options: Create equations that describe numbers or relationships

Work with radicals and integer exponents.

Use polynomial identities to solve problems.

Reason about and solve one-variable equations and inequalities.

Represent and solve equations and inequalities graphically.

Generate and analyze patterns.

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

Interpret the structure of expressions.

Add and subtract within 20.

Represent and analyze quantitative relationships between dependent and independent variables.

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

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

Represent and solve problems involving addition and subtraction.

Represent and solve problems involving multiplication and division.

Rewrite rational expressions.

Solve equations and inequalities in one variable.

Work with addition and subtraction equations.

Perform arithmetic operations on polynomials.

Use the four operations with whole numbers to solve problems.

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

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

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

Write expressions in equivalent forms to solve problems.

Solve systems of equations.

Gain familiarity with factors and multiples.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

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

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

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

Write and interpret numerical expressions.

Analyze patterns and relationships.

Use properties of operations to generate equivalent expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.
problem_activity: Warm-up
The purpose of this warm-up is for students to reason about expressions with negative exponents on a number line. Students explore a common misunderstanding about negative exponents that is helpful to address before scientific notation is used to describe very small numbers.
For students’ reference, consider displaying a number line from a previous lesson that shows powers of 10 on a number line.
Launch
Give students 2 minutes of quiet work time, followed by a whole-class discussion.
Student Facing
Kiran drew this number line.
[IMG]
Andre said, “That doesn’t look right to me.”
Explain why Kiran is correct or explain how he can fix the number line.
Student Response
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Activity Synthesis
The important idea to highlight during the discussion is that the larger the size (or absolute value) of a negative exponent, the closer the value of the expression is to zero. This is because the negative exponent indicates the number of factors that are
\(\frac{1}{10}\)
. For example,
\(10^{\text-5}\)
represents 5 factors that are
\(\frac{1}{10}\)
and
\(10^{\text-6}\)
represents 6 factors that are
\(\frac{1}{10}\)
, so
\(10^{\text-6}\)
is 10 times smaller than
\(10^{\text-5}\)
.
Ask one or more students to explain whether they think the number line is correct and ask for their reasoning. Record and display their reasoning for all to see, preferably on the number line. If possible, show at least two correct ways the number line can be fixed.


correct_option_index: 1