Subtraction with Regrouping
Students will be able to use two different strategies to subtract three-digit numbers.
- Write the following problem on the board: 365 – 174.
- Distribute the whiteboards and ask students to solve the problem using a strategy of their choice. Then, ask students to turn to their elbow partner to compare strategies and answers.
- Choose students who used different strategies to share their steps to solve the problem.
- Solve the problem on the board using expanded form subtraction and highlight that you have to regroup. Define regrouping as changing groups of ones, tens, or hundreds into another value (e.g., changing 1 ten to 10 ones).
- Explain that they'll learn two strategies for solving subtraction problems to help them check their answers and better understand subtraction processes.
Explicit Instruction/Teacher modeling(8 minutes)
- Model completing the first problem using expanded form subtraction from the Three-Digit Subtraction, Part 1 worksheet. Explain that expanded notation subtraction is a strategy to subtract larger numbers by decomposing the numbers into their values (e.g., 156 = 100 + 50 + 6), stacking them on top of one another, subtracting them one column at a time from right to left, and finally adding the differences to get the total remaining.
- Ask partners to look at the problem you solved and explain to each other the steps you used to solve the problem.
- Model completing the first problem using standard algorithm subtraction. Explain that standard algorithm subtraction is subtraction where digits in each number are lined up based on their place value and subtracted one place value at a time, starting from the right to the left.
Guided Practice(15 minutes)
- Choose a student to model the next problem for the class. Correct and offer suggestions throughout the whole process. Allow other students to share ideas as well.
- Distribute the Three-Digit Subtraction, Part 1 worksheet and ask students to solve the rest of the problems in partners. Remind them they'll have to regroup (i.e., borrow from a higher place value to add to a lesser place value) to complete the subtraction problem.
- Have two pairs compare their answers, and allow them to adjust them as necessary.
- Choose students to share the difference between the two strategies, and to decide which they prefer to use when subtracting three-digit numbers.
Independent working time(12 minutes)
- Distribute the Three-Digit Subtraction, Part 2 worksheet and review the instructions.
- Have students complete the whole worksheet, and then compare their answers with their partners. If they have varying answers, ask them to change the answer and write a sentence about what they had to adjust.
- Allow students to use place value charts and base ten blocks as they complete the two subtraction strategies.
- Have them practice regrouping with two-digit numbers using the exercise Two-Digit Subtraction and Regrouping. Hand out paper for their work on both of the subtraction strategies.
- Challenge students with word problems in the exercise Three-Digit Subtraction Word Problems. Ask them to show their strategies on a sheet of paper.
- Pair advanced students with those who need additional support. Ask advanced students to explain their processes during the group work and to check their partner's answers for accuracy.
- Write the following problem on the board: 809 – 312. Distribute the index cards and ask students to solve the problem using the standard algorithm and expanded notation subtraction strategies.
- Use the index card as a formative assessment of their ability to regroup to solve subtraction problems.
Review and closing(5 minutes)
- Provide an incorrect subtraction example. Have students decide if it's incorrect and why. Allow them to use their whiteboards to solve the problem and then explain the error.
- Ask this question: "What are the benefits of knowing more than one way to subtract three-digit numbers?"
- Have students share and discuss in partners. Then, summarize for the class some of the responses you heard during their discussions.