standard_description: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^(3) = 5(^(1/3))^(3) to hold, so (5^(1/3))^(3) must equal 5.
problem_activity: Narrative
The purpose of this activity is for students to write three-digit numbers as the sum of the value of each digit,
expanded form
. Students connect the order and values of the addends in expanded form to the order and value of each place in a three-digit number. Use expanded form and its definition interchangeably throughout the activity so that students feel comfortable with the new vocabulary. When students represent numbers as sums by place value, they interpret the three-digit numbers in terms of its digits and the operation of addition (MP7).
MLR8 Discussion Supports.
Provide all students with an opportunity to produce mathematical language by inviting students to chorally repeat “expanded form” in unison 1–2 times.
Advances: Speaking
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Display Andre, Tyler, and Mai’s situation and the image of their blocks.
“What would the expression look like?”
1 minute: independent work time
1 minutes: partner discussion
Share responses.
Display 357 and
\(300 + 50 + 7\)
.
“We can represent the value of the blocks by writing a three-digit number.”
“A number can also be represented as a sum of the value of each of its digits. This is called
expanded form
.”
“Like a three-digit number, expanded form shows the sum starting with the place that has the greatest value on the left to the place with the least value on the right.”
As needed, discuss reasons why any expressions generated in the launch would or would not be examples of expanded form.
Activity
“Now you will practice writing the value of the base-ten diagrams in expanded form and as a three-digit number.”
7 minutes: partner work time
Student Facing
Andre has 3 hundreds. Tyler has 5 tens. Mai has 7 ones. They want to represent the amount they have using an equation.
[IMG]
Write an expression to represent the sum of their values.
__________ + __________ + __________
Write the total value as a three-digit number:
_______________
Write each number as the sum of hundreds, tens, and ones, and as a three-digit number.
[IMG]
Expanded form: _________________________
Three-digit number: _________________________
[IMG]
Expanded form: _________________________
Three-digit number: _________________________
[IMG]
Expanded form: _________________________
Three-digit number: _________________________
[IMG]
Expanded form: _________________________
Three-digit number: _________________________
Student Response
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Activity Synthesis
“What is the value of
\(40 + 100 + 3\)
? Explain how you know.” (143. I saw there was 1 hundred, 4 tens, and 3 ones. I just rearranged it in my head like expanded form.)
“We know we can rearrange the addends to add in any order when we find the value of a sum. When a number is written in expanded form the values are written in place value order.”
“How would we write 143 in expanded form?” (
\(100 + 40 + 3\)
)


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