Practice Test 8 - 5th Grade Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

Error detection: A student writes, "Because a square is a kind of rectangle, squares do not need to have 4 right angles." The class chart is Quadrilateral ⟶ Rectangle ⟶ Square. - Quadrilateral: 4 sides - Rectangle: 4 right angles - Square: 4 equal sides Which statement best fixes the student's error?
A coach has $\tfrac{1}{3}$ of a water bottle left and splits it equally among 2 players. Picture a rectangle model: the bottle is divided into 3 equal parts, then one part is divided into 2 equal smaller parts. Dividing a fraction by a whole number creates smaller equal parts. Which model description matches $\tfrac{1}{3} \div 2$ ?
A coach has 6 liters of water. Each athlete's bottle holds $\tfrac{1}{3}$ liter. Dividing by a unit fraction asks how many of those $\tfrac{1}{3}$ -liter amounts fit into 6 liters. If you think of 6 liters as being partitioned into groups of size $\tfrac{1}{3}$ liter, how many groups are there (that is, what is $6 \div \tfrac{1}{3}$ )?
A student builds a right rectangular prism from unit cubes. The base layer has 6 cubes in each row and 2 rows. The prism has 4 equal layers stacked with no gaps or overlaps. What is the volume of the prism?
A teacher has $\tfrac{1}{2}$ of a pan of brownies left. She wants to share this leftover amount equally among 4 students. She first thinks of the pan as 2 equal halves, then partitions that half into 4 equal smaller parts. Dividing a fraction by a whole number creates smaller equal parts. What is the result of $\tfrac{1}{2} \div 4$ ?
The thickness of a sheet of paper is 0.004 inches. If this measurement is written as $4 \times 10^n$ , what is the value of n? Then, if the thickness were 10 times greater, what would be the new value of n?
A recipe uses 600 milliliters of milk. Priya has a measuring cup marked in liters and says, "600 milliliters is 6 liters." Which claim about the units is incorrect?
Refer to the diagram. A student claims that since all polygons are closed figures made of line segments, and hexagons are polygons, then hexagons must also be closed figures made of line segments. Is this reasoning correct?
A student is working with the multiplication expression $8 \times \tfrac{5}{4}$ . The factors are 8 and $\tfrac{5}{4}$ . Since $\tfrac{5}{4}$ is greater than 1, multiplying by it makes the product larger than the other factor 8. Which statement explains the size of the product compared to 8 (without calculating)?
A swimmer practices for 2 hours, 30 minutes. Her coach writes that time down as 2.30 hours. Which of the following statements is correct?
A teacher has $864$ pencils to pack equally into boxes that hold $24$ pencils each. What is the quotient of $864 \div 24$ ?
David calculated $1,248 \div 24 = 52$ . To verify this, he checks by multiplying: $52 \times 24$ . He estimates this as $50 \times 25 = 1,250$ , which is close to $1,248$ . What does this tell him about his division answer?
Compare the two products $\frac{3}{2} \times 8$ and $\frac{3}{4} \times 8$ . The factors in each expression include 8 and a fraction. Without calculating, which statement is true?
In the number 9.672, which digit would you use to complete this statement: 'Nine and $\underline{\hspace{2em}}$ hundred seventy-two thousandths'?
Ana reads for the same amount of time each day. After reading for 6 days, she has read for 4.5 hours total. Which equation can be used to find $t$ , the number of hours Ana reads each day?
Two shapes are compared using a property hierarchy: - Quadrilaterals - Parallelograms (2 pairs of parallel sides) - Rectangles (4 right angles) - Rhombuses (4 equal sides) - Squares (4 right angles) Shape F is a rectangle that is not a square. Shape G is a rhombus that is not a square. Which statement correctly compares them using the hierarchy?
Kevin builds two different rectangular prisms using unit cubes. Prism A is 4 units long, 2 units wide, and 3 units high. Prism B is 6 units long, 2 units wide, and 2 units high. How do their volumes compare?
A student is using this hierarchy: - Quadrilateral: 4 sides - Parallelogram: 2 pairs of parallel sides - Rectangle: 4 right angles - Rhombus: 4 equal sides - Square: both a rectangle and a rhombus The student labels Shape E as a square. Shape E has 4 equal sides, but its angles are not right angles. Which statement correctly describes the error?
A teacher says, "Start with 48 stickers. Split them equally into 6 groups. Then add 9 more stickers." Which expression matches the teacher's description?
Anna is designing a rectangular playground that must have an area of 1,200 square feet. She wants the length to be 40 feet. After calculating the width needed, she realizes the playground would be too narrow for the planned activities. What should Anna do next in her problem-solving process?

Practice tests