Lesson Plan

## Adding and Subtracting by Splitting

### Objectives

In this unit, students will add and subtract three-digit numbers by splitting. Students will:

• split each addend into hundreds, tens, and ones. Then they will add the sums of the hundreds, tens, and ones to find the sum of the original two addends.
• split the minuend into hundreds, tens, and ones. Then they will take away the hundreds, tens, and ones in the subtrahend to find the difference.

#### Essential Questions

How are relationships represented mathematically?
How can mathematics support effective communication?
How is mathematics used to quantify, compare, represent, and model numbers?
What does it mean to estimate or analyze numerical quantities?
What makes a tool and/or strategy appropriate for a given task?
• How are relationships represented mathematically?
• What makes a tool and/or strategy appropriate for a given task?

### Vocabulary

• Expanded Form: A way to write numbers that shows the value of each digit (e.g., 4,372 = 4,000 + 300 + 70 + 2).

45–60 minutes

### Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.

### Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

### Suggested Instructional Supports

• View
Scaffolding, Active Engagement, Modeling, Explicit Instruction W: Inform students that splitting can be useful in adding and subtracting numbers. H: Show students how to split a three-digit number into hundreds, tens, and ones. Make a connection to expanded form. (e.g., 745 is the same as 700 + 40 + 5). E: Students will add and subtract three-digit numbers by splitting. R: The questions asked before, during, and after the lesson will cause students to reflect on their understanding of splitting to add and subtract three-digit numbers. E: Use the Adding and Subtracting by Splitting Worksheet and the responses to questions throughout the lesson to determine student understanding of using the splitting method to add and subtract three-digit numbers. T: The lesson may be tailored using the suggestions in the Extension section. O: The lesson was designed to help students gain a better understanding of adding and subtracting three-digit numbers. Students move from using base-ten blocks to using pictures of base-ten blocks to splitting.

### Instructional Procedures

• View

“In the last lesson we added and subtracted three-digit numbers using base-ten blocks. Today we are going to learn a strategy called splitting. What do you think of when you hear the word ‘splitting?’ (Answers will vary.) Just like we can split the things you named, we can split numbers to help us add and subtract. When we use this strategy, we use what we know about expanded form. We write each number in expanded form; then we add the hundreds, then the tens, then the ones. We then add the sum of each.”

Write 453 + 245 = on the whiteboard. “I can write 453 like this.” Write 400 + 50 + 3 on the whiteboard. “I can write 245 like this.” Write 200 + 40 + 5 on the whiteboard. “Now I can add my hundreds together, my tens together, and my ones together like this.” Write 400 + 200 = 600 on the board; write 50 + 40 = 90 on the board; write 3 + 5 = 8 on the board. “Now I can add 600 + 90 + 8. This equals 698, so the sum of 453 + 245 is 698.”

“Let me show you one more.” Write 138 + 451 = on the whiteboard. “I can write 138 like this.” Write 100 + 30 + 8 on the board. “I can write 451 like this.” Write 400 + 50 + 1 on the board. “Now I can add my hundreds together, my tens together, and my ones together like this.” Write
100 + 400 = 500, 30 + 50 = 80, and 8 + 1 = 9 on the board. “Now I can add 500 + 80 + 9. This equals 589, so the sum of 138 + 451 is 589.”

“Now let’s do one together.” Write 432 + 325 = on the board. “Write 432 in expanded form on your whiteboard.” Have a student come up and write 432 in expanded form on the board. (400 + 30 + 2)

“Now, write 325 in expanded form on your whiteboard.” Have a student come up and write 325 in expanded form on the board. (300 + 20 +5) “Now add your hundreds together.” Have a student come up and write 400 + 300 = 700 on the board. “Now your tens.” Have a student come up and write
30 + 20 = 50 on the board. “And now your ones.” Have a student come up and write 2 + 5 = 7 on the board. “Finally add together your sums of the hundreds, tens, and ones.” Have a student come up and write 700 + 50 + 7 = 757 on the board.

“Let’s try one more together.” Write 267 + 202 = on the board. “Write 267 in expanded form on your whiteboard.” Have a student come up and write 267 in expanded form on the board. (200 + 60 + 7) “Now write 202 in expanded form on your whiteboard.” Have a student come up and write 202 in expanded form on the board. (200 + 2, or 200 + 0 + 2) “Now add your hundreds together.” Have a student come up and write 200 + 200 = 400 on the board. “Now your tens.” Have a student come up and write 60 + 0 = 60 on the board. “And now your ones.” Have a student come up and write 7 + 2 = 9 on the board. “Finally, add together your sums of the hundreds, tens, and ones.” Have a student come up and write 400 + 60 + 9 = 469 on the board.

“We can solve three-digit subtraction problems by splitting as well.” Write 789 – 352 = on the board. “I can write 789 like this.” Write 700 + 80 + 9 on the board. “I can write 352 like this.” Write 300 + 50 + 2 on the board. “Now in order to find the difference I need to subtract my hundreds, then my tens, and then my ones like this.” Write 700 – 300 = 400 on the board; write 80 – 50 = 30 on the board; write 9 – 2 = 7 on the board. “Now I add these differences together to find the difference of 789 – 352, like this.” Write 400 + 30 + 7 = 437 on the board.

“Let’s try one together.” Write 865 – 420 = on the board. “Write 865 in expanded form on your whiteboard.” Have a student come up and write 800 + 60 + 5 on the board. “Write 430 in expanded form on your whiteboard.” Have a student come up and write 400 + 30 + 0 on the board. “Now in order to find the difference, we need to subtract the hundreds, tens, and ones.” Have a student come up and write 800 – 400 = 400 on the board. Have another student come up and write 60 – 30 = 30 on the board. Have yet another student come up and write 5 – 0 = 5 on the board. “Now we add these differences together to find the difference of 865 – 430.” Have a student come up and write 400 + 30 + 5 = 435 on the board. “So 865 – 430 = 435.” Write this on the board.

“Now you are going to use the splitting strategy to help you solve addition and subtraction problems.” Distribute to each student a copy of the Adding and Subtracting by Splitting Worksheet (M-2-2-2_Adding and Subtracting by Splitting Worksheet and KEY.docx). Move around the room observing and asking clarifying questions to evaluate which students can add and subtract three-digit numbers using the splitting strategy and which students need additional exploration.

Extension:

• Routine: Students play Top-It and/or Beat the Calculator (M-2-2-1_Top-It Directions.docx and M-2-2-1_Beat the Calculator Directions.docx). Students can split the hundreds, tens, and ones to help them compute. Students can also play games listed in Related Resources.
• Small Group: Guide students through additional two-digit and three-digit addition and subtraction problems using the splitting strategy by following the process used and the questions asked in Instructional Procedures.
• Expansion:

### Related Instructional Videos

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Final 3/14/14