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: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

Now, does the problem or activity shown below 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_neg_0

HS_0
standard_description: Summarize numerical data sets in relation to their context, such as by:
- Reporting the number of observations.
- Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
- Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
problem_activity: Activity
In this activity, students calculate the mean of a data set and interpret it in the context of the given situation. The first data set students see here has a dozen values, discouraging students from redistributing the values incrementally and encouraging them to use a more efficient method. In the second question, students analyze the values in data sets and use the structure (MP7) to decide whether or not it makes sense that a given mean would match the data set.
As students work and discuss, notice the reasons they give for why the data sets in the second question could or could not be Tyler's data set. Identify students who recognize that the mean of a data set cannot be expected to be higher or lower than most of the values of the data set, and that a fair-share value would have a value that is roughly in the middle of data values.
Launch
Keep students in groups of 2. Give them 6–7 minutes of quiet work time, and then time to discuss their responses with their partner.
Representation: Internalize Comprehension.
Activate or supply background knowledge about determining means of data sets. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
For the past 12 school days, Mai has recorded how long her bus rides to school take in minutes. The times she recorded are shown in the table.
9
8
6
9
10
7
6
12
9
8
10
8
Find the mean for Mai’s data. Show your reasoning.
In this situation, what does the mean tell us about Mai’s trip to school?
For 5 days, Tyler has recorded how long his walks to school take in minutes. The mean for his data is 11 minutes. Without calculating, predict if each of the data sets shown could be Tyler’s. Explain your reasoning.
data set A: 11, 8, 7, 9, 8
data set B: 12, 7, 13, 9, 14
data set C: 11, 20, 6, 9, 10
data set D: 8, 10, 9, 11, 11
Determine which data set is Tyler’s. Explain how you know.
Student Response
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Activity Synthesis
Select a couple of students to share how they found the mean of Mai's travel times. Poll the class briefly to see if others in the class found the mean the same way.
Then, focus the discussion on the second task and on what values could be reasonably expected of a data set with a particular mean. Ask students how they decided to rule out or keep certain sets of data as potentially belonging to Tyler. If not mentioned by students, highlight that the mean of a data set would be a value in the middle of the range of numbers in order for it to be a fair-share value.
Point out that, unlike hours of work or cats in crates, the times of travel here cannot actually be redistributed. The interpretation of mean translates into a thought experiment:
The mean is the travel time each day if all the travel times in the set were the same such that the combined travel time for this data set and the original data set was the same.
Speaking, Listening: MLR8 Discussion Supports.
Use this routine to support students’ explanations of which data set is Tyler’s. Invite students to use the sentence frame “Data set ___ is Tyler’s because . . . .” Invite listeners to use the sentence frame “I agree/disagree, because . . . .” This will help students explain their own reasoning and make the sense of the reasoning of others.
Design Principle(s): Support sense-making; Optimize output (for justification


aligns: yes