options: Work with addition and subtraction equations.

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

Represent and solve equations and inequalities graphically.

Understand the relationship between zeros and factors of polynomials.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving multiplication and division.

Use polynomial identities to solve problems.

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

Gain familiarity with factors and multiples.

Interpret the structure of expressions.

Multiply and divide within 100.

Write and interpret numerical expressions.

Add and subtract within 20.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Rewrite rational expressions.

Create equations that describe numbers or relationships

Represent and solve problems involving addition and subtraction.

Reason about and solve one-variable equations and inequalities.

Work with radicals and integer exponents.

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

Solve systems of equations.

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

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

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

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

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

Perform arithmetic operations on polynomials.

Generate and analyze patterns.

Analyze patterns and relationships.

Use the four operations with whole numbers to solve problems.

Analyze and solve linear equations and pairs of simultaneous linear equations.
problem_activity: Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for products of 4 and 6 as they relate to products of 5. These understandings help students develop fluency and will be helpful later when students consider solutions for and solve two-step word problems.
When students use products of 5 to determine products of 4 by thinking of them as one fewer group or one fewer object in each group, or work from products of 5 to determine products of 6 by thinking of them as one more group or one more object in each group, they look for and make use of structure (MP7).
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.
\(5 \times 7\)
\(4 \times 7\)
\(6 \times 7\)
\(4 \times 8\)
Student Response
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Activity Synthesis
“How does knowing
\(5\times7\)
help you find some of the other products?” (I can remove a group of 7 to find
\(4\times7\)
or add a group of 7 to find
\(6\times7\)
.)
Consider asking:
“Who can restate _____’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone approach the problem in a different way?”
“Does anyone want to add on to _____’s strategy?”


correct_option_index: 10