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expanded notation: 5th Grade 🌐 Ver en Español

Number and Operations
Numbers and Basic Operations
3rd Grade 4th Grade 5th Grade
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TEKS:

3rd3.2(A)
4th4.2(A)
5th5.2(A)
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Author Picture Areli Amador
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Structured Conversation Questions
Observational

What is expanded notation?

Expanded notation is...
Relational

How is expanded notation related to place value?

Expanded notation is related to place value because...
Inferential

How can you use expanded notation to compare two numbers?

I can use expanded notation to compare two numbers by...
Vocab Visual

David Chavlovich

This visual could be improved by... including fractions in decimal places, like 1/10 and 0.1. Use both examples

08-06-25

Areli Amador

Thank you for your feedback. I’ve added fractions along with decimal representations to the visual.

08-12-25

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Students might notice in this visual:
  • The number is written both in standard form and expanded notation.
  • Each digit is labeled with its place value: tens, ones, tenths, hundredths, thousandths.
  • Decimal digits are written as fractions in the expanded notation.
  • The value of each digit matches its place value position.
  • The expanded form breaks the number into separate parts using multiplication.
EXTENDING THE DISCUSSION
After the observational question, randomly call on one or more students to share what they or their partner answered. Then ask the class, “Did anyone notice…?” using the suggestions above or anything else you’ve noticed.
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Students might wonder:
  • Why are decimals written using fractions in expanded notation?
  • What would happen if you changed one digit—how would it change the total?
  • Can expanded notation be used with very large numbers?
  • What’s the difference between writing a decimal in expanded notation vs. a whole number?
  • Why does each part of expanded notation use multiplication?
EXTENDING THE DISCUSSION
After students have shared what they notice, ask the class, “Did anyone wonder…?” using the suggestions above or anything else you might think is interesting or relevant to the lesson.
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Example student responses

To the observational question, What is expanded notation?

LOW-LEVEL

Expanded notation is a way to write a number by breaking it into parts.

HIGH-LEVEL

Expanded notation is a way to show the value of each digit in a number using place value and multiplication.

RESPONDING TO RESPONSES
Emphasize and celebrate each student’s use of the key vocabulary to support a culture of “no wrong answers.”
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