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.


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.


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.


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: Relate addition and subtraction to length.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Tell and write time.

Work with time and money.

Represent and interpret data.

Describe and compare measurable attributes.

Measure and estimate lengths in standard units.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Convert like measurement units within a given measurement system.

Measure lengths indirectly and by iterating length units.

Geometric measurement: understand concepts of angle and measure angles.

Classify objects and count the number of objects in each category.
problem_activity: Narrative
In a previous lesson, students described an angle to a peer so that they might draw the angle accurately without seeing it. Students learned what an angle is and have reasoned about how to describe the size of an angle.
In this activity, students use the features of an analog clock (minute hand, hour hand, and position of numbers) to explain how to draw a given angle. In doing so, they use language related to turning one or both hands on the clock. In future activities, students will relate this idea to turning a ray around a fixed point.
The hands on an actual clock are designed so that moving the minute moves the hour hand. The examples here disregard this constraint. For the purposes of this activity, it is assumed that both hands can be moved freely, or that one hand can be held in place while the other moved freely.
Required Materials
Materials to Gather
Rulers or straightedges
Launch
Groups of 2
Give students access to rulers or straightedges.
Activity
“In an earlier lesson, we played a game where you described an angle to your partner to help them draw it without seeing it.”
“Read Andre’s explanation for how to draw an angle. Try to draw his angle, and then think of another way to describe how to draw the same angle.”
3 minutes: independent work time on the first two problems
“Share your drawing and description with your partner.”
“Discuss how you would explain how to draw the other angles.”
3–5 minutes: partner discussion and work time
Monitor for students who clearly describe turning a hand around the clock and who connect the hands to the rays of the angles.
Student Facing
Andre used the hands of a clock to explain how to draw an angle to his partner.
“Imagine both hands are pointing at the 12. Turn the minute hand so it's pointing at the 3.”
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Draw Andre’s angle.
What is another way to describe how to draw the same angle using the clock?
Use Andre’s way to explain how to draw these angles:
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[IMG]
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Student Response
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Activity Synthesis
“Let’s listen to some different directions for how to draw these angles. As you listen, try to sketch the angle and guess which one they are describing how to draw.”
Invite 2–3 students to share the directions they wrote for drawing one of the angles. Choose students to share in a different order than the angles are presented in the task.
For each, consider asking:
“Which angle did they describe (a, b, or c) and how do you know?”
“What words help you picture how to draw the angle?” (turn right, turn left, point at 4)
“We can describe the size of an angle by explaining how much one ray has turned from the other.”


correct_option_index: 13