few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


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:
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).

Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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 $P$.


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
problem_activity: Narrative
The purpose of this activity is for students to try the algorithms they saw earlier in the lesson. The important thing is that they combine hundreds and hundreds, tens and tens, and ones and ones, which should be a familiar idea from grade 2. The synthesis provides an opportunity to show a different way of recording newly composed tens and hundreds when compositions are required, which will be discussed in more detail in subsequent lessons. Provide access to base-ten blocks for students to use to support their reasoning about the algorithms, in case requested.
Students analyze and improve a given explanation of how to find a sum, filling in details and using more precise language to explain the calculation more fully (MP3, MP6).
This activity uses
MLR3 Clarify, Critique, Correct
.
Advances: reading, writing, representing
Engagement: Develop Effort and Persistence.
Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Organization, Social-Emotional Functioning
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
“Now you are going to have a chance to try the algorithms that Lin and Han used in the last activity. Take a minute to think about which algorithm you want to use for each problem.”
1 minute: quiet think time
Activity
“Work with your partner to try an algorithm to find the value of each sum.”
5 minutes: partner work time
Monitor for students who use Lin’s algorithm and Han's algorithm on the last problem.
Student Facing
Try using an algorithm to find the value of each sum. Show your thinking. Organize it so it can be followed by others.
\(475 + 231\)
\(136 + 389\)
\(670 + 257\)
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
Select previously identified students to share their work on the last expression.
MLR3 Clarify, Critique, Correct
Display the following partially correct answer and explanation:
[IMG]
I added the ones, the tens, and then hundreds.
Read the explanation aloud.
“What is unclear?”
1 minute: quiet think time
2 minute: partner discussion
“With your partner, work together to write a revised explanation.”
Display and review the following criteria:
Explanation for each step
Words such as: first, next, then
3–5 minute: partner work time
Select 1–2 groups to share their revised explanation with the class. Record responses as students share. (Sample explanation: First, I stacked the numbers vertically. Then, I added the ones to get 7 and recorded a 7 below the ones place. Next, I added 70 and 50 and got 120. I recorded 20 below the 7 and 100 below the 20. I added 600 and 200 to get 800 and recorded that below the 100. Then I added and wrote 927 as the answer.)
“What is the same and different about the explanations?” (Both explanations say that they added the ones, tens, and hundreds, but the revised explanation gives more detail about how to record each step.)
“How is this way of recording this work the same or different from Han’s method in the first activity?” (Han would record 120 in the second row where we record the tens. It was 12 tens, but that’s the same as 1 hundred and 2 tens. We could record 100 on one line and 20 on the next line.)


aligns: no