This is a solver for problems involving the time value of money (TVM). It emulates the TVM solver on the TI-83+ and TI-84 graphing calculators. Updated 6 November 2011 to work correctly when I% = 0.

The purpose of this task is to engage students in geometric modeling, and in particular to deduce algebraic relationships between variables stemming from geometric constraints. The modelling process is a challenging one, and will likely elicit a variety of attempts from the students.

In this interactive object, learners study the properties of a trapezoid and use a geometric formula to find its perimeter and area.

In this math meets life science lesson, learners measure the circumference of local trees in order to calculate diameters. Learners use this information and a growth rate table to estimate the age of the trees. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence. As an instructional task, it can help students build up their understanding of the relationship between rigid motions and congruence.

This Java applet provides opportunities for creative problem solving while encouraging young students to estimate length and angle measure. Using the Turtle Pond Applet, students enter a sequence of commands to help the turtle get to the pond. Children can write their own solutions using LOGO commands and input them into the computer. The turtle will then move and leave a trail or path according to the instructions given. (N.B. the applet is an upgrade of one that supported the Lesson "Get the Turtle to the Pond," cataloged separately.)

In this video segment from Cyberchase, Digit must a make a straight line between the two points and then follow the path created.

Jackie and Matt are looking at the same object along two different lines, in this video segment from Cyberchase.

This task combines two skills from domain G-C: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment (G-C.2), and computing lengths of circular arcs given the radii and central angles (G-C.5). It also requires students to create additional structure within the given problem, producing and solving a right triangle to compute the required central angles (G-SRT.8).

This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere. Students who are given this task must be familiar with the formula for the volume of a cylinder, the formula for the volume of a cone, and CavalieriŐs principle.

This lesson unit is intended to help you assess how well students are able to: recognize and use common 2D representations of 3D objects and identify and use the appropriate formula for finding the circumference of a circle.

This video is meant to be a fun, hands-on session that gets students to think hard about how machines work. It teaches them the connection between the geometry that they study and the kinematics that engineers use -- explaining that kinematics is simply geometry in motion. In this lesson, geometry will be used in a way that students are not used to. Materials necessary for the hands-on activities include two options: pegboard, nails/screws and a small saw; or colored construction paper, thumbtacks and scissors. Some in-class activities for the breaks between the video segments include: exploring the role of geometry in a slider-crank mechanism; determining at which point to locate a joint or bearing in a mechanism; recognizing useful mechanisms in the students' communities that employ the same guided motion they have been studying.

Students explore volume by trying to pack a moving truck with boxes of specified sizes.
The lesson is structured in the following way:
* Before the lesson, students attempt the Packing It In task individually. You review their responses and formulate questions that will help them improve their work.
* At the start of the lesson, students read your comments and consider ways to improve their work.
* In pairs or threes, students work together to develop a better solution, producing a poster to show their conclusions and their reasoning.
* Then, in the same small groups, students look at some sample student work showing different approaches to the problem. They evaluate the strategies used and seek to improve the arguments given.
* In a whole-class discussion, students compare different solution methods.
* Finally, students reflect individually on their learning.

In this Cyberchase video segment, the CyberSquad must locate each other using a map's grid to construct a coordinate system using letters and numbers.

In this activity, learners walk the sides and interior angles of various polygons drawn on the playground. As they do so, learners practice rotating clockwise 180 and 360 degrees. Learners discover there is a pattern to the sum of the interior angles of any polygon.

Students apply their knowledge of scale and geometry to design wearables that would help people in their daily lives, perhaps for medical reasons or convenience. Like engineers, student teams follow the steps of the design process, to research the wearable technology field (watching online videos and conducting online research), brainstorm a need that supports some aspect of human life, imagine their own unique designs, and then sketch prototypes (using Paint®). They compare the drawn prototype size to its intended real-life, manufactured size, determining estimated length and width dimensions, determining the scale factor, and the resulting difference in areas. After considering real-world safety concerns relevant to wearables (news article) and getting preliminary user feedback (peer critique), they adjust their drawn designs for improvement. To conclude, they recap their work in short class presentations.

This task asks students to classify shapes based on their properties. The task itself is straightforward, but there are a number of opportunities to present this task in class and push the level of discussion and reasoning. For example, the rule for the bottom circle is that all shapes must have all sides with the same length. Some students will likely conjecture that the rule is either that all shapes must be regular polygons or that all shapes must be equiangular. Either of these would be true except for the rhombus.

Though this would likely extend beyond the scope of 5th grade understanding, it might be interesting to look at the pentagon with the right angle. In the eyes of a 5th grader, it looks as if it might have sides of equal length. They have not yet derived any rules about the sum of interior angles in polygons, but they should be pushed to see that mathematicians cannot make assumptions based on the appearance of shapes. We only know that each of the shapes in the bottom circle is equilateral because the tick marks indicate that the sides are the same length. In that same line of reasoning, we must be careful to specify in part b that the rectangle does not have equal sides. A deep discussion would allow students to construct viable arguments and critique the reasoning of others (MP 3) and attend to precision (MP 6).

In this geometry lesson students classify triangles and explore side lengths of triangles to discover the Triangle Inequality Theorem. The resource includes an exploratory activity and student sheet (pdf), class discussion prompts, a small group spinner activity, extension suggestions, and links to two related resources (cataloged separately).

In these two geometry activities students explore the properties of triangles, discover what shapes triangles can form, and investigate what shapes can form triangles. Each activity includes a student recording sheet, extension ideas, and questions for students. Cataloged separateley within this site are the Patch Tool and the related How Many Triangles Can You Construct? activity.

The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence. In this problem, we considered SSA. Also insufficient is AAA, which determines a triangle up to similarity. Unlike SSA, AAS is sufficient because two pairs of congruent angles force the third pair of angles to also be congruent.