few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. 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.

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_pos_0

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im_task_000870_neg_0

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im_task_001160_neg_0

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standard_description: Count to 100 by ones and by tens.
problem_activity: Narrative
The purpose of this activity is for students to make connections between written numbers and expressions. In the activity synthesis, students see each teen number written as an equation. In this unit, when reading equations to students, read the equal sign as “is.” For example, read
\(10 + 3 = 13\)
as “10 plus 3 is 13.” The equal sign will be read as “equals” in the next unit.
MLR8 Discussion Supports.
Synthesis: At the appropriate time, give students 2–3 minutes to make sure that everyone in their group can explain how they organized the numbers and expressions. Invite groups to rehearse what they will say when they share with the whole class.
Advances: Speaking, Conversing, Representing
Engagement: Develop Effort and Persistence.
Some students would benefit from having clear examples of the expectation of group work in this activity. Invite students to generate a list of shared expectations for group work. Ask students to share explicit examples of what those expectations would look like in this activity.
Supports accessibility for: Social-Emotional Functioning
Required Materials
Materials to Copy
Numbers and Expressions Cards
Required Preparation
Create a set of cards from the blackline master for each group of 4.
Launch
Groups of 4
Give each group of students a set of cards.
“Work with your group to organize the cards in a way that makes sense to you.”
Activity
6 minutes: small-group work time
Monitor for students who organize the numbers and expressions as shown in the sample response.
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
Invite a group of students to share how they organized the numbers and expressions or display the image in student responses.
“What do you notice about the numbers and expressions when they are arranged this way?” (They’re in the order that we count. The first number stays the same. The second number is 1 more each time. All the expressions have a 10. The second number starts at 1 and is one more each time. The expressions match the numbers.)
“Which number does
\(10 + 1\)
represent? How do you know?” (11)
“
\(10 + 1\)
is 11. We can write that as
\(10 + 1 = 11\)
.”
Demonstrate writing equations for each number and expression.


aligns: no