Lesson 5.5Missing and Fractional Edges
Start hereWords, worked example, and sentence starters
Learning target I can find the volume of a rectangular prism with whole-number edges using length × width × height.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| VolumeSpanish: Volumen | How much space is inside a solid shape. | V = l × w × h |
| Rectangular prismSpanish: Prisma rectangular | A solid box shape with six flat rectangle sides. | A cereal box or shoe box — it has length, width, and height |
| Cubic unitsSpanish: Unidades cúbicas | The units used to measure space inside, like cubic inches. | cm³, in³, ft³ |
| Length, width, heightSpanish: Largo, ancho, altura | How long, how wide, and how tall a box is. | V = l × w × h: for a box 5 × 3 × 2, volume = 30 cubic units |
| NetSpanish: Plantilla (desarrollo plano) | A flat shape that folds up into a solid. | A cross-shaped pattern of 6 rectangles folds into a rectangular box |
| EdgeSpanish: Arista | The line where two flat sides of a solid meet. | A cube has 12 edges — 4 along the top, 4 along the bottom, 4 vertical |
How it worksWorked examplefinding a missing edge from the volume
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A box has a volume of 336 in³. It is 8 in. wide and 6 in. tall. Find its length.
- Substitute what you know. V = l × w × h → 336 = l × 8 × 6
- Multiply the two edges you already know. 8 × 6 = 48
- Divide the volume by that product. 336 ÷ 48 = 7
Answer: The length of the box is 7 inches.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A box has a volume of 720 cm³. It is 15 cm wide and 12 cm tall. Find its length.
- Substitute what you know. = l × ×
- Multiply the two edges you already know. × =
- Divide the volume by that product. ÷ = cm
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The volume is and the edges I know are and .
- I multiplied the two known edges and got .
- The missing edge is because .
- A fractional edge makes the volume than the base area.
Word bank volumedimensionedgebase areaheightcubic unitsmultiplydividemissingfractionhalfproduct
Watch outA common mistake
A common mistake in Volume with Whole Number Edges is multiplying only two of the three edges and stopping there — for example, seeing a box that is 6 in long, 4 in wide, and 3 in tall, multiplying just 6 × 4 = 24, and calling that the volume, when 24 is only the area of the bottom face (in square inches), not the volume of the whole box. The height must also be multiplied in: V = 6 × 4 × 3 = 72 cubic inches. A second common mistake is adding the three edges instead of multiplying them (6 + 4 + 3 = 13 instead of 6 × 4 × 3 = 72 cubic inches). Volume always MULTIPLIES all three edges, and the answer is always labeled in cubic units (in³), never square units (in²) or plain units (in).
Lesson 5.5Missing and Fractional Edges
Apply Day · Version ASupported practice
Learning target I can find the volume of a rectangular prism with whole-number edges using length × width × height.
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1Complete each step, then write the final answer.
A box is 2 units long, 2 units wide, and 3 units tall. Find its volume.
Show your workHint Count the cubes in one layer. Then multiply by the layers.
Final answer: -
2Complete each step, then write the final answer.
A box is 5 cm long, 4 cm wide, and 2 cm tall. Find its volume.
Show your workHint Multiply 5 × 4 first. Then multiply by 2.
Final answer: -
3Complete each step, then write the final answer.
A box is 7 in long, 3 in wide, and 2 in tall. Find its volume.
Show your workHint Multiply the length by the width. Then multiply by the height.
Final answer:
Lesson 5.5Missing and Fractional Edges
Apply Day · Version BCore practice
Learning target I can find the volume of a rectangular prism with whole-number edges using length × width × height.
-
1Complete each step, then write the final answer.
Mo says a box 6 cm long, 2 cm wide, and 3 cm tall has a volume of 11 cubic centimeters, because 6 + 2 + 3 = 11. What is the correct volume?
Show your workFinal answer: -
2Complete each step, then write the final answer.
A box has a base area of 35 square centimeters. Its height is 6 cm. Find its volume.
Show your workFinal answer: -
3Complete each step, then write the final answer.
A box is 8 ft long, 3 ft wide, and 2 ft tall. Find its volume.
Show your workFinal answer:
Lesson 5.5Missing and Fractional Edges
Apply Day · ChallengeExtension
Learning target I can find the volume of a rectangular prism with whole-number edges using length × width × height.
-
1Circle the letter of the best answer. Show how you know.
A rectangular time capsule container measures 8 inches long, 5 inches wide, and 3 inches tall. What is its volume?
- A16 cubic inches
- B40 cubic inches
- C120 cubic inches
- D158 cubic inches
FormulaPut the numbers inWork it outAnswer with its unit -
2Circle the letter of the best answer. Show how you know.
Box A is 8 in by 5 in by 3 in. Box B is 6 in by 4 in by 5 in. Which box holds more?
- ABox A
- BBox B
- CThey hold the same amount
Show your work -
3Complete each step, then write the final answer.
A box has a volume of 105 cubic inches. It is 7 inches long and 5 inches wide. How tall is it?
Show your workFinal answer: