options: Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Find arc lengths and areas of sectors of circles.

Apply geometric concepts in modeling situations.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Understand congruence in terms of rigid motions.

Translate between the geometric description and the equation for a conic section.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Make geometric constructions.

Experiment with transformations in the plane.

Understand similarity in terms of similarity transformations.

Explain volume formulas and use them to solve problems.

Apply trigonometry to general triangles.

Visualize relationships between two-dimensional and three-dimensional objects.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Analyze, compare, create, and compose shapes.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Use coordinates to prove simple geometric theorems algebraically.

Prove geometric theorems.

Understand and apply theorems about circles.

Reason with shapes and their attributes.

Understand and apply the Pythagorean Theorem.

Solve real-world and mathematical problems involving area, surface area, and volume.

Classify two-dimensional figures into categories based on their properties.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Draw, construct, and describe geometrical figures and describe the relationships between them.
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: 21