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: Convert like measurement units within a given measurement system.

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

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

Describe and compare measurable attributes.

Work with time and money.

Measure lengths indirectly and by iterating length units.

Geometric measurement: understand concepts of angle and measure angles.

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

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

Represent and interpret data.

Relate addition and subtraction to length.

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

Tell and write time.

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

Measure and estimate lengths in standard units.
problem_activity: Narrative
The purpose of this activity is for students to answer questions about the data represented by their picture graphs and bar graphs. Students switch workbooks with a new partner, which is an opportunity for students to view each other’s work and see different representations of data. While students are answering questions based on different graphs, identify the questions that are harder for students to answer. These questions can be discussed in the lesson synthesis. In upcoming lessons, students will have more opportunities to work with questions that require comparing categories.
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details were important or most useful to pay attention to. Display the sentence frame, “The next time I answer questions about a graph, I will . . . .“
Supports accessibility for: Conceptual Processing, Memory
Required Materials
Materials to Gather
Materials from a previous lesson
Required Preparation
Each student needs the picture graph and bar graph they created in the previous lesson.
Launch
Groups of 2: different partner than previous activity
“Tear out the page in your books labeled ‘Answering Questions Using Graphs.’”
Activity
“Now you are going to answer questions a different partner has written about their graphs.”
“Write your name and your partner’s name on the top of the page.”
“Trade graphs and questions with your partner. Answer each of the questions your partner wrote.”
6 minutes: independent work time
“Discuss the questions and answers with your partner to see if you agree.”
6 minutes: partner discussion
Monitor for students who mention the graph features like the title or labels when answering, "How did you know where to find the answer to each question?"
Student Facing
Answer your partner’s questions from Activity 1 using the graphs.
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
How did you know where to find the answer to each question?
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
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
Select 2
–
3 identified students to share a question they answered and how they knew where to find the answer.


correct_option_index: 9