• Use the A Teacher and A Train practice worksheet (M-3-6-2_A Teacher and A Train Practice Worksheet and KEY.docx) to evaluate levels of student mastery.
• The Lesson 2 Exit Ticket (M-3-6-2_Lesson 2 Exit Ticket and KEY.docx) can be used to assess students’ understanding of using the standard algorithm to add multidigit numbers.

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 using base-ten blocks.

Review: Representing Numbers Using Base-Ten Blocks

As a class, discuss the following examples. Be sure to show these examples using base-ten blocks that can easily be seen by all students in the class. This can be done using large magnetic demonstration base-ten blocks and a whiteboard, virtual base-ten blocks and an interactive whiteboard, base-ten blocks and a document camera, or overhead base-ten blocks and an overhead projector.

Use base-ten blocks to display the first example. Ask for a student to come to the front of the class to explain what number is represented and how the student determined that. Continue displaying each of the examples and asking for students to explain the number represented. Notice many of the examples require students to either trade 10 ones for 1 ten or trade 10 tens for 1 hundred. This is purposeful in that regrouping or trading is often necessary when adding or subtracting multidigit numbers, which is the focus of this lesson and the next lesson.

Introduce the lesson by asking students to help Hussein. “Hussein asked if we can help him. He had $35. He earned $12 more. Hussein wants help deciding how much money he has now. Today we will learn to add two-digit and three-digit numbers. For example, we will learn how to add 35 and 12 to help Hussein, and even learn to add some larger numbers too. First, though, let’s remember how we represent these numbers using base-ten blocks.”

Review these examples as a whole class. A set of examples is provided; however, you might choose instead to ask a student to represent a number using base-ten blocks and then ask the class to identify the number.

Use base-ten blocks to represent the first number, as shown here.

“What number is represented by these base-ten blocks?”

First ask students to work alone to identify the number represented. If personal whiteboards are available for students, ask students to remain quiet and write their answers on whiteboards. When everyone is finished, ask students to hold their personal whiteboards up so you can quickly assess student understanding. [A substitute for personal whiteboards is plastic report covers with white or light-colored cardstock inside. Small squares of fleece fabric work well as erasers.]

“What number is represented by these base-ten blocks?”

The next examples are purposeful in that students need to regroup or trade. For example, in the first example that follows 10 ones need to be traded for 1 ten. In the second example, 10 tens need to be traded for 1 hundred.

“What number is represented by these base-ten blocks?”

“What number is represented by these base-ten blocks?”

Now ask, “Are there any other ways to represent 120 using base-ten blocks?” Students will likely be able to give other examples, such as 120 ones, 12 tens, 7 tens and 50 ones to name a few. The goal is to help students be flexible with the way they think about any given number. This will help them be more prepared to trade and regroup as needed when adding and subtracting multidigit numbers in this lesson and Lesson 3.

Using Base-Ten Blocks to Add Two- and Three-Digit Numbers

“Remember Hussein? We are now ready to help him decide how much money he has.”

Write the problem that follows on the board. Introduce the problem. Ask students to model the two different dollar amounts using base-ten blocks. If two different colors of base-ten blocks are available, students can represent the sets using different colors. If not, students can just build the sets separately.

“Hussein had $35. He earned $12 more. How much money does Hussein have now?”

$35 + $12 = $47

After students represent the dollar amounts, ask them, “How much money does Hussein have now?” Students will likely put the sets together and count the total.

After students have determined the total, ask them, “What operation did we use to determine how much money Hussein has now?” Students will likely be able to recognize this as an addition problem. If not, focus on the fact that there are two dollar amounts and the goal is to put them together and find the total. This is often how students think of addition, as the putting together of sets.

Model for students writing the equation horizontally, as shown. The goal is for students to recognize and write the addition equation. At this point in the lesson, students should focus on using the base-ten blocks to find the sum. This experience will then be used to support students as they transition to the standard algorithm for adding multidigit numbers later in this lesson.

Continue with the following examples. Write the first example on the board. Ask students to work together in pairs on each example. When most students have finished, ask a pair of students to show the addition to the class and write the equation. Notice that some of these examples require students to trade or regroup.

Example:

Anya had $23. She earned $38 more. How much money does Anya have now?

Example:

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?

The bank donated $265 to the food shelf. The hospital donated $189 to the food shelf. Together, how much money did the bank and hospital donate to the food shelf?

Distribute a copy of the Adding Multidigit Numbers practice worksheet to all students (M-3-6-2_Adding Multidigit Numbers Practice Worksheet and KEY.docx). Ask students to work in pairs to find the sums. Also, distribute at least 10 hundreds, 15 tens, and 20 ones to each pair of students.

Instruct students to build the numbers using base-ten blocks and use the blocks to find the sums. Before students begin, use the examples to explain to students how to draw hundreds using squares, tens using vertical line segments, and ones using dots. This will help them record the work more efficiently.

“Build the numbers using base-ten blocks. Draw the base-ten blocks you used. As you see in the examples, use squares for hundreds, lines for tens, and dots for ones. This will make it easier for you to draw the blocks you used. Complete the equation also.”

Ask students not to write in the box on the right side of each example. This area will be used to help students with the standard algorithm.

When students are finished with the examples, help them learn how to use the standard algorithm for addition. Use the standard algorithm to discuss the counting and trading of base-ten blocks and to determine the correct sum for each example.

The Standard Algorithm for Addition

First, ask students to write the numbers vertically for each example. Then, explain that this allows the place values to be added together. To explain the standard algorithm, emphasize starting with the ones and 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 sums with base-ten blocks. It is important to help students understand 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 helps students truly understand the standard algorithm and use the algorithm with greater accuracy.

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.docx) either in class or as a homework assignment. This can be used to assess students’ understanding of the standard algorithm for the addition of multidigit numbers.

Extension:

• Return to the use of base-ten blocks to support students who might benefit from additional practice of addition of two- and three-digit numbers. Specific resources for these students are listed in the Small Group section.

Students who are ready for an additional challenge should be introduced to adding four- and five-digit numbers. Specific strategies for supporting these students are provided in the Expansion section.

• Routine: As real-life situations arise during the school year, have students practice adding multidigit numbers, such as adding the number of books read by different third grade classrooms, finding the total amount raised from fundraising activities, and so on. Many problem-solving exercises throughout the curriculum will likely also utilize students’ ability to add multidigit numbers.
• Small Group: Students who need additional practice can be pulled into small groups to work on adding two- and three-digit numbers using the standard algorithm.

One student in the group should roll a ten-sided number cube. The first number rolled is in the tens place and the second number is in the ones place. A second student should do the same to generate a second two-digit number. All students should write both two-digit numbers down. Students should then be encouraged to add these two-digit numbers. It will be very important to listen carefully to identify and correct errors in their thinking. This process should then be repeated using number cubes to generate three-digit numbers and find the sum.

If students continue to struggle, return to using the base-ten blocks to model the addition of multidigit numbers. Be sure to record each step using the standard algorithm.

This Web site provides free printable worksheets for students needing extra practice adding whole numbers:

http://www.sssoftware.com/freeworksheets/addition.html

• Expansion: Students in need of a challenge should work in groups of two or three to play the following game.

The first student should roll a ten-sided number cube four times. Each number rolled should be recorded and become one of the digits of a four-digit whole number. The second student should do the same, generating a second four-digit whole number. All players should work individually to find the sum of these numbers. After all sums are computed, one player should use a calculator to find the sum. Any player with the correct sum earns one point. The first student who earns 10 points is the winner. This game can also be modified to focus on the addition of five-digit numbers if students need an additional challenge.