| Seventh Grade
Draw and Construct Geometric
Objects
- G.SR.07.01 Use a ruler and other tools
to draw squares, rectangles, triangles, and parallelograms
with specified dimensions.
- G.SR.07.02 Use compass and straightedge
to perform basic geometric constructions: the perpendicular
bisector of a segment, an equilateral triangle, and
the bisector of an angle; understand informal justifications.
- Angle
Measurement
This interactive site allows students to see
Angles in a Circle and manipulate the angles to
see how they add up to 90,180, and 360 degrees.
Also has Trig for Higher level Math
- Animal
Weigh In
Outstanding
- The site allows students to compare and
estimate the weight of animals and gives them
several chances before it helps them out. (Metric,
standard, and non-standard units are all used)
A balance scale activity which has the student
drag weights to match the unit given. Students
are provided hints and can read the "key ideas"
section to learn more about weights. Some conversion
of weights is needed, such as converting pounds
to ounces or kilograms to grams. Some non-standard
weights are used, such as "stones.' Students can
use the key ideas section to determine what weight
is equivalent to a stone. This is an interactive
game.
- Bathroom
Tiles
Outstanding
- Students use an interactive game to perform
transformations using reflections and rotations.
Three levels of activities are given as well as
solutions and hints.
- Constructing
Your Own Set of Tangrams
Directions for constructing your own tangram.
Extension activities with the pieces are available
in which students will produce other shapes (http://forum.swarthmore.edu/trscavo/tangrams/activities.html)
and gain a better understanding of area (http://forum.swarthmore.edu/trscavo/tangrams/area.html)
with out formulas. These activities seem to be
all linked together.
- From
Corner to Corner
Students are supplied with an on-line ruler and
must use it to measure the side of a square and
a diagonal. Students then need to analyze the
data to develop a rule for estimating the length
of the diagonal given the length of the side without
actually measuring the length. Students then need
to consider if the rule would work for other shapes.
They also need to reflect on their rule and submit
a short explanation of why it works. (This could
also be extended to include the Pythagorean Theorem.)
- Inversions
by Scott Kim
This site has several examples of symmetry using
inversions of people's names. It contains
teacher lesson plans as well as several examples
of various symmetries and unusual tesselations.
- Lesson
on Perimeter of Polygons
Students will be given a brief description of
polygons and perimeter and will be able to determine
the perimeter of a number of polygons by interacting
with the lesson. This is a student activity.
- Math
Goodies: Circumference
Students practice computing the formulas for
circumference after reading the lesson.
- Measure
It!
Students measure a red bar with a ruler in either
centimeters or inches. Multiple choice answers
are provided. Students get immediate feedback
if their answers are correct or incorrect.
- Shape
Surveyor
This is an interactive student activity used to
find the perimeter and area of a rectangle.
- Welcome
To Symmetry
This unit is designed to recognize the MCTM Curriculum
and Evaluation Standards for School Mathematics
concerning the need to give increased attention
to "Coordinate and Transformation Approaches in
Geometry at the secondary level. The lesson also
demonstrates increased attention to: The active
involvement of students in constructing and applying
mathematical ideas; the use of a variety of instructional
formats; and the use of computers for learning
and doing mathematics. This has links to
teacher resources and a student page dealing with
symmetry (rotational, reflectional, translational).
- World
of Escher
This is a commercial site selling MC Escher tesselations.
It would be useful as a reference and has many
examples of his art as well as those sent in by
others. Check out "gallery" for Escher's
work and "contest" for other people.
Understand the Concept of
Similar Polygons, and Solve Related Problems
- G.TR.07.03 Understand that in similar polygons,
corresponding angles are congruent and the ratios
of corresponding sides are equal; understand the concepts
of similar figures and scale factor.
- From
Corner to Corner
Students are supplied with an on-line ruler and
must use it to measure the side of a square and
a diagonal. Students then need to analyze the
data to develop a rule for estimating the length
of the diagonal given the length of the side without
actually measuring the length. Students then need
to consider if the rule would work for other shapes.
They also need to reflect on their rule and submit
a short explanation of why it works. (This could
also be extended to include the Pythagorean Theorem.
- More
Tangram Activities
Students will use tangram pieces to complete the
following objectives: gain a better understanding
of area without formulas, compute the area of
polygons by decompostion, gain familiarity with
the names of certain polygons (e.g., rectangle,
trapezoid, and pentagon), learn the meaning of
the term "similar", and will develop geometric
intuition.
- G.TR.07.04 Solve problems about similar
figures and scale drawings.
- From
Corner to Corner
Students are supplied with an on-line ruler and
must use it to measure the side of a square and
a diagonal. Students then need to analyze the
data to develop a rule for estimating the length
of the diagonal given the length of the side without
actually measuring the length. Students then need
to consider if the rule would work for other shapes.
They also need to reflect on their rule and submit
a short explanation of why it works. (This could
also be extended to include the Pythagorean Theorem.
- More
Tangram Activities
Students will use tangram pieces to complete the
following objectives: gain a better understanding
of area without formulas, compute the area of
polygons by decompostion, gain familiarity with
the names of certain polygons (e.g., rectangle,
trapezoid, and pentagon), learn the meaning of
the term "similar", and will develop geometric
intuition.
- G.TR.07.05 Show that two triangles are
similar using the criteria: corresponding angles are
congruent (AAA similarity); the ratios of two pairs
of corresponding sides are equal and the included
angles are congruent (SAS similarity); ratios of all
pairs of corresponding sides are equal (SSS similarity);
use these criteria to solve problems and to justify
arguments.
- From
Corner to Corner
Students are supplied with an on-line ruler and
must use it to measure the side of a square and
a diagonal. Students then need to analyze the
data to develop a rule for estimating the length
of the diagonal given the length of the side without
actually measuring the length. Students then need
to consider if the rule would work for other shapes.
They also need to reflect on their rule and submit
a short explanation of why it works. (This could
also be extended to include the Pythagorean Theorem.
- More
Tangram Activities
Students will use tangram pieces to complete the
following objectives: gain a better understanding
of area without formulas, compute the area of
polygons by decompostion, gain familiarity with
the names of certain polygons (e.g., rectangle,
trapezoid, and pentagon), learn the meaning of
the term "similar", and will develop geometric
intuition.
- G.TR.07.06 Understand and use the fact that
when two triangles are similar with scale factor of
r, their areas are related by a factor of r2.
- Constant
Perimeter and Area Rectangles
This site has a few interactive graphics that
students can manipulate. One shows a rectangle
with a set perimeter amd students can drag a point
to see the various areas of such a rectangle.
Another graphic shows a rectangle with a set area,
and students can change the perimeter.
- Experiment
with Volume
This is a teacher lesson plan where students predict
whether the volume of different shapeed cylinders
would be the same.
- From
Corner to Corner
Students are supplied with an on-line ruler and
must use it to measure the side of a square and
a diagonal. Students then need to analyze the
data to develop a rule for estimating the length
of the diagonal given the length of the side without
actually measuring the length. Students then need
to consider if the rule would work for other shapes.
They also need to reflect on their rule and submit
a short explanation of why it works. (This could
also be extended to include the Pythagorean Theorem.
- Learning
about Length, Perimeter, Area, and Volume of Similar
Objects Using Interactive Figures: Side Length
and Area of Similar Figures
In this activity, students will explore the relationship
between perimeter and area. They will also explore
the relationships in scale between two similar
figures.
- More
Tangram Activities
Students will use tangram pieces to complete the
following objectives: gain a better understanding
of area without formulas, compute the area of
polygons by decompostion, gain familiarity with
the names of certain polygons (e.g., rectangle,
trapezoid, and pentagon), learn the meaning of
the term "similar", and will develop geometric
intuition.
- Polygon
Capture: A Geometry Game
This activity requires students to classify polygons
according to more thatn one property at a time.
So students must move from a simple description
of shapes to an analysis of how properties are
related, all in the context of an enjoyable game.
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