few_shots: 
Example:
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?


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.

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, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001392_neg_0

8
standard_description: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)
problem_activity: Problem 1
Katia and Gerard are stocking shelves at the grocery store. Katia stocks 3 shelves with 7 boxes of cereal on each shelf. Gerard stocks 7 shelves with 3 boxes of cereal on each shelf.
Katia says they put the same number of cereal boxes on each shelf. Gerard says they didn’t, since they stocked a different number of boxes on each of a different number of shelves. Who do you agree with, Katia or Gerard? Explain.
Problem 2
Fill in the facts you know on the multiplication table below.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "table-layout:fixed; width:100%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#3399ff; text-align:center"}, "strong": [{"_value": "\u00d7"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "1"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "2"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "3"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "4"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "5"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "6"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "7"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "8"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "9"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "10"}]}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "1"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "2"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "3"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "4"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "5"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "6"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "7"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "8"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "9"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "10"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}]}]}]}
Problem 3
Solve.
a.
$$4 \times 8 =a $$
b.
$$18 = b \times 6$$
c.
$$c= 35 \div 7$$
d.
$$9 = 18 \div d$$


aligns: no