Understanding Fractions
Lessons in this chapter
About Understanding Fractions
Halves and Quarters is one lesson long and carries the single idea the whole of fraction work rests on: the parts have to be equal.
Identify Halves and Quarters of Shapes has kids split shapes in two and in four and decide whether a given split is fair. A circle cut off-center has two parts but not two halves, and seeing why is the entire point of the lesson.
The language matters as much as the splitting. A half means one of two equal parts, a quarter means one of four. Kids who learn halves as “the big piece and the little piece” carry that misreading into 2nd grade and beyond.
Keeping it to shapes rather than numbers is deliberate. Fractions of a quantity, equivalent fractions and fraction arithmetic all come later, and all of them depend on this one idea being secure first.
The chapter is one lesson, Identify Halves and Quarters of Shapes, and it opens as a worksheet in the page. The questions show a shape already split and ask whether it is halves, quarters or neither, which is where the equal parts idea actually gets tested. It is free, scored as you go, and takes a single sitting.
Frequently asked questions
One lesson, Identify Halves and Quarters of Shapes. It asks a child to split a shape into two or four equal parts and to spot when a split is not equal, which is the idea the whole of later fraction work rests on. In the Common Core it sits in first grade Geometry (1.G) rather than in a fractions domain, because at this stage fractions are about partitioning shapes; fractions as numbers start in third grade.
That a half is one of two equal parts and a quarter is one of four, and that they can recognize whether a shape has been split fairly. Nothing beyond that is expected.
Because without it, any split into two counts as halves. A circle cut off-center has two pieces but not two halves, and a child who misses this gets every later fraction comparison wrong.
Because 1st grade only introduces the idea. Fractions of a Whole in 2nd grade, then Understanding Fractions in 4th, build the arithmetic on top of it.
Yes, and it is worth showing. A square can be halved down the middle, across, or corner to corner, and all three give two equal parts.
A half is one of two equal parts, a quarter is one of four. Two quarters make a half, which is usually the first equivalent fraction a child notices.