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

Solve systems of equations.

Understand the relationship between zeros and factors of polynomials.

Solve equations and inequalities in one variable.

Use polynomial identities to solve problems.

Gain familiarity with factors and multiples.

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

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

Use properties of operations to generate equivalent expressions.

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

Represent and analyze quantitative relationships between dependent and independent variables.

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

Multiply and divide within 100.

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

Rewrite rational expressions.

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

Represent and solve problems involving multiplication and division.

Interpret the structure of expressions.

Analyze patterns and relationships.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Perform arithmetic operations on polynomials.

Use the four operations with whole numbers to solve problems.

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.

Generate and analyze patterns.

Work with radicals and integer exponents.

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

Represent and solve equations and inequalities graphically.

Create equations that describe numbers or relationships

Write expressions in equivalent forms to solve problems.

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

Write and interpret numerical expressions.

Work with addition and subtraction equations.

Represent and solve problems involving addition and subtraction.
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: 25