Mathematics Cumulative Progress Indicators (CPIs) for the end of the designated grade span

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STANDARD 4.2     (GEOMETRY AND MEASUREMENT)     ALL STUDENTS WILL DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES, RELATIONSHIPS, AND MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA.

D.    Units of Measurement

 By the end of Grade 2, students will:

 1.         Directly compare and order objects according to measurable attributes.

·        Attributes – length, weight, capacity, time, temperature

 2.         Recognize the need for a uniform unit of measure.

 3.         Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems.

·        Length – inch, foot, yard, centimeter, meter

·        Weight – pound, gram, kilogram

·        Capacity – pint, quart, liter

·        Time – second, minute, hour, day, week, month, year

·        Temperature – degrees Celsius, degrees Fahrenheit

 4.         Estimate measures.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will:

 1.         Understand that everyday objects have a variety of attributes, each of which can be measured in many ways.

 2.         Select and use appropriate standard units of measure and measurement tools to solve real-life problems.

·        Length – fractions of an inch (1/4, 1/2), mile, decimeter, kilometer

·        Area – square inch, square centimeter

·        Weight – ounce

·        Capacity – fluid ounce, cup, gallon, milliliter

 3.         Incorporate estimation in measurement activities (e.g., estimate before measuring).

Building upon knowledge and skills gained in preceding grades, by the end of Grade 4, students will:

 1.         Understand that everyday objects have a variety of attributes, each of which can be measured in many ways.

 2.         Select and use appropriate standard units of measure and measurement tools to solve real-life problems

·        Length – fractions of an inch (1/8, 1/4, 1/2), mile, decimeter, kilometer

·        Area – square inch, square centimeter

·        Volume – cubic inch, cubic centimeter

·        Weight – ounce

·        Capacity – fluid ounce, cup, gallon, milliliter

 3.         Develop and use personal referents to approximate standard units of measure (e.g., a common paper clip is about an inch long).

 4.         Incorporate estimation in measurement activities (e.g., estimate before measuring).

 5.         Solve problems involving elapsed time.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 5, students will:

 1.         Select and use appropriate units to measure angles and area.

 2.         Convert measurement units within a system (e.g., 3 feet = ___ inches).

 3.         Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile)

 4.         Use measurements and estimates to describe and compare phenomena.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will:

 1.         Select and use appropriate units to measure angles, area, surface area, and volume.

 2.         Use a scale to find a distance on a map or a length on a scale drawing.

 3.         Convert measurement units within a system (e.g., 3 feet = ___ inches).

 4.         Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile)

 5.         Use measurements and estimates to describe and compare phenomena.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will:

 1.         Solve problems requiring calculations that involve different units of measurement within a measurement system (e.g., 4’3” plus 7’10” equals 12’1”).

 2.         Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.

 3.         Recognize that all measurements of continuous quantities are approximations.

Building upon knowledge and skills gained in preceding grades, by the end of Grade 8, students will:

 1.         Solve problems requiring calculations that involve different units of measurement within a measurement system (e.g., 4’3” plus 7’10” equals 12’1”).

 2.         Use approximate equivalents between standard and metric systems to estimate measurements (e.g., 5 kilometers is about 3 miles).

 3.         Recognize that the degree of precision needed in calculations depends on how the results will be used and the instruments used to generate the measurements.

4.         Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.

 5.         Recognize that all measurements of continuous quantities are approximations.

 6.         Solve problems that involve compound measurement units, such as speed (miles per hour), air pressure (pounds per square inch), and population density (persons per square mile).

Building upon knowledge and skills gained in preceding grades, by the end of Grade 12, students will:

 1.         Understand and use the concept of significant digits.

 2.         Choose appropriate tools and techniques to achieve the specified degree of precision and error needed in a situation.

·        Degree of accuracy of a given measurement tool

·        Finding the interval in which a computed measure (e.g., area or volume) lies, given the degree of precision of linear measurements