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100+ Free MTEL Math Elementary (68) Practice Questions

Pass your MTEL Mathematics (Elementary) Field 68 exam on the first try — instant access, no signup required.

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A teacher wants students to justify why 1/2 + 1/3 does not equal 2/5. Which explanation is mathematically correct?

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D
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Key Facts: MTEL Math Elementary (68) Exam

100 MC + 2 OR

Test Structure

MTEL field 68 test page

240

Passing Score

MTEL test information guide

$139

Registration Fee

MTEL field 68 test page

30%

Number Systems and Operations weight

MTEL field 68 objectives

20%

Algebraic Thinking and Relations weight

MTEL field 68 objectives

15% / 15%

Geometry / Measurement-Data-Probability weights

MTEL field 68 objectives

20%

Open-response Integration weight

MTEL field 68 objectives

4 hours

Testing Time

MTEL field 68 test page

MTEL Mathematics (Elementary), field 68, is a 100-question multiple-choice plus 2-open-response test scored on a 240 passing standard. The official framework weights four multiple-choice subareas: Number Systems and Operations (30%), Algebraic Thinking and Relations (20%), Geometry (15%), and Measurement, Data, and Probability (15%), with a fifth open-response subarea, Integration of Knowledge and Understanding, worth 20%. The current public fee is $139, the appointment runs about 4 hours 15 minutes, and calculators are not permitted. This 100-question bank mirrors that blueprint so candidates can practice the exact content domains.

Sample MTEL Math Elementary (68) Practice Questions

Try these sample questions to test your MTEL Math Elementary (68) exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In the number 47,308.6, what is the value of the digit 7?
A.7,000
B.700
C.70,000
D.70
Explanation: Reading from the right, the digits before the decimal occupy the ones, tens, hundreds, thousands, ten-thousands places. In 47,308.6 the 7 sits in the thousands place, so its value is 7 × 1,000 = 7,000.
2Which of the following numbers is prime?
A.21
B.29
C.27
D.33
Explanation: A prime number has exactly two distinct factors: 1 and itself. 29 has no divisors other than 1 and 29, so it is prime.
3What is the prime factorization of 60?
A.2³ × 5
B.2 × 3 × 5
C.2² × 3 × 5
D.2² × 15
Explanation: 60 = 4 × 15 = (2 × 2) × (3 × 5) = 2² × 3 × 5. A prime factorization expresses a number as a product of prime factors only.
4Which property of operations is shown by the equation 6 × (4 + 9) = (6 × 4) + (6 × 9)?
A.Identity property
B.Associative property
C.Commutative property
D.Distributive property
Explanation: The distributive property of multiplication over addition states that a × (b + c) = (a × b) + (a × c). Multiplying the 6 across the sum demonstrates this property.
5Which of the following numbers is irrational?
A.√7
B.0.25
C.3/8
D.√16
Explanation: An irrational number cannot be written as a ratio of two integers and its decimal expansion neither terminates nor repeats. √7 ≈ 2.6457... is non-terminating and non-repeating, so it is irrational.
6A student demonstrates that a set of 8 counters is still 8 even after the counters are spread farther apart. Which early number concept does this illustrate?
A.Subitizing
B.Conservation of number
C.One-to-one correspondence
D.Cardinality
Explanation: Conservation of number is the understanding that the quantity in a set stays the same regardless of how the objects are arranged or spaced. Recognizing 8 counters as still 8 after rearrangement demonstrates conservation.
7Express 0.000045 in scientific notation.
A.45 × 10⁻⁶
B.4.5 × 10⁵
C.4.5 × 10⁻⁵
D.4.5 × 10⁻⁴
Explanation: Scientific notation writes a number as a value between 1 and 10 times a power of 10. Moving the decimal point five places to the right to get 4.5 means the exponent is −5: 4.5 × 10⁻⁵.
8What is the value of 5³?
A.25
B.15
C.243
D.125
Explanation: An exponent indicates repeated multiplication of the base. 5³ = 5 × 5 × 5 = 125.
9Convert 3/5 to a percent.
A.60%
B.35%
C.53%
D.0.6%
Explanation: To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100. 3 ÷ 5 = 0.6, and 0.6 × 100 = 60%.
10A jacket originally priced at $80 is discounted by 25%. What is the sale price?
A.$55
B.$60
C.$75
D.$20
Explanation: A 25% discount removes 25% of $80, which is 0.25 × 80 = $20. The sale price is $80 − $20 = $60. Equivalently, the customer pays 75% of $80 = $60.

About the MTEL Math Elementary (68) Exam

The MTEL Mathematics (Elementary) test, field 68, assesses the mathematics content knowledge needed by Massachusetts elementary and middle-grades math teacher candidates. It uses 100 multiple-choice questions plus two open-response assignments across number systems, algebraic thinking, geometry, and measurement, data, and probability.

Questions

100 scored questions

Time Limit

4 hours of testing (about 4h 15m total appointment)

Passing Score

240 scaled score

Exam Fee

$139 (Massachusetts DESE / Pearson)

MTEL Math Elementary (68) Exam Content Outline

~30% of this bank

Number Systems and Operations

Matches Subarea I: place value and number theory, primes and factors, rational and irrational numbers, exponents and roots, and operations with whole numbers, decimals, percents, integers, and fractions, including real-world percent problems.

~20% of this bank

Algebraic Thinking and Relations

Matches Subarea II: patterns and functions, evaluating and simplifying expressions, solving equations and inequalities, systems, ratios and proportions, and linear relationships including slope, intercepts, and rate of change.

~18% of this bank

Geometry

Matches Subarea III: properties of two- and three-dimensional figures, the Pythagorean theorem, circles, composite figures, coordinate geometry, transformations, congruence, and similarity.

~27% of this bank

Measurement, Data, and Probability

Matches Subarea IV: measurement units and conversions, perimeter, area, volume, density, elapsed time, probability of simple and compound events, and descriptive statistics including mean, median, mode, range, and data interpretation.

How to Pass the MTEL Math Elementary (68) Exam

What You Need to Know

  • Passing score: 240 scaled score
  • Exam length: 100 questions
  • Time limit: 4 hours of testing (about 4h 15m total appointment)
  • Exam fee: $139

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

MTEL Math Elementary (68) Study Tips from Top Performers

1Prioritize Number Systems and Operations since it is the heaviest subarea at about 30 percent of the multiple-choice questions
2Drill fraction, decimal, and percent conversions until they are automatic because they appear throughout the test
3Practice without a calculator to build mental math and estimation speed, since calculators are not allowed
4Memorize core geometry and measurement formulas for perimeter, area, volume, the Pythagorean theorem, and circles
5Rehearse the two open-response assignments by writing clear, step-by-step mathematical justifications
6Review each missed practice question by subarea so you can target the objectives where you are weakest

Frequently Asked Questions

What is on the MTEL Mathematics (Elementary) (68) test?

Field 68 covers four multiple-choice subareas — Number Systems and Operations, Algebraic Thinking and Relations, Geometry, and Measurement, Data, and Probability — plus a fifth open-response subarea, Integration of Knowledge and Understanding. The number subarea carries the most weight at about 30 percent.

How many questions are on MTEL field 68 and how long is it?

The test has 100 multiple-choice questions and 2 open-response assignments. Candidates receive about 4 hours of testing time within a roughly 4-hour, 15-minute total appointment that includes a short tutorial and the nondisclosure agreement.

What is the passing score for MTEL Mathematics (Elementary) (68)?

The passing standard is a scaled score of 240, the same standard used across most MTEL tests. Your multiple-choice and open-response performance combine into the single scaled score reported for the test.

How much does the MTEL Mathematics (Elementary) test cost in 2026?

The current public registration fee for MTEL field 68 is $139. Always confirm the exact fee in your Pearson registration portal before checkout, and budget separately for any other MTEL tests your license requires.

Can I use a calculator on MTEL field 68?

No. Calculators are not permitted on the MTEL Mathematics (Elementary) test. Practice mental math, estimation, and paper-and-pencil computation strategies so you can work efficiently without one on test day.

How should I study for MTEL Mathematics (Elementary) (68)?

Study to the official objective weights, spending the most time on number systems and operations, then algebraic thinking. Use timed mixed practice for the multiple-choice section and rehearse written explanations for the two open-response assignments.