options: Apply and extend previous understandings of arithmetic to algebraic expressions.

Add and subtract within 20.

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

Interpret the structure of expressions.

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

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

Create equations that describe numbers or relationships

Use properties of operations to generate equivalent expressions.

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

Understand the relationship between zeros and factors of polynomials.

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

Represent and solve problems involving multiplication and division.

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

Solve equations and inequalities in one variable.

Use the four operations with whole numbers to solve problems.

Work with addition and subtraction equations.

Work with radicals and integer exponents.

Analyze patterns and relationships.

Perform arithmetic operations on polynomials.

Write and interpret numerical expressions.

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

Reason about and solve one-variable equations and inequalities.

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

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

Solve systems of equations.

Multiply and divide within 100.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve equations and inequalities graphically.

Use polynomial identities to solve problems.

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

Rewrite rational expressions.

Generate and analyze patterns.
problem_activity: Narrative
In this activity, students examine the rectangles drawn by their classmates and learn the term
factor pairs
. Students recognize the side lengths of each rectangle as a factor pair of its area.
This activity uses
MLR7 Compare and Connect
.
Advances: representing, conversing
Launch
Groups of 2
Activity
5–7 minutes: gallery walk
Monitor for different explanations students offer for how they know whether all possible rectangles with a given area have been found.
Student Facing
As you visit each poster, discuss with your partner:
What do you notice? Use the following sentence frames when you share:
“I notice that some of the posters . . . .”
“I notice the posters for numbers _____ and _____ are alike because . . . .”
How do you know that all possible rectangles were found for the given area?
Student Response
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Activity Synthesis
MLR7 Compare and Connect
“What is the same and what is different between the rectangles on the posters?”
30 seconds: quiet think time
1 minute: partner discussion
“How do you know that all possible rectangles have been found for the given area?” (We could not find any other numbers that multiply together to make the area.)
Display the rectangles for 21: 1 by 21 and 3 by 7.
“Are there any more rectangles we can draw? Why or why not?” (No, there are no more whole-number factors of 21. Or, no, because to get 21 we can multiply only 1 and 21, 3 and 7, 7 and 3, and 21 and 1.)
“We call 1 and 21 a
factor pair
of 21 because each of them is a factor of 21 and multiplying them gives 21. Another factor pair of 21 is 3 and 7.”
“Work with your partner to write down the factor pairs for the areas you were assigned.”
2 minutes: partner work time


correct_option_index: 12