A focused Grade 6 learning session for Volume of Rectangular Prisms using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving volume of rectangular prisms.
Volume of Rectangular Prisms means using units, estimates, and operations to solve measurement situations.
Question: What is the volume of the rectangular prism?
Why it works: Using \(V = L \times W \times H\), we have \(V = 5 \times 2 \times 3 = 30\) cm\(^3\).
Answer: \(30\) cm\(^3\)
Question: Find the volume.
Answer: \(26.25\) in\(^3\)
Question: Calculate the volume.
Answer: \(15\) m\(^3\)
Question: Maya is building a garden box with dimensions \(3\frac{1}{2}\) ft long, \(2\) ft wide, and \(1\frac{1}{2}\) ft deep. How many cubic feet of soil does she need?
Why it works: \(V = 3.5 \times 2 \times 1.5 = 7 \times 1.5 = 10.5\) ft\(^3\).
Answer: \(10.5\) ft\(^3\)
Volume of Rectangular Prisms becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A rectangular prism has length \(4\) ft, width \(3\) ft, and height \(2\frac{1}{2}\) ft. What is its volume?
Answer C: \(30\) ft\(^3\)
Volume \(=L\times W\times H=4\times3\times2.5=30\) ft\(^3\).
What is the volume of the rectangular prism?
Answer C: \(30\) cm\(^3\)
Using \(V = L \times W \times H\), we have \(V = 5 \times 2 \times 3 = 30\) cm\(^3\).
A storage box has dimensions \(2\frac{1}{2}\) m by \(1\frac{1}{2}\) m by \(2\) m. Find its volume.
Answer B: \(7.5\) m\(^3\)
\(V = 2.5 \times 1.5 \times 2 = 3.75 \times 2 = 7.5\) m\(^3\).
A rectangular prism has a base area of \(12\) in\(^2\) and a height of \(5\) in. What is its volume?
Answer D: \(60\) in\(^3\)
Using \(V = B \times h = 12 \times 5 = 60\) in\(^3\).
A rectangular prism has volume \(120\) cm\(^3\), width \(5\) cm, and height \(4\) cm. What is its length?
Answer B: \(6\) cm
From \(V = L \times W \times H\), we have \(120 = L \times 5 \times 4\). So \(L = 120 \div 20 = 6\) cm.
Maya is building a garden box with dimensions \(3\frac{1}{2}\) ft long, \(2\) ft wide, and \(1\frac{1}{2}\) ft deep. How many cubic feet of soil does she need?
Answer C: \(10.5\) ft\(^3\)
\(V = 3.5 \times 2 \times 1.5 = 7 \times 1.5 = 10.5\) ft\(^3\).
What is the volume of a rectangular prism with length \(6\) in, width \(4\) in, and height \(2\) in?
Answer D: \(48\) in\(^3\)
\(V = 6 \times 4 \times 2 = 24 \times 2 = 48\) in\(^3\).
What is the volume of this rectangular prism?
Answer C: \(35\) in\(^3\)
\(V = 3.5 \times 2.5 \times 4 = 8.75 \times 4 = 35\) in\(^3\).
A small box is \(7\) cm long, \(3\) cm wide, and \(2\) cm tall. What is its volume?
Answer D: \(42\) cm\(^3\)
\(V = 7 \times 3 \times 2 = 21 \times 2 = 42\) cm\(^3\).
A rectangular prism has volume \(45\) cubic inches. Its length is \(6\) inches and width is \(\frac{5}{2}\) inches. What is its height?
Answer D: \(3\) in
From \(V = L \times W \times H\): \(45 = 6 \times 2.5 \times H\), so \(45 = 15 \times H\), giving \(H = 3\) in.
Find the volume of a rectangular prism with length \(8\) ft, width \(\frac{3}{4}\) ft, and height \(5\) ft.
Answer C: \(30\) ft\(^3\)
\(V = 8 \times 0.75 \times 5 = 6 \times 5 = 30\) ft\(^3\).
