standard_description: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
problem_activity: Problem 1
Nolan gives some Fruit-by-the-Foot to his
$$3$$
friends to share equally.
a.   If he has
$$3$$
feet of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive?
b.   If he has
$$1$$
foot of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive?
c.   If he has
$${1\over2}$$
foot of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive?
d.   If he has
$${1\over3}$$
foot of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive?
Problem 2
Priya and Mai used the diagrams below to find the value of
$$\frac13 \div 4$$
.
{"table": [{"_attributes": {"align": "center", "class": ["table"], "style": "width: 80%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: left;"}, "p": [{"strong": [{"_value": "Priya\u2019s diagram:"}]}]}, {"p": [{"_attributes": {"style": "text-align: left;"}, "strong": [{"_value": "Mai\u2019s diagram:"}]}]}]}, {"td": [{"img": [{"_attributes": {"height": "50", "src": "https://d21royfkw9g4l6.cloudfront.net/uploads/2022/05/05/g5mathu5l19_at2a.png", "width": "234"}}]}, {"img": [{"_attributes": {"height": "50", "src": "https://d21royfkw9g4l6.cloudfront.net/uploads/2022/05/05/g5mathu5l19_at2b.png", "width": "234"}}]}]}]}]}]}
a.   What is the same about the diagrams?
b.   What is different?
c.   Find the value that makes the equation true.
$$\frac13 \div 4 =$$
____
Problem 3
a.    Solve. Then check your work.
$${{1\over5}\div2}$$
$${{1\over6}\div4}$$
$${{1\over9}\div6}$$
b.   What do you notice in Part (a)? What do you wonder?


aligns: no