few_shots: 
Example:
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).

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_001097_pos_0

7
standard_description: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
problem_activity: Problem 1
Three students are partitioning a number line into fourths. Their work is shown.
Chadwick’s number line:
[IMG]
Allan's number line:
[IMG]
Dobrilla's number line:
[IMG]
Whose partitioning makes the most sense to you? Explain your reasoning.
Problem 2
a.
| Locate and label                               $$\frac{3}{4}$$                              and                               $$\frac{6}{4}$$                              . | .. image:: https://d21royfkw9g4l6.cloudfront.net/kQe2ZUaTBYoyNxM10w8iGO_7BJFW5.png |
|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------|
b.
| Locate and label                                 $$\frac{7}{8}$$                                and                                 $$\frac{12}{8}$$                                . | .. image:: https://d21royfkw9g4l6.cloudfront.net/kQe2ZUaTBYoyNxM10w8iGO_7BJFW5.png |
|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------|
c.
| Locate and label                                 $$\frac{2}{3}$$                                and                                 $$\frac{4}{3}$$                                . | .. image:: https://d21royfkw9g4l6.cloudfront.net/kQe2ZUaTBYoyNxM10w8iGO_7BJFW5.png |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------|
d.
| Locate and label                                 $$\frac{2}{6}$$                                and                                 $$\frac{7}{6}$$                                . | .. image:: https://d21royfkw9g4l6.cloudfront.net/3oblwjHOuDBzsytcrLOy5H_XO8XTR.png |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------|
e.   How did you partition the number line when you were locating the numbers
$$\frac{7}{8}$$
and
$$\frac{12}{8}$$
? Explain your reasoning.
f.   What patterns did you notice in the fractions you located?
Problem 3
Locate and label a point on the number line for
$$\frac{7}{3}$$
. Be as exact as possible.
[IMG]


aligns: no