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: 
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.

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.
|                                                          | **           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 following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_000972_pos_0

6

fl_problem_001097_neg_0

7

fl_problem_001392_pos_0

8
standard_description: Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”
problem_activity: Problem 1
Elena and Zack want some change to buy penny candy. Their mom keeps rolls of 10 pennies to give to them for just this purpose. Their mom gives them 5 rolls and 4 loose pennies. How can Zack and Elena split the change they got from their mom evenly?
Problem 2
Elena used base-ten diagrams to find 3.72 ÷ 3. She started by representing 3.72.
[IMG]
She made three groups, each with 1 one. Then, she put the tenths and hundredths in each of the three groups. Here is her diagram for 3.72 ÷ 3.
[IMG]
Elena’s diagram for 3.72 has 7 tenths. The one for 3.72 ÷ 3 has only 6 tenths. Why?
Where did the extra hundredths (small squares) come from?
How would Elena calculate 95.6 ÷ 4?
Problem 3
Andre calculated 95.6 ÷ 4 using a method that was different from Elena’s method.
|           He started by writing the dividend, 95.6, and the divisor, 4.            | He then subtracted 4 groups of different amounts from 95.6, starting with 4 groups of 20... |                   …then 4 groups of 3, and then 4 groups of 0.9.                   |                 Andre calculated 20 + 3 + 0.9 and then wrote 23.9.                 |
|------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------|------------------------------------------------------------------------------------|
| .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2019/09/22/g5u6l9at3a.png |     .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2019/09/22/g5u6l9at3b.png      | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2019/09/22/g5u6l9at3c.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2019/09/22/g5u6l9at3d.png |
Andre subtracted 80.0 from 95.6. What does the 80 represent?
Andre wrote 3.0 above the 20.0 and then subtracted 12.0 from 15.6. How is the 12.0 related to the 3.0?
What do the numbers 20.0, 3.0, and 0.9 represent?
What is the meaning of the 0.0 at the bottom of Andre’s work?
Problem 4
Solve. Show or explain your work.
0.96 ÷ 6 = ___________
9.85 ÷ 5 = ___________
24.08 ÷ 8 = ___________
64.8 ÷ 6 = ___________


aligns: no