Kentucky Grade 4 Math

Which covers more: three fourths or five sixths?

Imagine two rectangular banners of exactly the same size. Three fourths of one and five sixths of the other are painted. This original model compares the painted fractions by representing each banner as an equal-length bar. Decide which fraction is greater and explain why counting the original shaded parts alone is not enough.

Make the parts comparable

Divide each fourth into three equal pieces. The first whole then has twelve equal pieces, and its three painted fourths become nine painted twelfths: 3/4 = 9/12. Divide each sixth into two equal pieces. The second whole also has twelve equal pieces, and its five painted sixths become ten painted twelfths: 5/6 = 10/12. Both representations keep the original painted amount. Since the wholes and the new part sizes match, ten painted pieces cover more than nine. Therefore 3/4 < 5/6. The drawing explains the comparison instead of asking students to trust a symbol without a model.

Explain why the fractions remain equivalent

Repartitioning does not paint or erase any part of a banner. It changes how the same region is counted. Splitting every fourth into three changes both the total count of parts and the painted count by that factor. Splitting every sixth into two does the same for the other banner. Increasing only a denominator would describe a different fraction. The equal-whole condition also matters: a larger physical banner could have a smaller painted fraction but a larger painted area. This task fixes the banner sizes so its fraction comparison can answer the question about covered area.

Check a tempting shortcut

Five shaded pieces are not automatically greater than three shaded pieces when their sizes differ. Nor does six in the denominator alone tell us that five sixths is smaller or larger than three fourths. The numerator and denominator work together. Ask the student to show where one sixth and one fourth appear before explaining the repartitioned bars. A response that says both fractions are greater than one half is true, but it does not decide which of these two is greater. The twelfths provide the finer comparison needed here.

Transfer the reasoning

Now compare three fourths with four sixths using the same equal-whole model. Four sixths becomes eight twelfths, so three fourths, or nine twelfths, is greater. Explain why the comparison changes when the second painted amount changes. Students can sketch and label the parts rather than memorize a cross-multiplication procedure. Kentucky’s selected Grade 4 references join visual equivalence with justified comparison and explicitly require fractions referring to the same whole. Use the complete document and local lesson sequence for the remaining fraction work; this one model is not a full-course checklist.

Selected references from Kentucky mathematics standards

The Kentucky mathematics standards directory links the current mathematics document, whose cover identifies adoption in 2019. 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 4 is within Kentucky’s general summative KSA 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 Kentucky’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.