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.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Your response, in json format:
{
  "explanation": "This task teaches students to understand addition as putting together counters, or adding to already placed counters.",
  "answer": "AB"
}

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} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response, in json format:
{
  "explanation": "This problem involves understanding fractions as numbers by comparing their quantities.",
  "answer": "F"
}

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?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Your response, in json format:
{
  "explanation": "This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.",
  "answer": "G"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Analyze functions using different representations.

Construct and compare linear and exponential models and solve problems.

Define, evaluate, and compare functions.

Build new functions from existing functions.

Prove and apply trigonometric identities.

Build a function that models a relationship between two quantities.

Use functions to model relationships between quantities.

Extend the domain of trigonometric functions using the unit circle.

Model periodic phenomena with trigonometric functions.

Understand the concept of a function and use function notation.

Interpret functions that arise in applications in terms of the context.

Interpret expressions for functions in terms of the situation they model.
problem_activity: Activity
In this activity, students investigate how the height of water in a graduated cylinder is a function of the volume of water in the graduated cylinder. Students make predictions about how the graph will look and then test their prediction by filling the graduated cylinder with different amounts of water, gathering and graphing the data (MP4).
Digital
Launch
Arrange students in groups of 3–4. Be sure students know how to measure using a graduated cylinder. If needed, display a graduated cylinder filled to a specific measurement for all to see and demonstrate to students how to read the measurement. Give each group access to a graduated cylinder and water.
Give groups 8–10 minutes to work on the task, follow with a whole-class discussion.
For classrooms with access to the digital materials or those with no access to graduated cylinders, an applet is included here. Physical measurement tools and an active lab experience are preferred.
Speaking: MLR8 Discussion Supports.
Display sentence frames to support small-group discussion. For example, “I think ____ , because _____ .” or “I (agree/disagree) because ______ .”
Design Principle(s): Support sense-making; Optimize output for (explanation)
Student Facing
Use the applet to investigate the height of water in the cylinder as a function of the water volume.
Before you get started, make a prediction about the shape of the graph.
Check Reset and set the radius and height of the graduated cylinder to values you choose.
Let the cylinder fill with different amounts of water and record the data in the table.
Create a graph that shows the height of the water in the cylinder as a function of the water volume.
Choose a point on the graph and explain its meaning in the context of 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.
Print
Launch
Arrange students in groups of 3–4. Be sure students know how to measure using a graduated cylinder. If needed, display a graduated cylinder filled to a specific measurement for all to see and demonstrate to students how to read the measurement. Give each group access to a graduated cylinder and water.
Give groups 8–10 minutes to work on the task, follow with a whole-class discussion.
For classrooms with access to the digital materials or those with no access to graduated cylinders, an applet is included here. Physical measurement tools and an active lab experience are preferred.
Speaking: MLR8 Discussion Supports.
Display sentence frames to support small-group discussion. For example, “I think ____ , because _____ .” or “I (agree/disagree) because ______ .”
Design Principle(s): Support sense-making; Optimize output for (explanation)
Student Facing
Your teacher will give you a graduated cylinder, water, and some other supplies. Your group will use these supplies to investigate the height of water in the cylinder as a function of the water volume.
Before you get started, make a prediction about the shape of the graph.
Fill the cylinder with different amounts of water and record the data in the table.
| volume (ml) |   |   |   |   |   |
|-------------|---|---|---|---|---|
| height (cm) |   |   |   |   |   |
Create a graph that shows the height of the water in the cylinder as a function of the water volume.
[IMG]
Choose a point on the graph and explain its meaning in the context of 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
Select groups to share the graph for the third question and display it for all to see. Consider asking students the following questions:
“What do you notice about the shape of your graph?”
“What is the independent variable of your graph? Dependent variable?”
“How does this graph differ from what you predicted the shape would be?”
“For the last question, what point did you choose, and what does that point mean in the context of this activity?”
“What would the endpoint of the graph be?” (There is a maximum possible volume for the cylinder. Once it’s filled, any extra water will spill out and not raise the water height.)
[IMG]
Ask students to predict how the graph would change if their cylinder had double the diameter. After a few responses, display this graph for all to see:Explain that each line represents the graph of a cylinder with a different radius. One cylinder has a radius of 1 cm, another has a radius of 2 cm, and another has a radius of 3 cm. Have students consider which line must represent which cylinder. Ask, “how did the slope of each graph change as the radius increased?” (As the radius is larger, the slope is less steep. This is because for a cylinder with a larger base, the same volume of water will not fill as high up the side of the cylinder.)


correct_option_index: 6