Success criteria
- I calculate a rectangular base area in square units.
- I connect unit cubes in each layer to that base area.
- I calculate
length × width × heightand use cubic units. - I can find a missing dimension and explain my check.
Learn and explain
The base area is 8 × 5 = 40 cm². One cube-high layer contains that many unit cubes. There are 3 equal layers, so the volume is 120 cm³. The formula V = l × w × h is the base-area formula repeated through the height—not a spell to memorize.
Explain to someone: Why is the answer in cubic centimetres rather than centimetres or square centimetres?
Independent practice
Find the volume of a prism measuring 9 cm × 4 cm × 6 cm.
Each layer has 9 × 4 cubes; 6 layers contain 216 cubes.
Which expression best shows a prism with 7 rows of 3 cubes in each of 5 layers?
The base has 7 × 3 cubes and that layer is repeated 5 times.
Unfamiliar transfer — mystery box
A box has volume 180 cm³, length 10 cm, and width 6 cm. Find its height, then sketch the layers that prove your answer.
What is the missing height?
One layer has 10 × 6 cubes. Dividing 180 by that layer gives 3 layers.
Delayed check
In one week, build or sketch a different prism with volume 120 cubic units. Label all three dimensions and verify with both layers and the formula.
Evidence path
Save the labelled mystery-box sketch to jeremy/portfolio/math/unit-4/lesson-12-volume/.
Next step
- Repair: if the units or layers are unclear, build two small prisms from blocks.
- Continue: if volume and missing dimensions are independent, decompose compound solids.
- Stretch: find every whole-number prism with volume 48 cubic units.