few_shots: 
Example:
Concept/skill: 
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:70%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "No solution"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Exactly 1 solution"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Infinite number of solutions"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9=4x+7}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y=3y+5}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y={x\\over2}}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${3x+6y-9=0}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${x=y}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${1.25x=1.25y}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9.9=6x+8y}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9x=2.5y-8.8}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${11x-2y=1.5}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${11x-2y=2.5}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {}]}]}]}]}
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Answer: 
No. Completing neither of these problems requires replacing one equation by the sum of that equation and a multiple of the other equation.

Now, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: fl_problem_001392_neg_0

8
standard_description: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
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