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Ohio's Academic Content Standards in MathematicsMeasurement Standard
Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools, and technologies.
| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Prekindergarten | | 1. | Begin to identify and use the language of units of time. For example: a. Day, night, week; b. Yesterday, today, tomorrow. (ORC Resources) | | 2. | Recognize that various devices measure time (e.g., clock, timer, calendar). (ORC Resources) | | 3. | Sequence or order events in the context of daily activities and play (e.g., wash your hands before and after snacks, who's next for the computer). (ORC Resources) | | 4. | Begin to use terms to compare the attributes of objects (e.g., bigger, smaller, lighter, heavier, taller, shorter, more and less). (ORC Resources) | | 5. | Order a set of objects according to size, weight or length. (ORC Resources) | | 6. | Measure length and volume (capacity) using non-standard units of measure (e.g., how many paper clips long is a pencil, how many small containers it takes to fill one big container using sand, rice, or beans). (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Kindergarten | | 1. | Identify units of time (day, week, month, year) and compare calendar elements; e.g., weeks are longer than days. (ORC Resources) | | 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. (ORC Resources) | | 3. | Measure length and volume (capacity) using uniform objects in the environment. For example, find:
a. how many paper clips long is a pencil; and
b. how many small containers it takes to fill one big container using sand, rice, beans. (ORC Resources) | | 4. | Order events based on time. For example:
a. activities that take a long or short time;
b. review what we do first, next, last; and
c. recall what we did or plan to do yesterday, today, tomorrow. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 1 | | 1. | Recognize and explain the need for fixed units and tools for measuring length and weight; e.g., rulers and balance scales. (ORC Resources) | | 2. | Tell time to the hour and half hour on digital and analog (dial) timepieces. (ORC Resources) | | 3. | Order a sequence of events with respect to time; e.g., summer, fall, winter and spring; morning, afternoon and night. (ORC Resources) | | 4. | Estimate and measure weight using non-standard units; e.g., blocks of uniform size. (ORC Resources) | | 5. | Estimate and measure lengths using non-standard and standard units; i.e., centimeters, inches and feet.
(ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 2 | | 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; and
d. time - hours, half-hours, quarter-hours, or minutes and time designations a.m. or p.m. (ORC Resources) | | 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. (ORC Resources) | | 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? (ORC Resources) | | 4. | Tell time to the nearest minute interval on digital and to the nearest 5 minute interval on analog (dial) timepieces. (ORC Resources) | | 5. | Estimate and measure the length and weight of common objects, using metric and U.S. customary units, accurate to the nearest unit. (ORC Resources) | | 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. (ORC Resources) | | 7. | Make and test predictions about measurements, using different units to measure the same length or volume. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 3 | | 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; and
d. temperature - degrees (Fahrenheit or Celsius). (ORC Resources) | | 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. (ORC Resources) | | 3. | Tell time to the nearest minute and find elapsed time using a calendar or a clock. (ORC Resources) | | 4. | Read thermometers in both Fahrenheit and Celsius scales. (ORC Resources) | | 5. | Estimate and measure length, weight and volume (capacity), using metric and U.S. customary units, accurate to the nearest 1/2 or 1/4 unit as appropriate. (ORC Resources) | | 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 2-1/2 inches and width 3 inches, fill a measuring cup to the 3/4 cup mark. (ORC Resources) | | 7. | Make estimates for perimeter, area and volume using links, tiles, cubes and other models. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 4 | | 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. (ORC Resources) | | 2. | Demonstrate and describe perimeter as surrounding and area as covering a two-dimensional shape, and volume as filling a three-dimensional object. (ORC Resources) | | 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). (ORC Resources) | | 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. (ORC Resources) | | 5. | Make simple unit conversions within a measurement system; e.g., inches to feet, kilograms to grams, quarts to gallons. (ORC Resources) | | 6. | Write, solve and verify solutions to multi-step problems involving measurement. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 5 | | 1. | Identify and select appropriate units to measure angles; i.e., degrees. (ORC Resources) | | 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. (ORC Resources) | | 3. | Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects. (ORC Resources) | | 4. | Demonstrate understanding of the differences among linear units, square units and cubic units. (ORC Resources) | | 5. | Make conversions within the same measurement system while performing computations. (ORC Resources) | | 6. | Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. (ORC Resources) | | 7. | Use benchmark angles (e.g.; 45°, 90°, 120°) to estimate the measure
of angles, and use a tool to measure and draw angles. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 6 | | 1. | Understand and describe the difference between surface area and volume. (ORC Resources) | | 2. | Use strategies to develop formulas for finding circumference and area of circles, and to determine the area of sectors; e.g., 1/2 circle, 2/3 circle, 1/3 circle, 1/4 circle. (ORC Resources) | | 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; and
b. measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms.
(ORC Resources) | | 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. (ORC Resources) | | 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. (ORC Resources) | | 6. | Describe what happens to the perimeter and area of a two-dimensional shape when the measurements of the shape are changed; e.g. length of sides are doubled. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 7 | | 1. | Select appropriate units for measuring derived measurements; e.g., miles per hour, revolutions per minute. (ORC Resources) | | 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. (ORC Resources) | | 3. | Estimate a measurement to a greater degree of precision than the tool provides. (ORC Resources) | | 4. | Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system. (ORC Resources) | | 5. | Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems. (ORC Resources) | | 6. | Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms. (ORC Resources) | | 7. | Develop strategies to find the area of composite shapes using the areas of triangles, parallelograms, circles and sectors. (ORC Resources) | | 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. (ORC Resources) | | 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. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 8 | | 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. (ORC Resources) | | 2. | Use proportional relationships and formulas to convert units from one measurement system to another; e.g., degrees Fahrenheit to degrees Celsius. (ORC Resources) | | 3. | Use appropriate levels of precision when calculating with measurements. (ORC Resources) | | 4. | Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find:
a. the surface area of a cylinder as a function of its height and radius; and
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. (ORC Resources) | | 5. | Determine surface area for pyramids by analyzing their parts. (ORC Resources) | | 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. (ORC Resources) | | 7. | Apply proportional reasoning to solve problems involving indirect measurements or rates. (ORC Resources) | | 8. | Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor. (ORC Resources) | | 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.) (ORC Resources) | | 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. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 9 | | 1. | Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second. (ORC Resources) | | 2. | Use unit analysis to check computations involving measurement. (ORC Resources) | | 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. (ORC Resources) | | 4. | Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures. (ORC Resources) | | 5. | Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 10 | | 1. | Explain how a small error in measurement may lead to a large error in calculated results. (ORC Resources) | | 2. | Calculate relative error. (ORC Resources) | | 3. | Explain the difference between absolute error and relative error in measurement. (ORC Resources) | | 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. (ORC Resources) | | 5. | Determine the measures of central and inscribed angles and their associated major and minor arcs.
(ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 11 | | 1. | Determine the number of significant digits in a measurement. (ORC Resources) | | 2. | Use radian and degree angle measures to solve problems and perform conversions as needed. (ORC Resources) | | 3. | Derive a formula for the surface area of a cone as a function of its slant height and the circumference of its base. (ORC Resources) | | 4. | Calculate distances, areas, surface areas and volumes of composite three-dimensional objects to a specified number of significant digits. (ORC Resources) | | 5. | Solve real-world problems involving area, surface area, volume and density to a specified degree of precision. (ORC Resources) |
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| | | | PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | | Grade 12 | | 1. | Solve problems involving derived measurements; e.g., acceleration and pressure. (ORC Resources) | | 2. | Use radian measures in the solution of problems involving angular velocity and acceleration. (ORC Resources) | | 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. (ORC Resources) |
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