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 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_neg_0

HS_0
standard_description: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
problem_activity: Activity
The mathematical purpose of this activity is for students to create data displays and calculate statistics using technology. Students plot the survey data they collected from a statistical question in a previous lesson.
Launch
Arrange students in groups of two. Tell them that they will be using technology to create data displays and calculate statistics for data they collected from a survey question in a previous lesson.
Conversing, Representing, Writing: MLR 2 Collect and Display.
As pairs are working, listen for and collect vocabulary, phrases, and methods students use for creating dot plots, boxplots, and histograms using technology, such as data set, skewed distribution, median, the box plot for the IQR. Consider grouping language for each data display in different areas, and be sure to include the spreadsheet formulas. Continue to update collected student language throughout the entire activity and the entire unit. Remind students to borrow language from the display as needed. This will help students to expand their notation of recursive definitions.
Design Principle(s): Support sense-making; Maximize meta-awareness
Engagement: Develop Effort and Persistence.
Provide prompts, reminders, guides, rubrics, checklists that focus on increasing the length of on-task orientation in the face of distractions. For example, create an exemplar dot plot highlighting specific features, such as the scale and labels, as well as calculations for the mean and median.
Supports accessibility for: Attention; Social-emotional skill
Student Facing
Use the data you collected from the numerical, statistical question from a previous lesson. Use technology to create a dot plot, boxplot, and histogram for your data. Then find the mean, median, and interquartile range for the data.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
A stem and leaf plot is a table where each data point is indicated by writing the first digit(s) on the left (the stem) and the last digit(s) on the right (the leaves). Each stem is written only once and shared by all data points with the same first digit(s). For example, the values 31, 32, and 45 might be represented like:
\(\displaystyle \begin{array}{r|l l} 3 & 1 & 2\\ 4 & 5 \end{array}\)
Key: 3 | 1 means 31
A class took an exam and earned the scores:
86, 73, 85, 86, 72, 94, 88, 98, 87, 86, 85, 93, 75, 64, 82, 95, 99, 76, 84, 68
Use technology to create a stem and leaf plot for this data set.
How can we see the shape of the distribution from this plot?
What information can we see from a stem and leaf plot that we cannot see from a histogram?
What do we have more control of in a histogram than in a stem and leaf plot?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Students may lose one data display when they begin to create the next one. Explain to students that it is important to copy their solutions into a more permanent place so they can refer to it later.
Activity Synthesis
The goal of this activity was for students to create graphs and find statistics using technology. Here are some questions for discussion.
“What were some challenges that you faced using technology and how did you overcome them?” (I was not sure what buttons to press to get to the spreadsheet. I checked with my partner and figured it out.)
“What width did you use for your histogram? Why?” (I used 5 because my data set has values ranging from 1 to 42. I could have used 10 but then I would have only had 5 bars.)
“What is the appropriate measure of center for your data set?” (The median was appropriate because my data set has a skewed distribution.)
“Which display allows you to calculate the IQR the most easily?” (The box plot because it displays Q1 and Q3.)
“Can you find the median using your histogram?” (No, the data is grouped into intervals, so a histogram cannot be used to find the middle value for the median.)


aligns: no