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.


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:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Standard options: 
A. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
B. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Thought: By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.
Answer: B

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Thought: This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.
Answer: C

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

K

im_task_000157

3

fl_problem_000674

5
options: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
problem_activity: Activity
The purpose of this task is for students to sketch a graph from a story. In order to make the sketch, students must select two quantities from the story to graph, decide which is the independent variable and which is the dependent variable, and create and label their axes based on their decisions (MP4).
Monitor for displays that are correct but different from each other in important ways for students to focus on during the discussion. For example, they may differ by what variables were graphed such as:
distance from home as a function of time
distance from park as a function of time
total distance traveled as a function of time
Digital
Launch
Arrange students in groups of 2–3. Distribute tools for creating a visual display. Before students begin, it may be necessary to demonstrate how to “create a set of axes” so that a first-quadrant graph can be sketched and is large enough to be seen from a distance. Group work time followed by a whole-class discussion.
If using the digital activity, the Activity Narrative is still valid, and student graphs will be used to drive the class discussion. What varies from the print activity is students will have access to an applet to create their graphs. Students will be able to share their graphs by projecting their screen. They may need to save their graph by either exporting the image or “printscreen” to a word document.
Action and Expression: Provide Access for Physical Action.
Provide access to tools and assistive technologies such as the applet or graphing software. Some students may benefit from a checklist or list of steps to be able to use the applet or software.
Supports accessibility for: Organization; Conceptual processing; Attention
Conversing, Representing, Writing: MLR2 Collect and Display.
As students work in groups, capture the vocabulary and phrases students use to describe the relationship between the variables they selected over time. Listen for students who refer to the story to justify their decisions as they create the shape of the graph. Record their language on a visual display that can be referenced in future discussions. This will help students to produce and make sense of the language needed to communicate about the relationship between quantities represented by functions graphically and in story contexts.
Design Principle(s): Support sense-making; Maximize meta-awareness
Student Facing
You will use the tools in the applet for creating a visual display that shows your response to each question.
Here is a story: “Noah was at home. He got on his bike and rode to his friend’s house and stayed there for awhile. Then he rode home again. Then he rode to the park. Then he rode home again.”
Sketch a graph of this story.
What are the two quantities? Label the axes with their names and units of measure. (For example, if this were a story about pouring water into a pitcher, one of your labels might say “volume (liters).”)
Which quantity is a function of which? Explain your reasoning.
Based on your graph, is his friend’s house or the park closer to Noah's home? Explain how you know.
Read the story and all your responses again. Does everything make sense? If not, make changes to your work.
Note: To change the values on the axes, select the Move Graphics tool, click near the end of the axis you want to change, and drag it to grow or shrink it.
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Arrange students in groups of 2–3. Distribute tools for creating a visual display. Before students begin, it may be necessary to demonstrate how to “create a set of axes” so that a first-quadrant graph can be sketched and is large enough to be seen from a distance. Group work time followed by a whole-class discussion.
If using the digital activity, the Activity Narrative is still valid, and student graphs will be used to drive the class discussion. What varies from the print activity is students will have access to an applet to create their graphs. Students will be able to share their graphs by projecting their screen. They may need to save their graph by either exporting the image or “printscreen” to a word document.
Action and Expression: Provide Access for Physical Action.
Provide access to tools and assistive technologies such as the applet or graphing software. Some students may benefit from a checklist or list of steps to be able to use the applet or software.
Supports accessibility for: Organization; Conceptual processing; Attention
Conversing, Representing, Writing: MLR2 Collect and Display.
As students work in groups, capture the vocabulary and phrases students use to describe the relationship between the variables they selected over time. Listen for students who refer to the story to justify their decisions as they create the shape of the graph. Record their language on a visual display that can be referenced in future discussions. This will help students to produce and make sense of the language needed to communicate about the relationship between quantities represented by functions graphically and in story contexts.
Design Principle(s): Support sense-making; Maximize meta-awareness
Student Facing
Your teacher will give you tools for creating a visual display. With your group, create a display that shows your response to each question.
Here is a story: “Noah was at home. He got on his bike and rode to his friend’s house and stayed there for awhile. Then he rode home again. Then he rode to the park. Then he rode home again.”
Create a set of axes and sketch a graph of this story.
What are the two quantities? Label the axes with their names and units of measure. (For example, if this were a story about pouring water into a pitcher, one of your labels might say “volume (liters).”)
Which quantity is a function of which? Explain your reasoning.
Based on your graph, is his friend’s house or the park closer to Noah's home? Explain how you know.
Read the story and all your responses again. Does everything make sense? If not, make changes to your work.
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?
It is the year 3000. Noah’s descendants are still racing around the park, but thanks to incredible technological advances, now with much more powerful gadgets at their disposal. How might their newfound access to teleportation and time-travel devices alter the graph of stories of their daily adventures? Could they affect whether or not the distance from home is a function of the time elapsed?
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 try and start graphing before they have clearly articulated and labeled their axes with their chosen variables. Encourage groups to make sure all are in agreement on what variables they are graphing before they create their display.
Activity Synthesis
Select previously identified groups to share their visual displays for all to see throughout the discussion. Give students 2–3 minutes of quiet think time to review the 3 displays and identify differences and similarities. Invite students to share what they identified and record and display the responses for all to see. If not brought up by students, ask:
“What is the same and different about the two quantities that each group chose to use in their visual display?”
“Did each group use the same units of measure? Why does it make sense to use the unit of measure seen in any of these examples?”
“Why does it make sense to have time be the independent variable in this situation?"
“Do all of these examples make sense in relation to the situation?”
Conclude the discussion by refocusing students on the input-output pairs described by the different graphs. For example, on a graph where distance from home is a function of time, there should be three inputs where the output is zero since he starts at home, returns home from his friend’s house, and ends at home.
Alternatively, have the class do a “gallery walk” in which students leave written feedback on sticky-notes for the other groups. Here is guidance for the kind of feedback students should aim to give each other:
“What is one thing that group did that would have made your project better if you had done it?”
“What is one thing your group did that would have improved their project if they did it too?”
“Does their answer make sense in the situation?”
“Is their answer about which house is closer to the park clear and correct?”
“If there was a mistake, what could they be more careful about in similar problems?”


correct_option_index: 1