In Grade 1 you cut shapes into Halves and Fourths. Now you will cut them into thirds, too.
Why it works
Equal shares are the same size, so everyone gets a fair amount. A whole is 2 halves, 3 thirds or 4 fourths. When you share with more people, each person gets less, so a fourth is smaller than a third, and a third is smaller than a half.
Worked example: Halves that look different
Square B is cut from corner to corner. Are the two parts halves?
- The two triangles are the same size: one would fit exactly on top of the other.
- So yes, they are halves, even though they are a different shape from the halves of A.
Answer: Yes
Worked example: Which share is bigger?
Which is bigger: a half or a fourth of the same pizza?
- A half is 1 of 2 equal shares. A fourth is 1 of 4 equal shares.
- More shares means smaller shares.
Answer: a half
Key idea
Equal shares are the same size. Two equal shares are halves, three are thirds and four are fourths (or quarters). A whole is 2 halves, 3 thirds or 4 fourths.
Common mistake
Thinking equal shares must be the same shape. The halves of square B are triangles and the halves of A are rectangles, but each one is exactly half of the same square. Check: same size, not same shape.
Grown-up tip: Cut sandwiches or toast into halves, thirds or fourths in different ways, and ask whether the shares are fair.