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: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

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_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
problem_activity: Activity
In this activity, each group is assigned a situation for which they will design and perform a simulation to estimate the probability. Students will give a short presentation on the methods and results of their simulation for the class after they have designed and run the simulation. Students will need to attend to precision (MP6) as well as present arguments (MP3) for the simulation method they chose. At this stage, students have experienced a large number of simulation methods and should be able to design their own to represent the situations using the appropriate tools (MP5).
Launch
Arrange students in groups of 3. Assign each group a question slip from the blackline master. Provide access to number cubes, compasses, protractors, rulers, paper bags, colored snap cubes, scissors, and coins. Give students 15 minutes for group work followed by a whole-class discussion.
Student Facing
Your teacher will give your group a paper describing a situation.
Design a simulation that you could use to estimate a probability. Show your thinking. Organize it so it can be followed by others.
Explain how you used the simulation to answer the questions posed in the situation.
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
Ask each group to share their situation, their method of simulating the situation, and their results. Students should explain why their chosen method works to simulate the situation they were given. In particular, all important outcomes should be represented with the same probability as stated in the situation.
If all groups that have the same situation use the same simulation method, ask for ideas from the class about alternate methods that could be used for the situation.
For reference, the computed probabilities for each situation are:
\(\frac{5}{32} \approx 0.16\)
\(\frac{1}{64} \approx 0.02\)
\(\frac{59049}{100000} \approx 0.59\)
\(\frac{2072}{3125} \approx 0.66\)
\(\frac{181}{3125} \approx 0.06\)
Representation: Internalize Comprehension.
Use color and annotations to illustrate student thinking. As students show their representations of simulations and explain their reasoning, use color and annotations to scribe their thinking on a display of each problem so that it is visible for all students.
Supports accessibility for: Visual-spatial processing; Conceptual processing
Listening, Speaking: MLR8 Discussion Supports.
To help students explain why their chosen method works, provide sentence frames such as: “This simulation was designed so that . . .” and “The simulation and the actual event have the same probabilities because . . . .” As partners are sharing, encourage the listener to press for more explanation by asking: “Can you explain why the probabilities of the simulation and actual event match?” or “Is there another simulation that could provide the same probability?” This will help students practice justifying their simulation from their interpretation of the situation.
Design Principle(s): Maximize meta-awareness; Cultivate conversation


aligns: no