Kindergarten understanding and communicating the reason for using a variety of tools and measurement systems in specific problem-solving situations

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1 Complex Information: While engaged in grade appropriate tasks, the student demonstrates an understanding of measurement by: Pre-Kindergarten Simple Information: (Vocabulary and Details) use non-standard measurement to develop a sense of length, height, and weight (e.g. use links to measure the length and height of a table; weigh blocks with counting bear scale) use a chart to show the times and class schedule -measure, weight, length, height Kindergarten using a thermometer to measure temperature (e.g. one thermometer placed inside the classroom and one outside the classroom will show if it is hotter inside or outside) applying basic concepts of time (e.g. counting the number of days until a class party; Friday comes after Thursday and before Saturday) comparing and ordering objects according to length/capacity/weight using non-standard units (e.g. object A is three pencils long, object B is one pencil long, and object C is five pencils long, ordered from shortest to longest: B, A, C) -longer than/as long as, shorter than/as short as 1 st Grade measuring/estimating length to nearest inch/centimeter (e.g. an object that is five and three-quarter inches long measured to the nearest inch would be six inches long) comparing and ordering object according to length/capacity/weight using standard and non-standard units (e.g. object A is 4 paper clips long or 2 inches; object B is 2 paper clips long or 1 inch; object C is 8 paper clips long or 8 inches, therefore the order is B,A,C) telling time using both analog and digital clocks to the nearest half hour (the small hand is on the 2, the large hand is on the 5, the time to the nearest half-hour is 2:30) locating days, dates, and months on a calendar (e.g. October is before November and after September using a standard calendar) -measuring cup, standard measures of length

2 2 nd Grade describing the use of basic measurement tools (ruler, yard stick, meter stick, tape measure)(e.g. an object greater than three feet in length cannot be measured on a single yard stick) measuring/estimating length to nearest inch/foot/yard/centimeter/meter (e.g. a plant that measures three feet and four inches to the nearest foot is three feet) measuring/estimating capacity using cups and pints (e.g. measuring/estimating capacity using cups and pints) comparing and telling time using both analog and digital clocks to the nearest minute(e.g. 4:35:34 to the nearest minute would be 4:35) -time interval, standard measures of time, standard measures of weight 3 rd Grade estimating/measuring length, weight, and capacity in metric and standard units (e.g., measuring multiple objects and distances with both a metric and standard ruler to determine the length of each object/distance in both inches and centimeters; weighing multiple objects on a scale to determine the weight of each object in both pounds and kilograms; measuring the volume of various containers using both metric and standard measuring cups to determine the capacity of each container in both cups and liters) determining elapsed time to the day with calendars, without crossing months, and to the hour with a clock (e.g., using a clock to find out how many hours the class was at a school field trip) comparing and telling time using both analog and digital clocks to the nearest minute using AM and PM (e.g. 3:59 in the afternoon is 3:59 PM) finding the perimeter of a polygon (e.g. a polygon with sides of 4, 4, 3, and 3 has a perimeter of 14) estimating/calculating area using squares (e.g. using a square with an known area of 9, a larger rectangle that can fit two squares inside would have an area of 18 (9 + 9)) estimating/calculating volume of objects using cubes (e.g. using a cube with a known volume of 27, a larger object that can fit three cubes inside would have a volume of 81 ( )) -English system of measurement, metric system, elapsed time, perimeter, area, volume

3 4 th Grade selecting and applying appropriate units and tools to measure time and temperature (F and C) (e.g. a 100 yard dash should be measured by a stop watch in seconds) selecting and applying appropriate units (U. S. customary and metric) and tools to measure length (e.g. a person should be measured by a tape measure in feet and inches) estimating and measuring length to nearest 1/4 inch, 1/8 inch, and millimeter (e.g. a pencil that is between 5 and 1/4 inches and 5 and 1/2 inches long that is less than half way to 5 and 1/2 inches measured to the nearest quarter inch would be 5 and 1/4 inches) calculating elapsed time (hour and minute) (e.g. the elapsed time between 10:15 am and 6:35 pm is 8 hours 20 minutes) using formulas to find perimeter/area of triangles, rectangles, and squares (e.g. the formula for finding the area of a rectangle is Area = length x width) demonstrating that shapes with the same perimeters can have different areas and shapes with same areas can have different perimeters (e.g. a rectangle with top and bottom lengths of 6 and left and right widths of 2 has a perimeter of 16 and an area of 12) using formulas to find the volume of a cube (e.g. Volume = length x width x height) -equivalent representation, unit conversion, time zone, perimeter formula for triangle, perimeter formula for square, perimeter formula for rectangle

4 5 th Grade selecting and applying appropriate units and tools to measure time and temperature (e.g., explaining and modeling how to use various tools to measure time; explaining and exemplifying basic distinctions between various tools used to measure time and which tool would be most advantageous to measure time in a given situation) selecting and applying appropriate units and tools to measure length using U. S. customary and metric units (e.g. a room in a building is usually measured in feet and inches) converting units of measure within the same system (larger unit to smaller) (e.g. 10 centimeters is 100 millimeters) comparing various temperatures (F and C) (e.g., making comparisons of the boiling point of water in both Fahrenheit and Celsius; making comparisons of the freezing point of water in both Fahrenheit and Celsius; making comparisons of classroom temperature in both Fahrenheit and Celsius) calculating perimeter of rectangles from measured dimensions(e.g. a rectangle with top and bottom lengths of 8 and left and right widths of 3 would have a perimeter of 22 (P = 2l + 2w = 2(8) + 2(3) = = 22) using formulas to find areas of a triangle, parallelogram, and trapezoid from diagrams or word problems (e.g. a triangle with a base length of 10 and height of 7 would have an area of 35 (A = (1/2)bh = (1/2)(10)(7) = (5)(7) = 35)) finding the surface area and volume of rectangular solids (e.g. the formula for the volume of a rectangular solid is V = lwh) finding the area of complex shapes (e.g. simple shapes can be used to find the area of complex shapes) -Fahrenheit, Celsius, volume formula for rectangular solid, area formula for trapezoid, surface area 6 th Grade Converting common measurements to equivalent measurements within the metric system Understand, select, and use units of appropriate methods for estimating measurement

5 7 th Grade Understand, select, and use units of appropriate methods for estimating measurement Understand relationships among units and convert from one unit to another within the same system Determining appropriate units of measure to describe perimeter and area (e.g., explaining and exemplifying why a given unit of measure would not be appropriate to describe perimeter, i.e., using feet to describe a rectangle with sides measured in inches) Formulas to find perimeter and area of parallelograms and rectangles (e.g., explaining and modeling the steps required to find the area of a parallelogram) Using circumference and diameter to approximate the value of (e.g., explaining and exemplifying basic reasons why computing the ratio of the circumference and diameter of various circles can provide an approximation of the constant value of ) Using formulas to find circumference and area of circles (e.g., explaining and modeling the steps required to find the area of a circle) Using formulas to find perimeter and area of triangles and trapezoids (e.g., explaining and modeling the steps required to find the area of a trapezoid) Using formulas to find the perimeter and area of regular and irregular plane figures (e.g., explaining and modeling the steps required to find the area of an irregular polygon) Describing surface area and volume using appropriate units of measure (e.g., explaining and exemplifying why surface area is described in square units) Using formulas to find surface area and volume of rectangular prisms and cylinders. (e.g., explaining and modeling the steps required to find the volume of a cylinder) Surface area, volume, capacity, cubic units, cube, cubic centimeter, lateral area.

6 8 th Grade Select and apply appropriate units (U. S. customary and metric) and tools to estimate and measure length, mass, and capacity (e.g., explaining and modeling how to use a variety of tools to measure the weight of a given object) Understand relationships among units and convert from one unit to another within the same system (e.g. converting units using conversion rates, factor/label method, rate/factor method or using equation.) Solve problems involving scale factors, using ratios and proportions (e.g. determine the scale factor and use a proportion to find actual distances on a map; evaluate the size of an actual object given a scale model using a proportion; determine the constant of proportionality given a graph). ratio, rate, unit rate, conversion rate, factor label method, equal ratios, proportion, cross product, constant of proportionality, scale drawing, scale