Decomposing to Add

Objective

Students will learn to add two-digit numbers by decomposing one addend and using counting strategies to find the sum. They will understand that breaking down numbers makes addition easier and more intuitive.

Curriculum Area

• Mathematics
• Grade Level: 2nd Grade
• Common Core State Standards: CCSS.MATH.CONTENT.2.NBT.B.5 - Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Materials

• Whiteboard and markers
• Number cards (10-99)
• Base-ten blocks or linking cubes
• Chart paper
• Worksheets with addition problems
• Pencils and erasers
• Interactive math application (optional, if technology is available)

Time Allotment

• Total Duration: 45 minutes

Lesson Outline

1. Introduction (5 minutes)

• Begin with a brief discussion on addition. Ask students if they have ever found it difficult to add larger numbers and how they usually solve such problems.
• Introduce the concept of "decomposing" or breaking down numbers to make addition easier.
• Explain the goal: "Today, we're going to learn an exciting new way to add two-digit numbers by breaking them down!"

2. Explicit Instruction (10 minutes)

• Use the whiteboard to write a sample problem: 47 + 25.
• Break down 25 into 20 and 5 on the board.
• Add: 47 + 20 = 67 and then 67 + 5 = 72.
• Discuss each step as you perform it, emphasizing how decomposing helps simplify the process.
• Utilize base-ten blocks or linking cubes to visually demonstrate the problem. Show 47 using blocks, add a group of 20, and finally add 5 more, counting aloud.

3. Guided Practice (10 minutes)

• Hand out number cards to each student, ensuring each has a card from 10 to 99.
• Pair students up and have them pick two cards to create a two-digit addition problem.
• Each pair should work together to decompose one addend and solve the problem using counting strategies.
• Walk around the classroom, offering support and ensuring students understand the decomposition process. Encourage students to verbally explain their thinking.

4. Independent Practice (15 minutes)

• Provide each student with a worksheet containing various two-digit addition problems designed to be decomposed.
• Students work independently to solve the problems using the strategy taught.
• Include space for students to show their work and a “Challenge Zone” with a couple of slightly more difficult problems for those who finish early.

5. Closure and Reflection (5 minutes)

• Reconvene as a class and invite students to share one problem they solved and explain the decomposing process they used.
• Discuss the benefits and any challenges they faced using this strategy.
• Ask students: "How does decomposing help you when adding two-digit numbers?"

Assessment

• Observe students during guided and independent practice to ensure understanding.
• Review completed worksheets to assess each student's grasp of the decomposing strategy.
• Use informal questioning during the lesson to check for comprehension in real-time.

Accommodations and Extensions

• Accommodations: Provide additional visual aids or manipulatives for students who need extra support. Offer one-on-one assistance as needed.
• Extensions: Challenge advanced students to create their addition problems using three-digit numbers and apply the same decomposing strategy.

Reflection for Teachers

• After the lesson, reflect on what worked well and what might need adjustments. Consider student engagement and understanding. Was there a strong grasp of the decomposing concept? How might the lesson be improved next time?

By breaking down complex addition into manageable parts, students will enhance their mathematical fluency and build confidence in working with numbers. This creative approach supports a deeper understanding of number concepts and fosters an enthusiastic learning environment in the classroom.