STAAR Grade 6 Math

1. Question 1 · Number and Operations

   The sixth-grade science club is taking a field trip to a museum. There are 418 students and 26 chaperones going on the trip. Each bus holds 52 people. What is the least number of buses needed so everyone has a seat?
   • A.8
   • B.9
   • C.10
   • D.17
   Show answer and explanation

   Answer: B. 9

   Add to find the number of people: 418 + 26 = 444. Then 444 ÷ 52 = 8 remainder 28. Eight buses would leave 28 people without seats, so one more bus is needed, for a total of 9 buses.

2. Question 2 · Proportionality

   The tape diagram shows the ratio of tomato plants to pepper plants in a community garden. There are 48 plants in all. How many pepper plants are in the garden?
   • A.6
   • B.18
   • C.30
   • D.80
   Show answer and explanation

   Answer: C. 30

   The diagram has 3 + 5 = 8 equal parts that total 48 plants, so each part is 48 ÷ 8 = 6 plants. Pepper plants fill 5 parts: 5 × 6 = 30. The number 18 is the number of tomato plants.

3. Question 3 · Expressions, Equations, and Relationships

   What is the value of the expression 5 × 2³ − (12 + 6) ÷ 3?
   • A.24
   • B.30
   • C.34
   • D.994
   Show answer and explanation

   Answer: C. 34

   Work inside the parentheses first: 12 + 6 = 18. Next the exponent: 2³ = 8. Then multiply and divide: 5 × 8 = 40 and 18 ÷ 3 = 6. Finally, 40 − 6 = 34. Using 2³ = 6 by mistake gives 24.

4. Question 4 · Expressions, Equations, and Relationships

   Point R is at (−5, 6) on a coordinate plane. Lucia reflects point R across the x-axis. In which quadrant is the reflected point located?
   • A.Quadrant I
   • B.Quadrant II
   • C.Quadrant III
   • D.Quadrant IV
   Show answer and explanation

   Answer: C. Quadrant III

   A reflection across the x-axis keeps the x-coordinate and changes the y-coordinate to its opposite, so (−5, 6) becomes (−5, −6). A point with a negative x-coordinate and a negative y-coordinate is in Quadrant III. Point R itself is in Quadrant II.

5. Question 5 · Measurement and Data

   Eight library club members recorded the minutes they read on Saturday: 25, 30, 30, 35, 35, 35, 40, and 120. Which statement about the data is true?
   • A.The mean of the data is 35 minutes.
   • B.The range of the data is 35 minutes.
   • C.The mode of the data is 30 minutes.
   • D.The median describes a typical value better than the mean because 120 is an outlier.
   Show answer and explanation

   Answer: D. The median describes a typical value better than the mean because 120 is an outlier.

   The mean is 350 ÷ 8 = 43.75 minutes, which is pulled up by the outlier 120. The median is 35 minutes, which is closer to most of the data, so it better describes a typical value. The range is 120 − 25 = 95, and the mode is 35.

6. Question 6 · Number and Operations

   The band is selling candy bars to raise money for a trip. The band ordered 1,248 candy bars, and the candy bars come packed in boxes of 24. How many boxes of candy bars did the band order?
   • A.42
   • B.52
   • C.502
   • D.520
   Show answer and explanation

   Answer: B. 52

   Divide the total number of candy bars by the number in each box: 1,248 ÷ 24 = 52. Check by multiplying: 52 × 24 = 1,248. An answer such as 520 comes from placing a zero in the quotient by mistake.

7. Question 7 · Proportionality

   At the zoo's bird exhibit, the ratio of penguins to puffins is 5 to 3. There are 40 penguins in the exhibit. How many puffins are in the exhibit?
   • A.8
   • B.24
   • C.38
   • D.64
   Show answer and explanation

   Answer: B. 24

   The ratio 5 : 3 must be scaled so the penguin part is 40. Since 40 ÷ 5 = 8, multiply both parts by 8: 5 × 8 = 40 penguins and 3 × 8 = 24 puffins. The value 64 is the total number of birds.

8. Question 8 · Expressions, Equations, and Relationships

   The robotics team's number for a competition is 252. Which expression shows the prime factorization of 252?
   • A.2² × 3² × 7
   • B.2 × 3² × 14
   • C.2³ × 3 × 7
   • D.4 × 9 × 7
   Show answer and explanation

   Answer: A. 2² × 3² × 7

   Build a factor tree: 252 = 2 × 126 = 2 × 2 × 63 = 2 × 2 × 3 × 21 = 2 × 2 × 3 × 3 × 7. With exponents, this is 2² × 3² × 7. The expressions with 14, 4, or 9 equal 252 but use factors that are not prime, and 2³ × 3 × 7 equals 168.

9. Question 9 · Expressions, Equations, and Relationships

   At a band fundraiser, Noah runs a math game. To win a prize, a player must choose the expression that has a value of 30. Which expression should the player choose?
   • A.2 + 3² × 5
   • B.2 × 3² + 5
   • C.4² + 3 × 5
   • D.(2 + 3)² + 5
   Show answer and explanation

   Answer: D. (2 + 3)² + 5

   Evaluate each expression using the order of operations. (2 + 3)² + 5 = 5² + 5 = 25 + 5 = 30. The others give 2 + 9 × 5 = 47, 2 × 9 + 5 = 23, and 16 + 15 = 31. Only the first expression equals 30.

10. Question 10 · Measurement and Data

    Item	Number Sold
    Candles	18
    Popcorn	30
    Cookie dough	42
    Wrapping paper	30

    The table shows the number of each item the band sold at its fundraiser. What percent of all the items sold were cookie dough?
    • A.25%
    • B.35%
    • C.42%
    • D.54%
    Show answer and explanation

    Answer: B. 35%

    First find the total: 18 + 30 + 42 + 30 = 120 items. The relative frequency of cookie dough is 42/120 = 7/20 = 35/100 = 35%. Writing 42% treats the count as a percent, but the total is 120, not 100.

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