options: Explain volume formulas and use them to solve problems.

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.

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

Define trigonometric ratios and solve problems involving right triangles.

Apply trigonometry to general triangles.

Use coordinates to prove simple geometric theorems algebraically.

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

Prove geometric theorems.

Understand and apply the Pythagorean Theorem.

Reason with shapes and their attributes.

Prove theorems involving similarity.

Find arc lengths and areas of sectors of circles.

Understand and apply theorems about circles.

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

Understand congruence in terms of rigid motions.

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

Analyze, compare, create, and compose shapes.

Experiment with transformations in the plane.

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

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

Make geometric constructions.

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

Understand similarity in terms of similarity transformations.

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

Apply geometric concepts in modeling situations.

Draw, construct, and describe geometrical figures and describe the relationships between them.
problem_activity: Warm-up
The purpose of this warm-up is to remind students that the translation of a line is parallel to the original line, and to plant the seed that a line can be taken to a parallel line by translating it. They inspect several lines to decide which could be translations of a given line. Then they describe the translations by specifying the number of units and the direction the original line should be translated.
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet think time and access to geometry toolkits. Ask them to share their responses with a partner afterwards.
Student Facing
[IMG]
The diagram shows several lines. You can only see part of the lines, but they actually continue forever in both directions.
Which lines are images of line
\(f\)
under a translation?
For each line that is a translation of
\(f\)
, draw an arrow on the grid that shows the vertical translation distance.
Student Response
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Anticipated Misconceptions
Students may think that lines
\(i\)
and
\(h\)
can’t be images of line
\(f\)
because the part of
\(i\)
and
\(h\)
we can see is shorter than the part of
\(f\)
we can see. Tell these students that all of the lines go on indefinitely in both directions.
Activity Synthesis
Invite students to share how they know that lines
\(h\)
and
\(i\)
are translations of
\(f\)
. The main reason to bring out is that they are parallel to
\(f\)
. It might be worth demonstrating with a transparency that we can translate
\(f\)
to match up with
\(h\)
and
\(i\)
, but to match up with the other lines, we would need to rotate (or reflect) the transparency. If using a transparency to demonstrate the number of units to translate
\(f\)
up or down, it is helpful to draw a dot on a specific point on both the underlying graph and on the transparency.


correct_option_index: 3