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Teacher Certification · 5158

Praxis Pennsylvania Grades 4-8 Subject Concentration: Mathematics Practice Test

Mathematics for Pennsylvania grades 4–8 spans number and proportional reasoning, algebraic relationships, geometry, measurement, statistics, and probability. Practice questions sample calculations and interpretations involving ratios, rates, equations, angle measures, data summaries, and chance. These concepts support middle-grades work such as explaining solution steps, connecting representations, and identifying whether a numerical result fits a problem’s conditions.

Exam overview

Exam providerETS Praxis
Exam code5158
CategoryTeacher Certification

About the Praxis Pennsylvania Grades 4-8 Subject Concentration: Mathematics Exam

The question bank samples skills used to reason across mathematical representations. Number and ratio problems call for simplifying comparisons, scaling quantities, and dividing totals evenly; rate questions connect distance, time, and constant speed. Algebra items ask you to test ordered pairs in a linear equation or find where two equations have the same solution. Geometry tasks apply angle relationships, while statistics questions involve calculating and interpreting a mean. Probability items distinguish outcomes with and without replacement and relate favorable outcomes to all possible outcomes. As you work, attend to units, the meaning of each quantity, and whether a result is reasonable in context. For teaching mathematics in grades 4–8, being able to model a strategy, explain why it works, and recognize common errors helps make student reasoning visible.

Sample Practice Questions

Review a selection from this exam's published US Practice Tests practice bank.

Question 1

A line has equation y = 2x − 5. Which ordered pair lies on the line?

  1. A(0, 5)
  2. B(2, −1)
  3. C(3, 1)
  4. D(−1, −7)
Show answerCorrect answer: C

Substitute x = 3 into the equation: y = 2(3) − 5 = 1. Thus (3, 1) is on the line.

Question 2

A recipe uses 3 cups of flour for every 2 cups of oats. If the recipe uses 9 cups of flour, how many cups of oats are needed to keep the ratio the same?

  1. A4
  2. B6
  3. C9
  4. D13.5
Show answerCorrect answer: B

The flour amount is multiplied by 3, from 3 cups to 9 cups. Multiply the oats amount by 3 as well: 2 × 3 = 6 cups.

Question 3

A car travels 150 miles in 3 hours at a constant speed. At that speed, how far will it travel in 4.5 hours?

  1. A200 miles
  2. B215 miles
  3. C225 miles
  4. D250 miles
Show answerCorrect answer: C

The car's speed is 150 ÷ 3 = 50 miles per hour. In 4.5 hours it travels 50 × 4.5 = 225 miles.

Question 4

A bag contains 5 red marbles and 7 blue marbles. What is the probability of selecting a red marble at random?

  1. A5/7
  2. B5/12
  3. C7/12
  4. D1/5
Show answerCorrect answer: B

There are 5 + 7 = 12 marbles altogether, of which 5 are red. The probability is therefore 5/12.

Question 5

Which ordered pair is the solution to the system y = x + 2 and y = 8 − x?

  1. A(2, 4)
  2. B(3, 5)
  3. C(4, 6)
  4. D(5, 3)
Show answerCorrect answer: B

Set the expressions for y equal: x + 2 = 8 − x. Then 2x = 6, so x = 3. Substituting gives y = 3 + 2 = 5; the solution is (3, 5).

Question 6

What is the mean of the data set 4, 7, 7, 10, and 12?

  1. A7
  2. B8
  3. C9
  4. D10
Show answerCorrect answer: B

Add the values: 4 + 7 + 7 + 10 + 12 = 40. Divide by the 5 values: 40 ÷ 5 = 8.

Question 7

A triangle has angles measuring 47° and 68°. What is the measure of its third angle?

  1. A55°
  2. B65°
  3. C75°
  4. D85°
Show answerCorrect answer: B

The interior angles of a triangle sum to 180°. The third angle is 180° − 47° − 68° = 65°.

How to use this practice test

The free practice session presents up to 20 randomly selected questions from the available 50-question bank. Solve each item before checking the displayed results, then use missed or uncertain questions to identify specific skills to revisit, such as solving a system, simplifying a ratio, or calculating probability without replacement.

Preparation tips

  • For ratio and rate problems, label the quantities and units, then use equivalent ratios or a unit rate to justify the calculation.
  • Check an ordered pair in a linear equation by substituting both coordinates; for a system, verify that the pair satisfies both equations.
  • Review angle-sum reasoning for triangles and write the known angle measures before finding an unknown.
  • Distinguish probability with replacement from probability without replacement; update the number of possible outcomes after each draw when needed.
  • Calculate the mean by summing all data values and dividing by the number of values, and explain what that average represents.
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