Math: Measurement and Data
5.MD (A, B, C)
5.MD (A, B, C)
I can convert like measurement units within a given measurement system.
In other words, I can tell you that 12 inches = 1 foot, and 3 feet = 1 yard. Using the metric system: 1,000 meters = 1 kilometer, and 1,000 mm = 100 cm = 1 meter. I can convert different-sized measurements within the same measurement system. (5.MD.A.1) I can use measurement conversions to solve real-world problems. I can represent and interpret data. (5.MD.A.1) Examples: 1) 7 m = ___ cm Answer: 100 cm = 1 m. So 7 m = 7 × 100 = 700 cm. 2) If 1 yard = 3 ft., and a classroom is 12 yards long, how many feet long is the classroom? 3) We know 2 cups = 1 pint. If the cafeteria workers use 36 cups of milk to make coffee cake, how many pints of milk will they order to make the recipe? U.S. Customary System Review: U.S. units of length (inches, feet, yards, miles or in., ft., yd., & mi.) Review: U.S. units of weight (ounces and pounds, or oz. & lb.) Review: U.S. units of volume (cup, pint, quart, gallon, or c., pt., qt., & gal.) Video: Converting Units - U.S. Volume Video: Same length in different units (yards, inches) Practice: Convert units (U.S.) Metric System: Review: Metric units of length (millimeter, centimeter, meter, kilometer or mm., cm., m. & km.) Review: Metric units of mass (similar to weight) (grams, kilograms or g. & kg.) Review: Metric units of volume (liters, milliliters, or l. & mL.) Video: Converting units: metric distance Video: Converting units: centimeters to meters Practice: Convert units (metrics) Time: Video: Converting units -- minutes to hours I can make a line plot to show a data set of measurements involving fractions. (5.MD.B.2)
Example: You survey 30 students, asking each how much sugar they had in a given day. You get the following data: 5 students ate 1/8 cup. 4 ate 1/4 cup. 3 ate 3/8 cup. 7 ate 1/2 cup. 4 ate 5/8 cup. 5 ate 3/4 cup and 2 ate 7/8 cup. Make a line plot to show your data. Solution: I can use addition, subtraction, multiplication and division of fractions to solve problems involving information presented on a line plot. I can understand the concept of measurement in geometry with regards to volume. (5.MD.B.2)
Example: Using the line plot above, how many students ate less than a 1/2 cup of sugar? Solution: Each "X" equals one person. Sine we need to add up the columns of Xs for fractions that are less than 1/2 we only need to add up the first 3 columns. There are 5 Xs above 1/8, 4 above 1/4, and 3 above 3/8. 5 + 4 + 3 = 12, so 12 students ate less than a 1/2 cup of sugar. Video: Line Plot Distribution: Trail Mix Practice: Interpreting Line Plots with Fraction Addition and Subtraction Practice Line Plots (Dot Plots) with Fraction Operations |
I can recognize volume as a characteristic of solid figures and understand how it can be measured. (5.MD.C.3)
Lesson from LearnZillion: Identify and Label 3-Dimensional Figures Below, you can see how to measure the volume of a box, also known as a rectangular prism (or solid). These solutions use "unit cubes." You can also use formulas, like "Volume = Length × Width × Height" OR "Volume = Length × Depth × Height" I can understand a "unit cube" as a cube with side lengths of 1 unit and can use it to measure volume. (5.MD.C.3.A)
Lesson from LearnZillion: Identify the difference between a square unit and a cubic unit I can understand that a solid figure filled with a number of unit cubes is said to have a volume of that many cubes. (5.MD.C.3.B)
I can measure volume by counting unit cubes. (5.MD.C.4 ) Video: Measuring Volume with Unit Cubes : Video: Measuring Volume as Area Times Length Practice: Volume with Unit Cubes Practice: Compare Volume Using Unit Cubes Practice: Volume of Rectangular Prisms with Unit Cubes Lesson from LearnZillion: Find Volume by Counting Cubes I can solve real world problems involving volume by thinking about multiplication of addition. (5.MD.C.5)
Example: A box has the dimensions of 5 cm x 2 cm x 4 cm. Can you create a box with different dimensions but that holds the same number of cubic centimeters (volume)? Solution: The formula for finding the volume of a box (rectangular solid) is: Volume = Length × Width × Depth, or V = L×W×D It doesn't matter which value is assigned to the length, width or depth. So Volume = 5 × 2 × 4 = 20 cubic cm. Now find 3 numbers, that when multiplied, equal 20. One answer: 1 × 2 × 10 = 20 Can you come up with another answer? Video: Volume Word Problem: Water Tank Practice: Volume Word Problems Angles (in circles) Video: Angle Measurement & Circle Arcs Video: Measure Angles with a Circular Protractor Video: Angles in Circles Word Problem Practice: Angles in Circles Practice: Angles in Circles Word Problems If you'd like to read the CA State Standards:
Convert like measurement units within a given measurement system. 1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. Represent and interpret data. 2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5. Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems |