GACE Middle Grades Mathematics

The Middle Grades Mathematics assessment, offered as part of the Georgia Assessments for the Certification of Educators, is composed of one test. The test consists of 45 selected-response questions. The content areas covered by the test are: arithmetic, algebra, geometry, and data. The topics covered by the arithmetic and algebra subarea are: knowledge and application of numbers and operations; algebra and its processes; and functions and their graphs. The topics covered by the geometry and data subarea are: geometry, measurement, probability, statistics, and discrete mathematics.


The examination must be completed within two hours. Test-takers will receive performance indices indicating their success in each subarea of the examination. Scores will be available approximately a month after the date of the examination; unofficial results are posted on the internet, and an official score report is mailed to the test-taker, the Professional Standards Commission, and the institution specified by the test-taker during registration.

GACE Middle Grades Mathematics Practice Questions

1. Express 2/3 x 9/5 as a mixed number.

A: 18/15
B: 10/27
C: 1 1/5
D: 1 1/15

2. George’s house is three-quarters of a mile from school. If he walks at an average speed of 3 miles per hour, how long does it take him to walk to and from school each day?

A: 15 minutes
B: 30 minutes
C: 45 minutes
D: 50 minutes

3. What is the greatest common factor of 18 and 21?

A: 3
B: 6
C: 9
D: 10

4. Select the answer in which the fractions are arranged from least to greatest.

A: 3/8, 1/3, 4/7, 2/5
B: 1/3, 3/8, 2/5, 4/7
C: 3/8, 4/7, 1/3, 2/5
D: 1/3, 2/5, 3/8, 4/7

5. If x = 3 and y = -3, what is the value of (3 + x)(3 – y)?

A: 25
B: 36
C: 40
D: 49

Answer Key

1. C. When multiplying fractions, multiply numerator by numerator and denominator by denominator. Remember that a mixed number contains a whole number and a fraction less than one.
2. B. Time is equal to distance divided by rate. Remember that the total distance is 1.5 miles and that .5 hours is equal to half an hour, or thirty minutes.
3. A. The factors of a number are those terms that can be multiplied by some other number to derive the number.
4. B. The easiest way to solve this problem is to convert the fractions to decimals by dividing numerators by denominators.
5. B. Remember that two negative symbols make a positive.