few_shots: Example 1:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Thought: This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.
Answer: B

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:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


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


Thought: This set of problems involves solving linear equations and pairs of linear equations.
Answer: L

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6

fl_problem_001097

7

fl_problem_001392

8
options: Understand and apply theorems about circles.

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

Analyze, compare, create, and compose shapes.

Understand congruence in terms of rigid motions.

Make geometric constructions.

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

Find arc lengths and areas of sectors of circles.

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

Prove geometric theorems.

Experiment with transformations in the plane.

Explain volume formulas and use them to solve problems.

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

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

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

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

Understand similarity in terms of similarity transformations.

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

Apply trigonometry to general triangles.

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

Prove theorems involving similarity.

Understand and apply the Pythagorean Theorem.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Use coordinates to prove simple geometric theorems algebraically.

Apply geometric concepts in modeling situations.

Reason with shapes and their attributes.

Define trigonometric ratios and solve problems involving right triangles.

Classify two-dimensional figures into categories based on their properties.
problem_activity: Narrative
The purpose of this activity is for students to identify shapes as flat and solid as they sort shapes into groups. A sorting task gives students opportunities to analyze the structure of the shapes and identify common properties and characteristics (MP7).
If the sorting mat provided in the student workbook is too small for students to sort the shapes, consider giving students two pieces of construction paper, or ask students to put the solid shapes on one side of the table and the flat shapes on the other side.
MLR8 Discussion Supports.
Invite each partner to identify each shape aloud: Flat shape or solid shape. Encourage students to challenge each other when they disagree.
Advances: Conversing
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy for how they will sort the shapes.
Supports accessibility for: Conceptual Processing, Organization
Required Materials
Materials to Gather
Geoblocks
Solid shapes
Materials to Copy
Flat Shapes Cards K
Required Preparation
Each group of 2 needs a set of solid shapes and a set of cards.
Launch
Groups of 2
Give each group of students a set of solid shapes and a set of flat shapes cards.
Activity
“Work with your partner to sort the shapes into two groups. Write a number to show how many shapes are in each group.”
3 minutes: partner work time
“Pair up with another group. Show them how you sorted your shapes. Did you sort all of the shapes in the same way?”
3 minutes: small-group work time
“What could you call each group of shapes to show why you put those shapes together?”
Monitor for a group that sorts by flat shapes and solid shapes.
Student Facing
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[IMG]
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Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Advancing Student Thinking
If students identify a pyramid as flat because “it looks like a triangle,” consider asking:
“What is the same about all of the shapes in this group?”
Display a pyramid and a triangle next to each other and ask “What do you notice about these shapes? What is different about them?”
Activity Synthesis
Invite previously selected students to share the way they sorted the shapes into flat shapes and solid shapes.
“This group has flat shapes. This group has solid shapes.”
Display a square.
“Should this shape go with the flat shapes or the solid shapes? Why?” (It is a flat shape. If we put it on our desk, it doesn’t stick up.)
Display a cube.
“Should this shape go with the flat shapes or the solid shapes? Why?” (It is a solid shape. It sticks up and takes up space.)


correct_option_index: 13