A focused Grade 5 learning session for Finding Volume Using Formulas using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can use formulas to find volume.
Finding Volume Using Formulas is the Grade 5 skill of students find the volume of right rectangular prisms using the formulas V = l × w × h and V = B × h, where B is the area of the base. They connect the formulas to counting layers of unit cubes and apply them to solve problems.
Strong understanding comes from naming what the numbers, shapes, units, or data values represent, then showing the idea with a model or clear steps before solving.
The key to this topic is understanding the structure behind the work, not just following a rule. Students should be able to talk through what is happening, point to a model, and explain why the answer makes sense.
Question: Which rectangular prism has a volume of 120 cubic units?
| Prism | Length | Width | Height |
|---|---|---|---|
| A | 10 | 4 | 3 |
| B | 6 | 5 | 5 |
| C | 8 | 5 | 4 |
| D | 12 | 3 | 2 |
How the model helps: Check each prism so there is only one match. A: \(10 \times 4 \times 3 = 120\). B: \(6 \times 5 \times 5 = 150\). C: \(8 \times 5 \times 4 = 160\). D: \(12 \times 3 \times 2 = 72\). Prism A has volume 120 cubic units.
Question: Which rectangular prism has the greatest volume?
| Prism | Dimensions | ||
|---|---|---|---|
| A | 6 \(\times\) 5 \(\times\) 3 | ||
| B | 7 \(\times\) 4 \(\times\) 4 | ||
| C | 8 \(\times\) 3 \(\times\) 4 | ||
| D | 5 \(\times\) 5 \(\times\) 4 |
Answer: Prism B
Question: A rectangular container has dimensions 15 cm, 10 cm, and 8 cm. A smaller container has dimensions 12 cm, 8 cm, and 5 cm. What is the difference in their volumes?
| Container | Length | Width | Height | Volume |
|---|---|---|---|---|
| Large | 15 | 10 | 8 | \(1200\) |
| Small | 12 | 8 | 5 | \(480\) |
Answer: 720 cubic centimeters
Question: A storage box is shaped like a rectangular prism. It measures 10 inches by 7 inches by 5 inches. What is the volume? \LabeledPrismPic[0.64]{10 in}{7 in}{5 in}
Answer: 350 cubic inches
Why it works: Volume = \(10 \times 7 \times 5 = 350\) cubic inches.
Finding Volume Using Formulas gets easier when students read the model, track what each number means, and explain why the answer fits the situation.
Think in layers of cubic units, then justify the formula with the model.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A shipping company uses rectangular boxes with the following dimensions: What is the volume of one shipping box?
Answer C: Height: \( 10 \) inches
The base is \(12 \times 8 = 96\) square inches. With a height of 10 inches, the volume is \(96 \times 10 = 960\) cubic inches.
A rectangular prism has a length of 5 cm, width of 4 cm, and height of 3 cm. What is the volume? \LabeledPrismPic[0.66]{5 cm}{4 cm}{3 cm}
Answer D: 60 cm3
Volume = length \(\times\) width \(\times\) height = \(5 \times 4 \times 3 = 60\) cm3.
A fish tank is 6 feet long, 3 feet wide, and 4 feet tall. How many cubic feet of water will it hold?
Answer D: 72 cubic feet
Volume = \(6 \times 3 \times 4 = 72\) cubic feet.
Which rectangular prism has a volume of 120 cubic units?
Answer A: Prism A
Check each prism so there is only one match. A: \(10 \times 4 \times 3 = 120\). B: \(6 \times 5 \times 5 = 150\). C: \(8 \times 5 \times 4 = 160\). D: \(12 \times 3 \times 2 = 72\). Prism A has volume 120 cubic units.
A storage box is shaped like a rectangular prism. It measures 10 inches by 7 inches by 5 inches. What is the volume? \LabeledPrismPic[0.64]{10 in}{7 in}{5 in}
Answer C: 350 cubic inches
Volume = \(10 \times 7 \times 5 = 350\) cubic inches.
A classroom is 9 meters long, 8 meters wide, and 3 meters high. What is the volume of air in the classroom?
Answer D: 216 cubic meters
Volume = \(9 \times 8 \times 3 = 216\) cubic meters.
A swimming pool is shaped like a rectangular prism with dimensions 20 feet long, 15 feet wide, and 6 feet deep. How many cubic feet of water can it hold? \LabeledPrismPic[0.64]{20 ft}{15 ft}{6 ft}
Answer C: 1800 cubic feet
Volume = \(20 \times 15 \times 6 = 1800\) cubic feet.
What is the volume of a rectangular box with dimensions 8 inches, 6 inches, and 4 inches?
Answer D: 192 cubic inches
Volume = \(8 \times 6 \times 4 = 192\) cubic inches.
A rectangular prism is 10 cm long, 6 cm wide, and 4 cm high. What is its volume?
Answer B: 240 cubic centimeters
Volume is length \(\times\) width \(\times\) height: \(10 \times 6 \times 4 = 240\) cubic centimeters.
A shipping container measures 12 meters long, 2 meters wide, and 2 meters tall. What is its volume in cubic meters? \LabeledPrismPic[0.66]{12 m}{2 m}{2 m}
Answer C: 48 cubic meters
Volume = \(12 \times 2 \times 2 = 48\) cubic meters.
Which two prisms have the same volume?
Answer C: R and S
Compute each volume: P \(= 5 \times 4 \times 6 = 120\); Q \(= 10 \times 3 \times 5 = 150\); R \(= 8 \times 6 \times 2 = 96\); S \(= 4 \times 4 \times 6 = 96\). Only R and S have the same volume (96 cubic units).
