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Free ISEE Math Practice Test — Grade 5

Math only, deliberately — the real ISEE (published by ERB) also has verbal and reading sections, which we don't cover.

20 real practice questions at ISEE Lower Level difficulty, drawn from the same calibrated bank our adaptive practice uses. Work through them right here — every question has the answer and a step-by-step explanation one tap away.

Question 1 · GeometryIntro
The school band stores small instrument cases in a rectangular box. The box is 5 feet long, 3 feet wide, and 2 feet tall. What is the volume of the box?
A17 cubic feet
B30 cubic feet
C15 cubic feet
D10 cubic feet
Show answer & explanation
Let's work it out
1.To find the volume of a rectangular box (rectangular prism), multiply all three dimensions together: length × width × height.
2.The box is 5 feet long, 3 feet wide, and 2 feet tall, so the volume is 5 × 3 × 2 = 30 cubic feet.
Answer: B) 30 cubic feet
Question 2 · Coordinate GraphsIntro
A wildlife map of a nature preserve uses a coordinate grid measured in kilometers. A ranger marks a bird feeder at a spot that is 2.5 kilometers east of the entrance (the origin) and 4 kilometers north. Which ordered pair gives the location of the bird feeder?
A(3, 4)
B(4, 2.5)
C(2.5, 4)
D(4, 4)
Show answer & explanation
Let's work it out
1.East-west distance is the x-coordinate and north-south distance is the y-coordinate.
2.The feeder is 2.5 km east, so x = 2.5, and 4 km north, so y = 4, giving the ordered pair (2.5, 4).
Answer: C) (2.5, 4)
Question 3 · Coordinate GraphsEasy
Coordinate gridCoordinate grid, x-axis from 0 to 7, y-axis from 0 to 7. Points: P at (2, 4), Q at (5, 1), R at (6, 5), S at (1, 6). x y 12345671234567PQRS
The grid shows four labeled points. Where is Point P? Write the coordinates for Point P so you could plot it again on a new grid.
A(2, 4)
B(2, 5)
C(3, 4)
D(2, 6)
Show answer & explanation
Let's work it out
1.To find the ordered pair for Point P, first count how far right it is from the origin along the x-axis, which is 2 units, then count how far up it is along the y-axis, which is 4 units.
2.Written as an ordered pair in (x, y) order, the coordinates are (2, 4).
Answer: A) (2, 4)
Question 4 · Data & StatisticsEasy
Pattern sequencePattern sequence: 1/4, 1/2, 3/4, 3/4. Line plot values (in inches). 1/4→1/2→3/4→3/4Line plot values (in inches)
A line plot shows these four measurements (in inches): 34\frac{3}{4}, 12\frac{1}{2}, 14\frac{1}{4}, 34\frac{3}{4}. What is the total of all four measurements?
A920\frac{9}{20}
B112\frac{1}{2}
C214\frac{1}{4}
D234\frac{3}{4}
Show answer & explanation
Let's work it out
1.Convert each measurement to fourths: 34\frac{3}{4} stays 34\frac{3}{4}, 12\frac{1}{2} becomes 24\frac{2}{4}, 14\frac{1}{4} stays 14\frac{1}{4}, and 34\frac{3}{4} stays 34\frac{3}{4}.
2.Add the numerators over the common denominator: 34\frac{3}{4}+24\frac{2}{4}+14\frac{1}{4}+34\frac{3}{4}=94\frac{9}{4}.
3.Converting to a mixed number: 94\frac{9}{4}=214\frac{1}{4} inches.
Answer: C) 214\frac{1}{4}
Question 5 · Coordinate GraphsEasy
Coordinate gridCoordinate grid, x-axis from 0 to 7, y-axis from 0 to 8. Points: A at (1, 2), B at (5, 2), C at (5, 6), D at (1, 6). Also shown: a quadrilateral with vertices (1, 2), (5, 2), (5, 6), (1, 6). x y 123456712345678ABCD
Points A, B, C, and D are plotted on the coordinate grid. Point A is at (1, 2), Point B is at (5, 2), Point C is at (5, 6), and Point D is at (1, 6). A fifth point E is placed at the intersection of the two diagonals of rectangle ABCD. What are the coordinates of point E?
A(3, 4)
B(4, 3)
C(5, 4)
D(3, 6)
Show answer & explanation
Let's work it out
1.Rectangle ABCD has vertices A(1,2), B(5,2), C(5,6), D(1,6).
2.The diagonals of a rectangle bisect each other, so their intersection is the midpoint of either diagonal.
3.Midpoint of AC: x = 1+52\frac{1+5}{2} = 3, y = 2+62\frac{2+6}{2} = 4.
4.So E = (3,4).
5.Verify with diagonal BD: midpoint = (5+12\frac{5+1}{2}, 2+62\frac{2+6}{2}) = (3,4).
6.Correct.
Answer: A) (3, 4)
Question 6 · Coordinate GraphsEasy
Coordinate gridCoordinate grid, x-axis from 0 to 7, y-axis from 0 to 6. Points: Pencils at (1, 1), Notebooks at (2, 4), Erasers at (4, 2), Rulers at (6, 5). x y 1234567123456PencilsNotebooksErasersRulers
Maya is mapping her school store on a coordinate grid. Each grid square represents one shelf section. The grid shows the locations of four products. Maya wants to place a new sign at point P = (5, 3). Which grid point is the correct location for Maya’s sign?
A3 right, 5 up
B4 right, 3 up
C0 right, 5 up
D5 right, 3 up
Show answer & explanation
Let's work it out
1.To plot (5, 3), start at the origin and move 5 units to the right along the x-axis, then move 3 units up.
2.The correct location is 5 right and 3 up from the origin.
Answer: D) 5 right, 3 up
Question 7 · Arithmetic & Number SenseStandard
Paper Chain Strips
StripLength
Strip 1150 cm
Strip 2150 cm
Strip 3150 cm
Destiny is making a paper chain for an art project. The diagram shows three paper strips, each 150 centimeters long, laid end to end. What is the total length of all three strips combined, in millimeters?
A450
B45
C1500
D4500
Show answer & explanation
Let's work it out
1.Each strip is 150 cm long.
2.Since 1 cm equals 10 mm, convert: 150 x 10 = 1500 mm per strip.
3.With three strips laid end to end, multiply: 3 x 1500 = 4500 mm.
Answer: D) 4500
Question 8 · GeometryStandard
QuadrilateralQuadrilateral. Side lengths: 3/2 ft, 5/4 ft, 3/2 ft, 5/4 ft. 3/2 ft5/4 ft3/2 ft5/4 ft
A rectangular tile-placement game board is 3/2 feet long and 5/4 feet wide. A player must place a decorative border strip along every edge of the board. How many feet of border strip are needed in total?
A11/4
B6 1/4
C15/8
D5 1/2
Show answer & explanation
Let's work it out
1.The total length of border strip needed equals the perimeter of the rectangular board.
2.Perimeter = 2 × (length + width) = 2 × (3/2 + 5/4).
3.Converting 3/2 to fourths gives 6/4, so 6/4 + 5/4 = 11/4.
4.Multiplying by 2 gives 22/4 = 11/2 = 5 1/2 feet.
5.The correct answer is D.
Answer: D) 5 1/2
Question 9 · Data & StatisticsStandard
Number lineNumber line from 0.5 to 1.25, marked every 0.25. Points are marked at 0.5, 0.5, 0.75, 0.75, 0.75, 0.75, 1, 1, 1.25, 1.25. 0.50.7511.25
The line plot shows the lengths, in yards, of ribbon strips left in a craft box. Priya joins the strips end to end, uses 212\frac{1}{2} yards to border a wall hanging, and uses all the remaining ribbon to make tassels requiring 34\frac{3}{4} yard each. How many tassels can she make?
A12
B6
C8
D10
Show answer & explanation
Let's work it out
1.The ribbon strips have a total length of 812\frac{1}{2} yards.
2.The border leaves 812\frac{1}{2} - 212\frac{1}{2} = 6 yards, and 6 divided by 34\frac{3}{4} equals 8.
3.Priya can make 8 tassels.
Answer: C) 8
Question 10 · Arithmetic & Number SenseStandard
Maya's Purchase
ItemPrice EachQuantity
Notebook$4.753
Pen$1.356
At the school supply sale, notebooks cost $4.75 each and pens cost $1.35 each. Maya buys 3 notebooks and 6 pens. The table shows her purchase. What is the total amount Maya spends?
A$24.15
B$20.85
C$23.70
D$22.35
Show answer & explanation
Let's work it out
1.Multiply quantity by price for each item type, then add the two subtotals.
2.3 notebooks at $4.75 each: 3 × $4.75 = $14.25.
3.6 pens at $1.35 each: 6 × $1.35 = $8.10.
4.Total: $14.25 + $8.10 = $22.35, which is answer E.
Answer: D) $22.35
Question 11 · GeometryStandard
Project Room Dimensions
RoomLength (m)Width (m)
A8.45.2
B10.67.8
The table shows the dimensions of two rectangular project rooms in a school. The school plans to install new carpet only in Room B. What is the area of Room B, in square meters?
A55.12
B82.68
C36.80
D43.68
Show answer & explanation
Let's work it out
1.Room B has a length of 10.6 meters and a width of 7.8 meters.
2.Its area is 10.6 times 7.8.
3.Multiplying: 10 times 7.8 = 78.0, and 0.6 times 7.8 = 4.68, giving a total area of 82.68 square meters.
Answer: B) 82.68
Question 12 · Data & StatisticsStandard
Number lineNumber line from 0.125 to 0.875, marked every 0.125. Points are marked at 0.125, 0.375, 0.375, 0.5, 0.5, 0.625, 0.625, 0.875. 0.1250.250.3750.50.6250.750.875
The line plot contains eight values. Which value must be removed so that the remaining seven values can be redistributed equally into shares of 12\frac{1}{2}?
A12\frac{1}{2}
B78\frac{7}{8}
C18\frac{1}{8}
D34\frac{3}{4}
Show answer & explanation
Let's work it out
1.The eight plotted values have a sum of 4.
2.For the remaining seven values to be redistributed equally into shares of 12\frac{1}{2}, their total must equal 7 × 12\frac{1}{2} = 72\frac{7}{2} = 312\frac{1}{2}.
Answer: A) 12\frac{1}{2}
Why the other choices are tempting: The value that must be removed is therefore 4 - 312\frac{1}{2} = 12\frac{1}{2}, which is option A.
Question 13 · GeometryStandard
Gift Box Dimensions
DimensionMeasurement (inches)
Length9
Width5
Height4
A craft store sells gift boxes in different sizes. The table shows the dimensions of one box. What is the volume of this gift box in cubic inches?
A45
B18
C36
D180
Show answer & explanation
Let's work it out
1.Volume of a rectangular box equals length times width times height.
2.Using the values from the table, 9 times 5 equals 45, and 45 times 4 equals 180 cubic inches.
Answer: D) 180
Question 14 · Data & StatisticsStandard
Number lineNumber line from 999.5 to 1000.5, marked every 0.25. Points are marked at 999.5, 999.5, 999.75, 999.75, 1000.25, 1000.25, 1000.5. 999.5999.7510001000.251000.5
The line plot contains seven values. If adding x allows all eight values to be redistributed equally into shares of 1,000, what is x?
A2,00012\frac{1}{2}
B4,000
C1,000
D1,00012\frac{1}{2}
Show answer & explanation
Let's work it out
1.The seven plotted values have a sum of 6,99912\frac{1}{2}.
2.Eight shares of 1,000 require a total of 8,000, so x = 8,000 - 6,99912\frac{1}{2} = 1,00012\frac{1}{2}.
Answer: D) 1,00012\frac{1}{2}
Question 15 · Arithmetic & Number SenseHard
At a weekend community build, Jamal and his grandmother are each stacking boards to make a raised garden wall. The wall Jamal is building starts the morning at 12\frac{1}{2} foot tall, and he adds 34\frac{3}{4} foot to its height every hour. The wall his grandmother is building starts at 2 feet tall, and she adds 14\frac{1}{4} foot to its height every hour. After how many hours of building will the two walls first be exactly the same height?
A5
B4
C2
D3
Show answer & explanation
Let's work it out
1.List each wall height hour by hour.
2.Jamal: 12\frac{1}{2}, then 1 14\frac{1}{4}, then 2, then 2 34\frac{3}{4}.
3.Grandmother: 2, then 2 14\frac{1}{4}, then 2 12\frac{1}{2}, then 2 34\frac{3}{4}.
4.The two lists first show the same height, 2 34\frac{3}{4} feet, after 3 hours.
5.This makes sense because the walls start 1 12\frac{1}{2} feet apart and Jamal closes the gap by 34\frac{3}{4} - 14\frac{1}{4} = 12\frac{1}{2} foot every hour, and 1 12\frac{1}{2} divided by 12\frac{1}{2} is 3.
Answer: D) 3
Question 16 · Fractions & DecimalsHard
Maya is making decorative banners for a craft fair. She cuts two pieces of ribbon from an 8-yard spool: one piece that is 1 and 34\frac{3}{4} yards long and another piece that is 2 and 34\frac{3}{4} yards long. How many yards of ribbon remain on the spool after both cuts?
A4 and 14\frac{1}{4}
B4 and 12\frac{1}{2}
C3 and 12\frac{1}{2}
D3 and 14\frac{1}{4}
Show answer & explanation
Let's work it out
1.First, find the total ribbon used by adding 1 and 34\frac{3}{4} and 2 and 34\frac{3}{4}.
2.Add the whole-number parts: 1 + 2 = 3.
3.Add the fraction parts: 34\frac{3}{4} + 34\frac{3}{4} = 64\frac{6}{4} = 1 and 24\frac{2}{4} = 1 and 12\frac{1}{2}.
4.Combine: 3 + 1 and 12\frac{1}{2} = 4 and 12\frac{1}{2} yards used.
5.Subtract from the full 8-yard spool: 8 − 4 and 12\frac{1}{2} = 3 and 12\frac{1}{2} yards remain.
Answer: C) 3 and 12\frac{1}{2}
Question 17 · Arithmetic & Number SenseHard
A rectangular auditorium has 28 rows of seats. Each row has 35 seats. On the day of a performance, 126 seats were empty. How many seats were filled?
AA) 826
BB) 854
CC) 868
DD) 840
Show answer & explanation
Let's work it out
1.Step 1: Find the total number of seats in the auditorium by multiplying the number of rows by the seats per row: 28 × 35 = (28 × 30) + (28 × 5) = 840 + 140 = 980.
2.Step 2: Subtract the empty seats from the total: 980 − 126 = 854.
Answer: B) B) 854
Why the other choices are tempting: The answer is 854, which is option B.
Question 18 · Fractions & DecimalsHard
A wildlife center monitored 80 turtle eggs. Of these, 13 were infertile, and another 19 were fertile but did not hatch. What decimal represents the portion of all the eggs that hatched?
A0.4
B0.7625
C0.6
D0.48
Show answer & explanation
Let's work it out
1.A total of 13 + 19 = 32 eggs did not hatch, so 80 - 32 = 48 eggs hatched.
2.The portion that hatched was 4880\frac{48}{80} = 35\frac{3}{5}, and 35\frac{3}{5} equals 0.6.
Answer: C) 0.6
Question 19 · Fractions & DecimalsHard
A recipe calls for 3 and 12\frac{1}{2} cups of sugar to make a full batch of cookies. Lena wants to make only 23\frac{2}{3} of the full batch. How many cups of sugar does Lena need?
A2 and 12\frac{1}{2} cups
B2 and 13\frac{1}{3} cups
C2 and 23\frac{2}{3} cups
D2 and 56\frac{5}{6} cups
Show answer & explanation
Let's work it out
1.Step 1: Convert 3 and 12\frac{1}{2} to an improper fraction: 3 and 12\frac{1}{2} = 72\frac{7}{2}.
2.Step 2: Multiply 72\frac{7}{2} by 23\frac{2}{3}: 7x22x3\frac{7 x 2}{2 x 3} = 146\frac{14}{6} = 73\frac{7}{3}.
3.Step 3: Convert 73\frac{7}{3} to a mixed number: 7 divided by 3 = 2 remainder 1, so 73\frac{7}{3} = 2 and 13\frac{1}{3}.
Answer: B) 2 and 13\frac{1}{3} cups
Why the other choices are tempting: The answer is 2 and 13\frac{1}{3} cups, which is option B.
Question 20 · Fractions & DecimalsHard
A number line is marked with the fractions 12\frac{1}{2}, 23\frac{2}{3}, 34\frac{3}{4}, 45\frac{4}{5}, and 56\frac{5}{6}. How many of these fractions are greater than 79\frac{7}{9}?
A1
B2
C3
D0
Show answer & explanation
Let's work it out
1.Step 1: Convert each fraction to a decimal or find a common denominator to compare with 79\frac{7}{9} (approximately 0.7778). 12\frac{1}{2} = 0.5000 -- less than 79\frac{7}{9} 23\frac{2}{3} = 0.6667 -- less than 79\frac{7}{9} 34\frac{3}{4} = 0.7500 -- less than 79\frac{7}{9} 45\frac{4}{5} = 0.8000 -- greater than 79\frac{7}{9} 56\frac{5}{6} = 0.8333 -- greater than 79\frac{7}{9} Step 2: Verify 34\frac{3}{4} vs 79\frac{7}{9} using cross multiplication: 3 x 9 = 27 vs 4 x 7 = 28.
2.Since 27 < 28, we have 34\frac{3}{4} < 79\frac{7}{9}.
3.Confirmed.
4.Step 3: Verify 45\frac{4}{5} vs 79\frac{7}{9}: 4 x 9 = 36 vs 5 x 7 = 35.
5.Since 36 > 35, we have 45\frac{4}{5} > 79\frac{7}{9}.
6.Confirmed.
7.Step 4: Verify 56\frac{5}{6} vs 79\frac{7}{9}: 5 x 9 = 45 vs 6 x 7 = 42.
8.Since 45 > 42, we have 56\frac{5}{6} > 79\frac{7}{9}.
9.Confirmed.
10.Two fractions (45\frac{4}{5} and 56\frac{5}{6}) are greater than 79\frac{7}{9}.
Answer: B) 2

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