Addition with Regrouping
Students will be able to use two addition strategies to add three-digit numbers.
- Display the example box from the Three-Digit Addition: Part 1 worksheet and ask students to turn and talk to their partners about what they see and notice about the mathematical problem and solution strategies.
- Ask students to share some of their impressions about the problem (e.g., they decompose the numbers to add more simple numbers, there are two strategies to solve the same problem, expanded notation takes up more space, etc.).
- Tell students that today they'll learn how to use the two strategies to solve addition problems.
Explicit Instruction/Teacher modeling(10 minutes)
- Explain that the first strategy is expanded notation addition and the second is standard algorithm addition. Define Expanded notation additionAs a strategy to add larger numbers by decomposing the numbers into their values (i.e., 56 = 50 + 6), stacking them on top of one another, adding one column at a time, and finally adding the sums to get the total.
- Model using the expanded notation addition strategy with the first problem on the Three-Digit Addition: Part 1 worksheet. Emphasize Regrouping,Or changing groups of ones to tens and tens to hundreds. Define regrouping while completing the first problem.
- Define Standard algorithm additionAs addition where the addends in each number are lined up based on their place value and added up one place value at a time starting from the right to the left. (This is a good time to emphasize that the value of the one they carryover is the regrouping of 10s or 100s.)
- Model completing standard algorithm addition with the first problem of the Three-Digit Addition: Part 1 worksheet. (Tip: refer to the numbers as their place value numbers. So, if there’s a six in the hundreds place, refer to it as 600 rather than six.)
- Explain that these are just two of many ways to add larger numbers accurately. Emphasize that it is helpful to know multiple strategies to solve the same problem so that we can check our own calculations and correct simple errors.
Guided practise(15 minutes)
- Ask students to turn and talk to their partner and answer the following questions:
- What do you notice about the two strategies?
- Which seems easier to use and why?
- Choose two students to share their ideas with the class. Refer to students’ first impressions about the addition strategies from the introduction and ask students to confirm or deny some of their original ideas.
- Create a carousel activity with the pre-made chart papers placed around the room. Separate students into six groups and give each group their own colored pencil. Have them solve the addition problem using the expanded notation addition and standard algorithm addition strategies. Then, have two groups switch charts and check the answer and strategies by solving the problem again using their assigned colour.
- Allow the groups that switched charts to meet to share their answers and explain the changes they made, if any.
- Choose one student to explain the steps of how the group solved their addition problem.
Independent working time(15 minutes)
- Distribute the Three-Digit Addition: Part 2 worksheet and read the directions. Have students complete the worksheet on their own.
- Allow students to check their answers with their partners. Have them adjust their answers with a colored pen to highlight the changes they've made.
- Allow students to place their numbers in a place value chart to help them determine the expanded notation. Have them use base ten blocks to visualize place value.
- Have students complete less problems but explain their strategies. They can complete problems from the Three-Digit Addition: Part 1 worksheet as their independent work.
- Provide the Multi-Digit Addition exercise for additional practise (see optional resource under materials). Allow them to solve the addition problems with their chosen strategy.
- Ask them to model for students who need support how they solved their problem. Assign them as group leaders during the carousel activity and presentation.
- Write the following problem on the board: 368 + 567. Distribute note cards and have students complete the problem using their chosen method.
- Ask students to explain their process to their elbow partner.
Review and closing(5 minutes)
- Ask students to share why they think they should learn different strategies for addition problems with regrouping. Ask them if their impressions about the strategies from the beginning changed at all.
- Take a quick poll with their fingers to choose which strategy students prefer. Have them hold one finger up for expanded notation addition and two fingers up for standard algorithm addition.
- Explain that they can use both of these strategies with subtraction as well.