<p>During this lesson, students will subtract two- and three-digit numbers. They will:&nbsp;<br>- use base-ten blocks to calculate the difference between two and three digit numbers.&nbsp;<br>- use the standard algorithm to calculate the difference between two and three digit numbers.&nbsp;</p>

<p>- What are the mathematical representations for relationships?&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>- An Alligator Wearing a Vest practice worksheet (M-3-6-3_An Alligator Wearing a Vest Practice Worksheet and KEY)<br>- Subtracting Multidigit Numbers practice worksheet (M-3-6-3_Subtracting Multidigit Numbers Practice Worksheet and KEY)<br>- Lesson 3 Exit Ticket (M-3-6-3_Lesson 3 Exit Ticket and KEY)</p>

<p>- The An Alligator Wearing a Vest practice worksheet (M-3-6-3_An Alligator Wearing a Vest Practice Worksheet with KEY) can be used to determine how well students can use the standard algorithms to add and subtract multidigit numbers.<br>- Use the Lesson 3 Exit Ticket (M-3-6-3_Lesson 3 Exit Ticket with KEY) to quickly assess students’ ability to subtract multidigit numbers using the standard algorithm.</p>

<p>Explicit instruction, modeling, scaffolding, and active engagement&nbsp;<br>W: Students will learn how to subtract two and three digit values using base-ten blocks and the standard algorithm. Students will discover that regrouping is often required in order to subtract.&nbsp;<br>H: Real-world examples will emphasize the need of learning to subtract multidigit numbers.&nbsp;<br>E: Encourage students to express subtraction with base-ten blocks. The use of base-ten blocks will help students understand the requirement for regrouping, which is common when subtracting multidigit numbers. These concrete examples will help students understand the standard algorithm for subtraction of multidigit numbers.&nbsp;<br>R: Students will model each subtraction problem with base-ten blocks before reviewing how the standard algorithm represents the same problem. The Subtracting Multidigit Numbers Practice Worksheet will be used in class. At the end of the lesson, students will complete the An Alligator Wearing a Vest practice worksheet to review multidigit addition and subtraction.&nbsp;<br>E: Students will be tested on their ability to correctly complete the Subtracting Multidigit Numbers and An Alligator Wearing a Vest practice worksheet. Students will also be evaluated with the Lesson 3 Exit Ticket.&nbsp;<br>T: The lesson can be changed to match the needs of the students by following the ideas in the Extension section. Specific suggestions are made to help students who may benefit from more practice in the Small Group, while the Expansion section offers extra challenges to students who have mastered the lesson concepts.&nbsp;<br>O: The lesson is scaffolded, with students first using base-ten blocks to subtract multidigit numbers. Students then use this experience to understand how the standard algorithm describes similar concrete situations. Students then use the standard algorithm to subtract multidigit numbers. Finally, students practice adding and subtracting multidigit numbers with the standard algorithms.</p>

<p><strong>Using Base-Ten Blocks to Subtract Two- and Three-Digit Numbers</strong><br><br>Write the following problem on the board. Introduce the problem. Ask students to use base-ten blocks to represent the greater number. After students have represented the greatest number, ask them, <strong>"How many baseball cards does Ryan have now?"</strong> Students will most likely begin to subtract or delete the smaller amount.<br><br>Example:<br><br>Ryan had 57 baseball cards. He gave 36 of the cards to his friends. How many baseball cards does Ryan have left?<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_12.png" width="534" height="190"><br><br>After students have determined the difference, ask them, <strong>"What operation did we use to calculate how many baseball cards Ryan has left?"</strong> Students are likely to recognize this as a subtraction problem. If not, focus on the fact that Ryan gave away some of the baseball cards. This is often how students think of subtraction: taking away or deleting a number.<br><br>Model for students to write the equation horizontally, as shown. The purpose is for students to recognize and write the subtractive equation. At this point in the lesson, students should concentrate on using base-ten blocks to calculate the difference. This experience will be used to support students when they transition to the standard algorithm for subtracting multidigit number later in this lesson.<br><br>Continue with the next examples. Write the first example on the whiteboard. Ask students to work in pairs on each example. When most of the students have finished, assign a pair of students to demonstrate the subtraction to the class and write the equation. Some of these situations require students to trade or regroup.<br><br>Example:<br><br>There are 482 students drinking milk at lunch. Of these students, 150 are drinking white milk. The rest are drinking chocolate milk. How many students are drinking chocolate milk?<br><br><img src="https://storage.googleapis.com/worksheetzone/images/pic 2.png" width="505" height="181"><br><br>Example:<br><br>Anya had $63. She spent $48. How much money does Anya have left?<br><br><img src="https://storage.googleapis.com/worksheetzone/images/pic 3.png" width="536" height="183"><br><br>Example:<br><br>Hiro wants to visit his grandma. The flight will cost $375. Hiro has already saved $239. How much more does he need to save?<br><br><img src="https://storage.googleapis.com/worksheetzone/images/pic 4.png" width="555" height="196"><br><br>Example: 417 – 164<br><br><img src="https://storage.googleapis.com/worksheetzone/images/pic 5.png" width="554" height="191"><br><br>Distribute a copy of the Subtracting Multidigit Numbers Practice Worksheet (M-3-6-3_Subtracting Multidigit Numbers Practice Worksheet and KEY) and base-ten blocks to each student. Divide at least 10 hundreds, 15 tens, and 20 ones among each pair of students. Ask students to work in pairs to calculate the sums.&nbsp;<br><br>Instruct students to construct the greater number with base-ten blocks and subtract the base-ten blocks representing the lesser number to get the difference. Before students begin, use the examples to show them how to draw hundreds with squares, tens with vertical line segments, and one with dots. This will help them record their work more efficiently.<br><br><strong>"Find the differences using base-ten blocks. Draw the base-ten blocks you used, then cross off the ones you removed. As shown in the examples, use squares for hundreds, lines for tens, and dots for one. This will make it easy to draw the blocks you chose. Complete the equation as well."&nbsp;</strong><br><br>Ask students not to fill out the box on the right side of each example. This area will be used to help students learn the standard algorithms.&nbsp;<br><br>When students have finished the exercises, teach them how to use the standard algorithm for subtraction. Use the standard algorithm to describe counting and trading base-ten blocks, as well as determining the correct difference for each example.<br><br><strong>The Standard Algorithm for Subtraction</strong><br><br>First, have students write the numbers vertically for each example. Then explain how this permits place values to be subtracted. To explain the standard algorithm, begin with the ones, regrouping or trading if needed, and then continuing with each place value from right to left. Be sure to make the connections to finding the differences with base-ten blocks. It is important to teach students that a 1 is written above a place value when 10 of one type of base-ten block is exchanged for 1 of another in order to have enough to subtract from. This allows students to truly understand the standard algorithm and apply it with higher accuracy.<br><br><strong>Extension:</strong></p><p><br>Return to the use of base-ten blocks to help students who could benefit from more practice subtracting two- and three-digit numbers. Specific resources for these students are listed in the Small Groups section.&nbsp;<br>Students who are ready for a new challenge should be taught to subtract four and five-digit numbers. Specific strategies for supporting these students are provided in the Expansion section.<br><br><strong>Routine:</strong> As real-life situations arise during the school year, have students practice subtracting multidigit numbers, such as determining how many more books one third grade class read than another, how much more money one classroom raised for the school through fundraising activities than another, and so on. Many problem-solving exercises throughout the curriculum will likely make use of students' skills to add multidigit numbers.<br><strong>Small group:</strong> Students that require more practice can be divided into small groups to concentrate on subtracting two- and three-digit integers using the standard algorithm. One student from the group should roll a ten-sided number cube. The first number rolled is in the tens, while the second number is in the ones place. A second student should repeat the process to generate another two-digit number. Every student should write down both two-digit numbers. Students should be encouraged to subtract these two-digit numbers. It will be important to listen carefully in order to discover and correct mistakes in their thinking. The process should then be repeated with number cubes to generate three-digit numbers and find the difference.<br><br>This website offers free printable worksheets for students who need further practice adding whole numbers:<br><a href="http://www.sssoftware.com/freeworksheets/subtraction.html">http://www.sssoftware.com/freeworksheets/subtraction.html</a><br><br><strong>Expansion:</strong> Students looking for a challenge can form groups of two or three to play the following game. The first student must roll a ten-sided number cube four times. Each rolled number should be recorded and used as one of the four digits of a whole number. The second student should do the same thing, producing a second four-digit whole number. Each player should work independently to get the difference of these numbers. After all differences have been computed, one player should use a calculator to determine the sum. Any player with the correct sum wins one point. The first student to earn ten points is the winner.</p>