Grade 3 · Mathematics

Answer: C

The whole has eight equal parts, so each part is 1/8. Three colored parts are three copies of 1/8. Therefore the colored quantity is 3/8; the denominator counts all equal parts, including uncolored parts.

A: This reverses the number of selected parts and the number of equal parts in the whole.

B: This treats the three colored parts as the whole instead of counting all eight equal parts.

D: This names the uncolored quantity instead of the colored quantity.

Answer: A

A unit fraction names one equal part of a whole. There are six equal lengths in this strip, so one piece is 1/6 of the strip. The chosen whole remains the original strip.

B: The six counts pieces in one whole, not the number of whole strips.

C: Five counts the other pieces and leaves out the selected piece.

D: A half requires two equal parts in the whole, not six.

Answer: C

Each selected part has size 1/4. Count one copy for each of the three parts: 1/4 + 1/4 + 1/4 = 3/4. Selecting more parts changes the numerator, not the unit size.

A: These are thirds, but the whole was divided into fourths.

B: This counts only two of the three selected parts.

D: Each addend already counts three parts, so this counts too many.

Answer: A

A fourth is one of four equal-size parts of a specified whole. Counting four unequal sections does not establish fourths. Jo must check their areas before using 1/4 to name one section.

B: Uncolored parts still belong to the whole; coloring all parts is unnecessary.

C: One rectangle can serve as a whole for a fraction model.

D: The numerator counts selected unit parts, not the number of sections in the whole.

Answer: C

Each piece is 1/3 of one strip. Sam takes five such pieces, so the quantity is 5/3. Three thirds make one whole and two thirds remain. The quantity can exceed one whole without changing the size of each third.

A: Six parts belong to two strips; the denominator must describe parts in one chosen whole.

B: This leaves out the three parts from the first strip.

D: This counts the pieces in the first strip against both strips and ignores the two additional selected pieces.

Answer: D

Both pieces are correctly called one half because each is one of two equal parts of its own sheet. Their physical areas differ because their wholes differ. Comparing fraction pieces by size requires attention to the size of the chosen whole.

A: A fraction describes a quantity relative to a chosen whole, not a fixed physical area.

B: Each sheet was divided into two equal parts, so halves is the correct name.

C: Both sheets have two equal parts; the difference is the area of the whole.

Answer: B

One whole is the interval from 0 to 1. Four equal spaces make each space one fourth of a unit. The first endpoint after zero is one fourth-length jump from zero, so its value is 1/4.

A: Five boundary marks enclose four spaces; the denominator counts spaces.

C: There are four equal spaces in the whole, not three.

D: Four counts parts of one unit; it does not mean four whole units from zero.

Answer: D

Each jump measures 1/6. Five jumps measure 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 5/6. A sixth jump would reach 6/6, or 1, so the point is one sixth before 1.

A: This reverses the number of jumps and the number of sixths in one whole.

B: This is the endpoint after one jump, not five.

C: The size of each jump is one sixth, so the denominator does not become five.

Answer: D

Four fourth-length jumps from zero reach 4/4 = 1. Seven fourths require three additional fourth-length jumps. The location is between 1 and 2 and one fourth-length jump before 2.

A: That location is 1/4 because it is one fourth-length jump from zero.

B: That location is 5/4, not 7/4.

C: That location is 9/4, beyond the target.

Answer: B

The four equal spaces together span two units. Two of the spaces therefore span one unit, making each space half a unit. Check by adding four halves: 1/2 + 1/2 + 1/2 + 1/2 = 2.

A: This ignores that the four spaces cover two units, not one.

C: Eight such spaces would cover only one unit, and four would cover half a unit.

D: Two units is the length of the entire interval, not each of its four equal parts.

Answer: B

Start with the mark at zero. Each of six successive spaces adds one new endpoint, so there are seven marks. Counting boundary marks as if they were spaces would give an incorrect fraction denominator.

A: Six marks enclose only five spaces when both endpoints are included.

C: Five marks enclose only four spaces.

D: Neighboring spaces share a boundary; they do not require two separate new marks each.

Answer: A

Thirds are the unit-fraction lengths established between 0 and 1. Three jumps reach 1, and a fourth equal jump reaches 4/3. The same scale must continue beyond one; changing the jump length changes the number represented.

B: That construction locates 3/4, not 4/3.

C: That point is 1/3 and counts only one of the four jumps.

D: Counting zero as the first jump ends at 1 instead of one third beyond it.