Module 2 explores two-dimensional and three-dimensional shapes.  Students learn about flat and solid shapes independently as well as how they are related to each other and to shapes in their environment.  Students begin to use position words when referring to and moving shapes.  Students learn to use their words to distinguish between examples and non-examples of flat and solid shapes.

Kindergarten comes to a close with another opportunity for students to explore geometry in Module 6. Throughout the year, students have built an intuitive understanding of two- and three-dimensional figures by examining exemplars, variants, and non-examples. They have used geometry as a context for exploring numerals as well as comparing attributes and quantities. To wrap up the year, students further develop their spatial reasoning skills and begin laying the groundwork for an understanding of area through composition of geometric figures.

In this lesson, students use dimensions of round and square hay bales to calculate and compare volumes. They also calculate unit prices to determine which hay bale is the better value. Finally, students explore how to fit round and square bales into a barn to maximize volume, and decide which type of hale bale is the best choice. A class handout, plus solutions for the teacher, leads the problem-solving activity.

The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.

By the end of this lesson, students have created their own dartboard and practiced how to change the scale of an object and how to measure and draw angles using a protractor. The dartboard can later serve to emphasize properties of angles and angle pairs. The practice they will get in this lesson drawing concentric circles and measuring angles will help them in their quest to more accurately create circle graphs. Directions, handouts, student questions, and assessment options are all included.

The purpose of this task is for students to apply the concepts of mass, volume, and density in a real-world context. There are several ways one might approach the problem, e.g., by estimating the volume of a person and dividing by the volume of a cell.

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

In this problem, the variables a,b,c, and d are introduced to represent important quantities for this esimate: students should all understand where the formula in the solution for the number of leaves comes from. Estimating the values of these variables is much trickier and the teacher should expect and allow a wide range of variation here.

This activity has students explore the patterns that emerge when connecting midpoints of triangles. The activity includes a student worksheet, discussion questions, and an interactive fractal tool.

As written, this problem gives students all of the information they need to estimate the thickness of a soda can.

his is a version of ''How thick is a soda can I'' which allows students to work independently and think about how they can determine how thick a soda can is. The teacher should explain clearly that the goal of this task is to come up with an ''indirect'' means of assessing how thick the can is, that is directly measuring its thickness is not allowed.

This rich task is an excellent example of geometric concepts in a modeling situation and is accessible to all students. In this task, students will provide a sketch of a paper ice cream cone wrapper, use the sketch to develop a formula for the surface area of the wrapper, and estimate the maximum number of wrappers that could be cut from a rectangular piece of paper.

This short video and interactive assessment activity is designed to teach fifth graders about identifying basic 2d shapes in composite figures.

This short video and interactive assessment activity is designed to teach fifth graders about identifying basic 2d shapes in a set.

This short video and interactive assessment activity is designed to teach second graders about identifying ellipses and polygons.

This short video and interactive assessment activity is designed to teach third graders about identifying ellipses and polygons.

This short video and interactive assessment activity is designed to teach fourth graders about identifyinging lines of symmetry in letters.

This short video and interactive assessment activity is designed to teach fifth graders about identifying lines of symmetry in various shapes.

This short video and interactive assessment activity is designed to teach third graders about identifying parallel lines.

This short video and interactive assessment activity is designed to teach second graders about identifying parallel and perpendicular lines.