<p>In this lesson, students will add two- and three-digit numbers. They will:&nbsp;<br>- calculate the sum of two and three-digit numbers using base-ten blocks.&nbsp;<br>- use the standard algorithm to calculate the sum of 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>- A Teacher and A Train practice worksheet (M-3-6-2_A Teacher and A Train Practice Worksheet and KEY)<br>- Adding Multidigit Numbers practice worksheet and (M-3-6-2_Adding Multidigit Numbers Practice Worksheet and KEY)<br>- Lesson 2 Exit Ticket (M-3-6-2_Lesson 2 Exit Ticket and KEY)</p>

<p>- Use the A Teacher and A Train practice worksheet (M-3-6-2_A Teacher and A Train Practice Worksheet with KEY) to assess student mastery.&nbsp;<br>- The Lesson 2 Exit Ticket (M-3-6-2_Lesson 2 Exit Ticket and KEY) can be used to evaluate students’ understanding of using the standard algorithm to add multidigit integers.</p>

<p>Explicit instruction, modeling, scaffolding, and active engagement&nbsp;<br>W: Students will learn to add two- and three-digit numbers using base-ten blocks and the standard algorithm. Students will understand that regrouping is necessary when the sum in any place value is greater than or equal to ten.&nbsp;<br>H: Introduce Hussein and his interest in calculating the sum of two-digit numbers. Hook students by providing this real-world example to emphasize the importance of learning how to add multidigit numbers.<br>E: Encourage students to represent addition with base ten blocks. Using base-ten blocks, students will experience the need for regrouping, which is common when adding multidigit numbers. This will provide students with practical experiences that will help them in mastering the standard algorithm for adding multidigit integers.&nbsp;<br>R: Students will model addition problems with base-ten blocks and review the standard algorithm. The Adding Multidigit Numbers Practice Worksheet will be used in class. At the end of Lesson 3, students will use the An Alligator Wearing a Vest practice worksheet to review addition and subtraction of multidigit numbers.<br>E: Students will be evaluated based on their responses to the Adding Multidigit Numbers practice worksheet. Students will also be evaluated with the Lesson 2 Exit Ticket.&nbsp;<br>T: The lesson can be adapted to meet the needs of students using the suggestions in the Extension section. Specific suggestions are made to help students who may benefit from more practice, while the Expansion section offers extra challenges to students who have mastered the lesson concepts.<br>O: The lesson is scaffolded so that students first use base-ten blocks to add multidigit integers. Students then use this experience to understand how the standard algorithm describes similar concrete situations. Finally, students practice using the standard algorithm to add multidigit numbers.</p>

<p>This lesson focuses on adding two and three digit numbers. To prepare students for the lesson, review how to represent two and three-digit numbers with base-ten blocks.<br><br><strong>Review: Representing Numbers Using Base-Ten Blocks</strong><br><br>Discuss the following examples as a class. 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.<br><br>Use base-ten blocks to present the first example. Ask a student to come to the front of the class to explain what number is represented and how the student determined that. Continue displaying the samples and asking students to clarify the numbers represented. Many of the examples ask students to swap 10 ones for 1 ten or 10 tens for 1 hundred. This is intentional because regrouping or trading is frequently required when addition or subtracting multidigit numbers, which is the topic of this and the following lesson.<br><br>Begin the lecture by asking students to help Hussein. <strong>"Hussein asked if we can help. He had $35. He earned $12 more. Hussein wants help deciding how much money he has now. Today we'll learn how to add two and three digit integers. For example, we'll learn how to add 35 and 12 to help Hussein, as well as how to add some larger numbers. First, let us recall how we express these numbers with base-ten blocks.”</strong><br><br>Review these examples as a class. A collection of examples is provided; however, you may ask a student to represent a number with base-ten blocks and then have the class determine the number.<br><br>Use base-ten blocks to represent the first number, as shown here.<br><br><strong>“What number is represented by these base-ten blocks?”</strong><br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_3.png" width="260" height="140"><br><br>First, assign students to work alone to identify the number represented. If personal white boards are available for students, ask students to remain quiet and write their answers on whiteboards. When everyone has completed, ask students to hold up their personal whiteboards so that you may quickly assess their understanding. [Plastic report covers with white or light-colored cardstock inside serve as an alternative for personal whiteboards. Small squares of fleece fabric make good erasers.]<br><br><strong>“What numbers is represented by these base-ten blocks?”</strong><br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_4.png" width="266" height="140"><br><br>The following examples are purposely in that students must regroup or trade. For example, in the first example, 10 ones must be exchanged for 1 ten. In the second example, 10 tens must be traded for 1 hundred.<br><br><strong>“What number is represented by these base-ten blocks?”</strong><br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_5.png" width="460" height="158"><br><br><strong>“What number is represented by these base-ten blocks?”</strong><br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_6.png" width="456" height="159"><br><br>Continue with the question, <strong>"Are there any other ways to represent 120 using base-ten blocks?"</strong> Other examples that students may be able to provide are 120 ones, 12 tens, 7 tens, and 50 ones. The idea is to help students be adaptable in how they think about any given number. This will make students more prepared to trade and regroup as needed when adding and subtracting multidigit numbers in this and Lesson 3.<br><br><strong>Using Base-Ten Blocks to Add Two- and Three-Digit Numbers</strong><br><br><strong>“Remember Hussein? We are now ready to help him decide how much money he has.”</strong><br><br>Write the next problem on the board. Introduce the problem. Ask students to create models of the two different dollar amounts using base-ten blocks. If there are two different colors of base-ten blocks available, students can choose various colors to symbolize the sets. If not, students can just create the sets separately.<br><br><strong>“Hussein had $35. He earned $12 more. How much money does Hussein have now?”</strong><br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_7.png" width="308" height="146"><br><br>After the students have represented the dollar amounts, ask,<strong> "How much money does Hussein have now?"</strong> Students will most likely combine the sets and count the total.&nbsp;<br><br>After students have calculated the sum, ask them, <strong>"What operation did we use to determine how much money Hussein has now?"</strong> Students are likely to recognize this as an addition problem. If not, focus on the fact that there are two dollar amounts and the purpose is to add them together to determine the total. This is often how students think of addition, as the putting together of sets.<br><br>Model for students to write the equation horizontally, as shown. The purpose is for students to recognize and create an addition equation. At this point in the lesson, students should concentrate on using the base-ten blocks to calculate the sum. This experience will be used to help students move to the standard algorithm for adding multidigit numbers later in the class.&nbsp;<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 done, ask a pair of students to demonstrate the addition to the class and write the equation. Some of these situations require students to trade or regroup.<br><br>Example:<br><br>Anya had $23. She earned $38 more. How much money does Anya have now?<br><br><img src="https://storage.googleapis.com/worksheetzone/images/5.png" width="422" height="191"><br><br>Example:<br><br>The grocery store donated $147 to the food shelf. The school donated $250 to the food shelf. How much money did they donate to the food shelf in all? &nbsp;<img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_2345.jpeg" width="476" height="268"></p><p><br>The bank donated $265 to the food shelf. The hospital donated $189 to the food shelf. How much money did the bank and hospital donate together?<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_8.png" width="474" height="278"><br>&nbsp;</p><p>Distribute a copy of the Adding Multidigit Numbers Practice Worksheet (M-3-6-2_Adding Multidigit Numbers Practice Worksheet and KEY) to each student. Ask students to work in pairs to calculate the sums. Distribute at least 10 hundreds, 15 tens, and 20 ones to each pair of students.&nbsp;<br><br>Instruct students to construct the numbers using base-ten blocks and use the blocks to calculate the sums. 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 to record their work more efficiently.<br><br><strong>"Build the numbers with base-ten blocks. Draw the base-ten blocks that you used. 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 assist students learn the standard algorithms.<br><br>When the students have finished the examples, teach them how to use the standard algorithm for addition. Use the standard algorithm to discuss the counting and trading of base-ten blocks, as well as determining the right sum in each example.<br><br><strong>The Standard Algorithm for Addition</strong><br><br>First, have students write the numbers vertically for each example. Then explain how this allows the place values to be added. To explain the standard algorithm, begin with the ones, regrouping or trading if needed, and then proceed with each place value from right to left. Make sure to link the base-ten blocks to find the sums. 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 traded for 1 of another. This allows students to truly understand the standard algorithm and apply it with higher accuracy.<br><br>Students can then complete the A Teacher and A Train practice worksheet (M-3-6-2_A Teacher and A Train Practice Worksheet and KEY) as a class or homework assignment. This can be used to examine students knowledge of the standard algorithm for adding multidigit numbers.<br><br><strong>Extension:</strong><br><br>Return to the use of base-ten blocks to help students who could benefit from more practice adding 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 add four and five-digit numbers. Specific strategies for supporting these students are provided in the Expansion section.&nbsp;<br><br><strong>Routine:</strong> As real-life situations arise during the school year, have children practice adding multidigit numbers, such as adding the number of books read in different third grade classrooms, calculating the total amount raised from fundraising activities, 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 adding two- and three-digit integers using the standard algorithm.<br>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 add 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 calculate the sum.<br><br>If students continue to struggle, go back to use base-ten blocks to teach multidigit addition. Make sure to record each step following the standard algorithm.&nbsp;<br><br>This website offers free printable worksheets for students who need further practice adding whole numbers:<br><br>http://www.sssoftware.com/freeworksheets/addition.html<br><br><strong>Expansion:</strong> Students looking for a challenge can form groups of two or three to play the following game.<br>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 sum of these numbers. After all sums 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. If students need more of a challenge, this game can be adjusted to focus on the addition of five-digit numbers.</p>