few_shots: Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
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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.


Standard options: 
A. 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.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


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

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
$$-\frac{1}{4}$$


Standard options: 
A. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
B. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
C. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


Thought: 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).
Answer: B

Example 3:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Thought: 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. Solving this problem does not require use of the Pythagorean identity.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

fl_problem_001097

7

fl_problem_001894

HS_0
options: 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.

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
problem_activity: Activity
In this info gap activity, students practice analyzing box plots and thinking carefully about what questions they could help to answer. They connect features of box plots to information about IQR, range, median, and minimum and maximum values of several data sets on sea turtles (MP7). Along the way, they see the usefulness of box plots in comparing distributions and characteristics of different populations.
The info gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly precise questions until they get the information they need (MP6).
Here is the text of the cards for reference and planning:
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Launch
Tell students that they will now practice using box plots to answer questions about populations of sea turtles. Provide students with the following background information: Sea turtles are air-breathing amphibians that spend most of their time floating in seaweed beds. Females come on shore to lay their eggs. One nesting place for several species of sea turtles is the Outer Banks of North Carolina. All sea turtles are considered to be endangered and only about 1 in 1,000 newly hatched sea turtles survives, which is why their nesting areas are protected.
Arrange students in groups of 2. Give each group a pair of cut-up cards from the blackline master—a Problem Card for one partner and a Data Card for the other. Remind students of the protocol for asking and answering questions, as shown on the task statement. Give students 10 minutes to complete the activity. If any groups finish early, offer a second pair of cards and ask the partners to switch roles.
Engagement: Develop Effort and Persistence.
Display or provide students with a physical copy of the written directions. Check for understanding by inviting students to rephrase directions in their own words. Keep the display of directions visible throughout the activity.
Supports accessibility for: Memory; Organization
Conversing
: This activity uses
MLR4 Information Gap
to give students a purpose for discussing information necessary to connect features of a box plot to information about the five-number summary. Display questions or question starters for students who need a starting point such as: “Can you tell me . . . (specific piece of information)”, and “Why do you need to know . . . (that piece of information)?”
Design Principle(s): Cultivate Conversation
Student Facing
Your teacher will give you either a Problem Card or a Data Card about sea turtles that nest on the Outer Banks of North Carolina. Do not show or read your card to your partner.
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If your teacher gives you the
problem card
:
Silently read your card and think about what information you need to be able to answer the question.
Ask your partner for the specific information that you need.
Explain how you are using the information to solve the problem.
Continue to ask questions until you have enough information to solve the problem.
Share the
problem card
and solve the problem independently.
Read the
data card
and discuss your reasoning.
If your teacher gives you the
data card
:
Silently read your card.
Ask your partner
“What specific information do you need?”
and wait for them to
ask
for information.
If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.
Before sharing the information, ask “
Why do you need that information?
” Listen to your partner’s reasoning and ask clarifying questions.
Read the
problem card
and solve the problem independently.
Share the
data card
and discuss your reasoning.
Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.
Student Response
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Activity Synthesis
Invite students to share their experiences with the Info Gap activity. Consider discussing some of the following questions.
For students who had a Problem Card:
“How did you decide what information to ask for? How did the information on your card help?”
“How easy or difficult was it to explain why you needed the information you were asking for?”
“Give an example of a question that you asked, the clue you received, and how you made use of it.”
“How many questions did it take for you to be able to solve the problem? What were those questions?”
“Was anyone able to solve the problem with a different set of questions?”
For students who had a Data Card:
“When you asked your partner why they needed a specific piece of information, what kind of explanations did you consider acceptable?”
“Were you able to tell from their questions what statistical question they were trying to answer? If so, how? If not, why might that be?”


correct_option_index: 0