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


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response, in json format:
{
  "explanation": "An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation. Solving this problem does not require use of the Pythagorean identity.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS
options: Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?
problem_activity: Narrative
In this activity, students solve addition problems using money based on the Pattern Block Puzzles they sketched in the last activity.
The launch of the activity is an opportunity for students to reason which of the two designs will cost more before they complete any computations.
MLR7 Compare and Connect.
Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “Did anyone solve the problem the same way, but would explain it differently?”, “What did the representations have in common?”, “How were they different?”
Advances: Representing, Conversing
Launch
Groups of 2
“At the Pattern Block Store, each pattern block shape has a different price.”
Display the price list.
“Which of the two puzzles that you sketched do you think will cost more to make? Puzzle 1 or 2?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Activity
“Use the price list to figure out how much your two puzzles would cost.”
5 minutes: independent work time
5 minutes: partner discussion
As students work, look for different addition strategies. Monitor for students who:
add like quantities first
add bigger or smaller coins first
add some coins mentally
Student Facing
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "shape"}, {"_attributes": {"scope": "col"}, "_value": "cost"}]}]}], "tbody": [{"tr": [{"td": [{"figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "150143", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "Pattern block. Hexagon.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/cv5e6biplridvvjo2ed3aj5h1l0e?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-150143.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-150143.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T164143Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0347509318fc91e6302bb64febc22d05e7fffde820a42d8a1c974d802d04e917"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}]}, {"figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-image-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "37582", "data-record-model": "ImageFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "Coin. A quarter.", "class": ["h-max-height--5-lines"], "role": "image", "src": "https://cms-im.s3.amazonaws.com/mbgbaf4nkk0vsawoqjlubrf00b4z?response-content-disposition=inline%3B%20filename%3D%22quarter-back.png%22%3B%20filename%2A%3DUTF-8%27%27quarter-back.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T164143Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5ac6aff10bd46b5365f46ffeab054cd6ff7d700dfc9c660e3d011fd4c9676951"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}]}]}, {"td": [{"figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "150144", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "Pattern block. Trapezoid.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/jbxq4b7lr973twd7cju57q0oulmj?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-150144.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-150144.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T164143Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=cc2008c7b66cc9ba4e3feaf6d1cf65f2728db5a857421988d5a8147858504207"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}]}, {"figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-image-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "37583", "data-record-model": "ImageFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "A dime.", "class": ["h-max-height--3-lines"], "role": "image", "src": "https://cms-im.s3.amazonaws.com/cc7y30885x6mfqcvcubex3157eqw?response-content-disposition=inline%3B%20filename%3D%22dime-front.png%22%3B%20filename%2A%3DUTF-8%27%27dime-front.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T164143Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ed89067d01fbdb1013e28bfcff88ddb6c25812308117e2bbcefd3ce44f699d7a"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}]}]}, {"td": [{"figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "150145", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "Pattern block. Rhombus.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/eifk4j1l1h1tmht1t4etxeq8tveu?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-150145.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-150145.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T164143Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=58c5ac52a6d4f25d2d6c3c613126807263a2a66bf9e4aef477a79db9cedd3c1b"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}]}, {"figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-image-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "37584", "data-record-model": "ImageFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "Nickel.", "class": ["h-max-height--4-lines"], "role": "image", "src": "https://cms-im.s3.amazonaws.com/eafp6vkvl2h847xnayhv4z1hsgpk?response-content-disposition=inline%3B%20filename%3D%22nickel-front.png%22%3B%20filename%2A%3DUTF-8%27%27nickel-front.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T164143Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=364dd5652c695c8ea37c72709081c93a7d637b3606704f096422eac5b76b6266"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}]}]}, {"td": [{"figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "150146", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "Pattern block. Triangle.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/nwbexfpbl484uucueevlb0pvhxm8?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-150146.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-150146.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T164143Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f63c01510af539188608375c3095abe0b87f05e2c40893f0cba48aec0cb42d1c"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}]}, {"figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-image-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "37585", "data-record-model": "ImageFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "Penny.", "class": ["h-max-height--4-lines"], "role": "image", "src": "https://cms-im.s3.amazonaws.com/s4d93o4nmnqcgb18bzjs965plev5?response-content-disposition=inline%3B%20filename%3D%22penny-back.png%22%3B%20filename%2A%3DUTF-8%27%27penny-back.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T164143Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b1fa77470c010d1273eed7fa1b9b1afb99d84f2212108c0c6bfbdf297fa2308e"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}]}]}]}]}]}
How much would the two puzzles you sketched cost at the Pattern Block Store? Show or explain your reasoning.
Puzzle 1:
Puzzle 2:
Student Response
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Activity Synthesis
Invite previously selected students to share.
“Is it possible to redesign the puzzle to save more money?” (Yes, I can switch a blue rhombus with two triangles.)


correct_option_index: 1