Hawaii Grade 6 Math

Try the original problem

An invented craft pattern uses three blue beads for every two green beads. A version with twenty beads must keep the same color ratio. Find each color’s count and explain why two thirds of the total is not the green count.

Follow the reasoning

One complete ratio group has three blue and two green beads, five altogether. Twenty beads contain four such groups. Multiplying both color counts by four gives twelve blue and eight green, and 12 + 8 = 20. The ratio 3:2 compares blue with green. For a part-to-whole comparison, green is two out of five beads, so its fraction of the total is 2/5, not 2/3.

Check a common wrong turn

Using 2/3 of twenty treats the blue count as if it were the total. The result also would not give the stated three-to-two pattern. Check both conditions: the color counts must have the required ratio and add to the given total. Scaling only one color changes the relationship.

Transfer the idea

If a version has twenty-four blue beads, its scale factor from the original blue group is eight. It therefore needs sixteen green beads and forty beads altogether. Explain why this question gives a part while the first gives the whole. Make an equivalent-ratio table and plot the blue-green count pairs if useful. Keep each column labeled so the meaning of a ratio survives the calculation.

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 6 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.