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.


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:
Thought: This task teaches students to understand addition as putting together counters, or adding to already placed counters.
Answer: AB

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


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Your response:
Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

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


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Your response:
Thought: This problem applies trigonometric identities, including the angle addition formula for cosine.
Answer: A

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

K

fl_problem_001097

7

fl_problem_001894

HS_0
options: Understand the place value system.

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.

Work with numbers 11–19 to gain foundations for place value.

Use place value understanding and properties of operations to add and subtract.

Extend the counting sequence.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

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.

Understand place value.
problem_activity: Narrative
The purpose of this activity is for students to interpret and solve a story problem by adding or subtracting within 100. Students solve an Add To, Start Unknown problem, one of the more difficult problem types from grade 1. Students begin the activity by looking at the problem displayed, rather than in their books. At the end of the launch, students open their books and work on the problem.
Monitor for students who use methods that show adding or subtracting by place to share in the synthesis. Students who choose to use connecting cubes or base-ten blocks or who draw a diagram to represent the situation are using tools strategically (MP5). During the synthesis, invite all students to explain why these methods work using their understanding of place value.
This activity uses
MLR6 Three Reads
. Advances: reading, listening, representing. Some students may benefit from continued use of MLR6 to support reading comprehension in Activity 2.
Required Materials
Materials to Gather
Base-ten blocks
Connecting cubes
Launch
Groups of 2
Give students access to connecting cubes and base-ten blocks.
“Have you ever been on a field trip? Where did you go?”
“Did everyone on your field trip stay together the whole time or did you split into smaller groups?”
MLR6 Three Reads
Display only the story problem, without revealing the question.
“We are going to read this problem 3 times.”
1st Read: “Some students were on the bus to go to the zoo. Then 34 more students got on. Now there are 55 students on the bus.”
“What is this story about?”
1 minute: partner discussion.
Listen for and clarify any questions about the context.
2nd Read: “Some students were on the bus to go to the zoo. Then 34 more students got on. Now there are 55 students on the bus.”
“What are all the things we can count in this story?” (number of students who started the story on the bus, number of students who got on next, the total number of students on the bus, the number of buses)
30 seconds: quiet think time
2 minutes: partner discussion
Share and record all quantities.
Reveal the question.
3rd Read: Read the entire problem, including the question aloud.
“What are different ways we can solve this problem?” (We could subtract the number of students who got on the bus second from the total. We could add to the number of students who got on the bus until we get to the total.)
30 seconds: quiet think time
1–2 minutes: partner discussion
Activity
5 minutes: independent work time
Monitor for students who:
use base-ten blocks or base-ten diagrams to show adding tens to tens or ones to ones
use base-ten blocks or base-ten diagrams to show subtracting from tens or ones from ones
Student Facing
Some students were waiting on the bus to go to the zoo. Then 34 more students got on. Now there are 55 students on the bus. How many students were on the bus at first?
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Student Response
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Activity Synthesis
Invite previously identified students to share.
Record student methods using equations.
“How are these methods the same?” (They both show tens and ones. They both thought of keeping the tens with the tens and ones with the ones.)


correct_option_index: 3