options: Experiment with transformations in the plane.

Prove geometric theorems.

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

Understand congruence in terms of rigid motions.

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.

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

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

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

Understand and apply theorems about circles.

Understand similarity in terms of similarity transformations.

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

Explain volume formulas and use them to solve problems.

Use coordinates to prove simple geometric theorems algebraically.

Reason with shapes and their attributes.

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

Apply geometric concepts in modeling situations.

Understand and apply the Pythagorean Theorem.

Analyze, compare, create, and compose shapes.

Prove theorems involving similarity.

Find arc lengths and areas of sectors of circles.

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

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

Define trigonometric ratios and solve problems involving right triangles.

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

Make geometric constructions.

Apply trigonometry to general triangles.
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: 5