options: Use polynomial identities to solve problems.

Perform arithmetic operations on polynomials.

Work with radicals and integer exponents.

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

Gain familiarity with factors and multiples.

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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Generate and analyze patterns.

Use properties of operations to generate equivalent expressions.

Write and interpret numerical expressions.

Multiply and divide within 100.

Add and subtract within 20.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving multiplication and division.

Solve equations and inequalities in one variable.

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

Understand the relationship between zeros and factors of polynomials.

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

Interpret the structure of expressions.

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

Work with addition and subtraction equations.

Use the four operations with whole numbers to solve problems.

Rewrite rational expressions.

Solve systems of equations.

Analyze patterns and relationships.

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

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving addition and subtraction.

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

Represent and solve equations and inequalities graphically.

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

Create equations that describe numbers or relationships
problem_activity: Narrative
The purpose of this activity is for students to partition rectangles to create rows and columns of equal-size squares. In the launch, students build an array with tiles and then represent it on a rectangle with tick marks as guidance. They will partition rectangles without tick marks in the next activity.
MLR2 Collect and Display.
Synthesis: Direct attention to words collected and displayed from the previous lessons. Include the word “partition.” Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading
Required Materials
Materials to Gather
Inch tiles
Rulers
Launch
Groups of 2
Give students rulers and inch tiles.
Activity
“Use 8 tiles to make a rectangle. Your tiles should be in 2 rows.”
1 minute: independent work time
“Now, draw lines in the rectangle to show the squares. It should have the same number of equal-size squares as the rectangle you made out of tiles. You may use a ruler if it helps you.”
1 minute: independent work time
“You will draw lines to partition 2 more rectangles into equal-size squares. You can also use the tiles to build it first, if that helps.”
10 minutes: independent work time
Student Facing
Build a rectangle with 8 tiles arranged in 2 rows. Use a ruler to partition the rectangle to match the rectangle you made.
[IMG]
Use a ruler to partition the rectangle using the tick marks as a guide.
[IMG]
How many rows of equal-size squares did you make?
How many columns did you make?
Write 2 equations to represent the total number of equal-size squares.
Use a ruler to partition the rectangle using the tick marks as a guide.
[IMG]
How many rows of equal-size squares did you make?
How many columns did you make?
Write 2 equations to represent the total number of equal-size squares.
Student Response
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Advancing Student Thinking
If students create equations that match the total number of squares, but do not represent the sum of squares in each row or the sum of squares in each column, consider asking:
“How does your equation match the array?”
“Can you write an equation with equal addends that shows the sum of each row or column?”
Activity Synthesis
Invite 1
–
2 students to share their rectangles and equations for their rectangle with 3 rows and 5 columns. (
\(3 + 3 + 3 + 3 + 3 = 15\)
or
\(5 + 5 + 5 = 15\)
)
Draw a rectangle and partition to show:
[IMG]
“How is this partition different from what we did in this activity?” (The squares aren’t the same size and the last column has 4 not 3.)


correct_option_index: 30