options: Prove theorems involving similarity.

Understand similarity in terms of similarity transformations.

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

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

Explain volume formulas and use them to solve problems.

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

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

Apply geometric concepts in modeling situations.

Use coordinates to prove simple geometric theorems algebraically.

Experiment with transformations in the plane.

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

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

Define trigonometric ratios and solve problems involving right triangles.

Prove geometric theorems.

Make geometric constructions.

Analyze, compare, create, and compose shapes.

Understand congruence in terms of rigid motions.

Understand and apply the Pythagorean Theorem.

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

Find arc lengths and areas of sectors of circles.

Apply trigonometry to general triangles.

Understand and apply theorems about circles.

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

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

Reason with shapes and their attributes.

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

Visualize relationships between two-dimensional and three-dimensional objects.
problem_activity: Activity
The purpose of this activity is to give students an opportunity to solve a relatively complicated application problem that requires an understanding of aspect ratio, the Pythagorean Theorem, and realizing that a good way to compare the sizes of two screens is to compare their areas. The previous activities in this lesson are meant to prepare students to understand the situation and suggest some strategies for tackling the problem.
Monitor for students using different approaches and strategies. Students may benefit from more time to think about this problem than is available during a typical class meeting.
Launch
Provide access to calculators that can take the square root of a number. The task statement is wordy, so consider using the Three Reads protocol to ensure students understand what the problem is saying and what it is asking.
We chose not to provide diagrams drawn to scale in the student materials, since it makes it somewhat obvious that the new phone design has a smaller screen area. However if desired, here is an image to show or provide to students:
[IMG]
Reading, Listening, Conversing: MLR6 Three Reads.
Use this routine to support reading comprehension of this word problem. Use the first read to orient students to the situation. Ask students to describe what the situation is about without using numbers (customers think that newly released smartphones have smaller screens). Use the second read to identify quantities and relationships. Ask students what can be counted or measured without focusing on the values (aspect ratios for phones manufactured before and after 2017). After the third read, invite students to brainstorm possible strategies they can use determine whether or not the new phones have a smaller screen, and by how much.
Design Principle(s): Support sense-making
Student Facing
Before 2017, a smart phone manufacturer’s phones had a diagonal length of 5.8 inches and an aspect ratio of
\(16:9\)
. In 2017, they released a new phone that also had a 5.8-inch diagonal length, but an aspect ratio of
\(18.5:9\)
. Some customers complained that the new phones had a smaller screen. Were they correct? If so, how much smaller was the new screen compared to the old screen?
Student Response
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Activity Synthesis
Invite students to share their ideas and progress with the class. If appropriate, students may benefit from an opportunity to clearly present their solution in writing.


correct_option_index: 17