Grade: K
Measurement Standard
Measurement Units
Standard Number: 1
Identify units of time (day, week, month, year) and compare calendar elements; e.g., weeks are longer than days
Use Measurement Technique & Tools
Standard Number: 2
Compare and order objects of different lengths, areas, weights and capacities; and use relative terms, such as longer, shorter, bigger, smaller, heavier, lighter, more and less
Standard Number: 3
Measure length and volume (capacity) using uniform objects in the environment
a how many paper clips long is a pencil
b how many small containers it takes to fill one big container using sand, rice, beans
Standard Number: 4
Order events based on time
a activities that take a long or short time
b review what we do first, next, last
c recall what we did or plan to do yesterday, today, tomorrow
Grade: Gr. 1
Measurement Standard
Measurement Units
Standard Number: 1
Recognize and explain the need for fixed units and tools for measuring length and weight; e.g., rulers and balance scales
Standard Number: 2
Tell time to the hour and half hour on digital and analog (dial) timepieces
Use Measurement Technique & Tools
Standard Number: 3
Order a sequence of events with respect to time; e.g., summer, fall, winter and spring; morning, afternoon and night
Standard Number: 4
Estimate and measure weight using non-standard units; e.g., blocks of uniform size
Standard Number: 5
Estimate and measure lengths using non-standard and standard units; i.e., centimeters, inches and feet
Grade: Gr. 2
Measurement Standard
Measurement Units
Standard Number: 1
Identify and select appropriate units of measure for
a length – centimeters, meters, inches, feet, or yards
b volume (capacity) – liters, cups, pints, or quarts
c weight – grams, ounces, or pounds
d time – hours, half-hours, quarter-hours, or minutes and time designations a.m. or p.m.
Standard Number: 2
Establish personal or common referents for units of measure to make estimates and comparisons; e.g., the width of a finger is a centimeter, a large bottle of soda pop is 2 liters, a small paper clip weighs about one gram
Standard Number: 3
Describe and compare the relationships among units of measure, such as centimeters and meters; inches, feet and yards; cups, pints and quarts; ounces and pounds; and hours, half-hours, and quarter-hours; e.g., how many inches in a foot
Standard Number: 4
Tell time to the nearest minute interval on digital and to the nearest 5 minute interval on analog (dial) timepieces
Use Measurement Technique & Tools
Standard Number: 5
Estimate and measure the length and weight of common objects, using metric and U.S. customary units, accurate to the nearest unit
Standard Number: 6
Select and use appropriate measurement tools; e.g., a ruler to draw a segment 3 inches long, a measuring cup to place 2 cups of rice in a bowl, a scale to weigh 50 grams of candy
Standard Number: 7
Make and test predictions about measurements, using different units to measure the same length or volume
Grade: Gr. 3
Measurement Standard
Measurement Units
Standard Number: 1
Identify and select appropriate units for measuring
a length – miles, kilometers and other units of measure as appropriate
b volume (capacity) – gallons
c weight – ounces, pounds, grams, or kilograms
d temperature – degrees (Fahrenheit or Celsius)
Standard Number: 2
Establish personal or common referents to include additional units; e.g., a gallon container of milk; a postage stamp is about a square inch
Standard Number: 3
Tell time to the nearest minute and find elapsed time using a calendar or a clock
Standard Number: 4
Read thermometers in both Fahrenheit and Celsius scales
Use Measurement Technique & Tools
Standard Number: 5
Estimate and measure length, weight and volume (capacity), using metric and U.S. customary units, accurate to the nearest or unit as appropriate
Standard Number: 6
Use appropriate measurement tools and techniques to construct a figure or approximate an amount of specified length, weight or volume (capacity); e.g., construct a rectangle with length 2 inches and width 3 inches, fill a measuring cup to the cup mark
Standard Number: 7
Make estimates for perimeter, area and volume using links, tiles, cubes and other models
Grade: Gr. 4
Measurement Standard
Measurement Units
Standard Number: 1
Relate the number of units to the size of the units used to measure an object; e.g., compare the number of cups to fill a pitcher to the number of quarts to fill the same pitcher
Standard Number: 2
Demonstrate and describe perimeter as surrounding and area as covering a two-dimensional shape, and volume as filling a three-dimensional object
Standard Number: 3
Identify and select appropriate units to measure
a perimeter – string or links (inches or centimeters).
b area – tiles (square inches or square centimeters)
c Volume – cubes (cubic inches or cubic centimeters).
Use Measurement Technique & Tools
Standard Number: 4
Develop and use strategies to find perimeter using string or links, area using tiles or a grid, and volume using cubes; e.g., count squares to find area of regular or irregular shapes on a grid, layer cubes in a box to find its volume
Standard Number: 5
Make simple unit conversions within a measurement system; e.g., inches to feet, kilograms to grams, quarts to gallons
Standard Number: 6
Write, solve and verify solutions to multi-step problems involving measurement
Grade: Gr. 5
Measurement Standard
Measurement Units
Standard Number: 1
Identify and select appropriate units to measure angles; i.e., degrees
Standard Number: 2
Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length
Standard Number: 3
Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects
Standard Number: 4
Demonstrate understanding of the differences among linear units, square units and cubic units
Use Measurement Technique & Tools
Standard Number: 5
Make conversions within the same measurement system while performing computations
Standard Number: 6
Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms
Standard Number: 7
Use benchmark anglesto estimate the measureof angles, and use a tool to measure and draw angles
Grade: Gr. 6
Measurement Standard
Measurement Units
Standard Number: 1
Understand and describe the difference between surface area and volume
Use Measurement Technique & Tools
Standard Number: 2
Use strategies to develop formulas for finding circumference and area of circles; and to deteermine the area of sectors.
Standard Number: 3
Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by
a estimating lengths using string or links, areas using tiles or grid, and volumes using cubes
b measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms
Standard Number: 4
Determine which measure (perimeter, area, surface area, volume) matches the context for a problem situation; e.g., perimeter is the context for fencing a garden, surface area is the context for painting a room
Standard Number: 5
Understand the difference between perimeter and area, and demonstrate that two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters
Grade: Gr. 7
Measurement Standard
Measurement Units
Standard Number: 1
Select appropriate units for measuring derived measurements; e.g., miles per hour, revolutions per minute
Standard Number: 2
Convert units of area and volume within the same measurement system using proportional reasoning and a reference table when appropriate; e.g., square feet to square yards, cubic meters to cubic centimeters
Use Measurement Technique & Tools
Standard Number: 3
Estimate a measurement to a greater degree of precision than the tool provides
Standard Number: 4
Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system
Standard Number: 5
Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems
Standard Number: 6
Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms
Standard Number: 7
Develop strategies to find the area of composite shapes using the areas of triangles, parallelograms, circles and sectors
Standard Number: 8
Understand the difference between surface area and volume and demonstrate that two objects may have the same surface area, but different volumes or may have the same volume, but different surface areas
Standard Number: 9
Describe what happens to the surface area and volume of a three-dimensional object when the measurements of the object are changed; e.g., length of sides are doubled
Grade: Gr. 8
Measurement Standard
Measurement Units
Standard Number: 1
Compare and order the relative size of common U.S. customary units and metric units; e.g., mile and kilometer, gallon and liter, pound and kilogram
Standard Number: 2
Use proportional relationships and formulas to convert units from one measurement system to another; e.g., degrees Fahrenheit to degrees Celsius
Use Measurement Technique & Tools
Standard Number: 3
Use appropriate levels of precision when calculating with measurements
Standard Number: 4
Derive formulas for surface area and volume and justify them using geometric models and common materials
a the surface area of a cylinder as a function of its height and radius
b that the volume of a pyramid (or cone) is one-third of the volume of a prism (or cylinder) with the same base area and height
Standard Number: 5
Determine surface area for pyramids by analyzing their parts
Standard Number: 6
Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs
Standard Number: 7
Apply proportional reasoning to solve problems involving indirect measurements or rates
Standard Number: 8
Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor
Standard Number: 9
Demonstrate understanding of the concepts of perimeter, circumference and area by using established formula for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones
Standard Number: 10
Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision
Grade: Gr. 9
Measurement Standard
Measurement Units
Standard Number: 1
Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second
Use Measurement Technique & Tools
Standard Number: 2
Use unit analysis to check computations involving measurement
Standard Number: 3
Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively.
Standard Number: 4
Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures
Standard Number: 5
Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system
Grade: Gr. 10
Measurement Standard
Use Measurement Technique & Tools
Standard Number: 1
Explain how a small error in measurement may lead to a large error in calculated results
Standard Number: 2
Calculate relative error
Standard Number: 3
Explain the difference between absolute error and relative error in measurement
Standard Number: 4
Give examples of how the same absolute error can be problematic in one situation but not in another; e.g., compare “accurate to the nearest foot” when measuring the height of a person versus when measuring the height of a mountain
Standard Number: 5
Determine the measures of central and inscribed angles and their associated major and minor arcs
Grade: Gr. 11
Measurement Standard
Measurement Units
Standard Number: 1
Determine the number of significant digits in a measurement
Standard Number: 2
Use radian and degree angle measures to solve problems and perform conversions as needed
Use Measurement Technique & Tools
Standard Number: 3
Derive a formula for the surface area of a cone as a function of its slant height and the circumference of its base
Standard Number: 4
Calculate distances, areas, surface areas and volumes of composite three-dimensional objects to a specified number of significant digits
Standard Number: 5
Solve real-world problems involving area, surface area, volume and density to a specified degree of precision
Grade: Gr. 12
Measurement Standard
Use Measurement Technique & Tools
Standard Number: 1
Solve problems involving derived measurements; e.g., acceleration and pressure
Standard Number: 2
Use radian measures in the solution of problems involving angular velocity and acceleration
Standard Number: 3
Apply informal concepts of successive approximation, upper and lower bounds, and limits in measurement situations; e.g., measurement of some quantities, such as volume of a cone, can be determined by sequences of increasingly accurate approximations.
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