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.
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fl_problem_001097

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fl_problem_001894

HS_0
options: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Apply geometric concepts in modeling situations.

Apply trigonometry to general triangles.

Understand and apply theorems about circles.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Prove theorems involving similarity.

Reason with shapes and their attributes.

Understand and apply the Pythagorean Theorem.

Translate between the geometric description and the equation for a conic section.

Prove geometric theorems.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Use coordinates to prove simple geometric theorems algebraically.

Explain volume formulas and use them to solve problems.

Analyze, compare, create, and compose shapes.

Visualize relationships between two-dimensional and three-dimensional objects.

Understand similarity in terms of similarity transformations.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Classify two-dimensional figures into categories based on their properties.

Solve real-world and mathematical problems involving area, surface area, and volume.

Understand congruence in terms of rigid motions.

Find arc lengths and areas of sectors of circles.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Define trigonometric ratios and solve problems involving right triangles.

Experiment with transformations in the plane.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Make geometric constructions.

Graph points on the coordinate plane to solve real-world and mathematical problems.
problem_activity: Narrative
The purpose of this activity is for students to apply what they’ve learned about quadrilaterals to design a wax print pattern. First, students analyze wax prints that have quadrilaterals incorporated into the pattern. Then, students design their own wax print that incorporates rhombuses, rectangles, or squares and a quadrilateral that doesn’t belong to any of these subcategories.
MLR8 Discussion Supports.
Synthesis: During group presentations, invite the student(s) who are not speaking to follow along and point to the corresponding parts of the display.
Advances: Speaking, Representing
Action and Expression: Internalize Executive Functions.
To support working memory, provide students with access to sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization
Required Materials
Materials to Gather
Colored pencils, crayons, or markers
Materials to Copy
Square Dot Paper Standard
Launch
Groups of 2
Display the image.
“Today’s lesson is going to focus on African wax prints. African wax prints are colorful cotton fabrics commonly used for clothing in West Africa. Take a minute to think about the pattern. What do you notice? What do you wonder?” (Students may notice: The pattern is colorful. There are rhombuses in the pattern. There are triangles in the pattern. There are quadrilaterals that aren’t rhombuses, rectangles, or squares in the pattern. Students may wonder: How do they make these patterns? What other shapes could be used to make these patterns? What types of clothing are made with this cloth? Where can you buy this type of fabric?)
1 minute: partner discussion
Share responses.
“You’re going to create your own wax print pattern. Independently read over the directions and think about how you’ll create your pattern.”
2–3 minutes: quiet think time
“Are there any questions about how you’ll create your wax print pattern?”
Answer any questions students have.
Give each student a sheet of dot paper and colored pencils, crayons, or markers.
Activity
“Work independently to create your wax print pattern.”
5–7 minutes: independent work time
“You can continue working on your own or work with a partner or small group to finish your pattern. Even if you choose to work alone, be available if your partner wants to think through something together.”
3–5 minutes: partner, small group, or independent work time
Monitor for students who use a rhombus, rectangle, or square in their pattern to highlight in the synthesis. Adjust the synthesis if all shapes aren’t used.
Student Facing
Your teacher will give you some dot paper for drawing.
Use the dot paper to design your own wax print pattern. Your pattern should:
use a rhombus, rectangle, or square
use a quadrilateral that is not a rhombus, rectangle, or square
have each shape repeat at least 5 times
Color the pattern in a way that highlights the shapes you chose or choices you made.
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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
Display previously selected patterns one at a time.
For each pattern, ask, “How did this student use rectangles (or rombuses, or squares) in their design?”


correct_option_index: 6