options: Write expressions in equivalent forms to solve problems.

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

Rewrite rational expressions.

Multiply and divide within 100.

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

Use polynomial identities to solve problems.

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

Represent and solve problems involving multiplication and division.

Generate and analyze patterns.

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

Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

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

Add and subtract within 20.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

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

Gain familiarity with factors and multiples.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Work with addition and subtraction equations.

Interpret the structure of expressions.

Represent and solve equations and inequalities graphically.

Solve systems of equations.

Create equations that describe numbers or relationships

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

Represent and analyze quantitative relationships between dependent and independent variables.

Perform arithmetic operations on polynomials.

Understand the relationship between zeros and factors of polynomials.

Use the four operations with whole numbers to solve problems.

Work with radicals and integer exponents.

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Narrative
In this activity, students are given expressions that represent strategies for finding the area of rectangles. The strategies are based on the distributive property and the associative property of multiplication. Students interpret the expressions by marking or shading area diagrams and connect each expression to the product of two factors (MP2). For instance, they see that to find the value of
\(2 \times (2 \times 6)\)
is to find the value of
\(4 \times 6\)
or
\(6 \times 4\)
.
MLR8 Discussion Supports:
Synthesis: Create a visual display of the diagrams. As students share their strategies, annotate the display to illustrate connections. For example, trace the area showing 5 columns of 3, and write
\(5 \times 3\)
.
Advances: Speaking, Representing
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite students to select at least 2 of the 3 problems to complete.
Supports accessibility for: Organization, Attention, Social-emotional skills
Required Materials
Materials to Gather
Colored pencils, crayons, or markers
Launch
Groups of 2
“Take a minute to read the directions of the activity. Then, talk to your partner about what you are asked to do.”
1 minute: quiet think time
1 minute: partner discussion
Answer any clarifying questions from students.
Give students access to colored pencils, crayons, or markers.
Activity
“Mark or shade each diagram to represent how each student found the area.”
3–5 minutes: independent work time
“Share with your partner how you used the rectangles to show each expression.”
3–5 minutes: partner discussion
Student Facing
Here are some rectangles and expressions that show how three students saw the area of the rectangles.
Noah
[IMG]
\((5\times 3)+(2 \times 3)\)
Priya
[IMG]
\(2 \times (2 \times 6)\)
Tyler
[IMG]
\((5 \times 8) + (3 \times 8)\)
For each rectangle:
Name the two factors that can be multiplied to find its area.
Mark or shade each rectangle to show how each student saw the area. Be prepared to explain your reasoning.
Student Response
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Activity Synthesis
“What are the two factors you can multiply to find the area of Noah’s rectangle?” (7 and 3)
“How are those numbers related to the expression that he wrote:
\((5\times 3)+(2 \times 3)\)
?”  (
\(7 \times 3\)
is 21. Finding
\(5\times3\)
, which is 15, then adding
\(2\times3\)
, which is 6, also gives 21.)
“Where do you see the two factors in his expression?” (The 7 is 5 and 2 combined. The 3 is in the
\(5 \times 3\)
and
\(2 \times 3\)
.)
Repeat the line of questioning with Priya’s rectangle and expression.


correct_option_index: 3