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: 
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Answer: 
Yes. This problem solves a real-world problem involving mixing ingredients for cookies. A student doing this problem would need to reason about equivalent ratios of butter amounts to sugar amounts.

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_pos_0

6

fl_problem_001097_neg_0

7

fl_problem_001392_pos_0

8
standard_description: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
problem_activity: Task
Your teacher was just awarded \$1,000 to spend on materials for your classroom.  She asked all 20 of her students in the class to help her decide how to spend the money.  Think about which supplies will benefit the class the most.
{"table": [{"_attributes": {"class": ["regular", "centered"]}, "tbody": [{"tr": [{"th": [{"_value": "Supplies"}, {"_value": "Cost"}]}, {"td": [{"_value": "A box of 20 markers"}, {"_value": "\\$5"}]}, {"td": [{"_value": "A box of 100 crayons"}, {"_value": "\\$8"}]}, {"td": [{"_value": "A box of 60 pencils"}, {"_value": "\\$5"}]}, {"td": [{"_value": "A box of 5,000 pieces of printer paper"}, {"_value": "\\$40"}]}, {"td": [{"_value": "A package of 10 pads of lined paper"}, {"_value": "\\$15"}]}, {"td": [{"_value": "A box of 50 pieces of construction paper"}, {"_value": "\\$32"}]}, {"th": [{"_value": "Books and maps"}, {}]}, {"td": [{"_value": "A set of 20 books about science"}, {"_value": "\\$250"}]}, {"td": [{"_value": "A set of books about the 50 states"}, {"_value": "\\$400"}]}, {"td": [{"_value": "A story book (there are 80 to choose from)"}, {"_value": "\\$8"}]}, {"td": [{"_value": "A map: there is one of your city, one for every state, one of the country, and one of the world to choose from"}, {"_value": "\\$45"}]}, {"th": [{"_value": "Puzzles and games"}, {}]}, {"td": [{"_value": "Puzzles (there are 30 to choose from)"}, {"_value": "\\$12"}]}, {"td": [{"_value": "Board games (there are 40 to choose from)"}, {"_value": "\\$15"}]}, {"td": [{"_value": "Interactive computer games (math and reading)"}, {"_value": "\\$75"}]}, {"th": [{"_value": "Special Items"}, {}]}, {"td": [{"_value": "A bean bag chair for the reading corner"}, {"_value": "\\$65"}]}, {"td": [{"_value": "A class pet"}, {"_value": "\\$150"}]}, {"td": [{"_value": "Three month's supply of food for a class pet"}, {"_value": "\\$55"}]}, {"td": [{"_value": "A field trip to the zoo"}, {"_value": "\\$350"}]}]}]}]}
Write down the different items and how many of each you would choose. Find the total for each category.
Supplies
Books and maps
Puzzles and games
Special items
Create a bar graph to represent how you would spend the money.  Scale the vertical axis by \$100.  Write all of the labels.
What was the total cost of all your choices?  Did you have any money left over?  If so, how much?
Compare your choices with a partner. How much more or less did you choose to spend on each category than your partner? How much more or less did you choose to spend in total than your partner?


aligns: yes