few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Concept/skill: 
Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

Example 2:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

Example 3:
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.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_pos_0

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fl_problem_001097_pos_0

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HS_0
standard_description: Derive the equation of a parabola given a focus and directrix.
problem_activity: Narrative
The purpose of this activity is to reintroduce students to Put Together, Total Unknown story problems. In this type of problem, there is no action, so students must recognize the addends must be joined to make up the total. Students were introduced to this type of story problem in kindergarten and solved within 10 using objects or drawings. Students also solved Put Together, Total Unknown problems in Unit 1 in the context of data.
Students begin the activity by looking at the problem displayed, rather than in their books. The three reads routine gives students an opportunity to make sense of the problem before looking for a solution. Because there is no action in a put together problem, students identify the important quantities and think about how they might represent them before they solve the problem (MP1). At the end of the launch, students open their books and work on the problem. Students solve in any way they choose including using objects, drawings, words, or numbers, and write an equation to match the story problem.
This activity uses
MLR6 Three Reads.
Advances: reading, listening, representing.
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to 10-frames and connecting cubes or two-color counters.
Activity
MLR6 Three Reads
Display only the problem stem, without revealing the question(s).
“We are going to read this problem 3 times.”
1st Read: “Kiran has some fish in his fish tank. He has 4 red fish and 5 blue fish.”
“What is this story about?”
1 minute: partner discussion
Listen for and clarify any questions about the context.
2nd Read: “Kiran has some fish in his fish tank. He has 4 red fish and 5 blue fish.”
“What are all the things we can count in this story?” (the number of red fish, the number of blue fish, the total number of fish)
30 seconds: quiet think time
2 minutes: partner discussion
Share and record all quantities.
Reveal the question(s).
3rd Read: Read the entire problem, including question(s) aloud.
“What are different ways we can solve this problem?” (I can use red and blue connecting cubes. I can draw the fish and count them.)
30 seconds: quiet think time
1 minute: partner discussion
"Solve the problem."
3 minutes: independent work time
“Share your thinking with your partner.”
2 minutes: partner discussion
Monitor for students who solve in the following ways and can explain their thinking clearly:
objects or drawings and count all
objects or drawings and count on
numbers and count on
Student Facing
Kiran has some fish in his fish tank.
He has 4 red fish and 5 blue fish.
How many fish does he have in all?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Student Response
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Activity Synthesis
Invite previously identified students to share in sequence above.
After each student shares, “How does this representation match the story problem?”
Display
\(4+5=\boxed{9}\)
.
"Where do you see the parts of this equation in this representation? The story problem?” (4 means the 4 red fish, 5 is the blue fish, 9 is how many he has altogether.)


aligns: no