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

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

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

Prove theorems involving similarity.

Reason with shapes and their attributes.

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

Use coordinates to prove simple geometric theorems algebraically.

Apply trigonometry to general triangles.

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

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

Understand and apply the Pythagorean Theorem.

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

Find arc lengths and areas of sectors of circles.

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

Define trigonometric ratios and solve problems involving right triangles.

Make geometric constructions.

Explain volume formulas and use them to solve problems.

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

Apply geometric concepts in modeling situations.

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

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

Analyze, compare, create, and compose shapes.

Prove geometric theorems.

Experiment with transformations in the plane.

Understand and apply theorems about circles.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
problem_activity: Warm-up
This warm-up introduces students to a scale without units and invites them to interpret it using what they have learned about scales so far.
As students work and discuss, notice those who interpret the unitless scale as numbers having the same units, as well as those who see “1 to 100” as comparable to using a scale factor of 100. Invite them to share their thinking later.
Launch
Remind students that, until now, we have worked with scales that each specify two units—one for the drawing and one for the object it represents. Tell students that sometimes scales are given without units.
Arrange students in groups of 2. Give students 2 minutes of quiet think time and another minute to discuss their thinking with a partner.
Student Facing
A map of a park says its scale is 1 to 100.
What do you think that means?
Give an example of how this scale could tell us about measurements in the park.
Student Response
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Anticipated Misconceptions
Students might think that when no units are given, we can choose our own units, using different units for the 1 and the 100. This is a natural interpretation given students’ work so far. Make note of this misconception, but address it only if it persists beyond the lesson.
Activity Synthesis
Solicit students’ ideas about what the scale means and ask for a few examples of how it could tell us about measurements in the park. If not already mentioned by students, point out that a scale written without units simply tells us how many times larger or smaller an actual measurement is compared to what is on the drawing. In this example, a distance in the park would be 100 times the corresponding distance on the map, so a distance of 12 cm on the map would mean 1,200 cm or 12 m in the park.
Explain that the distances could be in any unit, but because one is expressed as a number times the other, the unit is the same for both.
Tell students that we will explore this kind of scale in this lesson.


correct_option_index: 20