standard_description: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
problem_activity: Narrative
The purpose of this activity is to provide further practice relating the different forms of decimals. This includes expanded form, word form, and decimal form. Using the balance and weight of gold nuggets as a context, students go back and forth between different ways of representing these weights (MP2). The synthesis highlights the meaning of the digits in a decimal and how that relates to the expanded form of the decimal.
Launch
Display the image.
“What decimal can I write for the weight of the gold nugget?” (0.124)
Write equation:
\(0.124 = \left(1 \times 0.1\right) + \left(2 \times 0.01\right) + \left(4 \times 0.001\right)\)
“How does the balance show the expanded form of 0.124?” (There is 1 tenth of an ounce weight, 2 hundredth of an ounce weights, and 4 thousandth of an ounce weights.)
Activity
8–10 minutes: independent work time
Monitor for students who see, in the first problem, that the digits in the decimal for the gold weights are the same as the number of weights for that decimal place value.
Student Facing
[IMG]
Weights are used to balance some gold nuggets. Write the weight of each gold nugget in expanded form.
three 0.1 ounce weights, five 0.01 ounce weights, and eight 0.001 ounce weights
six 0.1 ounce weights and two 0.001 ounce weights
two 0.01 ounce weights and six 0.1 ounce weights
Here are the weights of some gold nuggets in word form. Write the weights in expanded form.
two hundred eighty three thousandths of an ounce
four hundred nine thousandths of an ounce
A gold nugget weighs 0.527 ounces.
What is the value of each of the digits in the decimal 0.527?
How does the expanded form of 0.527 show the value of each digit in the decimal?
Student Response
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Activity Synthesis
Invite students to share the expanded form of the decimal 0.527.
Display the expression:
\(\left(5 \times 0.1 \right) +\left(2 \times 0.01\right) +\left( 7 \times 0.001\right)\)
“What is the value of the 5 in 0.527?” (5 tenths)
“How does the expanded form show this?” (It shows the 5 is
\(5 \times 0.1\)
or 5 tenths.)
“What is the value of the 7 in 0.527?” (7 thousandths)
“How does the expanded form show this?” (It shows the 7 is
\(7 \times 0.001\)
or 7 thousandths.)
“How is going from word form to expanded form different than going from decimal form to expanded form?” (The decimal form shows the place values. With the word form, everything is given in terms of thousandths, so I need to figure out what the individual place values of the number are.)


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