1/6 (one-sixth) and 1/8 (one-eighth) extend unit fraction understanding to smaller pieces. More parts means smaller pieces per part.
Fold paper or use grids to create 6 and 8 equal parts. Compare sizes with halves and fourths.
Dividing unevenly; not recognizing that more parts means smaller pieces.
You already understand that 1/2 means one out of two equal parts, 1/3 means one out of three equal parts, and 1/4 means one out of four equal parts. Sixths and eighths extend the exact same pattern to finer divisions. One-sixth (1/6) means the whole has been cut into 6 equal pieces, and you are talking about 1 of those pieces. One-eighth (1/8) means 8 equal pieces, 1 of which you are describing. The denominator simply tells you how many equal pieces the whole was split into.
The most important thing to internalize about sixths and eighths is the relationship between the denominator and the size of each piece: more parts always means smaller pieces (as long as the whole stays the same). You already know that 1/4 is smaller than 1/2 because cutting something into 4 pieces gives smaller slices than cutting it into 2. Extending this: 1/6 is smaller than 1/4, and 1/8 is smaller than 1/6. A pizza cut into 8 slices gives you a thinner slice than a pizza cut into 2 slices, even though 8 is a bigger number than 2. The big number in the denominator describes *more cuts*, not *more food*.
A useful way to see this is with a strip of paper. Fold it in half to see halves, then fold again to see fourths, and again to see eighths — each fold doubles the number of pieces and cuts their size in half. You cannot fold to get sixths as easily, but you can draw a rectangle divided into 6 equal columns. Lay that next to a rectangle divided into 4 equal columns and you can see directly that each sixth is narrower than each fourth.
This understanding sets you up to compare unit fractions: given two unit fractions, the one with the larger denominator is the *smaller* fraction. 1/8 < 1/6 < 1/4 < 1/3 < 1/2 < 1. This ordering might look surprising — it runs opposite to how the denominators are ordered — but it flows directly from the logic above. Every time you see a unit fraction, picture the whole being divided and ask: how fine are the cuts? The finer the cuts, the smaller each piece.