Add and Subtract within 1,000,000
10 min
Narrative
This Warm-up prompts students to analyze an example of subtraction using both the standard algorithm and expanded form. The numbers require decomposing multiple units, which are shown in both strategies. The observations prepare students to later reason with similar subtraction problems in which more than one decomposition is needed.
Launch
- Groups of 2
- Display subtraction calculations.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Subtract. Seventy thousand, plus five thousand, plus nine hundred, plus forty, plus zero, minus, ten thousand, plus two thousand, plus seven hundred, plus eighty, plus six, equals sixty thousand, plus three thousand, plus one hundred, plus fifty, plus four.
Sample Response
Students may notice:
- One calculation uses the standard algorithm and the other uses expanded form.
- In Problem A, the 9, 4, and 0 in 75,940 are crossed out. In Problem B, 900, 40, and 0 are crossed out.
- The tens place has 2 new numbers at the top. There are 3 different units being decomposed.
- The result of the subtraction is not shown in the first example, but it is shown in the second example.
- Why are there multiple numbers above the two numbers being subtracted?
- Why is the difference not shown in the first example?
- Would the first example also get a difference of 63,154?
Activity Synthesis (Teacher Notes)
- “How are the two examples alike? How are they different?” (In the second one the numbers are written in expanded form, including the numbers that show regrouping.)
- “We’ve seen subtraction problems with decomposed units before. How are these different?” (In the problems we have seen so far, only one place needed to be decomposed in order to subtract. In these examples, more than one place needs to be decomposed.)
Standards
Addressing
- 4.NBT.4·Fluently add and subtract multi-digit whole numbers using the standard algorithm.
- 4.NBT.B.4·Fluently add and subtract multi-digit whole numbers using the standard algorithm.
15 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Add and Subtract within 1,000,000
10 min
Narrative
This Warm-up prompts students to analyze an example of subtraction using both the standard algorithm and expanded form. The numbers require decomposing multiple units, which are shown in both strategies. The observations prepare students to later reason with similar subtraction problems in which more than one decomposition is needed.
Launch
- Groups of 2
- Display subtraction calculations.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Subtract. Seventy thousand, plus five thousand, plus nine hundred, plus forty, plus zero, minus, ten thousand, plus two thousand, plus seven hundred, plus eighty, plus six, equals sixty thousand, plus three thousand, plus one hundred, plus fifty, plus four.
Sample Response
Students may notice:
- One calculation uses the standard algorithm and the other uses expanded form.
- In Problem A, the 9, 4, and 0 in 75,940 are crossed out. In Problem B, 900, 40, and 0 are crossed out.
- The tens place has 2 new numbers at the top. There are 3 different units being decomposed.
- The result of the subtraction is not shown in the first example, but it is shown in the second example.
- Why are there multiple numbers above the two numbers being subtracted?
- Why is the difference not shown in the first example?
- Would the first example also get a difference of 63,154?
Activity Synthesis (Teacher Notes)
- “How are the two examples alike? How are they different?” (In the second one the numbers are written in expanded form, including the numbers that show regrouping.)
- “We’ve seen subtraction problems with decomposed units before. How are these different?” (In the problems we have seen so far, only one place needed to be decomposed in order to subtract. In these examples, more than one place needs to be decomposed.)
Standards
Addressing
- 4.NBT.4·Fluently add and subtract multi-digit whole numbers using the standard algorithm.
- 4.NBT.B.4·Fluently add and subtract multi-digit whole numbers using the standard algorithm.