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 60 selected-response questions (80% of the test score) and 2 constructed-response assignments (20% of the test score). The content areas covered by the first test are: numbers and operations; measurement and geometry; patterns, algebra, and functions; data analysis and probability; and mathematical processes and perspectives. The topics covered by the numbers and operations subarea are: the structure of the base ten numeration system; number theory; the different representations of real numbers; and basic operations on real numbers. The topics covered by the measurement and geometry subarea are: the principles and applications of measurement; and Euclidean, coordinate, and transformational geometry. The topics covered by the patterns, algebra, and functions subarea are: patterns, relations, and functions; the properties and techniques of algebraic operations; and linear functions and their applications. The topics covered by the data analysis and probability subarea are: the processes of collecting, organizing, describing, analyzing, and interpreting data; and the basic theory and applications of probability. The topics covered by the mathematical processes and perspectives subarea are: the various representations used to communicate mathematical ideas and concepts; and the basic mathematical reasoning, proof, and problem solving strategies.

The examination must be completed within four hours. The total test score is placed on a scale of 100 to 300, with 220 as the lowest passing score. Scores are based on the number of selected-response questions answered correctly and the scores assigned by judges to the constructed responses. Test-takers will also 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.