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: 
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: 
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_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
problem_activity: Narrative
In this activity, students approach 10,000 by counting up in different ways. Each count ends by reaching 10,000. Students count by different amounts and describe patterns and relationships between numbers. The activity is designed to highlight familiar counting patterns as a way to support naming and writing multi-digit numbers. The final questions in the task ask students to consider the magnitude of each number in relation to 10,000.
When students count by large numbers and examine the counted numbers, they observe patterns in how the different digits in the numbers change (MP7).
Representation: Access for Perception.
Provide access to a variety of tools that students may use to approach the task. These might include: a class set of base-ten blocks, colored pencils to color-code place values or highlight the digit that changes, and a visual display reminding students of sketches they can make to represent numbers with thousands and ten-thousands.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Attention
Launch
Groups of 2
“Read the directions for problem 1 and share your understanding of the directions with a partner.”
“What questions do you have before we begin?”
Activity
5 minutes: independent work time
10 minutes: partner work time
As students work,
listen for how students say the numbers and support them in using place value understanding to say the numbers correctly.
look for use of extra digits when writing numbers (for example, students write 90,500 instead of 9,500) and support students with making the revisions by having them say the numbers.
Student Facing
Record each count in the given spaces. The first number has been recorded for you.
Count by 1,000
5,000 , _____________, _____________, _____________, _____________, _____________
Count by 100
9,500 , _____________, _____________, _____________, _____________, _____________
Count by 10
9,950 , _____________, _____________, _____________, _____________, _____________
Count by 1
9,995, _____________, _____________, _____________, _____________, _____________
Complete each statement:
Ten-thousand is 1 more than _____________.
Ten-thousand is 1,000 more than _____________.
Ten-thousand is 10 more than _____________.
Ten-thousand is 100 more than _____________.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students interpret the part a of the last problem to mean “name a number that is 10,000 more than 1,” consider clarifying by asking: “The number 10 is 1 more than what number?” and “The number 100 is 1 more than what number?” Then, restate the sentence in part a: “Ten-thousand is 1 more than what number?”
Activity Synthesis
“How is counting by 100 and 1,000 like counting by 1 and 10?” (When counting by thousands, only the thousands change. This is also the case when counting by ones, tens, and hundreds.)
Have students share their answers for the last problem.
Consider asking: “Who can restate what _____ shared?”
If needed, discuss the placement of the comma in each number.


aligns: no