Practice Test 11 - 5th Grade Math

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

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1. A photographer is organizing 156 photos into albums. Each album holds 24 photos. He calculates $156 \div 24 = 6.5$ and wants to plan his album arrangement efficiently. If he prefers to keep related photos together rather than splitting them across albums, which interpretation helps him make the best decision?
2. A solid made of unit cubes has 2 layers. The bottom layer has 4 rows of 2 cubes each. The top layer has 2 rows of 2 cubes each, sitting on one end of the bottom layer. No cubes are hidden. The volume can be found by counting cubes. What is the volume of the solid?
3. A solid is made of unit cubes. There are no hidden cubes. The volume can be found by counting cubes. The solid has 2 layers: - Bottom layer: 10 cubes arranged as 5 cubes in a row and 2 rows (a 5-by-2 layer) - Top layer: 5 cubes arranged as 5 cubes in a row placed directly above the back row of the bottom layer only Which counting method is correct for finding the volume?
4. A solid is made from unit cubes, and there are no hidden cubes. The volume can be found by counting cubes. Front view shows 3 cubes across and 2 cubes tall, but the solid is only 1 cube deep (just one row going back). What is the volume of the solid?
5. A rectangular prism made of unit cubes has a length that is twice its width. The width is 3 cubes, and the height is 4 cubes. If 8 cubes fall out from various positions, what is the remaining volume?
6. A recipe calls for $2.5$ cups of flour for $8$ servings. How many cups of flour are needed to make $12$ servings of the same recipe?
7. Maya calculated that $567 - 289 = 278$. To check her work, she estimates using $600 - 300 = 300$. Her estimate is $22$ more than her calculated answer. Should she be concerned about this difference?
8. During 6 days, a plant grew these heights in centimeters: 2.5, 3.1, 2.8, 2.5, 3.4, 2.9. What is the mean height rounded to the nearest tenth?
9. A classroom has 6 yards of string for a project. The teacher is deciding between cutting pieces that are each $\tfrac{1}{2}$ yard long or pieces that are each $\tfrac{1}{3}$ yard long. Dividing by a unit fraction asks how many of those fractional pieces fit into 6 yards. Which claim is incorrect?
10. A right rectangular prism is built from unit cubes. The base layer has 2 rows of 10 cubes (20 cubes in one layer). The prism is 5 layers tall, and the layers line up so the prism is completely packed with no gaps or overlaps. This means the volume by packing equals the volume by multiplying the three dimensions. What is the volume of the prism?
11. A baker has 4 cups of flour. One mini-batch uses $\tfrac{1}{2}$ cup. Dividing by a unit fraction asks how many $\tfrac{1}{2}$-cup groups fit into 4 cups. Which statement correctly tells what the quotient $4 \div \tfrac{1}{2}$ represents?
12. In the number $70{,}105.909$, the digit 9 is in the tenths place and another 9 is in the thousandths place. Which statement correctly compares the two 9s?
13. A bulletin board shows this hierarchy based on properties: - Quadrilaterals - Kites: 2 pairs of equal sides next to each other - Parallelograms: 2 pairs of parallel sides - Rhombuses: 4 equal sides - Squares: 4 right angles Shape C has 4 equal sides and 2 pairs of parallel sides, and it also has 4 right angles. Which statement correctly classifies Shape C?
14. A student compares Shape G and Shape H using a property-based hierarchy: - Quadrilateral: 4 sides - Rectangle: 4 right angles - Rhombus: 4 equal sides - Square: both a rectangle and a rhombus Shape G has 4 right angles and 2 long sides and 2 short sides (not all equal). Shape H has 4 equal sides but does not have 4 right angles. Which statement correctly compares them in the hierarchy?
15. Lisa builds a rectangular prism using unit cubes. The base layer contains 18 unit cubes arranged in a rectangle. She builds the prism to a height of 4 layers. If the length of the base is 6 units, what is the width of the base?
16. A student models $1.20$ as $120$ hundredths and wants to find $1.20 \div 3$. They know decimal operations rely on place value understanding. Which strategy correctly solves the problem?
17. A music teacher has 5 minutes to practice a tricky part. She will practice it in chunks that are $\tfrac{1}{5}$ minute long. This division answers "how many $\tfrac{1}{5}$-minute chunks fit into 5 minutes." Imagine a timeline from 0 to 5 minutes marked every $\tfrac{1}{5}$ minute. What is the correct answer to the problem?
18. A rectangular garden plot is drawn on a coordinate grid. Three of its corners are located at $(2, 3)$, $(2, 9)$, and $(8, 3)$. What are the coordinates of the fourth corner needed to complete the rectangle?
19. A pizza is cut into slices where each slice is $\frac{1}{12}$ of the whole pizza. If Kevin eats $\frac{2}{3}$ of the available slices and there were originally 9 slices available, what fraction of the whole pizza did Kevin eat?
20. A class has 24 markers to share. The markers are sorted into 6 equal groups. Then the class uses 5 of the groups for an art project. This matches $\frac{5}{6}\times 24$. How does partitioning help explain $\frac{5}{6}\times 24$?

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