few_shots: 
Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_neg_0

HS_0
standard_description: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
problem_activity: Narrative
The purpose of this activity is for students to relate multiplying a non-unit fraction by a whole number to multiplying a unit fraction by the same whole number. After finding the value of
\(\frac{1}{5} \times 3\)
in a way that makes sense to them, they then consider the value of the products
\(\frac{2}{5} \times 3\)
and
\(\frac{3}{5} \times 3\)
. In the synthesis students address how they can use the value of
\(\frac{1}{5} \times 3\)
to find the value other expressions.
Launch
Groups of 2
Activity
8 minutes: independent work time
Monitor for students who:
draw a diagram
use division to solve
recognize a relationship between
\(\frac{1}{5}\times3\)
,
\(\frac{2}{5}\times3\)
, and
\(\frac{3}{5}\times3\)
.
Student Facing
Find the value of each expression. Explain or show your reasoning. Draw a diagram if it is helpful.
\(\frac{1}{5} \times 3\)
\(\frac{2}{5} \times 3\)
\(\frac{3}{5} \times 3\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Ask previously selected students to share their solutions.
Display:
\(\frac{1}{5} \times 3\)
,
\(\frac{2}{5} \times 3\)
,
\(\frac{3}{5} \times 3\)
“How are the expressions the same?” (They all have a 3. They all have some fifths and there is a product.)
“How are the expressions different?” (The number of fifths is different. There is 1 and then 2 and then 3.)
“How can you use the value of
\(\frac{1}{5} \times 3\)
to help find the value of
\(\frac{2}{5} \times 3\)
?” (I can just double the result because it’s
\(\frac{2}{5}\)
instead of
\(\frac{1}{5}\)
.)
“What about
\(\frac{3}{5} \times 3\)
?” (That’s just another
\(\frac{1}{5} \times 3\)
.)
Display diagram from student solution or a student generated diagram like it.
“How does the diagram show
\(\frac{1}{5} \times 3\)
?” (There is 3 total and
\(\frac{1}{5}\)
of it is shaded.)
Display:
\(\frac{2}{5} \times 3\)
.
“How could you adapt the diagram to show
\(\frac{2}{5} \times 3\)
?” (I could fill in 2 of the fifths in each whole instead of 1.)
“In the next activity we will study a diagram for
\(\frac{2}{5} \times 3\)
more.”


aligns: no