few_shots: 
Example 1:
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.

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Concept/skill: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
[IMG]
Draw a circle with center $P$ and with  radius $r \gt 0$.  Explain why the circle
meets each ray of angle $A$ in a single point.  Label these points $Q$ and $R$ respectively.
Draw circles with centers $Q$ and $R$ respectively and radius $r$.  These circles meet at $P$ and a second point to be labelled $B$.
Show that ray $\overrightarrow{PB}$  bisects angle $P$.


Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

Answer: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

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

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
problem_activity: Narrative
The purpose of this activity is for students to compare shapes by covering them with pattern blocks. Students experience tiling as a way to see which shape covers the most space. There are several ways to tile the shapes, but it may prove most useful to use the same units, such as triangles. The rectangle can only be fully tiled with square pattern blocks. To compare shapes B and C, students will need to notice that the rectangle and parallelogram can be made the same length, but the square pattern blocks used to tile the rectangle are taller than the blocks used to tile the parallelogram.
[IMG]
[IMG]
The work here prepares students to tile figures with square tiles in the next lesson and to think of area in terms of square units.
MLR8 Discussion Supports.
Synthesis: Create a visual display of shapes A, B, and C. As students discuss their comparisons, annotate the display with their observations. For example, when comparing shape B to C, write “same length, but taller.”
Advances: Speaking, Listening
Action and Expression: Develop Expression and Communication.
Synthesis: Identify connections between strategies that result in the same outcomes but use differing approaches.
Supports accessibility for: Conceptual Processing
Required Materials
Materials to Gather
Pattern blocks
Scissors
Materials to Copy
Pattern Blocks to Compare Shapes
Required Preparation
Each group of 2 needs at least 2 hexagons and trapezoids,  4 squares and rhombuses, and 8 triangles.
Launch
Groups of 2
Give each student a copy of the blackline master.
Give each group pattern blocks.
Display the first two shapes (the hexagon and the heart-shaped octagon).
“What do you notice? What do you wonder?” (Students may notice: Both shapes could be made with pattern blocks. The second shape looks like the first shape, but it’s been bent. Students may wonder: Which shape covers more space? Which shape is larger?)
1 minute: quiet think time
Share and record responses.
“Which shape covers more space? How do you know?” (We can cover them with the same blocks, so they cover the same amount of space.)
2 minutes: partner discussion
Share and record responses.
Activity
“Let's continue comparing shapes. Work with your partner to decide which of these shapes covers the most space. Use pattern blocks if they are helpful.”
5 minutes: partner work time
Monitor for students who:
use pattern blocks to determine which shape covers the most space
notice that shape B and C would be the same length if one of the ends of B was moved over, but C covers more space because it is taller
Student Facing
Your teacher will give you handouts with some shapes on them.
Use pattern blocks to decide which shape covers the most space. Be ready to explain your reasoning.
[IMG]
Student Response
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Activity Synthesis
Ask selected students to share strategies for tiling each shape with pattern blocks and how the tiling helped them decide which shape covers the most space.
“When we decide which shape covers the most space, we are talking about the area of a shape. We can think about the
area as the amount of space covered by a shape.”
“Which of these shapes has the greatest area?” (C takes up the most space, so it has the greatest area.)


aligns: no