Vermont Grade 5 Math

Two layers of fifteen unit cubes

A right rectangular prism has edge lengths 5 cm, 3 cm, and 2 cm. Find its volume. Explain why 5 × 3 = 15 is not the full volume. Check by separating the length into non-overlapping parts of 3 cm and 2 cm.

Follow the reasoning

The 5 cm by 3 cm base has area 15 cm². One layer of one-centimetre cubes contains fifteen cubes, and the 2 cm height contains two layers. Thus V = 5 × 3 × 2 = 30 cm³. The base area measures a flat region, while the volume measures three-dimensional space. Splitting the length gives one prism of 3 × 3 × 2 = 18 cm³ and another of 2 × 3 × 2 = 12 cm³. Their non-overlapping volumes add to 30 cm³, confirming the layer calculation without counting any space twice.

Check the explanation

The stated edge lengths describe a right rectangular prism. This calculation does not give the total surface area or a real container’s usable interior capacity unless the supplied dimensions describe that interior. Write square units for area and cubic units for volume.

Try the next step

Keep the 5 cm by 3 cm base and increase the height to 4 cm. Explain why four layers give 60 cm³, twice the original volume. The base area stays 15 cm² even though the volume changes.

Vermont reference for this worked activity

The Vermont mathematics standards directory identifies Common Core State Standards adoption in 2010. The linked publisher PDF is the June 2010 CCSS mathematics edition; the upload directory date does not establish a new adoption. Read the complete requirements and the school’s current curriculum sequence. The reference below selects one worked focus.

This selected reference identifies the activity focus. The complete standard and grade curriculum include additional work. These labels do not certify alignment of every independent lesson, worksheet, or quiz in the broader directory.

Choose a next task from the student’s explanation

Use a different set of numbers to check whether the student can explain the same relationship. If the explanation is unclear, return to the model; if the reasoning is sound but a calculation is wrong, work through a shorter calculation and check it against the model. Use the related learning resources alongside the teacher’s assigned goals.

The Vermont Agency of Education Academic Proficiency overview lists general VTCAP English and mathematics assessment in Grades 3–9. Grade 5 is included in that mathematics range. Follow the school’s current directions and accommodations. Independently published practice follows its own timing, tools, question count, and scoring; its result does not establish a state performance level. This original activity is not an official state assessment question. Read Vermont assessment guidance.

State sources and the selected complete PDF page checked October 6, 2026. Confirm later guidance and local assignments before planning assessment preparation.