Vermont Grade 6 Math

The same center can hide a different spread

Two invented groups each complete the same short sorting task. Group A’s five times are 4, 4, 5, 6, and 6 minutes. Group B’s five times are 1, 4, 5, 6, and 9 minutes. Find each group’s mean and median. Then find the mean absolute deviation from the mean and explain what it adds.

Follow the reasoning

Each group’s times total 25 minutes, so each mean is 25 ÷ 5 = 5 minutes. In each ordered list, the third value is 5, so each median is also 5 minutes. For A, the absolute distances from the mean are 1, 1, 0, 1, and 1 minutes; their mean is 4 ÷ 5 = 0.8 minute. For B, the distances are 4, 1, 0, 1, and 4, giving 10 ÷ 5 = 2 minutes. The larger mean absolute deviation describes greater average distance from the shared center in B. Equal means and medians therefore do not establish identical distributions or equal consistency.

Check the explanation

These are fictional records of five observations per group. They do not establish population differences, ability, or a cause for the variation. Use absolute distances before averaging; signed differences from the mean would cancel and would not measure spread.

Try the next step

Add a new observation of 5 minutes to each record. The means stay 5 minutes, but the mean absolute deviations become 4 ÷ 6 = 2/3 minute and 10 ÷ 6 = 5/3 minutes. Explain why adding a central observation lowers each average distance without changing the old observations.

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 6 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.