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

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

Write the problem that follows on the board. Introduce the problem. Ask students to model the greater number using base-ten blocks. After students represent the greater number, ask students “How many baseball cards does Ryan have now?” Students will likely begin to take away or remove the lesser number.

Example:

Ryan had 57 baseball cards. He gave 36 of the cards to his friends. How many baseball cards does Ryan have left?

After students have determined the difference, ask students “What operation did we use to determine how many baseball cards Ryan has left?” Students will likely be able 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, as taking away or removing some number.

Model for students writing the equation horizontally, as shown. The goal is for students to recognize and write the subtraction equation. At this point in the lesson, students should focus on using the base-ten blocks to find the difference. This experience will then be used to support students as they transition to the standard algorithm for subtracting 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 subtraction to the class and write the equation. Notice that some of these examples require students to trade or regroup.

Example:

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?

Example:

Anya had $63. She spent $48. How much money does Anya have left?

Example:

Hiro wants to go visit his grandma. The flight will cost $375. Hiro has already saved $239. How much more does he need to save?

Example: 417 – 164

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

Instruct students to build the greater number using base-ten blocks and take away the base-ten blocks representing the lesser number to find the difference. 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.

“Find the differences using base-ten blocks. Draw the base-ten blocks you used and cross out those you removed. 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 subtraction. Use the standard algorithm to discuss the counting and trading of base-ten blocks and to determine the correct difference for each example.

The Standard Algorithm for Subtraction

First, ask students to write the numbers vertically for each example. Then, explain that this allows the place values to be subtracted. 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 differences 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 in order to have enough to subtract from. This helps students truly understand the standard algorithm and use the algorithm with greater accuracy.

Extension:

• Return to the use of base-ten blocks to support students who need additional practice to understand the subtraction of two- and three-digit numbers. More specific suggestions can be found in the Small Group section.

Students who are ready for an additional challenge should be introduced to subtracting 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 subtracting multidigit numbers, such as finding out how many more books one third grade class read than another, finding out how much more money one classroom raised for the school through fund raising activities than another, and so on. Many problem-solving exercises throughout the curriculum will likely also utilize students’ ability to subtract multidigit numbers.
• Small Group: Students who need additional practice can be pulled into small groups to work on subtracting 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 subtract 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 difference.

This Web site provides free printable worksheets for students needing additional practice subtracting whole numbers:

http://www.sssoftware.com/freeworksheets/subtraction.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 difference of these numbers. After all differences are computed, one player should use a calculator to find the difference. Any player with the correct difference earns one point. The first student who earns 10 points is the winner.