The purpose of this task is for students to apply a reflection to a single point. The standard 8.G.1 asks students to apply rigid motions to lines, line segments, and angles.

This goal of this task is to provide experience applying transformations to show that two polygons are similar.

This is the first version of a task asking students to find the areas of triangles that have the same base and height, and is the most concrete.

This is the second version of a task asking students to find the areas of triangles that have the same base and height.

The purpose of this task is two-fold. One is to provide students with a multi-step problem involving volume. The other is to give them a chance to discuss the difference between exact calculations and their meaning in a context.

This is the third in a series of four tasks that gradually build in complexity. The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. Here, we are given the volume and are asked to find the height. In order to do this, students must know that 1 ℓ=1000 cm3. This fact may or may not need to be included in the problem, depending on students’ familiarity with the units.

This is the last in a series of four tasks that gradually build in complexity. The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. This problem is based on Archimedes’ Principle that the volume of an immersed object is equivalent to the volume of the displaced water. While the stone itself is an irregular solid, relating it to the displaced water in a rectangular tank means that the actual volume calculation is that of a rectangular prism, and therefore, fits in with content standard 6.G.2.

The purpose of this task is for students to translate between information provided on a map that is drawn to scale and the distance between two cities represented on the map.

The purpose of this task is to have students explore various cross sections of a cube and use precise language to describe the shape of the resulting faces.

The purpose of this task is for students to solve a volume problem in a modeling context (MP.4).

This goal of this task is to give students familiarity using the formula for the area of a circle while also addressing measurement error and addresses both 7.G.4 and 7.RP.3.

The goal of this task is to motivate and prepare students for the formal definition of dilations and similarity transformations.

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

This task shows the congruence of two triangles in a particular geometric context arising by cutting a rectangle in half along the diagonal.

The purpose of this task is for students to study the impact of dilations on different measurements: segment lengths, area, and angle measure.

The purpose of this task is to apply rigid motions and dilations to show that triangles are similar.

In this task, using computer software, you will apply reflections, rotations, and translations to a triangle. You will then study what happens to the side lengths and angle measures of the triangle after these transformations have been applied. In each part of the question, a sample picture of the triangle is supplied along with a line of reflection, angle of rotation, and segment of translation: the attached GeoGebra software will allow you to experiment with changing the location of the line of reflection, changing the measure of the angle of rotation, and changing the location and length of the segment of translation.

The purpose of this task is for students to practice plotting points in the coordinate plane and finding the areas of polygons. This task assumes that students already understand how to find areas of polygons by decomposing them into rectangles and triangles;

The purpose of this task is for students to apply the calculation of distances on a coordinate plane to a real life context (6.G.3).

The goal of this task is to study the circumferences of different sized circles, both using manipulatives and from the point of view of scaling.