Domain: 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. Convert like measurement units within a given measurement system. Standard Clarification/Example: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) Use these conversions in solving multi-step, real world problems. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. (4.MD.1) Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, Metric Standard Unit Equivalent Measurement
including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. (4.MD.2) Recall how the value of a decimal changes when the decimal point moves left or right. (5.NBT2) Recall how to multiply and divide decimals to hundredths. (5.NBT7) Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. (5.NF.3) Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) Use these conversions in solving multi-step, real world problems. 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. system Convert Conversion Domain: 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. Represent and interpret data.
Standard Clarification/Example: 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. Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 1/8). (4.MD.4 and 5.MD.2) Solve word problems involving addition and subtraction of fractions. (5.NF.2) Solve real world problems involving multiplication of fractions and mixed numbers (5.NF.6). Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. (5.NF.7C) Use operations on fractions for this grade to solve problems involving information presented in line plots. Line plot Data set Measurements Fractions Unit Unit fractions
Domain: 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. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Standard Clarification/Example: 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. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (3.MD.2) Recall that a square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area. Volume Cube
(3.MD.5a) Recognize that 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. Side length Attribute Solid figure Unit cube Cubic unit
Domain: 3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 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. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Standard Clarification/Example: 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. Recall that a plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. (3.MD.5b) Recognize that 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. Solid figure Gap
Overlap Cubic units Domain: 4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
Standard Clarification/Example: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). (3.MD.6) 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. (5.MD.3a) 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. (5.MD.3b) Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units (dice, sugar cubes, etc). Solid figure Gap Overlap Volume Unit Cubic units Cubic centimeter Cubic inch Cubic foot Domain: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
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 wholenumber products as volumes, e.g., to represent the associative property of multiplication. Standard Clarification/Example: 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. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying side lengths. (3.MD.7a) Measure volumes by counting unit cubes, using cubic cm, cubic in, Solid figure Gap
cubic ft, and improvised units. (5.MD.4) Apply properties of operations as strategies to multiply and divide. 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication) (3.OA.5) 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. Overlap Volume Unit Area Side lengths Cubic units Cubic centimeter Cubic inch Cubic foot Domain: 5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 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. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
Standard Clarification/Example: 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. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. (3.MD.7b) Apply the area and perimeter formulas for rectangles in real world and mathematical problems. (4.MD.3) Apply properties of operations as strategies to multiply and divide. 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication) (3.OA.5) 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. Formula Cubic units Right rectangular prism Base Height Edge Domain: Geometric measurement: understand concepts of volume and relate
volume to multiplication and to addition. 5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 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. Standard Clarification/Example: 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. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Formula Volume
Apply properties of operations as strategies to multiply and divide. 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication) (3.OA.5) 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. (5.MD.5b) 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. Cubic units Right rectangular prism Base Height Edge