Fractions of shapes in 3rd grade

The shape has $2$ equal parts, so each part is $\frac{1}{2}$. Sara's $\frac{1}{2}$ matches the shape exactly. The statement saying Sara is correct describes her claim.

1. 1Look at the shape and count the equal parts.
2. 2The shape has $2$ equal parts. So each part is $\frac{1}{2}$ of the shape.
3. 3Sara said one part is $\frac{1}{2}$. This matches the shape exactly.
4. 4Sara's fraction matches the shape. Her claim is correct.

Common mistake. A common mistake is assuming there must be a mistake when Sara is in fact correct. The shape has $2$ equal parts, and Sara wrote $\frac{1}{2}$ — the denominator $2$ matches the number of parts exactly.

The idea underneath. The denominator of a unit fraction tells you the total number of equal parts. To check someone's unit-fraction claim, count the actual parts in the shape and compare with their denominator.

Answer. 1

The rectangle has $4$ equal parts, so each part is $\frac{1}{4}$ of the whole rectangle.

1. 1Look at the rectangle. Count how many equal parts it is divided into.
2. 2The rectangle is divided into $4$ equal parts.
3. 3One out of $4$ equal parts is $\frac{1}{4}$. The numerator $1$ shows that we are naming one part, and the denominator $4$ tells how many equal parts make up the whole rectangle.

Common mistake. A common mistake is typing $4$ instead of $\frac{1}{4}$, which names the count of parts rather than the size of one part. The unit fraction $\frac{1}{4}$ shows that each piece is one of $4$ equal pieces in the whole.

The idea underneath. When a whole is split into $4$ equal parts, each part is $\frac{1}{4}$. The denominator names how many equal pieces fill the whole, and the numerator $1$ names one of those pieces.

The answer is: Both Maya and Mateo are correct. Shape A (the rectangle) is divided into 3 equal vertical strips, so Maya's claim is true, and Shape B (the circle) is divided into 3 equal pie slices, so Mateo's claim is also true.

1. 1Look at Shape A (the rectangle). It is divided into 3 vertical strips. Each strip has the same width and height, so the 3 parts have equal area. Maya's claim is correct.
2. 2Look at Shape B (the circle). It is divided into 3 pie slices. All 3 slices are the same size, so the 3 parts have equal area. Mateo's claim is correct.
3. 3Both Maya's claim and Mateo's claim are correct. The best statement is: Both Maya and Mateo are correct.

Common mistake. A common mistake is counting parts and assuming any 3 parts means equal-area thirds. Equal area requires every part to have the same size, not just the same count. Always check that the parts look the same size before deciding.

The idea underneath. Equal-area parts all cover the same amount of space. Counting parts tells you how many there are. Check each shape to see whether all its parts have equal area.

The correct picture shows the triangle divided into $4$ bands that are all the same size. Equal parts must have the same size AND the right count.

1. 1We need a triangle that has $4$ parts AND all parts the same size. Look carefully at each picture to check both things.
2. 2Count the parts in each picture and check whether they are the same size. One picture has only $3$ equal bands, one picture has $5$ equal bands, and one picture has $4$ bands that are not the same size.
3. 3The remaining picture has $4$ bands that are all the same size. That picture shows the triangle divided into $4$ equal parts.

Common mistake. A common mistake is counting the parts but forgetting to check that they are all the same size. A triangle with $4$ parts that are not the same size does NOT show $4$ equal parts.

The idea underneath. To check for equal parts, you need TWO things: the right number of parts AND each part the same size as the others. Missing either one means the partition is not equal.