Practice Test 1 - 5th Grade Math

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

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1. Liam filled a water bottle that holds 1 whole liter. He drank $\frac{7}{8}$ liter and then drank $\frac{1}{3}$ liter more from another identical full bottle. The fractions refer to the same-sized whole liter. He rewrote $\frac{7}{8}=\frac{21}{24}$ and $\frac{1}{3}=\frac{8}{24}$. What is the total amount he drank?
2. A science class pours water into a container, using the same 1-liter measuring cup each time. They pour $\frac{5}{6}$ liter, then pour $\frac{1}{4}$ liter more. The fractions must refer to the same whole (1 liter). One student rewrites them as equivalent fractions: $\frac{5}{6}=\frac{10}{12}$ and $\frac{1}{4}=\frac{3}{12}$. What is the total amount of water poured?
3. A right rectangular prism is a gift box with length 9 cm, width 2 cm, and height 7 cm. The base is the 9 cm by 2 cm rectangle, and the height is 7 cm. The volume formula gives the same result as packing the box with 1-cm cubes. How does the base area help find volume?
4. A class has the same-sized whole set of 30 library books to label. The students finish $\tfrac{4}{5}$ of the books on Monday. On Tuesday, they label $\tfrac{2}{3}$ of the books that were finished on Monday (adding special stickers). Fraction multiplication represents taking part of a quantity. What is the correct answer to the problem: How many books get special stickers on Tuesday?
5. A small garden bed is a rectangle that is $\tfrac{2}{3}$ meter long and $\tfrac{1}{2}$ meter wide. You tile it with unit fraction squares that are $\tfrac{1}{3}$ meter by $\tfrac{1}{2}$ meter. The tiling shows 2 squares along the length and 1 square along the width. Multiplying the side lengths should give the same area as the tiling. What is the area of the garden bed?
6. Lucia solved a problem about the total cost of buying school supplies and got $23.47. The problem involved buying 3 notebooks at $2.79 each and 2 pens at $1.89 each. How should Lucia evaluate the reasonableness of her solution?
7. A teacher removes the lowest score from a set of 9 test scores. After removal, the mean increases by 3 points and the median increases by 2 points. If the new mean is 78, what was the original lowest score?
8. The Martinez family receives $268.00 from their garage sale. They want to use this money for: new curtains ($89.75), a lamp ($45.25), picture frames ($23.50), and put the rest toward a new couch that costs $165.00. How much more money do they need for the couch?
9. A bus ride to a museum takes 1 hour 20 minutes. A student says, "That is 120 minutes." Which statement is correct?
10. Sofia calculates $92 \div 6$ for a problem about organizing books on shelves. She gets $15\frac{2}{6}$ and simplifies the fraction to get $15\frac{1}{3}$. In what situation would keeping the unsimplified form $15\frac{2}{6}$ be more helpful than $15\frac{1}{3}$?
11. A recipe uses $\tfrac{5}{6}$ cup of flour. Jordan already put in $\tfrac{1}{3}$ cup of flour using the same measuring cup size. Fraction operations depend on understanding fraction size (both amounts must be parts of the same 1-cup whole). What fraction of a cup of flour does Jordan still need to add?
12. Which item should Ben bring back to the store to prove he actually bought the toy there?
13. Comparison using shared attributes: A bulletin board shows this relationship: Quadrilateral ⟶ Trapezoid. - Quadrilateral: 4 sides - Trapezoid: at least 1 pair of parallel sides Which statement about the shapes is true?
14. A rope is $4\frac{1}{5}$ feet long. It is cut into pieces that are each $\frac{3}{5}$ feet long. How many pieces will there be?
15. A student is finding the value of ${25 - [3 \times (4 + 1)]}$. What is the value of the expression?
16. After booking everything as planned, what should the Wong family do with their remaining vacation money?
17. 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?
18. A class has $\tfrac{1}{2}$ of a pitcher of juice. They share this $\tfrac{1}{2}$ pitcher equally among 3 students. What does the quotient $\tfrac{1}{2} \div 3$ represent?
19. Refer to the figure showing a large rectangular prism made up of smaller identical cubes. If each small cube has a volume of 8 cubic units, and you can count 3 cubes along the length, 2 cubes along the width, and 4 cubes along the height, what is the total volume of the large prism?
20. A runner plans to run 4 miles (original number: 4). She considers two plans: • Plan A: $4 \times \frac{9}{8}$ miles • Plan B: $4 \times \frac{3}{8}$ miles Which statement correctly explains why one plan gives a distance greater than 4 and the other gives a distance less than 4? (Products: $4\times\frac{9}{8}$ and $4\times\frac{3}{8}$.)

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