standard_description: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
problem_activity: Problem 1
Three students are partitioning a number line into fourths. Their work is shown.
Chadwick’s number line:
[IMG]
Allan's number line:
[IMG]
Dobrilla's number line:
[IMG]
Whose partitioning makes the most sense to you? Explain your reasoning.
Problem 2
a.
{"table": [{"_attributes": {"class": ["table"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "width:40%"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{3}{4}$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{6}{4}$$"}], "_values": ["Locate and label", "and", "."]}, {"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/kQe2ZUaTBYoyNxM10w8iGO_7BJFW5.png"}}]}]}]}]}]}
b.
{"table": [{"_attributes": {"class": ["table"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "width:40%"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{7}{8}$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{12}{8}$$"}], "_values": ["Locate and label", "and", "."]}, {"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/kQe2ZUaTBYoyNxM10w8iGO_7BJFW5.png"}}]}]}]}]}]}
c.
{"table": [{"_attributes": {"class": ["table"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "width:40%"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{2}{3}$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{4}{3}$$"}], "_values": ["Locate and label", "and", "."]}, {"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/kQe2ZUaTBYoyNxM10w8iGO_7BJFW5.png"}}]}]}]}]}]}
d.
{"table": [{"_attributes": {"class": ["table"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "width:40%"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{2}{6}$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{7}{6}$$"}], "_values": ["Locate and label", "and", "."]}, {"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/3oblwjHOuDBzsytcrLOy5H_XO8XTR.png"}}]}]}]}]}]}
e.   How did you partition the number line when you were locating the numbers
$$\frac{7}{8}$$
and
$$\frac{12}{8}$$
? Explain your reasoning.
f.   What patterns did you notice in the fractions you located?
Problem 3
Locate and label a point on the number line for
$$\frac{7}{3}$$
. Be as exact as possible.
[IMG]


aligns: no