South Dakota Grade 4 Math

Seventeen students, packs of four

Two fictional groups of 9 and 8 students each need one pencil. Pencils are sold only in sealed packs of 4. There are no pencils already available. Find the fewest packs needed, then explain how many pencils remain after giving one to each student. Compare that answer with the number of complete groups of four students that can be formed.

Follow the reasoning

The two groups contain 9 + 8 = 17 students. Dividing 17 by 4 gives 4 with remainder 1: 17 = 4 × 4 + 1. Four packs contain only 16 pencils, leaving one student without a pencil. Buying five packs provides 20 pencils, and 20 − 17 = 3 pencils remain. Five is the fewest packs because four are insufficient and five cover the need. In contrast, 17 students form only 4 complete groups of four, with one student outside those complete groups. The same division supports different answers because the questions ask different things.

Read the question before rounding

Do not automatically round every division result up. Packs needed must include capacity for the remaining student; complete groups count only full groups. Buying 4.25 packs is not allowed by the stated sale condition. The example gives no price, so the calculation does not establish a purchase cost.

Try the next step

If one of the 17 students already has a pencil, only 16 pencils are needed. Four packs then suffice and no pencils remain. Explain which condition changed and write an equation for the new need before dividing.

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 4. 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.