South Dakota Grade 3 Math

Thirds become sixths

Two drawings represent the same length of ribbon. The first divides that whole into three equal parts and marks two. The second divides the same whole into six equal parts and marks four. Explain why the marked amounts are equal, even though the numbers in the fraction names differ.

Follow the reasoning

Split each third into two equal smaller pieces. The whole now contains six sixths, and the two marked thirds contain four sixths. The marking reaches the same position because the whole and marked length have stayed unchanged. Thus 2/3 = 4/6. Both the total number of parts and the selected number double when the partition changes. The six parts are smaller than the three parts; counting four pieces rather than two does not make the marked amount larger.

Keep the whole fixed

The conclusion uses equal-sized wholes and equal parts within each drawing. Two thirds of a much longer ribbon could exceed four sixths of a shorter ribbon. Fraction equivalence as numbers uses the same unit whole; the fraction name alone does not establish equal lengths of two different physical objects.

Try the next step

Divide the same whole into four equal parts, mark three, and split every part into two. Explain why 3/4 = 6/8. Then mark both fraction names at the same point on a number line from 0 to 1.

South Dakota mathematics references and edition transition

The South Dakota mathematics directory links both its 2018 and newly adopted 2026 editions. The assessed-standards timeline identifies 2026–27 as the mathematics transition year, 2027–28 for implementation, and 2028–29 for assessment of the new edition. This activity links the selected 2018 requirement for current teaching and identifies a related 2026 reference separately. Follow the school’s adopted materials and transition plan.

The 2018 document places numbered clauses beneath grade/domain headings; the reference above combines that heading and clause number. The 2026 edition reorganizes and renumbers requirements. These are selected related references, not a complete edition crosswalk, full curriculum, or certified alignment of every practice resource.

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 department’s current 2026–27 assessment table places the general English language arts and mathematics assessments in Grades 3–8, including Grade 3. Follow the school’s current directions and accommodations. Independently published practice has its own timing, tools, question count, and scoring; its result does not establish a state performance level. Read the current South Dakota assessment table.

State sources and the selected complete PDF page checked October 6, 2026. Confirm later guidance and local assignments before planning assessment preparation.