standard_description: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
problem_activity: Problem 1
a.   Fill in the following blanks to make true statements. Use base ten blocks to help you.
1 thousand is the same as _______ hundreds.
1 hundred is the same as _______ tens.
1 ten is the same as _______ ones.
1 one is the same as _______ tenths.
b.   Below is an area model that represents 1 one. It is partitioned into tenths. Partition it to show what you would expect the next smallest unit to look like so that it continues the pattern in Part (a).
[IMG]
c.   Use what you notice in Part (a) and (b) to write a similar sentence that starts “1 tenth is the same as…”
Problem 2
The shaded part of this diagram represents 1 hundredth. We can write this as the fraction
$$\frac{1}{100}$$
or as the decimal
0.01.
[IMG]
Fill out the following table to represent each given number.
|                                                                                                  **            Diagram           **                                                                                                  | **            Unit Form           ** | **            Fraction Form           ** | **            Decimal Form           ** |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------|------------------------------------------|-----------------------------------------|
| |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png|  |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png| image:: https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png |             7 hundredths             |                                          |                                         |
| |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png|  |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png| image:: https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png |                                      |            $$\frac{32}{100}$$            |                                         |
| |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png|  |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png| image:: https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png |                                      |                                          |                  0.85                   |
| |https://d21royfkw9g4l6.cloudfront.net/xJTfKSJObLTngvzpCrjGcc_LY71VX.png|  |https://d21royfkw9g4l6.cloudfront.net/xJTfKSJObLTngvzpCrjGcc_LY71VX.png| image:: https://d21royfkw9g4l6.cloudfront.net/xJTfKSJObLTngvzpCrjGcc_LY71VX.png |                                      |                                          |                                         |
Problem 3
a.   Explain why
$${{1\over10}={10\over100}}$$
. Draw a picture to illustrate your explanation.
b.   Explain why
$${0.20 = 0.2}$$
. Draw a picture to illustrate your explanation.
Problem 4
Jani and Kai are representing a decimal number. Here are the area models they drew:
|                                                                                                                 Jani                                                                                                                 |                                                                                                                 Kai                                                                                                                  |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| |https://d21royfkw9g4l6.cloudfront.net/pCjOWHyq93ljOqoarBpFRi_XAG8G1.png|  |https://d21royfkw9g4l6.cloudfront.net/pCjOWHyq93ljOqoarBpFRi_XAG8G1.png| image:: https://d21royfkw9g4l6.cloudfront.net/pCjOWHyq93ljOqoarBpFRi_XAG8G1.png | |https://d21royfkw9g4l6.cloudfront.net/IX0bwHJs13FGRL7TldfH6i_9P5SGX.png|  |https://d21royfkw9g4l6.cloudfront.net/IX0bwHJs13FGRL7TldfH6i_9P5SGX.png| image:: https://d21royfkw9g4l6.cloudfront.net/IX0bwHJs13FGRL7TldfH6i_9P5SGX.png |
a.   What value do you think Jani and Kai are trying to model? How do you know?
b.   Draw pictures to show what Kai might have drawn for each area model in Anchor Task 2.


aligns: no