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

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.

Analyze patterns and relationships.

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

Multiply and divide within 100.

Work with addition and subtraction equations.

Interpret the structure of expressions.

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

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

Use properties of operations to generate equivalent expressions.

Write expressions in equivalent forms to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Write and interpret numerical expressions.

Create equations that describe numbers or relationships

Generate and analyze patterns.

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

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

Solve systems of equations.

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Rewrite rational expressions.

Solve equations and inequalities in one variable.

Understand the relationship between zeros and factors of polynomials.

Reason about and solve one-variable equations and inequalities.

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

Represent and solve equations and inequalities graphically.

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

Use polynomial identities to solve problems.

Perform arithmetic operations on polynomials.
problem_activity: Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have about equal groups in multiplication expressions and see a pattern as one factor is decreased. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to use multiplication to answer questions about array situations.
When students notice that as the number being multiplied by 2 decreases the product decreases by a group of 2, they look for and express regularity in repeated reasoning (MP8).
Launch
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time
Activity
Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.
Student Facing
Find the value of each expression mentally.
\(10\times2\)
\(9\times2\)
\(8\times2\)
\(7\times2\)
Student Response
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Activity Synthesis
“What do you notice about the products as we worked through this series of problems?” (They decrease by 2.)
“Why does the product decrease by 2 each time?” (The number of groups decreased by 1.)


correct_option_index: 5

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