ALEX Classroom Resource

Students:
Given right rectangular prisms with whole number edge lengths,

• Use associative property of multiplication to find volume and relate it to packing a solid with unit cubes.
• Apply formula V = l × w × h, where V represents volume and l, w, and h represent the three dimensions of the prism (length, width, height) and relate the formula to a unit cube filled model.
• Apply formula V = B × h, where V represents volume, B is the base-area, and h represents the height (number of layers of the base-area) and relate the formula to a unit cube filled model.

• Given a solid figure composed of two or more right rectangular prisms in real-world or mathematical contexts, find the total volume by decomposing the figure into non-overlapping rectangular prisms and find the sum of the volumes.

Students know:

• Measurable attributes of area and how it relates to finding the volume of objects.
• Units of measurement for volume, specifically unit cubes.

Students are able to:

• Solve word problems involving volume.
• Use associative property of multiplication to find volume.
• Relate operations of multiplication and addition to finding volume.
• Apply formulas to find volume of right rectangular prisms.
• Find volume of solid figures composed of two rectangular prisms.

Students understand that:

• Volume is a derived attribute based on a length unit and can be computed as the product of three length measurements or as the product of one base area and one length measurement.
• Volume is an extension of area and can be found as the area of the base being repeated for a given number of layers.

Learning Objectives:
M.5.19.1: Define volume.
M.5.19.2: Recognize angle measure as additive.
M.5.19.3: Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
M.5.19.4: Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
M.5.19.5: Recognize the formula for volume.
M.5.19.6: Recall the attributes of three-dimensional solids.
M.5.19.7: Recall basic multiplication facts.
M.5.19.8: Fluently add.
M.5.19.9: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
M.5.19.10: Measure and estimate liquid volumes.
M.5.19.11: Recall basic multiplication facts.
M.5.19.12: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
M.5.19.13: Recognize the formula for volume.
M.5.19.14: Recall basic multiplication facts.
M.5.19.15: Describe attributes of three-dimensional figures.
M.5.19.16: Describe attributes of two-dimensional figures.
M.5.19.17: Identify solid figures.

Students:

• Understand that the application of volume formulas and the relationship between these three formulas can be used in combinations when determining solutions involving real-world cylinders, cones, and spheres.

Students know:

• the volume formulas for cylinders, cones, and spheres.
• That 3.14 is an approximation of pi commonly used in these volume formulas.
• That composite three dimensional objects in the real-world can be created by combining cylinders, cones, and spheres in part or whole.

Students are able to:

• calculate the volume of cones, cylinders, and spheres given in real-world contexts. often times approximating solutions to a specified decimal place.
• Identify the components of a composite figure as being portions of or whole cylinders, cones, and spheres.
• Combine the results of calculations to find volume for real-world composite figures.

Students understand that:

• the application of volume formulas and the relationship between these three formulas can be used in combinations when determining solutions involving real-world cylinders, cones, and spheres.

Students:

• Understand that the application of volume formulas and the relationship between these three formulas can be used in combinations when determining solutions involving real-world cylinders, cones, and spheres.

Students know:

• The volume formulas for cylinders, cones, and spheres.
• That 3.14 is an approximation of pi commonly used in these volume formulas.
• That composite three dimensional objects in the real-world can be created by combining cylinders, cones, and spheres in part or whole.

Students are able to:

• Calculate the volume of cones, cylinders, and spheres given in real-world contexts. often times approximating solutions to a specified decimal place.
• Identify the components of a composite figure as being portions of or whole cylinders, cones, and spheres.
• Combine the results of calculations to find volume for real-world composite figures.

Students understand that:

• the application of volume formulas and the relationship between these three formulas can be used in combinations when determining solutions involving real-world cylinders, cones, and spheres.

Learning Objectives:
M.8.30.1: Define formula, volume, cone, cylinders, spheres, and height.
M.8.30.2: Discuss the measure of volume and give examples.
M.8.30.3: Solve problems with exponents, with or without a calculator.
M.8.30.4: Recall how to find circumference of a circle, with or without a calculator.
M.8.30.5: Identify parts of a circle.
M.8.30.6: Calculate the volume of three-dimensional figures.
M.8.30.7: Solve real-world problems using the volume formulas for three-dimensional figures, with or without a calculator.