Major Cluster

Verify experimentally the properties of rotations, reflections, and translations:

8 Lessons

14 Activities

Lines are taken to lines, and line segments to line segments of the same length.

10 Lessons

5 Activities

Angles are taken to angles of the same measure.

9 Lessons

4 Activities

Parallel lines are taken to parallel lines.

7 Lessons

2 Activities

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

11 Lessons

17 Activities

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

12 Lessons

12 Activities

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

7 Lessons

15 Activities

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

10 Lessons

19 Activities

Major Cluster

Explain a proof of the Pythagorean Theorem and its converse.

7 Lessons

7 Activities

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

14 Lessons

20 Activities

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

4 Lessons

4 Activities

Additional Cluster

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

18 Lessons

18 Activities