II. Geometry and Measurement

 
  1. Shape and Shape Relationships
  2. Position
  3. Measurement

 

Additional Links to General Mathematics Sites

 

3. Measurement

Middle School

  1. Benchmark 1. "Select and use appropriate tools; measure objects using standard units in both the metric and common systems and measure angles in degrees."
    1. Angle Measurement - Measurement (II.3.MS.1)
      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 - Measurement (II.3.MS.1&2)
      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. Be a Weather Watcher - Measurement (II.3.MS.1&6)
      This activity is part of Project SkyMath: module Section 1, Activity 2. In this activity students measure temperature in both Fahrenheit and Celsius.
    4. Converting from One Unit of Measurement to Another - Measurement (II.3.MS.1,2&5)
      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.
    5. From Corner to Corner - Measurement (II.3.MS.1,5&6)
      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.)
    6. Lesson on Perimeter of Polygons - Measurement (II.3.MS.1)
      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.
    7. Math Goodies: Circumference and Area of Circles - Measurement (II.3.MS.1)
      Students practice computing the formulas for circumference and area of circles after reading the lesson on each topic.
    8. Measure It! - Measurement (II.3.MS.1)
      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.
    9. Shape Surveyor - Measurement (II.3.MS.1)
      This is an interactive student activity used to find the perimeter and area of a rectangle.
  2. Benchmark 2. "Identify the attribute to be measured and select the appropriate unit of measurement for length, mass (weight), time, temperature, perimeter, area, volume and angle."
    1. Angle Tank Attack - Measurement (II.3.MS.2)
      A fun game to review angle measurments. Angles in a triangle, Angles interior. Students answer the angle questions with a video game response. A great way to get students to practice and review all types of angles.
    2. Animal Weigh In - Measurement (II.3.MS.1&2)
      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. Converting from One Unit of Measurement to Another - Measurement (II.3.MS.1,2&5)
      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.
    4. Interior Angles - Measurement (II.3.MS.2)
      The sum of the measures of the interior angles of a triangle is 180 degrees. Finding the measure of the angles of the other regular polygons. This is a student activity.
    5. Math Goodies: Perimeter and Area of Polygons - Measurement (II.3.MS.2)
      Introduces area and perimeter formulas.  This can also be used as a review of these formulas.  Formulas included are perimeter of polygons, area of rectangles, parallelograms, triangles, and trapezoids.  Short quiz at the end of each session to check for learning.
    6. Math Warehouse - Measurement (II.3.MS.2)
      Great site for students and teachers, both can see and interact with slope, Ordered pairs, and Algebraic equations.
  3. Benchmark 3. "Estimate measures with a specified degree of accuracy and decide if an estimate or a measurement is "close enough."
    1. Golden Ratio - Measurement (II.3.MS.3)
      This is an estimate of the ratio of the length to width in rectangles. This is a teacher lesson plan.
    2. Learning about Length, Perimeter, Area, and Volume of Similar Objects Using Interactive Figures: Side Length and Area of Similar Figures - Measurement (II.3.MS.3&4)
      In this activity, students will explore the relationship between perimeter and area. They will also explore the relationships in scale between two similar figures.
  4. Benchmark 4. "Interpret measurements and recognize that two objects may have the same measurement on one attribute (e.g., area) but not necessarily on another (e.g., perimeter)."
    1. Constant Perimeter and Area Rectangles - Measurement (II.3.MS.4)
      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. Experiment with Volume - Measurement (II.3.MS.4)
      This is a teacher lesson plan where students predict whether the volume of different shapeed cylinders would be the same.
    3. Learning about Length, Perimeter, Area, and Volume of Similar Objects Using Interactive Figures: Side Length and Area of Similar Figures - Measurement (II.3.MS.3&4)
      In this activity, students will explore the relationship between perimeter and area. They will also explore the relationships in scale between two similar figures.
    4. Polygon Capture: A Geometry Game - Measurement (II.3.MS.4)
      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.
  5. Benchmark 5. "Use proportional reasoning and indirect measurements to draw inferences."
    1. Converting from One Unit of Measurement to Another - Measurement (II.3.MS.1,2&5)
      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 - Patterns (I.3.MS.1,5&6)
      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 - Measurement (II.3.MS.5)
      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.
  6. Benchmark 6. "Apply measurement to describe the real world and to solve problems."
    1. Be a Weather Watcher - Measurement (II.3.MS.1&6)
      This activity is part of Project SkyMath: module Section 1, Activity 2. In this activity students measure temperature in both Fahrenheit and Celsius.
    2. Figure This! Math Challenges for Families - Shape and Shape Relationships (II.3.MS.6)
      Figure This! Mathematics Challenges for Families provides interesting math challenges that middle-school students can do at home with their families. Each challenge features a description of the important math involved, a note on where the math is used in the real world, a hint to get started, complete solutions, a "Try This" section, additional relational related problems with answers, questions to thinks about, fun facts related to the math, and resources for further exploration. Math Challenge #39 is an examples of problems that would help teach this particular objective.
    3. Flight Path - - Measurement (II.3.MS.6)
      Students will use their skills in adding distances to plan a flight across the United States. A group project is added as an extension project. Teacher plans are also included.
    4. From Corner to Corner - Patterns (II.3.MS.1,5&6)
      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. Popcorn: Which Shape Holds the Most  - Measurement (II.3.MS.6)
      Students will compare cylinders made by using an 8.5 by 11 inch piece of paper to determine which cylinder could hold the most popcorn. The concept of volume is explored both in a hands on appoach and represented numerically. Extension activities include developing packaging to hold the most product while using a minimal amount of material.
    6. State Internet Search: A Mathematical Introduction To State Reports - Measurement (II.3.MS.6)
      As a mathematical beginning to their state reports students complete a 2 day assignment which involves critical thinking, reasoning, graphing, and locating information on Web sites. This site is best suited for grades 4-7.

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