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: Add, subtract, multiply, and divide decimals to hundredths, 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 and explain the reasoning used.
problem_activity: Narrative
The purpose of this activity is for students to match situations to expressions and then find the value of the expressions (MP2). Students see expressions that show both quotients of a whole number by a fraction and quotients of a fraction by a whole number. They need to think carefully about the situations to make sure the expression they choose matches the situation (MP2).
Launch
Groups of 2
Display the image from student book:
[IMG]
“What do you notice? What do you wonder?” (They look like seeds. How many are in the bowls? Why are there 2 bowls?)
“The small bowl is filled with
\(\frac {1}{4}\)
cup of kernels. That is one serving of popcorn kernels. What does ‘one serving’ mean?” (It is the amount you are supposed to eat at one time.)
“About how many servings are in the big bowl?” (Answers vary. Sample responses range from 10 to 15.)
Activity
1–2 minutes: independent think time
5–8 minutes: partner work time
Monitor for students who:
draw diagrams to represent the situations
describe the relationship between the dividend and divisor using language such as “groups of”
use the value of the expression to describe why the expression matches the situation
Student Facing
Match each problem to an expression that represents the problem. Some expressions will not have a match. Be prepared to explain your reasoning.
One serving of popcorn is
\(\frac {1}{4}\)
cup of kernels. There are 3 cups of kernels in the bowl. How many servings are in the bowl?
[IMG]
One serving of orange juice is
\(\frac {1}{4}\)
liter. The container of juice holds 2 liters. How many servings are in the container?
One serving of granola is
\(\frac {1}{2}\)
cup. The bag of granola holds 5 cups. How many servings are in the bag?
\(\frac {1}{4} \div 3 \)
\(\frac {1}{2} \div 5\)
\(3 \div \frac {1}{4}\)
\(\frac {1}{4} \div 2\)
\(5 \div \frac {1}{2}\)
\(2 \div \frac {1}{4}\)
Find the value of each expression.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students do not correctly match the situations to the expressions, refer to each situation and ask, “How does the situation represent division?”
Activity Synthesis
Ask previously selected students to share their solutions.
“How did you decide which expression matched which situation?” (I thought about the number of things being divided and whether it was a fraction or a whole number. I thought about the size of the pieces.)
Display:
\(3 \div \frac {1}{4}= 12\)
“Describe how this equation represents the situation in the first problem.” (There are 3 cups of kernels in the bowl and a serving is
\(\frac {1}{4}\)
a cup, so there are 12 servings in the bowl.)
Display:
\(\frac {1}{4} \div 3 = \frac {1}{12}\)
“How do you know that this equation does not match the situation?” (The answer is a fraction. That doesn’t make sense because there is more than 1 serving in 3 cups.)


aligns: no