few_shots: 
Example:
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.

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
standard_description: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
problem_activity: Activity
In this activity, students get a chance to practice solving equations with a single variable. The equations resemble the types of equations students see in the associated Algebra 1 lesson after they substitute for a variable. Students will work in pairs and each partner is responsible for answering the questions in either column A or column B. Although each row has two different problems, they share the same answer. Ensure that students work their problems out independently and collaborate with one another when they do not arrive to the same answers. Students construct viable arguments and critique the reasoning of others (MP3) when they resolve errors by critiquing their partner's work or explaining their reasoning.
Launch
Arrange students in groups of 2.
Student Facing
Solve each equation.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "row"}, {"_attributes": {"scope": "col"}, "_value": "column A"}, {"_attributes": {"scope": "col"}, "_value": "column B"}]}]}], "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "1"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "28834"}, "_value": "\\(4(2x+8)-10 = 14\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "28861"}, "_value": "\\(4 + 2(\\text-3x+5)=20\\)"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "2"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "28897"}, "_value": "\\(3(x-4)+6 = 60\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "28936"}, "_value": "\\(3(\\frac12x + 9)-5=55\\)"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "3"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "28976"}, "_value": "\\(4(\\frac{x+3}{2})-5 = 10\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29019"}, "_value": "\\(7-2(6x+1)=\\text-49\\)"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "4"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29065"}, "_value": "\\(2x+(5-3x) = 14\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29114"}, "_value": "\\(1=5x+10-4x\\)"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "5"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29167"}, "_value": "\\(4x + 2(3-x)=16\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29213"}, "_value": "\\(x+2(x-4)+5=12\\)"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "6"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29263"}, "_value": "\\(2x - 2(3x-1) = 8\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29314"}, "_value": "\\(\\text-6x+2(4x+5)=7\\)"}]}]}]}]}]}
​​
Student Response
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Activity Synthesis
The purpose of the discussion is to recall strategies for solving equations with one variable. Select students to share their solutions including their reasoning for the steps they take.
Some questions for discussion:
"When there is a variable inside parentheses, how did you approach the problem?" (I distributed the value multiplying the parentheses to remove the parentheses then solved the equation as usual.)
"How could you check that your answer works using the original equation?" (I could substitute the value for
\(x\)
into the original equation and determine if the equation is true.)


aligns: no