<p>During this unit, students will use jumping to add and subtract three-digit numbers. Students are going to:&nbsp;<br>- use a blank number line as a visual aid to demonstrate their work.&nbsp;<br>- leap 100s, 10s, and 1s forward and backward.&nbsp;<br>- calculate the difference between two numbers to get the next or previous decade more effectively.</p>

<p>- What mathematical representations exist for relationships?&nbsp;<br>- How does effective communication benefit from mathematics?&nbsp;<br>- How can numbers be 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>- Decompose: Breaking apart a number into two equal parts (e.g., 6 can be decomposed into 1 and 5, 2 and 4, or 3 and 3).</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 Jumping Worksheet (M-2-2-3_Adding and Subtracting by Jumping 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>- Watch the students as they work through the M-2-2-3_Adding and Subtracting by Jumping Worksheet and KEY to see how they add and subtract.&nbsp;<br>- Observe student reactions during Instructional Procedures.&nbsp;<br>- Watch the students as they engage in the games found in the Related Resources, Beat the Calculator, and/or Top-It.</p>

<p>Explicit instruction, modeling, scaffolding, and active engagement&nbsp;<br>W: Explain to the students that adding and subtracting numbers can be done with the help of a number line.&nbsp;<br>H: Show a blank line of numbers. Tell students that this is the tool they will be using to practice adding and subtracting three-digit numbers.&nbsp;<br>E: Using an empty number line, students will add and subtract three-digit numbers.&nbsp;<br>R: Students will consider how well they understand adding and subtracting three-digit numbers using an empty number line as a result of the questions posed before, during, and after the lesson.&nbsp;<br>E: To assess understanding of using an empty number line to add and subtract three-digit numbers, use the Adding and Subtracting by Jumping Worksheet and the answers to the questions throughout the lesson.&nbsp;<br>T: You can modify the lesson by implementing the ideas mentioned in the Extension section.&nbsp;<br>O: The purpose of the lesson was to improve the students' comprehension of adding and subtracting three-digit numbers. Next, the students use pictures of base-ten blocks, split the blocks, jump on an empty number line, and then use base-ten blocks themselves.&nbsp;</p>

<p>First, assign the following choral counting exercises to your students:<br><br><strong>“Count forward by 100s, starting at 145, until I tell you to stop.”</strong>&nbsp;Stop students at 945.&nbsp;(145, 245, 345, 445, 545, 645, 745, 845, 945)<br><strong>“Count forward by 100s, starting at 279 until I tell you to stop.”&nbsp;</strong>Stop students at 1079.&nbsp;(279, 379, 479, 579, 679, 879, 979, 1079)<br><strong>“Count backward by 100s, starting at 932 and continuing until I tell you to stop.”</strong>&nbsp;Stop students at 32.&nbsp;(932, 832, 732, 632, 532, 432, 332, 232, 132, 32)<br><strong>“Count backward by 100s, starting at 1064 until I tell you to stop.”</strong>&nbsp;Stop students at 164.&nbsp;(1064, 964, 864, 764, 664, 564, 464, 364, 264, 164)<br><strong>“Count forward by 10s, starting at 264 until I tell you to stop.”</strong>&nbsp;Stop students at 344.&nbsp;(264, 274, 284, 294, 304, 314, 324, 334, 344)<br><strong>“Count backward by 10s, starting at 321 until I tell you to stop.” </strong>Stop students at 281.&nbsp;(321, 311, 301, 291, 281)<br><br><strong>"We divided each three-digit number into hundreds, tens, and ones in the previous lesson and added and subtracted them. I will demonstrate another method for adding and subtracting numbers to you today. It is known as jumping. An empty number line is used to record the jumps made when utilizing the jumping strategy. First, we jump forward or backward by 100s, then by 10s, and lastly by 1s. I will model this for you.”</strong><br><br>545 + 178 = on the board. Draw a line, place a dot on the left side, and label that dot 545. Say, <strong>"The second addend is 178. 178 has 100, so we jump from 545 to 100."</strong> Move the arrow forward from 545 on the number line and write +100. <strong>"If you jump from 545 to 100, you end up with 645.''</strong> Place a dot on the number line and write 645. <strong>"There are 7 10s in the number 178. 7 10 is 70, so jump forward 70."</strong> While counting the jumps, draw an arrow, write +10, draw a dot on the number line, and mark the number you landed on. Write and record it on the number line.<strong> "655, 665, 675, 685, 695, 705, 715. There are eight in the number 178, so we jump eight places forward from 715."</strong> 8 turns out he can break it down into two parts. <strong>"We know we can jump over 5 to get to 720, so we break down 8 into 5 and 3. That way we can jump three more to 723. ”</strong> After the equal sign, write 723. Write 268 + 237 = on the board.&nbsp;<br><br>Walk students through the process above. Be sure to use a number line to model what you want your students to do on the number line.&nbsp;<br><br><strong>"Where does the empty number line start?''</strong> Students draw a line on the board, place a dot on the left, and label it 268.&nbsp;<br><br><strong>"How many hundreds do you jump?'' </strong><i>(2)</i> Students jump 100, draw an arrow, write +100, place a dot on the number line, and label it 368. Students jump another 100, draw an arrow, write +100, place a dot on the number line, and label it 468.&nbsp;<br><br>Continue this process by asking the following questions and directing students to work on the number line:&nbsp;<br><br><strong>"How many tens do you jump?'' </strong><i>(3)&nbsp;</i><br><strong>"How many ones do you jump?'' </strong><i>(7)&nbsp;</i><br><strong>"What would you break down 1 into to arrive at the next decade (or set of decades)?''</strong> <i>(2 and 5)&nbsp;</i><br><br>Then use an empty number line. to model this subtraction problem 645 - 257 =. Follow the same steps as modeling the addition problem. Make sure to start on the right side of the number line so you can jump backward. Write 762 – 325 = on the board. Guide students through the process of jumping backward on a blank number line by asking the following questions about number line work.&nbsp;<br><br><strong>"What number should you write on the number line first?'' </strong><i>(762)&nbsp;</i><br><strong>''Would you like to write this number next to the number line?'' </strong><i>(Right)&nbsp;</i><br><strong>"How many ones of jumps back? </strong><i>(5)&nbsp;</i><br><strong>"How many tens of jumps back?" </strong><i>(2)&nbsp;</i><br><strong>"How many hundreds of jumps back?" </strong><i>(3)</i><br><strong>"What would you break down to get the previous decade (or group of 10)?"</strong><i> (2 and 3)&nbsp;</i><br><br><strong>"Then use the blank number line to solve addition and subtraction problems. I'll solve it."</strong> Distribute a copy of the Jump Addition and Subtraction Worksheet (M-2-2-3_Jump Addition and Subtraction Worksheet and KEY) to each student. Move around the room to observe and ask clarifying questions to assess which students can add and subtract three-digit numbers using an empty number line and which students need additional investigation.<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. When learning to compute, students can utilize an empty number line. Students can engage in the games found under Related Resources.<br><strong>Small Group: </strong>Use the empty number line to lead students through more addition and subtraction problems if they require more exploration. Utilize the same questions you asked in Instructional Procedures to help them along. Use two-digit numbers to practice the leaping concept with students who are struggling with three-digit numbers.<br><br><strong>Expansion:&nbsp;</strong><br>Students use three-digit numbers to write number stories (addition and subtraction).<br>Students use the recommended Top-It and/or Beat the Calculator Extensions (M-2-2-1_Top-It Directions and M-2-2-1_Beat the Calculator Directions) to play.<br>Students demonstrate their thinking by adding four-digit numbers.</p>