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: 
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Answer: 
Yes. This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.

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

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
problem_activity: Narrative
The purpose of this activity is to introduce students to a new unit, the hundred. Students used connecting cubes to make tens in grade 1 and used tens and ones to count to and represent numbers within 120.
In an earlier unit, students were introduced to base-ten blocks and used base-ten diagrams to represent sums and differences within 100. Students build on this understanding as they use blocks to represent a starting number (96) and add ones until they reach a total value of 100. As students discover they have 10 tens, monitor for language they use to describe the total value of the blocks and the connections they make to their previous work with ones, tens, and three-digit numbers (MP7).
Engagement: Provide Access by Recruiting Interest.
Give the students a context to connect to their own lives. Tell the students that the base-ten blocks represent gum. The ones are single sticks of gum and the tens are packs of gum.
Supports accessibility for: Conceptual Processing, Attention
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Display photo of 8 tens and 16 ones.
“Andre was using base-ten blocks to represent numbers. How many do you see? How do you see them?” (96. I see 8 tens and 16 ones. I see it as 9 tens and 6 ones.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Activity
“Work with a partner to follow along and see what Andre discovered as he adds more blocks.”
10 minutes: partner work time
Monitor for students who explain that the value is 100 by:
counting by 1 from 80 or by 1 from 96
counting by 10
Student Facing
How many do you see? How do you see them?
[IMG]
Andre added more blocks.
[IMG]
What is the value of Andre’s blocks now?
How many tens and ones are in this number?
Andre made the same number with the fewest amount of blocks possible. Draw a base-ten diagram to show what Andre’s number looks like now. Use your base-ten blocks to help.
Student Response
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Advancing Student Thinking
If students represent 100 with a diagram that includes tens and ones, consider asking:
“Can you explain how your diagram represents Andre’s total value using the fewest number of blocks possible?”
“Is there a way to represent the same amount without any ones?”
Activity Synthesis
Invite previously identified students to share how they know the value of Andre’s blocks is 100.
“If Andre used the fewest number of blocks, how many tens did he use?” (He had 10 tens.)
“What if Andre wanted to use the greatest amount of blocks to show this number? What would he do?” (He’d decompose all the tens to use only ones. He’d use 100 ones.)
“In this activity, you showed you know that 10 ones is the same as 1 ten. Just like 10 ones is the same as 1 ten, 10 tens is the same as 1 hundred.”
“A hundred is a unit that is made up of 10 tens.”


aligns: no