Represent Numbers in Different Ways
10 min
Narrative
This Warm-up prompts students to compare numbers represented in different ways. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology to talk about characteristics of the items in comparison to one another. During the discussion, ask students to explain the meaning of any terms they use, such as “place value,” “hundreds,” “tens,” ones,” “sum,” or “base-ten diagram.”
Launch
- Groups of 2
- Display the image and expressions.
- “Pick 3 representations that go together. Be ready to share why they go together.”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 2–3 minutes: partner discussion
- Share and record responses.
Student Task
Which 3 go together?
A.
B. 300+70+1
C. 300+60+10
D. 400−30
Solution Steps (5)
- 1Evaluate A: base-ten diagram→3 hundreds + 7 tens = 370
- 2Evaluate B: expanded form expression→300 + 70 + 1 = 371
- 3Evaluate C: expanded form expression→300 + 60 + 10 = 370
- 4Evaluate D: subtraction expression→400 - 30 = 370
- 5Identify which 3 go together by value→A, C, D all equal 370
Sample Response
Sample responses:
A, B, and C go together because:- They show addition or can be used to show addition.
- The tens are shown together.
- They show a value of 370.
- They are expressions.
Activity Synthesis (Teacher Notes)
- “Why do all 4 go together?” (The parts of the number have been separated into hundreds and tens or hundreds, tens, and ones.)
- “Remember that expanded form is a specific way of writing a number as a sum of hundreds, tens, and ones. It is written as a sum of the value of each digit, like in B.”
- “How would we write 482 in expanded form?” (400+80+2)
Standards
Building On
- 2.NBT.1·Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 2.NBT.3·Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
- 2.NBT.A.1·Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 2.NBT.A.3·Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
Building Toward
- 3.NBT.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
- 3.NBT.A.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
15 min
20 min
Knowledge Components
All skills for this lesson
Role Legend
Target
Essential
Supporting
Foundational
All lesson KCs
1 skills
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Represent Numbers in Different Ways
10 min
Narrative
This Warm-up prompts students to compare numbers represented in different ways. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology to talk about characteristics of the items in comparison to one another. During the discussion, ask students to explain the meaning of any terms they use, such as “place value,” “hundreds,” “tens,” ones,” “sum,” or “base-ten diagram.”
Launch
- Groups of 2
- Display the image and expressions.
- “Pick 3 representations that go together. Be ready to share why they go together.”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 2–3 minutes: partner discussion
- Share and record responses.
Student Task
Which 3 go together?
A.
B. 300+70+1
C. 300+60+10
D. 400−30
Solution Steps (5)
- 1Evaluate A: base-ten diagram→3 hundreds + 7 tens = 370
- 2Evaluate B: expanded form expression→300 + 70 + 1 = 371
- 3Evaluate C: expanded form expression→300 + 60 + 10 = 370
- 4Evaluate D: subtraction expression→400 - 30 = 370
- 5Identify which 3 go together by value→A, C, D all equal 370
Sample Response
Sample responses:
A, B, and C go together because:- They show addition or can be used to show addition.
- The tens are shown together.
- They show a value of 370.
- They are expressions.
Activity Synthesis (Teacher Notes)
- “Why do all 4 go together?” (The parts of the number have been separated into hundreds and tens or hundreds, tens, and ones.)
- “Remember that expanded form is a specific way of writing a number as a sum of hundreds, tens, and ones. It is written as a sum of the value of each digit, like in B.”
- “How would we write 482 in expanded form?” (400+80+2)
Standards
Building On
- 2.NBT.1·Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 2.NBT.3·Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
- 2.NBT.A.1·Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 2.NBT.A.3·Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
Building Toward
- 3.NBT.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
- 3.NBT.A.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.