Middle School Internet Sites (6-8)

Seventh Grade

1. Number & Operations (N)

2.  Algebra (A)

3. Geometry (G)

4. Data and Probability (D)

Strand 3. Geometry (G)

1. Draw and Construct Geometric Objects
2. Understand the Concept of Similar Polygons, and Solve Related Problems

3. Geometry (G)

Seventh Grade

Draw and Construct Geometric Objects

1. G.SR.07.01 Use a ruler and other tools to draw squares, rectangles, triangles, and parallelograms with specified dimensions.
2. 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.
   1. 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
    
   2. 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.
   3. 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.
   4. Be a Weather Watcher
      This activity is part of Project SkyMath: module Section 1, Activity 2. In this activity students measure temperature in both Fahrenheit and Celsius.
   5. 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.
   6. Converting from One Unit of Measurement to Another
      This activity is part of Project SkyMath: module Section 2, Activity 6. In this activity students describe how units of measure are mathematically related and develop formulas for converting between units of measure.
   7. 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.)
   8. 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.
   9. 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.
   10. 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.
   11. 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.
   12. Shape Surveyor
       This is an interactive student activity used to find the perimeter and area of a rectangle.
   13. 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).
   14. 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

1. 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.
   1. Converting from One Unit of Measurement to Another
      This activity is part of Project SkyMath: module Section 2, Activity 6. In this activity students describe how units of measure are mathematically related and develop formulas for converting between units of measure.
   2. 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.
   3. 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.
2. G.TR.07.04 Solve problems about similar figures and scale drawings.
   1. Converting from One Unit of Measurement to Another
      This activity is part of Project SkyMath: module Section 2, Activity 6. In this activity students describe how units of measure are mathematically related and develop formulas for converting between units of measure.
   2. 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.
   3. 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.
3. 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.
   1. Converting from One Unit of Measurement to Another
      This activity is part of Project SkyMath: module Section 2, Activity 6. In this activity students describe how units of measure are mathematically related and develop formulas for converting between units of measure.
   2. 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.
   3. 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.
4. 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.
   1. 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.
   2. Converting from One Unit of Measurement to Another
      This activity is part of Project SkyMath: module Section 2, Activity 6. In this activity students describe how units of measure are mathematically related and develop formulas for converting between units of measure.
   3. Experiment with Volume
      This is a teacher lesson plan where students predict whether the volume of different shapeed cylinders would be the same.
   4. 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.
   5. 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.
   6. 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.
   7. 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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