standard_description: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
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.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "Diagram"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "Unit Form"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "Fraction Form"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "Decimal Form"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "p": [{"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png"}}]}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "7 hundredths"}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "p": [{"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png"}}]}]}, {}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{32}{100}$$"}]}, {}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "p": [{"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png"}}]}]}, {}, {}, {"_attributes": {"style": "text-align: center;"}, "_value": "0.85"}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "p": [{"img": [{"_attributes": {"src": "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:
{"table": [{"_attributes": {"align": "center", "class": ["table"], "style": "width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center;"}, "_value": "Jani"}, {"_attributes": {"style": "text-align: center;"}, "_value": "Kai"}]}, {"td": [{"p": [{"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/pCjOWHyq93ljOqoarBpFRi_XAG8G1.png"}}]}]}, {"p": [{"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "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: yes