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

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

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