This task is designed to give students insight into the effects of translations, rotations, and reflections on geometric figures in the context of showing that two figures are congruent.

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b).

The construction of the perpendicular bisector of a line segment is one of the most common in plane geometry and it is undertaken here. In addition to giving students a chance to work with straightedge and compass, the problem uses triangle congruence both to show that the constructed line is perpendicular to AB and to show that it bisects AB.

This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. This helps pave the way toward what students will see later in trigonometry but some guidance will likely be needed in order to get students started on this path.

This short video and interactive assessment activity is designed to teach first graders about counting rectangles, squares, and triangles in composite figures.

This short video and interactive assessment activity is designed to teach fourth graders about counting right angles in a turn.

This challenging problem and brainteaser gives first graders an opportunity to compose and decompose squares.

This short video and interactive assessment activity is designed to teach third graders about counting vertices and sides in various shapes.

This short video and interactive assessment activity is designed to teach fourth graders about counting the angles in a closed figure.

This short video and interactive assessment activity is designed to teach fifth graders about counting the number of perpendicular lines.

In this video segment from Cyberchase, the CyberSquad must get into a vault before Hacker, Buzz and Delete by cracking a code of shapes and numbers.

This short video and interactive assessment activity is designed to teach third graders about describing patterns using letters.

This short video and interactive assessment activity is designed to teach fourth graders about describing patterns using letters.

This short video and interactive assessment activity is designed to teach third graders about determining unknown angles in parallelograms.

This short video and interactive assessment activity is designed to teach fourth graders about determining unknown angles in trapezoids.

This short video and interactive assessment activity is designed to teach third graders about determining unknown angles in trapezoids.

This short video and interactive assessment activity is designed to teach third graders about determining unknown angles within rectangles and squares.

This short video and interactive assessment activity is designed to teach fifth graders about determining unknown angles within rectangles and squares.

This short video and interactive assessment activity is designed to teach third graders about determining the unknown angle in an isosceles triangle.