Kansas Grade 3 Math

Two identical paper strips each represent one whole. Shade two of three equal parts on the first and two of four equal parts on the second. Compare 2/3 and 2/4. This original mathematical model uses equal-sized wholes; its measurements are chosen for illustration rather than collected from a classroom.

Explain what each number means

The denominator names the number of equal parts in one whole. The numerator names how many of those parts are selected. Both numerators are two, but a third of this whole is larger than a fourth. Selecting two larger parts produces the greater shaded amount, so 2/3 > 2/4. The symbol points its open side toward the greater number. Count equal parts in each strip before comparing the shading.

Check a tempting shortcut

Four is greater than three as a whole number, but that does not make two fourths greater than two thirds. The denominators describe the partitions rather than the amount selected by themselves. Also avoid a rule that every fraction with a smaller denominator must be larger: the equal-numerator condition matters. A different pair can require different reasoning. State both the shared numerator and the equal whole when explaining this comparison.

Keep the model’s conditions visible

Two parts from an unequally divided strip do not necessarily represent two thirds or two fourths. The parts within each strip must be equal. A photograph of a large strip beside a small one can also mislead if the reader compares physical areas while the wholes differ. These identical strips make the mathematical comparison clear. For a word problem about pieces of actual food, establish the size of the original wholes before comparing the amounts eaten.

Transfer the comparison

Draw two more identical strips and compare 1/3 with 1/4. Then compare 3/4 with 1/4: now the denominator is shared, so the equal part size stays fixed while the selected count changes. Explain which condition changes between the two pairs. If the result is correct but the explanation relies only on guessing from the drawing, return to the meaning of numerator and denominator. Kansas’s selected expectation includes recording and justifying comparisons; a labeled model and a sentence should work together.

Selected references from Kansas mathematics standards

The Kansas mathematics standards directory links the current mathematics document, whose cover identifies adoption in 2017 and review in 2024. 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 Kansas’s general summative KAP mathematics testing range. The linked learning resources have their own directions and scoring; a practice score does not establish an official state performance level. Read Kansas’s assessment overview.

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.