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: Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), 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 subtract a one-digit number from a two-digit number. In the previous activity, students shared many ways to subtract including using connecting cubes or base-ten blocks to show decomposing a ten. They build on this understanding as they use base-ten blocks to represent the starting number and subtract an amount that requires them to decompose a ten.
MLR8 Discussion Supports.
Synthesis: Display sentence frames to support students with preparing to explain their thinking in the whole-class discussion. “First, I _____ because . . . .” “I noticed _____ so I . . . .” If necessary, revoice student ideas to demonstrate mathematical language, and invite students to chorally repeat phrases that include relevant vocabulary in context.
Advances: Speaking, Conversing
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details they think are important to remember. Use the sentence frame: “The next time I subtract, I will know that I need to decompose a ten when . . . .“
Supports accessibility for: Conceptual Processing, Memory
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give each group access to base-ten blocks.
Activity
“Diego was representing numbers using base-ten blocks. Work with a partner to follow along and see what Diego discovered.”
“Use your blocks first to show what Diego does. Then answer any questions.”
8 minutes: partner work time
Monitor for students who talk about “exchanging” or “trading” a ten for ten ones.
Student Facing
Diego started with 5 tens and 5 ones. Represent Diego’s blocks with the base-ten blocks.
How many does he have?
Diego took away 2 tens.
Draw a representation to show what happened to Diego’s blocks.
Write an equation to show how many Diego has now.
Then, Diego took away 8 ones.
Draw a diagram to show what happened to Diego’s blocks.
Write an equation to show how many Diego has now. Be prepared to explain your reasoning.
Student Response
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Advancing Student Thinking
Some students may get the ones they need, but also keep the ten. Consider asking:
“Why did you add 10 ones to Diego’s blocks?”
“What is the value of the blocks now?”
“When you decompose a tower of ten, what happens to the tower? How could you show this with the base-ten blocks?”
Activity Synthesis
“What did you need to do with the blocks when Diego took away 8 ones?”
Select previously identified students to share.
“What is different about using base-ten blocks compared to the towers of ten?” (With the towers we could break it apart, but with the base-ten blocks we had to give a ten and take out 10 ones.)
“When you subtract by place, sometimes you need to decompose a ten to subtract ones. When we use connecting cubes, we can show those by breaking apart or decomposing a tower of ten.”
“When we use base-ten blocks, we can't break apart the ten into ones, but we can still show decomposing it by replacing 1 ten with 10 ones.”


aligns: no