Maryland Grade 3 Math

This original classroom activity is independent practice.

Try the problem

Two number lines each run from 0 to 1 with the same unit length. Partition the first into four equal intervals and mark the end of the second interval. Partition the second into eight equal intervals and mark the end of the fourth. Explain why 2/4 and 4/8 identify the same number. Do not count tick marks as if they were intervals.

Work through the explanation

Two fourths reach halfway from 0 to 1. Four eighths also reach halfway, so both marks locate the same point. Splitting each fourth-sized interval into two equal intervals changes the number and size of the parts together: two selected fourths become four selected eighths. It does not change the distance from 0. Thus 2/4 = 4/8 = 1/2. A correct explanation names the same unit interval and the equal partitions. The numerator counts the selected intervals from 0, and the denominator describes how many equal intervals make the whole. The point at 0 is the start, not a first fraction-sized step.

Check the reasoning

A student may say 4/8 is larger because four is larger than two. That ignores the different unit-fraction sizes. Another may divide the line into four tick marks, creating only three intervals. Check the spaces between consecutive marks and the endpoint labeled 1. Comparing shaded physical pieces from different-sized wholes can be misleading: half of a larger strip need not have the same physical length as half of a smaller one. The fraction numbers remain equal, while the model’s chosen whole determines its physical size. This task deliberately gives both models the same whole.

Try a related task

Make a strip model for 1/3 and 2/6 using identical whole strips, then relate both to the same point on a number line. Ask the child to explain what changed in the partition and what stayed fixed. Maryland’s Grade 3 fraction section limits denominators to 2, 3, 4, 6, and 8; choose follow-up examples within that section’s scope and the school’s sequence. Keep a drawing and explanation together when deciding whether more work on equal partitions or equivalence is needed.

Selected references from revised Maryland mathematics standards

The Maryland mathematics standards directory links grade-specific 2025 crosswalk documents. Their covers identify adoption in July 2025 and implementation in SY 2026–27. Read the 2025 standards columns; the 2010 columns show previous requirements. These selected references identify the worked activity’s focus. The expectations include numbered requirements, examples, and mathematical practices. Read the full document and confirm the school’s current instructional sequence.

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 3 is within Maryland’s statewide mathematics testing range. The linked learning resources have their own directions and scoring; a practice score does not establish an official state performance level. Maryland announced a transition from MCAP to MSTAR beginning in 2026–27. Older MCAP-named books and practice retain their published names and are independent supplements. Their timers, question counts, tools, and scoring are not official MSTAR specifications or predictions of a state performance level. Read the May 2026 state board report, PDF page 12 (archived copy).

The live MSDE site displayed a maintenance notice during review and linked an archived backup. These curriculum references use working archived copies of the revised state documents. Check the school’s sequence and MSDE for later updates. Check MSDE updates.

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.