Decomposing and Adding Place Values

Explicit Instruction/Teacher modeling

• Write 34 + 12 on the whiteboard vertically.
• Ask the students to look at the problem and think about whether you should add or subtract 34 and 12. Allow students time to discuss their ideas with a partner. Clarify that you should add because you see the addition sign. Explain to the students that the addition sign can also be called the plus sign. Elaborate that the addition sign, or plus sign, means you will combine 34 and 12 to find the total amount.
• Complete the problem in the traditional way, moving from right to left. Model how to add the ones place and then the tens place.
• Brainstorm different strategies they could use to solve the problem. Have students think-pair-share ideas with an elbow partner.
• Pass out an index card to each student. Instruct the students to write or draw a different way to solve the problem. Some examples of this are using the left to right method, drawing a picture, using base-ten blocks, turning it into a story problem, or any other creative ways that the student chooses to solve the problem.
• Bring the class back together and invite students to share their ideas and model solving the problem using a few of their ideas.
• Compile a list on the whiteboard under the heading "Strategies to Add" of all the ways students solved the problem.
• Validate all reasonable responses and explain to the students that today they are going to learn how to decompose three-digit numbers and use place value to add two three-digit numbers.

Guided Practice

• Write a three-digit addition problem on the whiteboard, such as 263 + 134.
• Ask the students if the strategies on the whiteboard would also work to solve the three-digit addition problem. Have students share their answers with a partner.
• Provide sentence frames, such as:
  • I think the strategies would work because ____.
  • I don't think the strategies would work because ____.
• Encourage students to talk about why the strategies transfer from solving two-digit addition problems to three-digit addition problems. Elicit deep thinking by asking students to reflect on what is similar between both types of problems (both use addition, both have the addition sign, etc).
• Agree that the strategies they recorded to add the two-digit numbers would also work to add three-digit numbers.
• Tell the students that today they will learn a new strategy called decomposing. Explain to the students that when we decompose a number, we break it down into its smaller parts.
• Model decomposing both addends starting from left to right/top to bottom (200 + 100 = ____ , 60 + 30 = ____, 3 + 4 = ____). Record the decompositions vertically.
• Ask for a student volunteer to come to the front of the room to model adding the numbers, starting with the hundreds and moving down to the ones. Next, instruct the students to add the three totals together (300 + 90 + 7 = 397).
• Have the students think-pair-share one or two things they notice about the new strategy of decomposing and adding place values. Provide sentence stems to support students in sharing out their ideas.
  • I notice that decomposing is ____.
  • I notice that the strategy is ____.

Group work time

• Present students with another three-digit addition problem (321 + 255).
• Ask students to explain to a partner how to solve the problem using decomposition and adding place values. Provide students with sequencing sentence frames to support them as they discuss their ideas: First, ____. Next, ____. Then, ____. Finally, ____.
• Provide students with a word bank with important vocabulary words/phrases they can use to complete the sentence frames (break down, add, place value, total).
• Ask for a few student volunteers to detail the process they would use with the rest of the class. Clarify any misconceptions.
• Put students in partnerships and give each student a personal whiteboard and whiteboard markers. Instruct students to decompose the addends and add the place values to find the total of the two three-digit numbers.
• Ask students to hold up their whiteboards when they are finished. Allow one or two students to share their answers with the rest of the class. Encourage students to ask questions and agree/disagree with their peers' process.