New Hampshire Grade 3 Math

A fraction’s denominator tells how many equal parts make the whole. When two fractions use the same whole and the same numerator, the size of each part can settle the comparison. The equal bars show why the count of shaded pieces alone is not enough.

Try this original activity

Compare 4/8 and 4/6 using the pictured equal-sized bars. Which is greater? Record the comparison with a symbol and explain what the denominators mean. Do not compare pieces from differently sized wholes.

Work through the reasoning

Each whole has the same length. Splitting it into eight equal parts makes each part smaller than splitting it into six equal parts. Four sixths therefore cover more of the whole than four eighths. The comparison is 4/8 < 4/6. The first shaded amount reaches halfway across its bar; the second reaches farther than halfway. Both numerators are four, but each fourth counted piece in the second bar belongs to a larger unit fraction. The bars provide a visual justification without requiring a new fraction algorithm. The different partitions matter; counting four shaded pieces in each bar does not make the shaded lengths equal.

Check the common mistake

Choosing 4/8 because eight is bigger confuses the number of parts with their size. The same-whole condition also matters. Four eighths of a very long ribbon could be longer than four sixths of a short ribbon, so do not make a physical-length comparison without equal wholes. The visual here deliberately gives both bars the same full width. Resizing the screen keeps their relative lengths but does not supply an inch measurement.

Try a related case

Compare 2/3 with 2/4 using two new equal bars. Thirds are larger than fourths, so two thirds are greater than two fourths: 2/3 > 2/4. Ask the student to shade and explain both fractions. This same-numerator reasoning does not settle every fraction pair when both numerator and denominator change.

Selected Common Core references for this activity

New Hampshire’s current school-approval rules, Ed 306.34, allow local boards to use the adopted 2010 Common Core mathematics standards or approved alternative academic standards. Confirm the school’s standards choice and local competencies first. The selected Common Core references below were checked in the original publisher’s 2010 document. They identify this activity’s focus, rather than a complete local course. Read the full requirements, mathematical practices, examples, and progression with the school’s curriculum.

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.

The 2025–2026 public NH SAS manual describes general mathematics testing in Grades 3–8, including Grade 3, using a computer-adaptive assessment. Confirm the learner’s assigned pathway, tools, and the school’s current administration directions. The reviewed manual is the 2025–2026 edition; confirm later-year directions with the school. Independently published practice may use its own timer, tools, question count, and scoring; these are not official administration specifications or a prediction of a state performance level. Read the public NH SAS manual resource page.

Read New Hampshire local curriculum rules for later guidance. 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.