Maryland Grade 5 Math

This original classroom activity is independent practice.

Try the problem

A model is made from two rectangular prisms placed side by side without overlapping. Prism A is 4 units long, 3 units wide, and 2 units high. Prism B is 2 units long, 3 units wide, and 1 unit high. Every unit cube has edge length 1 unit. Find the combined volume and explain how the calculation connects with layers of cubes. Why would multiplying the dimensions of the entire bounding box give a different result?

Work through the explanation

Each layer of Prism A contains 4 × 3 = 12 unit cubes. Two layers give 24 cubic units. Prism B has one layer of 2 × 3 = 6 cubes, so its volume is 6 cubic units. The non-overlapping model therefore has volume 24 + 6 = 30 cubic units. The side-by-side arrangement forms a step: its bounding box is 6 units long, 3 units wide, and 2 units high. That box would contain 36 cubic units, including 6 cubic units of empty space above the shorter prism. Counting that space would measure the containing box rather than the actual composite model. The calculation must account for the solids being measured and their arrangement.

Check the reasoning

Adding edge lengths, 4 + 3 + 2, does not count the cubes filling Prism A. Using square units would also describe area instead of volume. Ask a student to connect a 12-cube layer with the second layer before relying on a formula. The addition of volumes is valid here because the two prism interiors do not overlap. If they did, adding both full volumes would count the overlapping region twice. A drawing can hide the step or show only front-facing cubes; use a model or labeled dimensions to account for cubes behind and above those visible.

Try a related task

Build or draw a new non-overlapping composite model using a 3-by-2-by-2 prism and a 2-by-2-by-1 prism. Its volume is 12 + 4 = 16 cubic units. Explain each product through unit-cube layers and describe a decomposition that avoids overlap. Record whether the difficulty concerns counting cubes, interpreting a three-dimensional drawing, multiplying dimensions, or choosing units. Maryland’s 2025 crosswalk includes both cube-based measurement and additive volume reasoning; use the complete requirements and the school’s sequence.

Selected references from revised Maryland mathematics standards

The Maryland mathematics standards directory links grade-specific 2025 crosswalk documents. Their covers identify adoption in July 2025 and implementation in SY 2026–27. Read the 2025 standards columns; the 2010 columns show previous requirements. These selected references identify the worked activity’s focus. The expectations include numbered requirements, examples, and mathematical practices. Read the full document and confirm the school’s current instructional sequence.

Sources checked October 6, 2026. Read complete requirements, clarifications, limitations, and mathematical practices alongside the school’s sequence. This selected activity is an entry point for instruction.

Connect the explanation with practice

Use the lesson, worksheet, and quiz directory to choose a related skill. The existing resource links remain available; open each activity’s directions to understand its timer, tools, question count, and scoring.

Grade 5 is within Maryland’s statewide mathematics testing range. The linked learning resources have their own directions and scoring; a practice score does not establish an official state performance level. Maryland announced a transition from MCAP to MSTAR beginning in 2026–27. Older MCAP-named books and practice retain their published names and are independent supplements. Their timers, question counts, tools, and scoring are not official MSTAR specifications or predictions of a state performance level. Read the May 2026 state board report, PDF page 12 (archived copy).

The live MSDE site displayed a maintenance notice during review and linked an archived backup. These curriculum references use working archived copies of the revised state documents. Check the school’s sequence and MSDE for later updates. Check MSDE updates.

Keep one example of the student’s reasoning with the practice result. Choose a smaller model, a related question, or a new context according to the difficulty revealed in the worked activity.