few_shots: 
Example:
Concept/skill: 
Analyze and solve pairs of simultaneous linear equations.

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: 
Yes. The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.

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

shot_info: fl_problem_001392_pos_0

8
standard_description: Recognize and represent proportional relationships between quantities.
problem_activity: Problem 1
Robb’s Fruit Farm consists of 100 acres on which three different types of apples grow. On 25 acres, the farm grows Empire apples. Macintosh apples grow on 30 acres of the farm. The remainder of the farm grows Fuji apples.
Shade in the grid below to represent the portion of the farm each apple type occupies. Use a different color or pattern for each type of apple. What percent of the fruit farm is taken up by each type of apple? Fill in the table below.
[IMG]
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "table-layout: fixed; width: 100%;"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "background-color: rgb(238, 238, 238); text-align: center;"}, "_value": "Type of Apple"}, {"_attributes": {"scope": "col", "style": "background-color: rgb(238, 238, 238); text-align: center;"}, "_value": "Color in Grid"}, {"_attributes": {"scope": "col", "style": "background-color: rgb(238, 238, 238); text-align: center;"}, "_value": "Part:Whole Ratio"}, {"_attributes": {"scope": "col", "style": "background-color: rgb(238, 238, 238); text-align: center;"}, "_value": "Rate per 100 Acres"}, {"_attributes": {"scope": "col", "style": "background-color: rgb(238, 238, 238); text-align: center;"}, "_value": "% of Fruit Farm"}]}]}], "tbody": [{"tr": [{"td": [{}, {}, {}, {}, {}]}, {"td": [{}, {}, {}, {}, {}]}, {"td": [{}, {}, {}, {}, {}]}]}]}]}
Problem 2
Adam’s Fruit Farm also has 100 acres, but he grows more than just apples. Oranges take up 60 acres of his farm.
What percent of Adam’s farm is oranges? What percent is not oranges? Draw a 10x1 tape diagram to model the situation.
Problem 3
Represent the values of the following coins as percentages of $1 on the double number line.
dime
quarter
half-dollar
[IMG]
Problem 4
What percent of a dollar is the value of:
3 quarters?
6 quarters?
9 quarters?
Show your work using a double number line.


aligns: no