Hawaii Grade 5 Math

Try the original problem

A filled rectangular-prism model is three unit cubes long, two cubes wide, and four layers high. Every unit cube has edges one centimeter long, and the model has no gaps. How many cubes fill it, and what is its volume? Explain the role of each dimension rather than simply multiply three unlabeled numbers.

Follow the reasoning

One layer contains three rows or groups of two cubes, giving 3 × 2 = 6 cubes. Four equal layers contain 4 × 6 = 24 cubes. Each is one cubic centimeter, so the volume is 24 cubic centimeters. The product 3 × 2 × 4 describes the layer arrangement and the number of layers. A layer drawing and repeated addition, 6 + 6 + 6 + 6, support the same result.

Check a common wrong turn

Adding the edge lengths, 3 + 2 + 4 = 9, combines lengths and does not count the cubes filling the prism. Counting only visible faces also does not establish how many cubes are inside. The multiplication applies to this completely filled rectangular-prism arrangement; an irregular or partly empty arrangement would need its actual filled portions counted. Keep cubic units separate from the square units used for a surface area.

Transfer the idea

Remove one complete layer. Eighteen unit cubes remain, so the remaining filled prism has volume eighteen cubic centimeters. Then consider a model with only two of the four layers filled and distinguish its amount of cube material from the volume of the full outer prism. Explain what is being measured before using a formula. This helps connect counting, layers, and a volume calculation without treating every drawing as a solid filled box.

Selected references from Hawaiʻi’s revised mathematics document

The Hawaiʻi mathematics standards directory links the HCCS-M document approved in 2026. Its announced implementation schedule is elementary school in 2027–28, middle school in 2028–29, and high school in 2029–30. These references identify this activity’s focus in the revised document; they do not claim every school has already implemented it. Confirm the school’s current course and transition plan, including the placement of Grade 6.

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 Hawaiʻi’s Smarter Balanced mathematics testing range. The linked learning resources have their own directions and scoring; a practice score does not establish an official state performance level. Read Hawaiʻi’s assessment overview.

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.