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 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).

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.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
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_pos_0

7

fl_problem_001392_pos_0

8
standard_description: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
problem_activity: Problem 1
What is the measure, in wedges, of the following angle?
[IMG]
A ray that turns all the way around its endpoint and back to its starting place has made a full turn. We say that the ray has turned 360
degrees
.
[IMG]
How many degrees has the ray turned from where it started?
[IMG]
[IMG]
[IMG]
Problem 2
Determine how many degrees the wedge created in Lesson 5 measures, and use that to create a makeshift protractor to measure benchmark angles.
Use a similar process to create a makeshift protractor that measures in increments of 45°.
Problem 3
Using the makeshift protractors you made in Anchor Task #2, find the measure, in degrees, of each of the following angles. If an angle can’t be measured precisely with either protractor, make an estimate.
| 1.            |https://d21royfkw9g4l6.cloudfront.net/HGpdLmPiXL2wEUGq7M9oOB_HN2R71.png|  |https://d21royfkw9g4l6.cloudfront.net/HGpdLmPiXL2wEUGq7M9oOB_HN2R71.png| image:: https://d21royfkw9g4l6.cloudfront.net/HGpdLmPiXL2wEUGq7M9oOB_HN2R71.png |     1.            |https://d21royfkw9g4l6.cloudfront.net/FMs2nYL35BSek6I79QzcBc_7N2YKT.png|  |https://d21royfkw9g4l6.cloudfront.net/FMs2nYL35BSek6I79QzcBc_7N2YKT.png| image:: https://d21royfkw9g4l6.cloudfront.net/FMs2nYL35BSek6I79QzcBc_7N2YKT.png      |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| 1.            |https://d21royfkw9g4l6.cloudfront.net/6c8XNXS8LTq61hZkJBlXSF_CSHLNR.png|  |https://d21royfkw9g4l6.cloudfront.net/6c8XNXS8LTq61hZkJBlXSF_CSHLNR.png| image:: https://d21royfkw9g4l6.cloudfront.net/6c8XNXS8LTq61hZkJBlXSF_CSHLNR.png | 1.                     |https://d21royfkw9g4l6.cloudfront.net/uPouVZDNncCcCiLGZlYrBR_VUQXH3.png|  |https://d21royfkw9g4l6.cloudfront.net/uPouVZDNncCcCiLGZlYrBR_VUQXH3.png| image:: https://d21royfkw9g4l6.cloudfront.net/uPouVZDNncCcCiLGZlYrBR_VUQXH3.png |


aligns: no