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Grade 6 Mathematics Diagnostic

NC EOG-Aligned Readiness Assessment

📚 Mathematics 🎓 Grade 6 ⏱️ 67 minutes

Learning Objectives

  • Use ratios, unit rates, and percents to solve real-world problems.

  • Divide fractions, compute with decimals, and find common factors and multiples.

  • Reason about rational numbers, absolute value, and the coordinate plane.

  • Write, evaluate, and generate equivalent algebraic and numerical expressions.

  • Solve one-step equations and reason about one-variable inequalities.

  • Find area, surface area, and volume and work with polygons on the coordinate plane.

  • Summarize data using measures of center, spread, and data displays.

Progress 6 sections
1

Directions

~3 minutes

This diagnostic screens all five Grade 6 math domains. It follows the NC End-of-Grade emphasis, so ratio and rate reasoning and algebraic expressions appear most often. Read each question carefully and use scratch paper.

2

Ratios & Proportional Relationships

~16 minutes

Ratio table (flour to cookies).

Cups of flourCookies
224
336
| 5 | ? |

Question 1

A fruit bowl has 8 apples and 12 oranges. What is the ratio of apples to oranges in simplest form?

Question 2

A car travels 150 miles on 5 gallons of gas. What is the unit rate?

Question 3

Use the ratio table shown. How many cookies can be made with 5 cups of flour?

Question 4

Which is the better buy?

Question 5

What is 25% of 80?

Question 6

15 is 30% of what number?

Question 7

A $\$40$ shirt is marked 20% off. What is the sale price?

Question 8

A map uses the scale 1 inch = 2.5 miles. How many miles does 6 inches represent?

3

The Number System

~14 minutes
Two points on a coordinate plane
A four-quadrant coordinate plane from -6 to 6. Point A is plotted at (3, 2) and point B at (3, -4). A vertical segment connects them....
Question 9

What is $\frac{3}{4} \div \frac{1}{2}$?

Question 10

How many 1/4-cup scoops are in 3 cups of flour?

Question 11

Find $4.2 \times 0.5$.

Question 12

What is the greatest common factor (GCF) of 24 and 36?

Question 13

Which number is farthest to the left on a number line?

Question 14

Which statement is true?

Question 15

Use the coordinate plane shown. What is the distance between point A (3, 2) and point $B (3, -4)$?

4

Expressions & Equations

~16 minutes
Question 16

Evaluate $2^{4}$.

Question 17

Evaluate $3 + 2 \times 5^{2}$.

Question 18

Which expression represents 'the product of 7 and a number n, decreased by 4'?

Question 19

Evaluate $4x + 3$ when $x = 5$.

Question 20

Which expression is equivalent to $6(x + 2)$?

Question 21

Simplify $5x + 3 + 2x$.

Question 22

Solve $x + 8 = 15$.

Question 23

Which value of x makes the inequality $x > 5$ true?

5

Geometry

~10 minutes
Triangle with base and height
A triangle with a horizontal base labeled 10 centimeters and a dashed vertical height of 6 centimeters drawn to the base, meeting it at a right angle....
Net of a rectangular prism
A flattened net of a rectangular prism with edge lengths 3 by 2 by 4 centimeters, showing six rectangular faces arranged in a cross shape....
Rectangle on a coordinate plane
A first-quadrant coordinate grid showing a rectangle with vertices at (1,1), (5,1), (5,4), and (1,4)....
Question 24

Use the triangle shown (base 10 cm, height 6 cm). What is its area?

Question 25

Use the net shown for a 3 cm by 2 cm by 4 cm rectangular prism. What is its total surface area?

Question 26

A storage box measures 4 cm by 2.5 cm by 3 cm. What is its volume?

Question 27

Use the rectangle shown with vertices (1,1), (5,1), (5,4), and (1,4). What is its area?

6

Statistics & Probability

~8 minutes
Favorite fruit bar graph
A bar graph of favorite fruits: Apple 18, Banana 12, Grape 8, Orange 10 students....
Question 28

Find the mean of this data set: 4, 8, 6, 10, 7.

Question 29

Find the median of this data set: 3, 9, 5, 7, 12, 5.

Question 30

Use the bar graph shown. How many more students chose apples than grapes?

Question 31

Find the range of this data set: 12, 7, 15, 9, 20.