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: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Answer: 
No. This task does not involve an equation in two variables. There is only 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_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 100 can be thought of as a bundle of ten tens — called a “hundred.”
- The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
problem_activity: Narrative
The purpose of this activity is for students to subtract one-digit and two-digit numbers from a three-digit number using the methods that make sense to them. Each difference would require students to decompose a ten to subtract by place. They may count back or count on by place to find the difference. They may also use their understanding of place value and their experiences decomposing a ten when they subtracted within 100. In the synthesis, focus on connecting and comparing these different methods and making sense of representations that show decomposing a unit when subtracting by place.
When students use base-ten blocks, number lines, or equations to find the value of each difference they use appropriate tools strategically (MP5).
This activity uses
MLR7 Compare and Connect
. Advances: representing, conversing.
Engagement: Provide Access by Recruiting Interest.
Optimize meaning and value. Invite students to share ideas of items to sell (cupcakes, sports cards, video games, etc.) and use that as the context around the problems to solve. Discuss the action of selling to represent subtraction.
Supports accessibility for: Attention, Conceptual Processing
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Activity
“Find the value of each expression in any way that makes sense to you. Explain or show your reasoning.”
3–4 minutes: independent work time
3–4 minutes: partner discussion
Monitor for an expression that generates a variety of student methods or representations to share in the synthesis, such as:
using base-ten blocks
drawing a number line
writing their reasoning in words
writing equations
Student Facing
Find the value of each expression in any way that makes sense to you. Explain or show your reasoning.
\(354 - 7\)
\(354 - 36\)
\(354 - 48\)
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
MLR7 Compare and Connect
Invite one previously identified student who used a method that did not explicitly show decomposing a ten to share.
Invite one previously identified student to show how they decomposed a ten to subtract with base-ten blocks or a base-ten diagram.
“What is the same and what is different about the ways _____ and _____ represented the problem?” (____ used base-ten blocks and showed decomposing a ten. _____ showed a number line and counting back 36. They used the same numbers. They found the same difference.)


aligns: no