few_shots: 
Example:
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 and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

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_001097_pos_0

7
standard_description: 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.
problem_activity: Hummingbird feeders can be filled with a simple sugar water mixture. Two different recipes are shown below.
{"table": [{"_attributes": {"class": ["table"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"div": [{"_attributes": {"class": ["table-responsive"]}, "table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "width: 80%;"}, "caption": [{"_value": "Recipe 1"}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center;"}, "_value": "Water (cups)"}, {"_attributes": {"style": "text-align: center;"}, "_value": "Sugar (cups)"}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$2$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{2}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$4$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$16$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$4$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$28$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$7$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$32$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$8$$"}]}]}]}]}]}]}, {"div": [{"_attributes": {"class": ["table-responsive"]}, "table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "width: 80%;"}, "caption": [{"_value": "Recipe 2"}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center;"}, "_value": "Water (cups)"}, {"_attributes": {"style": "text-align: center;"}, "_value": "Sugar (cups)"}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$2\\frac{2}{3}$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$4$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$1\\frac{1}{2}$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$8$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$3$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$24$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$9$$"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$32$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$12$$"}]}]}]}]}]}]}]}]}]}]}
Compare the two different recipes. Which recipe is more sugary? Justify your response.


aligns: yes