Practice Test 10 - 5th Grade Math

18 of the 20 questions below are in this test; the other 2 can't be scored yet. Answer them in any order, then submit to see your score and every explanation.

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1. Marcus builds a rectangular prism using centimeter cubes. The base layer uses 18 cubes arranged in a rectangle. He builds the prism 4 layers high. Later, he discovers that 6 cubes from different layers are cracked and must be removed. What is the final volume in cubic centimeters?
2. A school library charges fines for overdue books. The fine is 25 cents per day for the first 5 days, then 50 cents per day after that. Maria returned a book that was 12 days overdue, and Tom returned a book that was 8 days overdue. What is the difference between their fines?
3. Examine the bar graph showing monthly rainfall. A student claims that September will definitely have less rainfall than August because there's a decreasing pattern. What's wrong with this reasoning, and what would make a better prediction?
4. A bulletin board is a rectangle that is $\tfrac{3}{4}$ foot wide and $\tfrac{2}{3}$ foot tall. Imagine tiling it with unit fraction squares that are $\tfrac{1}{4}$ foot by $\tfrac{1}{3}$ foot. This shows the area is measured in square feet, and multiplying the side lengths gives the same area as counting the tiles. What is the area of the bulletin board?
5. Look at this chart comparing two different surveys about favorite school lunches. What is the MAIN problem with comparing these two data sets?
6. A student looks at a 3D model made of identical small cubes. Each small cube has edge length 1 unit in length, width, and height. One unit cube takes up 1 cubic unit of space, and unit cubes are used to measure volume. What does one unit cube measure?
7. A math notebook shows this category chain: Quadrilateral Rectangle Square. Next to it, the notebook says: - Quadrilateral: 4 sides - Rectangle: 4 right angles - Square: 4 equal sides Choose the ONE false statement about the hierarchy.
8. A student writes the expression $18 - (6 + 4)$. What is the value of the expression $18 - (6 + 4)$?
9. A water bottle holds 1 whole liter (the same-sized whole). A student drank $1\frac{1}{2}$ liters over the day from refills, then drank $\frac{2}{3}$ liter more. These amounts refer to the same unit (liters). The student rewrites $\frac{1}{2}=\frac{3}{6}$ and $\frac{2}{3}=\frac{4}{6}$. What is $1\frac{1}{2}+\frac{2}{3}$ liters?
10. What is the flaw in this student's reasoning?
11. A student is solving $145 \times 63$ with the standard algorithm and must align digits by place value. Which step is correct for the partial product that uses the tens digit in 63?
12. A student has $\tfrac{1}{6}$ of a pan of brownies left. She wants to pack it into 3 equal snack containers. This division answers "how much brownie is in each container when $\tfrac{1}{6}$ is shared into 3 equal groups." Picture a fraction bar showing $\tfrac{1}{6}$ of the pan, then that part split into 3 equal pieces. What is the correct answer to the problem?
13. Dana has $\frac{1}{15}$ yard of fabric. She cuts it into 4 equal strips. She uses 2 strips for a project and then cuts one of the remaining strips into 3 smaller pieces. What fraction of the original yard does each of these smaller pieces represent?
14. Sarah needs to buy $6$ packages of stickers that cost $2.89 each. She estimates the total cost as $6 \times \$3 = \$18$. At the store, she brings $15. What can we conclude?
15. A student rounded $0.364$ to the nearest hundredth and got $0.36$. Rounding depends on the value of the next digit (the thousandths digit), which decides whether the hundredths digit stays the same or increases by 1. Which statement explains the rounding?
16. The net shown is missing one face. What type of face is needed to complete this net so it can fold into a rectangular prism?
17. During art class, Maya used $\frac{3}{4}$ of a sheet of paper for a poster and then used $\frac{2}{3}$ of a sheet of paper for a collage. Both fractions refer to the same-sized whole sheet of paper. She found equivalent fractions: $\frac{3}{4}=\frac{9}{12}$ and $\frac{2}{3}=\frac{8}{12}$. What is the total amount of paper she used?
18. A student writes two expressions: $8 \times (5 + 1)$ and $8 \times 5 + 1$. Which statement best explains how the parentheses change the value?
19. A baker uses the same whole tray of brownies. She has $2\tfrac{1}{3}$ trays made and gives away $\tfrac{3}{4}$ tray. She rewrites $\tfrac{1}{3}$ as $\tfrac{4}{12}$ and $\tfrac{3}{4}$ as $\tfrac{9}{12}$ so the fractions refer to the same-sized whole tray. How many trays does she have left?
20. The weights of backpacks in pounds: 8, 12, 8, 15, 10, 8, 13. A new backpack weighing 9 pounds is added. What happens to the mode of this data set?

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