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 the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 100 can be thought of as a bundle of ten tens — called a “hundred.”
- The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
problem_activity: Narrative
The purpose of this activity is for students to add or subtract to find unknown addends within 20. Students will find unknown addends when the total is 20. The known addends may encourage students to think about ways to make a ten and to use the sums and differences that they know (MP7).
MLR7 Compare and Connect.
Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “Why did the different approaches lead to the same outcome? What did the methods have in common? How were they different?”
Advances: Representing, Conversing
Engagement: Develop Effort and Persistence.
Students may benefit from feedback that emphasizes effort and time on task. For example, give feedback on the partner relationship and how students are able to work together to complete a task. Encourage both partners to share ideas and speak up to agree or disagree.
Supports accessibility for: Social-Emotional Functioning, Attention
Required Materials
Materials to Copy
Number Cards 0-19
Required Preparation
Create a set of cards for each group of 2.
Launch
Groups of 2
Give each group a set of cards.
Activity
“Let’s play another game to find unknown addends.”
Select a volunteer to be your partner.
“Partner A will draw a card and hold it on their forehead without looking.”
Prompt the volunteer to demonstrate.
“Partner B names a number that you can add to the number on the card to get to 20.”
Think aloud finding and naming the number.
“Partner A then names the number they are holding on their head.”
Prompt the volunteer to find the number.
“Check your work and write an equation to represent how you found an unknown addend in the turn. Share your equation with your partner. Switch roles and play again.”
12 minutes: partner work time
Monitor for students who:
use place value reasoning or look to make 10
use known addition or subtraction facts
make equivalent, but easier sums or differences
Student Facing
Directions:
Partner A holds a card on their forehead without looking.
Partner B names the number that you can add to the number on the card to get 20.
Partner A says the number on their card.
Record an equation to represent how you found the unknown addend.
{"table": [{"_attributes": {"border": "1", "style": "width:100%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "my equations"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "my partner\u2019s equations"}]}]}], "tbody": [{"tr": [{"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}]}]}]}
Student Response
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Activity Synthesis
“Mai thought of trying to make 2 tens. What number needs to be added to 12 to make 2 tens?”
“What other methods did you use to find the unknown addend?”
Invite previously identified students to share methods.
“Pull out the number cards for 0–9, as you will use them in the next activity.”


aligns: no