3. Geometry (G)
Seventh Grade
Draw and Construct Geometric Objects
- 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 and Area of Circles - Students practice computing the formulas for circumference and area of circles after reading the lesson on each topic.
- 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.
- 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 decomposition, 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 decomposition, 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 decomposition, 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 and 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 shaped 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.