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 attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
problem_activity: Narrative
The purpose of this activity is for students to use language to describe and distinguish quadrilaterals (MP6). The activity has the same structure as the activity where students tried to identify which rectangle on the coordinate grid their partner was thinking of. Students rely on what they remember about categories of quadrilaterals, such as rectangles and rhombuses. They can also use informal language such as tilted, arrow, or red pattern block. The goal of the synthesis is to share and gather language which was helpful for distinguishing the quadrilaterals.
This activity uses
MLR2 Collect and Display
. Advances: Conversing, Reading, Writing.
Representation: Internalize Comprehension.
Activate or supply background knowledge. Provide a graphic organizer that lists characteristics of different quadrilaterals for students to use as a reference as they ask questions about the shape.
Supports accessibility for: Memory, Attention, Conceptual Processing
Required Materials
Materials to Gather
Dry erase markers
Sheet protectors
Materials to Copy
Guess Which One
Required Preparation
Consider giving each student a sheet protector and a dry-erase marker so that students can easily reuse the blackline master for multiple rounds of the game.
Launch
Groups of 2
Distribute the blackline master with the sheet protectors and dry-erase marker to each group or instruct students to use the image of quadrilaterals in their workbook.
Activity
8 minutes: partner work time
MLR2 Collect and Display
Circulate, listen for and collect the language students use to describe the quadrilaterals as they sort. Listen for:
language and gestures used to describe angles, such as: wide, open, skinny, square, big, small, obtuse, acute, right
language and gestures used to describe sides, such as: straight, cross, intersect, parallel, perpendicular
language used to describe shapes, such as: square, tilted, flat, trapezoid, rhombus, diamond, arrow, parallelogram
Record students’ words and phrases on a visual display and update it throughout the lesson.
Student Facing
Play a round of Guess Which One.
Partner A: Select one of the quadrilaterals. Do not reveal your choice to your partner.
Partner B: Ask “yes” or “no” questions to guess which shape your partner picked. After each question, cross out or remove quadrilaterals based on your partner’s answer.
[IMG]
[IMG]
[IMG]
Use the space to record your questions for this round.
Han and Mai were playing Guess Which One. These are the last two shapes. What question can Mai ask to determine which shape is the one that Han picked?
[IMG]
If there is time: Switch roles and play Guess Which One again.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students do not ask specific questions during this task,
collect a set of questions during a practice round and ask, “Which questions could you ask to find out which shape your partner chose?”
Activity Synthesis
“Are there any other words or phrases that are important to include on our display?”
As students share responses, update the display, by adding (or replacing) language, diagrams, or annotations.
Remind students to borrow language from the display as needed.
Invite previously selected students to share.
Display rhombus card that is not a square.
“What are some names we can use to describe this shape?” (quadrilateral, diamond, parallelogram, rhombus)


aligns: yes