few_shots: Example 1:
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

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


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


Thought: This task asks students to solve an equation in one variable. Since the problem asks for many different solution methods, students are also encouraged to solve the problem graphically.
Answer: P, U

Example 3:
Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
[IMG]
Draw a circle with center $P$ and with  radius $r \gt 0$.  Explain why the circle
meets each ray of angle $A$ in a single point.  Label these points $Q$ and $R$ respectively.
Draw circles with centers $Q$ and $R$ respectively and radius $r$.  These circles meet at $P$ and a second point to be labelled $B$.
Show that ray $\overrightarrow{PB}$  bisects angle $P$.


Mathematical concept/skill options: 
A. Apply trigonometry to general triangles.
B. Understand similarity in terms of similarity transformations.
C. Analyze, compare, create, and compose shapes.
D. Prove geometric theorems.
E. Make geometric constructions.
F. Graph points on the coordinate plane to solve real-world and mathematical problems.
G. Understand congruence and similarity using physical models, transparencies, or geometry software.
H. Understand congruence in terms of rigid motions.
I. Draw, construct, and describe geometrical figures and describe the relationships between them.
J. Translate between the geometric description and the equation for a conic section.
K. Reason with shapes and their attributes.
L. Prove theorems involving similarity.
M. Explain volume formulas and use them to solve problems.
N. Find arc lengths and areas of sectors of circles.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Use coordinates to prove simple geometric theorems algebraically.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
S. Understand and apply theorems about circles.
T. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
U. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
V. Classify two-dimensional figures into categories based on their properties.
W. Apply geometric concepts in modeling situations.
X. Solve real-world and mathematical problems involving area, surface area, and volume.
Y. Experiment with transformations in the plane.
Z. Understand and apply the Pythagorean Theorem.
AA. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.


Thought: This task asks students to make geometric constructions, such as bisecting an angle.
Answer: E

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS_0

im_task_000870

HS_1

im_task_001160

HS_2
options: Measure and estimate lengths in standard units.

Work with time and money.

Tell and write time.

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

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

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

Classify objects and count the number of objects in each category.

Represent and interpret data.

Measure lengths indirectly and by iterating length units.

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

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

Geometric measurement: understand concepts of angle and measure angles.

Relate addition and subtraction to length.

Convert like measurement units within a given measurement system.

Describe and compare measurable attributes.
problem_activity: Narrative
In this activity, students create a line plot using the measurement data that they generated earlier and display their group’s line plot for all to see.
Encourage students to plan their line plot using the blank line in the activity statement before creating a poster version for display in a gallery walk. A template for a larger line plot is provided in the blackline master. Students can join the number lines on two copies of the blackline master to create a longer number line.
[IMG]
As students visit others’ data displays, they consider how the line plots are alike and how they are different, as well as why different scales might have been chosen for different objects measured.
Representation: Access for Perception.
Synthesis: Use gestures during the explanation of the line plot to emphasize important aspects of the line plot.
Supports accessibility for: Conceptual Processing, Attention
Required Materials
Materials to Gather
Glue or tape
Scissors
Tools for creating a visual display
Materials to Copy
Let's Make a Line Plot
Launch
Groups of 4
“Look at the data your group collected. What do you need to know to make a line plot that represents the data?” (The longest and shortest measurements. Whether the lengths are whole numbers or include halves and fourths of an inch.)
1 minute: group discussion
Share responses.
Give each group 2 copies of the blackline master, scissors, glue or tape, and tools for creating a visual display.
Activity
“Work with your group to create a line plot that represents your data. You will share your line plot with the class later.”
“You can use the blank number line on your page to plan your line plot before creating a final one to display.”
Consider asking:
“How do you plan to make the scale for the line plot so that it can show all your measurements?”
“What information or labels could be included to help others understand your line plot?”
Demonstrate how to join and tape (or glue) the 2 copies of the blackline master to make a large line plot.
“After you complete your final line plot, tape (or glue) your line plot on a poster.”
12–15 minutes: group work time
Student Facing
Create a line plot to represent the measurement data you collected. You will display and share your line plot with your class later.
You can use the blank number line here for your draft. Think about:
how to label the tick marks so that all the measurements are included
details to help others understand the data you collected
[IMG]
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
Ask students to display their posters.
MLR7 Compare and Connect
“As you visit the posters with your group, think about how the line plots are alike and how they are different. Be prepared to share your observations.”
5 minute: gallery walk
See lesson synthesis.


correct_option_index: 7