Fifth Grade - MATH
5: Math
Unit 8: Volume
Lesson 3
From Area to Volume
Students use an interactive tool to add and remove unit cubes to build rectangular prisms, with the lesson noting that "every time you add a cube to the prism, you're changing the prism's volume." Students practice attaching additional cubes and rectangular prisms on isometric paper and with the online tool to create more complex shapes. The materials identify volume in cubic units and instruct students to model prisms using centimeter cubes, reinforcing that volume is related to counts of unit cubes.
Lesson 4
Volume and Unit Cubes
Students build rectangular prisms from centimeter unit cubes and count cubes to find volume (Activity 2 and Day 2 Finding Volume), including completing steps that count cubes in one layer, count layers, then multiply to get volume. Students use repeated addition and multiplication to combine layers into a total volume (Activity 6 shows 154 + 154 + ... = 924 and 154 × 6 = 924). Students find volumes of non-rectangular/composite shapes by counting unit cubes on the "Volume and Cubes" worksheet and solve layered word problems (for example, the garden wall problem with total volume 48 cubic feet).
Lesson 7
Extending Work With Volume
Students are instructed in Activity 3 to add volumes of separate prisms (example: 48 + 36 + 24 = 108) and complete the "Volume is Additive!" page that includes a word problem about two gift boxes. In Activity 4 students build an L-shape with centimeter cubes, count total cubes, then break the shape into two rectangular prisms, compute each prism's volume (e.g., A = 84, B = 162) and add them to get the total (246). Student activity pages and answer keys provide step-by-step decomposition guidance and multiple practice problems where students find missing dimensions, compute individual prism volumes, and sum them, including contextual problems with boxes and cubes.
Lesson 8
Problem Solving
The Parent Plan Skills section explicitly states that students will "Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts," which directly names the target procedure. The lesson repeatedly teaches and has students practice the formulas V = l × w × h and V = b × h and applies them in multiple real-world problems (packing boxes, containers), providing the arithmetic skills needed to add volumes.
Lesson 9
Unit Review and Test
Students are asked to determine the volume of shapes made up of two non-overlapping rectangular prisms (the Unit Review lists "Determine the volume of a shape made up of two non-overlapping rectangular prisms (volume is additive)"). Students solve diagram problems that break an L-shaped or adjacent-prism figure into two rectangular prisms, compute each prism's volume (for example 2×3×5 = 30 and 3×3×4 = 36), and add the results to get the total volume. Students complete test and review items that require adding volumes of two prisms (e.g., composite volumes of 66 cubic in. and 72 cubic in.) and answer combined-volume word problems about two boxes.
Final Project
Volume Town
Students are required to create at least two buildings that are complex/composite shapes made from more than one box/prism, meeting the project requirement for composite rectangular prisms. Students are instructed to measure length, width, and height for each box, record dimensions, and use V = l × w × h to compute the volume of each rectangular prism. Students are explicitly told to add volumes together to find the total volumes for buildings made up of more than one box/prism and to record those totals in cubic centimeters.
Unit 9: Skills Review
Lesson 3
Measurement
Students are given a labeled L-shaped (complex) prism problem (Activity 1, Problem 7) that requires them to split the shape into two rectangular prisms, compute each prism's volume (3×2×7 and 6×2×3), and add the results to get the total volume (42 + 36 = 78). The Missing Dimensions activity and its answer key show an irregular L-shaped block explicitly described as composed of two rectangular prisms with labeled dimensions and a total volume, and students are asked to calculate the volume of that composed shape. The parent/answer key steps demonstrate students actually perform decomposition and addition of the two non-overlapping right rectangular prisms to find volume.
