&nbsp;<br>O: The goal of the lesson was to improve the students' comprehension of adding and subtracting three-digit numbers. From using base-ten blocks to using pictures of base-ten blocks, to splitting, students progress.&nbsp;</p>

<p><strong>"In the previous session, we used base-ten blocks to add and subtract three-digit numbers. We're going to learn a tactic today called splitting.&nbsp;When you hear the term "splitting," what comes to mind?</strong> (Answers will differ.)&nbsp;<strong>We can split numbers to aid in addition and subtraction, just as we can split the items you mentioned. This approach makes use of our understanding of expanded form. After writing each number in expanded form, we add the hundreds, tens, and ones. The sum of each is then added."</strong><br><br>On the whiteboard, write 453 + 245 =.<strong> "With this, I can write 453."&nbsp;</strong>On the whiteboard, write 400 + 50 + 3.&nbsp;<strong>"With this, I can write 245."</strong>&nbsp;On the whiteboard, write 200 + 40 + 5.&nbsp;<strong>"It allows me to add my ones, tens, and hundreds together in this way."</strong>&nbsp;Write 400 + 200 = 600, 50 + 40 = 90, and 3 + 5 = 8 on the board, respectively. <strong>"I can add 600 + 90 + 8 right now. This equals 698, so&nbsp;453 + 245 equals 698."</strong><br><br><strong>"Allow me to give you one more."&nbsp;</strong>On the whiteboard, write 138 + 451 =.&nbsp;<strong>"With this, I can write 138."</strong>&nbsp;On the board, write 100 + 30 + 8.&nbsp;<strong>"With this, I can write 451."</strong>&nbsp;On the board, write 400 + 50 + 1.&nbsp;<strong>"It allows me to add my ones, tens, and hundreds together in this way."&nbsp;</strong>On the board, write: 8 + 1 = 9, 30 + 50 = 80, and 100 + 400 = 500. <strong>"I can now add 500 + 80 + 9. This adds up to 589; thus, 138 +&nbsp;451 equals 589."</strong><br><br><strong>"Now let's do one together."&nbsp;</strong>On the board, write 432 + 325 =.&nbsp;<strong>"Write the expanded form of 432 on your whiteboard."</strong>&nbsp;Ask a student to stand up and write the number 432 in extended&nbsp;form&nbsp;on the board.&nbsp;(400 + 30 + 2)<br><br><strong>"Now, on your whiteboard, write 325 in expanded form."&nbsp;</strong>Allow a student to come up to the board and write 325 in expanded form. (300 + 20 + 5) <strong>"Now add up all of your hundreds." </strong>A student should step forward and write 400 + 300 = 700 on the board.<strong>&nbsp;"Now get your tens."</strong> Have a student come forward and write 30 + 20 = 50 on the board.<strong> "After that, your ones."&nbsp;</strong>Ask a&nbsp;student to stand up and write 2 + 5 = 7 on the board.<strong>&nbsp;"Combine your totals for the ones, tens, and hundreds at the end." </strong>Have a student approach and write the following on the board: 700 + 50 + 7 = 757.<br><br><strong>"Let's try one more together."&nbsp;</strong>On the board, write 267 + 202 =.&nbsp;<strong>"Write 267 on your whiteboard in expanded form."</strong>&nbsp;Bring up a student to write the expanded form of 267 on the board. (200 + 60 + 7)&nbsp;<strong>"Now, on your whiteboard, write 202 in expanded form."&nbsp;</strong>Bring up 202 and ask a student to write it on the board in expanded form. (200 + 2 or 200 + 0 + 2)<strong>&nbsp;"Now add up all of your hundreds."</strong>&nbsp;Approaching the board, ask a student to write 200 + 200 = 400.<strong>&nbsp;"Now get your tens."&nbsp;</strong>Ask a student to stand up and write on the board, 60 + 0 = 60.<strong>&nbsp;"And your ones now."</strong>&nbsp;Ask a student to stand up and write the equation 7 + 2 = 9 on the board. "<strong>Lastly, total up the hundreds, tens, and ones." </strong>Ask a student to stand up and write the equation 400 + 60 + 9 = 469 on the board.<br><br><strong>"We can also use splitting to solve three-digit subtraction problems."&nbsp;</strong>On the board, write 789 – 352 =.<strong>&nbsp;"With this, I can write 789."</strong>&nbsp;On the board, write 700 + 80 + 9.<strong>&nbsp;"With this, I can write 352."</strong>&nbsp;Write on the board: 300 + 50 + 2.&nbsp;<strong>"Now I have to deduct my hundreds, then my tens, and finally my ones like this to find the difference."</strong>&nbsp;On the board, write the following: 700 – 300 = 400; 80 – 50 = 30; and 9 – 2 = 7.&nbsp;<strong>"I now total these differences to determine the difference between 789 and 352, as shown here."&nbsp;</strong>Write on the board: 400 + 30 + 7 = 437.<br><br><strong>"Let's try one together."</strong> Indicate on the board that 865 – 420 =.&nbsp;Ask a student to come up and write 800 + 60 + 5 on the board after you say,<strong> "Write 865 in expanded form on your whiteboard.&nbsp;Write 430 in expanded form on your whiteboard."</strong> Ask a student to approach the board and inscribe 400 + 30 + 0.&nbsp;<strong>"Now we have to subtract the ones, tens, and hundreds to find the difference." </strong>Ask a student to come up and write 800 – 400 = 400 on the board. Ask a different student to approach and write 60 - 30 = 30 on the board. Ask a different pupil to stand up and write 5 – 0 = 5 on the board.&nbsp;<strong>"Let's combine these variations to determine the 865–430 difference."</strong> Have a student approach and write 400 + 30 + 5 = 435 on the board, so 865 – 430 = 435.&nbsp;Write this down on the whiteboard.<br><br><strong>"Now, to assist you in solving addition and subtraction problems, apply the splitting strategy."</strong>&nbsp;Give copies of the Adding and Subtracting by Splitting Worksheet (M-2-2-2_Adding and Subtracting by Splitting Worksheet and Key) to every student. Examine which students can add and subtract three-digit numbers using the splitting strategy by moving around the room, offering clarification when needed, and determining which students need more time to learn.<br><br><strong>Extension:</strong><br><br><strong>Routine: </strong>Students use the M-2-2-1_Top-It Directions and M-2-2-1_Beat the Calculator Directions to play Top-It and/or Beat the Calculator. For computational assistance, students can divide the ones, tens, and hundreds. Students can also engage in gaming through the Related Resources list.<br><br><strong>Small Group: </strong>Utilizing the splitting strategy, walk students through additional two- and three-digit addition and subtraction problems by following the steps and questions outlined in the Instructional Procedures.<br><br><strong>Expansion:</strong><br><br>Students use three-digit numbers to write addition and subtraction number stories.<br>Students use M-2-2-1_Top-It Directions and M-2-2-1_Beat the Calculator Directions to play the recommended Extensions for Top-It and/or Beat the Calculator.<br>Students demonstrate their thought processes by adding four-digit numbers.</p>