few_shots: 
Example:
Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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
$$-\frac{1}{4}$$


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, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: fl_problem_001097_pos_0

7
standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Problem 1
a.   A construction worker is tiling a backsplash. The backsplash is
$${4{{{1\over2}}}}$$
tiles long and
$${{1\over2}}$$
tile tall. How many tiles are needed in total for the whole backsplash? Give an exact answer that includes the fractions of a tile she will need.
b.   A runway measures
$${10{1\over3}}$$
yards long and
$${{3\over4}}$$
yards wide. What is the area, in square yards, of the runway?
Problem 2
a.   Kendra is making
$${{1\over2}}$$
of a recipe. The full recipe calls for
$${3 {1\over4}}$$
cups of flour. How many cups of flour should Kendra use?
b.   Claire walked
$${2{2\over5}}$$
miles. Jason walked
$${{2\over3}}$$
as far as Claire. How many miles did Jason walk?
Problem 3
Solve. Show or explain your work.
a.
$${{2\over3} \times 4{1\over4}}$$
b.
$${3{2\over5} \times {1\over2}}$$
c.
$${{5\over4} \times 3{1\over3}}$$


aligns: yes