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: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
problem_activity: Narrative
The purpose of this activity is for students to practice describing geometric attributes of a quadrilateral with increasing precision by playing a game. Students should be encouraged to ask questions like, “Are all the sides the same length?” rather than, “Is it a square?” to keep the focus on attributes of the quadrilateral rather than the name. As students decide which questions to ask they think about important attributes such as side lengths and angles and have an opportunity to use language precisely (MP6, MP7).
Students will use the quadrilaterals from the previous lesson to hide in the “mystery quadrilateral” folder, but will have a copy of all the shapes in their workbook to support them in asking questions to narrow down the shape. Students can also cover shapes in their workbook with counters as they rule out shapes.
MLR8 Discussion Supports.
Synthesis: Think aloud and use gestures to emphasize the attributes that students use to describe the shapes. For example, trace your finger along the angles and sides of the shape as students describe them.
Advances: Listening, Representing
Engagement: Develop Effort and Persistence.
Check in and provide each group with feedback that encourages collaboration and community.
Supports accessibility for: Social-Emotional Functioning
Required Materials
Materials to Gather
Counters
Folders
Materials from a previous lesson
Required Preparation
Each group of 2 needs a set of quadrilateral cards from the previous lesson.
Each group of 2 will need a folder to hide the card during this activity.
Launch
Groups of 2
“Now you’re going to play Mystery Quadrilateral with your partner. Re-read the directions for the game, then think about some words that may be helpful as you play.” (side, angle, right angle, equal, skinny, tall, slanted)
1 minute: quiet think time
Share and record responses.
Give each group a folder containing a set of the quadrilateral cards from the previous lesson.
“How could you use the images of all the quadrilaterals on your paper as you play?” (They can help me think about questions I could ask. I could mark off quadrilaterals as I figure out that they're not the mystery quadrilateral.)
Give students access to counters and let them know they can be used to cover shapes they want to cross out during the game.
Activity
“Play Mystery Quadrilateral with your partner. Be sure to take turns hiding the shape and guessing the shape.”
10–15 minutes: partner work time
Student Facing
Partner A: Choose a shape from the group of quadrilaterals. Place it in the mystery quadrilateral folder without your partner seeing it.
Partner B: Ask up to 5 “yes” or “no” questions to identify the quadrilateral. Then guess which quadrilateral is the mystery quadrilateral.
Partner A: Show your partner the mystery quadrilateral.
Switch roles and play again.
Student Response
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Activity Synthesis
“What shapes were the easiest to figure out and why?” (W was easy because it was so different with one angle pointing in. X was easy because it was the only square resting on a side.)
“What shapes were the most challenging to ask questions about and why?” (FF was challenging because none of the sides were the same length, and it was hard to get more information with “yes” or “no” questions. M and BB were hard to tell apart because they were so similar and it was hard to figure out what questions to ask.)


aligns: no