options: Understand solving equations as a process of reasoning and explain the reasoning.

Analyze patterns and relationships.

Solve systems of equations.

Use the four operations with whole numbers to solve problems.

Solve equations and inequalities in one variable.

Use polynomial identities to solve problems.

Understand and apply properties of operations and the relationship between addition and subtraction.

Generate and analyze patterns.

Work with equal groups of objects to gain foundations for multiplication.

Add and subtract within 20.

Work with radicals and integer exponents.

Understand properties of multiplication and the relationship between multiplication and division.

Represent and solve problems involving multiplication and division.

Write expressions in equivalent forms to solve problems.

Rewrite rational expressions.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Represent and solve equations and inequalities graphically.

Work with addition and subtraction equations.

Perform arithmetic operations on polynomials.

Understand the connections between proportional relationships, lines, and linear equations.

Create equations that describe numbers or relationships

Use properties of operations to generate equivalent expressions.

Understand the relationship between zeros and factors of polynomials.

Multiply and divide within 100.

Represent and solve problems involving addition and subtraction.

Interpret the structure of expressions.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Reason about and solve one-variable equations and inequalities.

Write and interpret numerical expressions.

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Represent and analyze quantitative relationships between dependent and independent variables.
problem_activity: Optional activity
In this activity, students consider a doubling relationship where the exponent is a variable. Monitor for students who connect this activity to the lessons on exponents, or who recognize that the quantities in this relationship are changing with respect to each other in a different manner than previous examples they have seen. Have these students share during the discussion.
Digital
Launch
Give students 5-7 minutes of quiet work time, followed by a whole-class discussion.
Receptive/Expressive Language: Peer Tutors.
Pair students with their previously identified peer tutors to aid in comprehension and expression of understanding.
Student Facing
A researcher who is studying mosquito populations collects the following data:
| day in                                   the study                                   \((d)\) | number of                                   mosquitoes                                   \((n)\) |
|----------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------|
|                                              1                                               |                                                2                                                 |
|                                              2                                               |                                                4                                                 |
|                                              3                                               |                                                8                                                 |
|                                              4                                               |                                                16                                                |
|                                              5                                               |                                                32                                                |
The researcher said that, for these five days, the number of mosquitoes,
\(n\)
, can be found with the equation
\(n = 2^d\)
where
\(d\)
is the day in the study. Explain why this equation matches the data.
Use the ordered pairs in the table to graph the relationship between number of mosquitoes and day in the study for these five days.
Describe the graph. Compare how the data, equation, and graph illustrate the relationship between the day in the study and the number of mosquitoes.
If the pattern continues, how many mosquitoes will there be on day 6?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Give students 5-7 minutes of quiet work time, followed by a whole-class discussion.
Student Facing
A researcher who is studying mosquito populations collects the following data:
| day in                           the study                           \((d)\) | number of                           mosquitoes                           \((n)\) |
|------------------------------------------------------------------------------|----------------------------------------------------------------------------------|
|                                      1                                       |                                        2                                         |
|                                      2                                       |                                        4                                         |
|                                      3                                       |                                        8                                         |
|                                      4                                       |                                        16                                        |
|                                      5                                       |                                        32                                        |
The researcher said that, for these five days, the number of mosquitoes,
\(n\)
, can be found with the equation
\(n = 2^d\)
where
\(d\)
is the day in the study. Explain why this equation matches the data.
Use the ordered pairs in the table to graph the relationship between number of mosquitoes and day in the study for these five days.
[IMG]
Describe the graph. Compare how the data, equation, and graph illustrate the relationship between the day in the study and the number of mosquitoes.
If the pattern continues, how many mosquitoes will there be on day 6?
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
The purpose of this discussion is to help students make connections between the table, graph, and equation that describe this situation. Ask students to share who connected this activity to the lessons on exponents, or who recognize that the quantities in this relationship are changing with respect to each other in a different manner than previous examples they have seen.
Consider asking some of these questions:
“Which of the data, equation, or graph gives you more of a feel for how the mosquito population changes with the day in the study?”
“Think back to the lesson on exponents with the dot pattern and the Genie activity. How do those situations compare with this mosquito situation? How would tables of data, graphs, and equations compare?”
“What are some similarities and differences you noticed between all the relationships you've seen in the last few lessons?”
Speaking, Listening: MLR8 Discussion Supports.
To support whole-class discussion, display sentence frames such as, “The dot pattern is similar to/ different than the mosquito situation because ________,” and “The genie situation is similar to/ different than the mosquito situation because ________.” This routine will support rich and inclusive discussion about the similarities and differences between all of the relationships students have seen in the last few lessons.
Design Principle(s): Optimize output (for comparison); Cultivate conversation


correct_option_index: 33