Understand Fractions as Equal Parts - 3rd Grade Math

1. What is the same about all three circles?
   Answer: Each circle has exactly 1 shaded part, even though the total number of parts is different Each circle has exactly 1 part shaded, even though the circles are divided into different numbers of total parts (3, 4, and 6), so A is correct. Choice B is incorrect because the circles are divided into different numbers of parts, not the same number. Choice C is incorrect because the number of shaded and unshaded parts is different in each circle. Choice D is incorrect because the denominators (3, 4, and 6) are different, not the same.
2. The distance from 0 to 1 on a number line is divided into 5 equal parts. Point P is at the 2nd tick mark after 0. What fraction does point P represent?
   Answer: $\frac{2}{5}$ Point P represents 2/5, since it is located at the 2nd tick mark out of 5 equal parts between 0 and 1. Choice B (3/5) would be the 3rd tick mark, not the 2nd. Choice C (2/3) uses the wrong number of equal parts (3 instead of 5). Choice D (5/2) flips the numerator and denominator, describing a fraction greater than 1 rather than the point's actual location.
3. The square is divided into 4 equal parts. Each part is what fraction?
   Answer: $1/4$ This question tests understanding fractions as equal parts (CCSS.3.NF.1), specifically that $1/b$ is the quantity formed by 1 part when a whole is partitioned into b equal parts, and $a/b$ is the quantity formed by a parts of size $1/b$. A fraction describes a part-to-whole relationship where the whole is divided into EQUAL parts. When a whole is divided into b equal parts, each individual part represents the fraction $1/b$. In this problem, the square is divided into 4 equal parts, so each part is $1/4$ of the whole. Each equal part represents $1/4$, meaning one part out of four equal parts. Choice C is correct because it accurately represents 1 part when the whole is divided into 4 equal parts, which is $1/4$. The numerator (1) represents one part, and the denominator (4) represents the total number of equal parts. Choice A is incorrect because $1/2$ would mean each part is half the whole, which would only be true if the square were divided into 2 equal parts, not 4. This error occurs when students don't correctly count the total number of equal parts. To help students understand fractions as equal parts: Use paper folding to physically create equal parts. Emphasize that when divided into 4 equal parts, each part is $1/4$. Practice identifying what fraction one part represents in different divisions.
4. Look at the two shapes. Shape A is divided to show $\frac{1}{4}$ and Shape B is divided to show $\frac{1}{6}$. What is different about how the wholes are divided?
   Answer: Shape A is divided into 4 equal parts, Shape B is divided into 6 equal parts The fraction $\frac{1}{4}$ means the whole (Shape A) is divided into 4 equal parts, and $\frac{1}{6}$ means the whole (Shape B) is divided into 6 equal parts. The denominator tells us how many equal parts each whole is divided into. Choice B focuses only on the numerators. Choice C confuses what is shaded versus total parts. Choice D reverses the denominators.
5. A teacher draws a shape on the board and divides it into equal parts. She colors some parts red and says this represents $\frac{3}{5}$. Then she erases 2 of the red parts but leaves the shape divisions the same. What fraction represents the red parts now?
   Answer: $\frac{1}{5}$ Originally, $\frac{3}{5}$ meant 3 red parts out of 5 total equal parts. When 2 red parts are erased, there is 3-2=1 red part remaining. Since the shape divisions stay the same, there are still 5 equal parts total. So the fraction is $\frac{1}{5}$. Choice B incorrectly changes the denominator to 3. Choice C doesn't make sense given the context. Choice D represents the number of parts erased, not what remains.
6. Maria cuts a pizza into 6 equal slices. She eats 2 slices and gives 1 slice to her brother. Look at the diagram showing the remaining pizza. What fraction represents the part of the pizza that is left?
   Answer: $\frac{3}{6}$ The pizza was cut into 6 equal parts. Maria ate 2 slices and gave away 1 slice, so 3 slices were removed. This leaves 3 out of 6 equal parts, which is $\frac{3}{6}$. Choice B incorrectly uses 3 as the denominator instead of the total parts. Choice C flips the numerator and denominator. Choice D represents only the slices Maria ate, not what's left.

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