Fifth Grade - MATH
5: Math
Unit 8: Volume
Lesson 2
Rectangular Prisms
Students build rectangular prisms using exactly 16 centimeter cubes and are instructed that their prisms must use all 16 cubes with no holes or gaps, which requires counting unit cubes. The Parent Plan explicitly says centimeter blocks (and sugar cubes as an alternative) may be used, indicating the use of cubic-centimeter unit cubes and an improvised unit option. The wrapping up statement has students recognize that the different prisms made from 16 cubes all have the same volume, connecting the count of unit cubes to the idea of equal amount of space.
Lesson 3
From Area to Volume
Students use an online interactive tool where they place and remove individual cube pieces to build rectangular prisms; the instructions state that "every time you add a cube to the prism, you're changing the prism's volume." The Parent Plan explicitly lists the skill "Create rectangular prisms using cubes" and suggests using centimeter cubes as a model. The student sheet and answer key name volume as measured in "cubic units" and ask students to identify dimensions and measurements needed (length, width, height) for volume.
Lesson 4
Volume and Unit Cubes
Students build rectangular prisms with centimeter cubes and record length, width, and height in Activity 2, explicitly using the number of unit cubes to represent volume. In Activity 3 students complete a "Finding Volume" page that has them color and count cubes in layers, multiply the number of cubes in one layer by the number of layers, and write volumes in cubic units (cm3). The "Volume and Cubes" sheet and its answer key include problems using inch cubes and foot-long cubes (cubic in and cubic ft) and students practice counting unseen cubes in composite shapes.
Lesson 5
Unit Cubes to Algorithm
Students are instructed to use 24 centimeter cubes to build a variety of rectangular prisms (Activity 1), to count and record dimensions that produce a volume of 24 cubic centimeters, and to fill a table showing length × width × height = volume. The Parent Plan repeatedly states that students will pack prisms with unit cubes and that volume is measured in cubic centimeters. The lesson also asks students to interpret and apply the volume formula and includes examples and questions using cubic inches and cubic feet.
Lesson 6
Practicing the Algorithm
Students build a rectangular prism using 24 centimeter cubes and note that it has a volume of 24 cubic centimeters, showing explicit counting of unit cubes. Several activities and images show prisms made of unit cubes (Volume Sort) and an interactive that originally asked students to count cubes, reinforcing counting unit cubes. Practice problems and the quiz require students to compute and label volumes in cubic centimeters, cubic inches, and cubic feet (e.g., problems with cm, in, and ft).
Lesson 7
Extending Work With Volume
Students are asked to use centimeter cubes to make three different rectangular prisms that have a volume of 20 cubic cm and to share their work, which requires constructing and counting unit cubes. Activity 4 explicitly directs students to use centimeter cubes to create an L shape and to count the total number of cubes to find the total volume. Multiple student pages and answer keys use cubic cm, cubic in., and cubic ft. in volume problems and provide opportunities to express answers in cubic units.
Lesson 8
Problem Solving
Students calculate volumes using the formulas V = l × w × h and V = b × h in multiple word problems (e.g., Diego's box in cubic inches, Danielle's cube in cubic inches, Charlie's box in cubic centimeters). Students determine the number of 1 cm unit cubes a prism can hold by using base area × height (Problem 4 yields 168 centimeter cubes). Students are asked to label answers with appropriate cubic units and may show units in word form or exponent form (e.g., cubic feet or ft3).
Lesson 9
Unit Review and Test
The Skills and Unit Review sections explicitly list "Measure volume by counting unit cubes" and include practice using an interactive cube tool where students add cubes to fill rectangular prisms. Activity 3 (Unit Test) Section 1 directs students to "Count the cubes to determine the volume" for multiple problems, with answer keys given in cubic units. Multiple student pages and answer keys require students to compute and label volumes in cubic cm, cubic in., and cubic ft (e.g., 40 cubic cm, 512 cubic in., 160 cubic ft).
Final Project
Volume Town
Students measure the length, width, and height of each building in centimeters and record l × w × h in the Dimensions column. Students calculate volumes using the formula l × w × h = V and write the volumes labeled as "cubic cm" or "cm3." Students find total volumes for buildings made of more than one box by adding the volumes of the non-overlapping rectangular prisms.
Unit 9: Skills Review
Lesson 3
Measurement
Students label dimensions and compute volumes for rectangular prisms using V = l × w × h and V = b × h in Activity 1, with examples given in meters, inches, centimeters, and feet (e.g., 8×4×5 = 160 cubic m; 3×6×1 = 18 cubic in; 5×5×5 = 125 cubic cm). Students complete problems that produce answers explicitly stated in cubic units (cubic cm, cubic in, cubic ft) and solve missing-dimension problems where volume is given in cubic units (e.g., 240 cubic ft, 288 cubic in.). The tasks include finding volumes of composite (L-shaped) prisms by decomposing into rectangular prisms and summing their volumes.