Vermont Grade 4 Math

More digits does not mean a larger decimal

Compare 0.8 and 0.75 as numbers. A student says 0.75 is larger because 75 is greater than 8. Use hundredths of the same unit whole to explain the comparison, then record it with the correct symbol.

Follow the reasoning

Eight tenths equals eighty hundredths: 0.8 = 0.80. Seventy-five hundredths is less than eighty hundredths, so 0.75 < 0.8. The student compares the written digit groups without accounting for their place values. A common unit makes the difference clear: both bars represent portions of the same whole, and the eighty-hundredth portion extends farther. The difference is five hundredths of that unit, or 0.05. Adding the trailing zero in 0.80 changes the representation but does not change the number.

Check the explanation

The decimal comparison as numbers uses one unit whole. In a physical context, eight tenths of a smaller object need not be longer than seventy-five hundredths of a larger object. Name the whole before comparing portions of objects.

Try the next step

Compare 0.6 and 0.60, then compare 0.60 and 0.65. Explain equality in the first comparison and a five-hundredth difference in the second. Use the same unit whole throughout.

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 4 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.