few_shots: 
Example 1:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Concept/skill: 
Recognize and represent proportional relationships between quantities.

Answer: 
No. Usually problems that teach recognizing and representing proportional relationships between quantities involve deciding whether two quantities are in a proportional relationship or identifying the constant of proportionality, and then representing proportional relationships by equations or explaining proportional relationship using coordinate graphs.

Example 2:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
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: 
Analyze and solve pairs of simultaneous linear equations.

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

shot_info: fl_problem_000972_neg_0

6

fl_problem_001097_neg_0

7

fl_problem_001392_pos_0

8
standard_description: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
problem_activity: Problem 1
Bisect the following angle using constructions. Write your steps for construction.
$${\overline{CA}\cong \overline{AB}}$$
[IMG]
Problem 2
You and your partner will be provided with a list of steps (in random order) needed to copy an angle using a compass and straightedge. Your task is to place the steps in the correct order, then follow the steps to copy the angle below.
[IMG]
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width:50%"}, "tbody": [{"tr": [{"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$B$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$B$$"}], "_values": ["Draw circle", ": center", ", any radius."]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$B$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$A$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$C$$"}], "_values": ["Label the intersections of circle", "with the sides of the angle as", "and"], "em": [{"_value": "."}]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$B$$"}], "_values": ["Label the vertex of the original angle as", "."]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${\\overrightarrow{ED}}$$"}], "_values": ["Draw", "."]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${\\overrightarrow{EG}}$$"}], "_values": ["Draw", "as one side of the angle to be drawn."]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$F$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$F$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$FA$$"}], "_values": ["Draw circle", ": center", ", radius", "."]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$E$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$E$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$EA$$"}], "_values": ["Draw circle", ": center", ", radius", "."]}]}, {"td": [{"em": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$E$$"}]}], "_values": ["Label intersection of circle", "with", "as", "."], "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${\\overrightarrow{EG}}$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$F$$"}]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$E$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$F$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$D$$"}], "_values": ["Label either intersection of circle", "and circle", "as", "."]}]}]}]}]}


aligns: no