AASA 6th Grade Math 2 — Questions and Answers
Question 1: A rectangle has a length of 12 cm and a width of 7 cm. What is the area of the rectangle?
- 84 sq cm (Correct answer)
- 38 sq cm
- 19 sq cm
- 96 sq cm
Correct answer: 84 sq cm
Area of a rectangle = length × width = 12 × 7 = 84 square centimeters.
To find the area of a rectangle, you use the formula: Area = length × width. Here, the length is 12 cm and the width is 7 cm, so Area = 12 × 7 = 84 square centimeters. The perimeter (38 cm) is a different measurement that adds all sides together, so be careful not to confuse the two formulas.
Question 2: What is the value of 3/4 ÷ 1/2?
- 3/2 (Correct answer)
- 3/8
- 2/3
- 1/4
Correct answer: 3/2
To divide fractions, multiply by the reciprocal: 3/4 × 2/1 = 6/4 = 3/2.
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/2 is 2/1. So 3/4 ÷ 1/2 becomes 3/4 × 2/1 = (3×2)/(4×1) = 6/4, which simplifies to 3/2 or 1 1/2. This is a key skill tested on the Arizona AASA 6th grade math assessment.
Question 3: A store sells notebooks for $2.50 each. If Marcus buys 6 notebooks and pays with a $20 bill, how much change does he receive?
- $5.00 (Correct answer)
- $15.00
- $7.50
- $2.50
Correct answer: $5.00
6 notebooks × $2.50 = $15.00. Change = $20.00 − $15.00 = $5.00.
This problem requires two steps. First, find the total cost: 6 × $2.50 = $15.00. Then find the change: $20.00 − $15.00 = $5.00. Decimal multiplication and multi-step word problems are important components of the AASA 6th grade math standards, which align with Arizona's emphasis on real-world mathematical applications.
Question 4: Which expression is equivalent to 4(3x + 5)?
- 12x + 20 (Correct answer)
- 12x + 5
- 7x + 9
- 7x + 20
Correct answer: 12x + 20
Using the distributive property: 4 × 3x = 12x and 4 × 5 = 20, so the result is 12x + 20.
The distributive property states that a(b + c) = ab + ac. Applying this: 4(3x + 5) = 4 × 3x + 4 × 5 = 12x + 20. A common mistake is to only multiply one term, yielding incorrect answers like 12x + 5. Arizona's 6th grade standards expect students to apply properties of operations to generate equivalent expressions.
Question 5: A number line shows points at −3, −1, 0, 2, and 4. Which of the following correctly orders these numbers from least to greatest?
- −3, −1, 0, 2, 4 (Correct answer)
- 0, −1, −3, 2, 4
- 4, 2, 0, −1, −3
- −1, −3, 0, 2, 4
Correct answer: −3, −1, 0, 2, 4
On a number line, numbers increase from left to right. The correct order from least to greatest is −3, −1, 0, 2, 4.
When ordering integers on a number line, values increase as you move to the right. Negative numbers are always less than positive numbers, and among negative numbers, one with a greater absolute value is actually smaller (−3 < −1). So the correct ascending order is −3, −1, 0, 2, 4. Understanding the number line and integer ordering is a foundational 6th grade AASA skill.
Question 6: A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of randomly drawing a blue marble?
- 1/2 (Correct answer)
- 1/3
- 3/10
- 2/5
Correct answer: 1/2
Total marbles = 3 + 5 + 2 = 10. Probability of blue = 5/10 = 1/2.
Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. There are 5 blue marbles out of a total of 3 + 5 + 2 = 10 marbles. So P(blue) = 5/10 = 1/2. Simplifying fractions and understanding basic probability are both part of the Arizona 6th grade math standards assessed on the AASA.
AASA 6th Grade Math 2
A rectangle has a length of 12 cm and a width of 7 cm.
What is the area of the rectangle?