6-8, 9-12
Each student constructs a tetrahedron and describes the linear, area and
volume measurements using non‑traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed.
6-8
Using a MIRA
TM geometry tool, students determine the relationships between radius, diameter, circumference and area of a circle.
6-8
Students explore the relationship between the lengths of the sides and diagonals of a square. Students will use their discoveries to predict the diagonal length of any square.
3-5, 6-8
The
Stomachion is an ancient tangram-type puzzle. Believed by
some to have been created by Archimedes, it consists of 14 pieces cut
from a square. The pieces can be rearranged to form other interesting
shapes. In this lesson, students learn about the history of the
Stomachion, use the pieces to create other figures, learn about symmetry and transformations, and investigate the areas of the pieces.
6-8
In this lesson, students will design a playground using manipulatives and multiple representations. Maximum area with a given perimeter will be explored using tickets. The playground will include equipment with given dimensions, which decreases the maximum area that can be created. This is an interesting demonstration of how a real-world context can change a purely mathematical result. Finally, scale models will be created on graph paper and a presentation will be made to a playground planning committee for approval.
6-8
In this lesson, students draw various polygons and investigate their interior angles. The investigation is done using both an interactive tool and paper and pencil to foster an understanding of how different patterns can lead to the same solution. After comparing results with a partner, students develop a formula showing the relationship between the number of sides of a polygon and the sum of the interior angles.
6-8, 9-12
This lesson allows students to explore linear equations and the effects of changing the slope and
y-intercept on a line. It gives students exposure to
y =
mx +
b,
and can be used as an introduction to the topic. Using graphing
calculators, students are challenged to overlap lines onto the sides of
polygons. To achieve this goal, students change slopes and
y-intercepts of lines, noting observations about behavior as they work. As students change the
y-intercept
of a line, they see it raise or lower the line. As students change the
slope, they see it affect the steepness of the line.
6-8
Students explore two different methods for dividing the area of a circle in half, one of which uses concentric circles. The first assumption that many students make is that half of the radius will yield a circle with half the area. This is not true, and it surprises students. In this lesson, students investigate the optimal radius length to divide the area of a circle evenly between an inner circle and an outer ring.
6-8
Darts is a popular game in which players throw 3 darts, one at a time, aiming for a target. Different regions of the board give different points. In this lesson, students learn how to change the scale of an object, and how to measure and draw angles using a protractor. By the end of the lesson, students have created their own dartboard. The dartboard can later serve to emphasize properties of angles and angle pairs. This activity is a good one to do prior to a lesson in which students construct circle graphs. The practice they will get in this lesson drawing circles and measuring angles will help them in their quest to more accurately create circle graphs.
6-8
Tile floors are common in many homes and businesses. They are durable, beautiful, and can add value to the home or business but they can also be costly. In this lesson, students will create and estimate the cost of a tile floor design using geometric shapes, ratios, proportions, and percents. All cost estimates are based on the purchase of full boxes of tiles so students have to weigh cost against design considerations. Cost estimates also include labor and taxes for a more realistic estimate of what it costs for a great looking floor.
