Measure what is measurable, and
make measurable what is not so.
Measurement is best learned through direct applications or as part of other mathematical topics. A measurable attribute of an object is a characteristic that is most readily quantified and compared. Many attributes, such as length, perimeter, area, volume, and angle measure, come from the geometric realm. Other attributes are physical, such as temperature and mass. Still other attributes, such as density, are not readily measurable by direct means.
In PreK - K, students begin to make qualitative comparisons between physical objects (e.g., which object is longer or shorter, which is lighter or heavier, which is warmer or colder), and begin to use nonstandard units of measurement for quantitative comparisons. Building on existing measurement ideas, students in grades 1 and 2 become competent with standard units of measurement. Students gain understanding of ratio and proportion in the middle grades, and apply their new found knowledge to making scale drawings and maps that accurately reflect the dimensions of the landscape or the objects they represent. Greater familiarity with ratios enhances students’ understanding of the derived attributes (speed, density, and trigonometric ratios), their applications, and the use of conversion factors to change a base unit in a measure.
At all levels, students develop respect for precision and accuracy by learning to select the tools and units of measurement appropriate to the situation. They also learn to analyze possible and real errors in their measurements and how those errors may be compounded in computations.
Exploratory Concepts and Skills
• Explore various models for finding the area of a triangle, parallelogram, and trapezoid, and develop strategies for more complex shapes.
• Investigate volumes and surface areas of a variety of three-dimensional objects.
• Explore volume and surface areas of rectangular prisms, cylinders, and spheres.
Standards:
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
6.M.1: Apply the concepts of perimeter and area to the solution of problems. Apply formulas where appropriate.
6.M.2: Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals.
6.M.3: Solve problems involving proportional relationships and units of measurement, e.g., same system unit conversions, scale models, maps, and speed.
6.M.4: Find areas of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same area. Develop strategies to find the area of more complex shapes.
6.M.5: Identify, measure, and describe circles and the relationships of the radius, diameter, circumference, and area (e.g., d = 2r, p = C/d), and use the concepts to solve problems.
6.M.6: Find volumes and surface areas of rectangular prisms.
6.M.7: Find the sum of the angles in simple polygons (up to eight sides) with and without measuring the angles.
There are 1,000 millimeters in a meter.
Number & Math Play - Average Speed
Louise runs the first half of a race at 5 miles per hour. Then she picks up her pace and runs the last half of the race at 10 miles per hour. What is her average speed on the course?
