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


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Your response:
Thought: This problem applies trigonometric identities, including the angle addition formula for cosine.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS
options: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Use equivalent fractions as a strategy to add and subtract fractions.

Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
The purpose of this activity is for students to practice identifying fractional intervals along a number line. This is Stage 2 of the center activity, Number Line Scoot. This activity encourages students to count by the number of intervals (the numerator). Students have to land exactly on the last tick mark, which represents 4, to encourage them to move along different number lines. While this activity does not focus on equivalence, it gives students exposure to this idea before they work more formally with it in the next section. In the synthesis, students relate counting on a number line marked off in whole numbers to their number lines marked off in fractional-sized intervals.
It may be helpful to play a few rounds with the whole class to be sure students are clear on the rules of the game. Keep the number line game boards for center use.
Engagement: Develop Effort and Persistence.
Check in and provide each group with feedback that encourages collaboration and community. For example, check in after the first round of Number Line Scoot.
Supports accessibility for: Attention, Social-Emotional Functioning
Required Materials
Materials to Gather
Base-ten blocks
Number cubes
Materials to Copy
Number Line Scoot Stage 2 Gameboard
Number Line Scoot Stage 2 Directions
Required Preparation
Each group of 2 students needs a number cube.
Each student needs at least 5 base-ten cubes to use as game pieces.
Launch
Groups of 2
Give each group of 2 a gameboard, two recording sheets, a number cube, and at least 10 base-ten cubes.
“Now you will play a game where you move, by fractions, along different number lines. To start, each player places a small cube on zero on each number line. The goal of the game is to get as many small cubes as you can to the 4 on any of the number lines.”
Roll the number cube, demonstrate where to record the rolled number and move that fraction along one of the number lines.
Activity
10 minutes: partner work time
As students work, monitor for students who count by the numerator once they have chosen a number line.
Activity Synthesis
Display a gameboard with a marker on
\(\frac{3}{4}\)
.
“If I rolled a 4, and chose to move
\(\frac{4}{4}\)
, how would you count the move?” (I would count 1, 2, 3, 4.)
“How did you know you have moved
\(\frac{4}{4}\)
?” (Because each space is
\(\frac{1}{4}\)
, so I need to move 4 times.)
Display a number line marked with only 0, 1, 2, 3, 4.
“How is counting along this number line the same and different than counting along your number lines?” (On the whole number one each space is 1 so we just count 1, 2, 3, 4. On our number lines we still count the jumps, but now each space is smaller than 1 so we need the denominator to tell us the size of each space.)


correct_option_index: 4