Fractions of a Whole
Lessons in this chapter
About Fractions of a Whole
Piece of Pie extends 1st grade’s halves and quarters in two directions: a new denominator, and fractions of a group rather than of a shape.
Split Shapes into Halves, Quarters and Thirds adds thirds, which is harder than it sounds because three equal parts cannot be made by halving and halving again. A child who splits by repeated halving can produce quarters and eighths but never thirds, and meeting that limit is useful.
Combine Equal Parts goes the other way: two quarters make a half, three thirds make a whole. This is the first equivalence kids see, and it is the idea that equivalent fractions and fraction addition are built on later.
Find Equal Parts of a Set is the genuinely new move. Half of a group of eight counters is four, which means a fraction can describe part of a collection and not just part of a shape. Kids who only ever see fractions as pizza slices struggle with this for years, so meeting it in 2nd grade is worth the effort.
Split Shapes into Halves, Quarters and Thirds, Combine Equal Parts and Find Equal Parts of a Set are three lessons and three worksheets, worked in the page and marked as your child answers. Fractions start as shapes here rather than as symbols, so most of the practice is cutting a whole up and putting it back together. All three are free.
Frequently asked questions
Splitting shapes into halves, quarters and thirds, combining equal parts back into a whole, and then finding equal parts of a set of objects rather than of a single shape. At 2nd grade the Common Core puts this in Geometry (2.G), where the standards ask for partitioning circles and rectangles into equal shares. The fractions domain itself opens in 3rd grade.
Halves, quarters and thirds: splitting a shape into them, combining them back, and finding them for a set of objects.
Because quarters can be made by halving twice, which kids can do by eye. Thirds cannot, so they have to judge three equal parts directly.
A fraction of a group of objects rather than of one shape. Half of eight counters is four. It is the same idea applied to a collection.
Because kids who only see fractions as parts of a shape cannot handle half of twelve sweets. Meeting both pictures early prevents that gap.
Two quarters make a half and three thirds make a whole. This is the first equivalence kids meet, and it leads directly to equivalent fractions later.