Unofficial practice for MTEL Elementary Mathematics (68): number, algebraic thinking, geometry, measurement, data and probability, every answer worked out.
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Unofficial practice questions, not affiliated with the Massachusetts Department of Elementary and Secondary Education or Pearson. Bank checked October 9, 2026.
A board 4 1/2 feet long is sawed into blocks that are each 3/8 foot long. Ignoring the width of the cuts, how many blocks are made?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0003
A calculator shows four fractions as decimals. For which fraction do the digits end, with no repeating block?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0002
A coat priced at $80 is marked down 25%. Sales tax of 6.25% is then charged on the sale price. What is the total cost?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0002
A hiker walks 5/6 mile east, turns back 3/8 mile west, then walks 1/4 mile east again. How far east of the start is the hiker?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0003
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Subarea I: Number systems and operations, continued
A lab spreads 6 × 10⁸ bacteria evenly over 1.5 × 10³ culture dishes. How many bacteria are on each dish?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0001
A number line model starts at −4 and moves 7 units to the left. Which expression does it represent?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0003
A printer uses 2 1/4 ounces of ink each hour. How much ink does it use in 3 2/3 hours?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0003
A student finds 6 × 47 by adding 6 × 40 and 6 × 7. Which property makes this method valid?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0001
A student simplifies −3² + |4 − 10| × 2. Which result follows the order of operations?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0003
A town's population grew from 12,500 to 14,000. What was the percent increase?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0002
The decimal form of 5/37 is 0.135135135…, with the block 135 repeating. Which digit is in the 50th place after the decimal point?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0002
The numbers −3, −√10, π and 22/7 are marked on a number line. Which list names them from left to right?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0001
To find 503 − 198, a student computes 505 − 200 instead. Why does this give the correct difference?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0002
What is the base-ten value of the base-five numeral 243?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0001
Which expression is the prime factorization of 396?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0001
Which fraction is not equivalent to 18/24?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0003
Which is the best estimate of 4,870 × 0.21?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0002
Which of the numbers √49, 22/7, 0.1666… and √27 cannot be written as a ratio of two integers?MTEL Elementary Mathematics (68) test objectives, subarea I Number Systems and Operations. Written to MTEL Elementary Mathematics (68), objective 0001
Subarea II: Algebraic thinking and relations 12
A line passes through (−2, 7) and (4, −5). How does y change each time x increases by 1?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0007
A school fair sold 150 wristbands for a total of $1,020. Day wristbands cost $8 and evening wristbands cost $5. How many day wristbands were sold?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0005
A table lists the x-values 2, 4 and 6. Which row of matching y-values makes y proportional to x?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0006
A taxi fare in dollars is F = 3.50 + 2.25m for a ride of m miles. Which equation gives m in terms of F?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0005
A tile pattern has 2 tiles in figure 1, 6 in figure 2, 12 in figure 3 and 20 in figure 4. If the pattern continues, how many tiles are in figure 10?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0004
A trail mix has nuts and raisins in the ratio 5 : 3 by weight. How many pounds of raisins are in 12 pounds of the mix?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0006
A water tank drains at a steady rate. It holds 200 liters after 2 minutes and 140 liters after 5 minutes. How much water did it hold when the draining began?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0007
In which relation is one input paired with two different outputs, so that y is not a function of x?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0004
On a trail map, 1.5 inches stands for 4 miles. Two campsites are 6.75 inches apart on the map. How far apart are the campsites?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0006
Plan A costs $30 a month plus $0.10 per text. Plan B has no monthly fee and costs $0.25 per text. For how many texts in a month do the two plans cost the same?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0007
The time needed to fill a tank varies inversely with the number of identical pumps running. Four pumps fill it in 9 hours. How long do six pumps take?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0004
What is the solution of −3x + 7 ≤ 22?MTEL Elementary Mathematics (68) test objectives, subarea II Algebraic Thinking and Relations. Written to MTEL Elementary Mathematics (68), objective 0005
Subarea III: Geometry 9
A circular pond has a circumference of 20π meters. What is its area?MTEL Elementary Mathematics (68) test objectives, subarea III Geometry. Written to MTEL Elementary Mathematics (68), objective 0008
A closed cylinder has a radius of 3 cm and a height of 10 cm. What is its total surface area?MTEL Elementary Mathematics (68) test objectives, subarea III Geometry. Written to MTEL Elementary Mathematics (68), objective 0008
A quadrilateral has four congruent sides and no right angles. Which statement about it must be true?MTEL Elementary Mathematics (68) test objectives, subarea III Geometry. Written to MTEL Elementary Mathematics (68), objective 0008
A rectangular window frame is 84 inches wide and 35 inches high. A length of tape is stretched from one corner to the opposite corner. How long is the tape?MTEL Elementary Mathematics (68) test objectives, subarea III Geometry. Written to MTEL Elementary Mathematics (68), objective 0008
A transversal crosses two parallel lines. A pair of alternate interior angles measures (4x − 6)° and (2x + 34)°. What is x?MTEL Elementary Mathematics (68) test objectives, subarea III Geometry. Written to MTEL Elementary Mathematics (68), objective 0009
A triangle has vertices (2, 4), (6, 4) and (2, 10). Every coordinate is multiplied by 1/2, a dilation about the origin. What is the area of the new triangle?MTEL Elementary Mathematics (68) test objectives, subarea III Geometry. Written to MTEL Elementary Mathematics (68), objective 0009
How many edges does a pentagonal prism have?MTEL Elementary Mathematics (68) test objectives, subarea III Geometry. Written to MTEL Elementary Mathematics (68), objective 0008
The point (2, −7) is turned 90° counterclockwise about the origin, and the result is slid 3 units to the left. What are the coordinates of the final point?MTEL Elementary Mathematics (68) test objectives, subarea III Geometry. Written to MTEL Elementary Mathematics (68), objective 0009
Quadrilateral ABCD has vertices A(0, 0), B(4, 2), C(5, 6) and D(1, 4). Which name fits it best?MTEL Elementary Mathematics (68) test objectives, subarea III Geometry. Written to MTEL Elementary Mathematics (68), objective 0009
Subarea IV: Measurement, data and probability 9
A box plot of commute times shows a minimum of 8 minutes, a first quartile of 15, a median of 22, a third quartile of 30 and a maximum of 55. Which statement does the plot support?MTEL Elementary Mathematics (68) test objectives, subarea IV Measurement, Data, and Probability. Written to MTEL Elementary Mathematics (68), objective 0012
A club with 7 members elects a president, a secretary and a treasurer. No member may hold two offices. In how many ways can the offices be filled?MTEL Elementary Mathematics (68) test objectives, subarea IV Measurement, Data, and Probability. Written to MTEL Elementary Mathematics (68), objective 0011
A leaking pipe loses 25 milliliters of water each minute. How many liters does it lose in one week?MTEL Elementary Mathematics (68) test objectives, subarea IV Measurement, Data, and Probability. Written to MTEL Elementary Mathematics (68), objective 0010
A rectangular board 30 cm by 20 cm has a circular target of radius 6 cm painted on it. A dart lands at a random point on the board. What is the probability that it lands in the target?MTEL Elementary Mathematics (68) test objectives, subarea IV Measurement, Data, and Probability. Written to MTEL Elementary Mathematics (68), objective 0011
A student's mean score on five tests is 82. What score on a sixth test raises the mean to 84?MTEL Elementary Mathematics (68) test objectives, subarea IV Measurement, Data, and Probability. Written to MTEL Elementary Mathematics (68), objective 0012
A train leaves at 10:45 a.m. and arrives at 2:20 p.m. the same day after traveling 172 miles. What is its average speed?MTEL Elementary Mathematics (68) test objectives, subarea IV Measurement, Data, and Probability. Written to MTEL Elementary Mathematics (68), objective 0010
A tray holds 5 blueberry muffins and 7 bran muffins. Two muffins are picked at random, one after the other, and neither is put back. What is the probability that both are blueberry?MTEL Elementary Mathematics (68) test objectives, subarea IV Measurement, Data, and Probability. Written to MTEL Elementary Mathematics (68), objective 0011
Five salaries are $38,000, $40,000, $41,000, $43,000 and $44,000. A sixth salary of $150,000 is added. Which measure changes least?MTEL Elementary Mathematics (68) test objectives, subarea IV Measurement, Data, and Probability. Written to MTEL Elementary Mathematics (68), objective 0012
The length and the width of a rectangular poster are each increased by 50%. By what percent does its area increase?MTEL Elementary Mathematics (68) test objectives, subarea IV Measurement, Data, and Probability. Written to MTEL Elementary Mathematics (68), objective 0010
How this list was compiled: Our own questions, written to the test objectives of MTEL Elementary Mathematics, field 68, as the test information guide prints them on the Massachusetts Tests for Educator Licensure website (https://www.mtel.nesinc.com/Content/StudyGuide/MA_SG_OBJ_68.htm and https://www.mtel.nesinc.com/TestView.aspx?f=HTML_FRAG/MA068_TestPage.html, read 2026-10-09): 100 multiple-choice questions and 2 open-response items in 4 hours; multiple-choice subareas I Number Systems and Operations (30% of the score, objectives 0001 to 0003), II Algebraic Thinking and Relations (20%, objectives 0004 to 0007), III Geometry (15%, objectives 0008 and 0009) and IV Measurement, Data, and Probability (15%, objectives 0010 to 0012), and the open-response subarea, 20%. This bank holds 18, 12, 9 and 9. Every answer is arithmetic or reasoning from the numbers in the question, and each was worked out a second time before the bank was written. Licence: Questions, choices and explanations are original work of this site.
How it works
This MTEL elementary math practice test follows Elementary Mathematics, field 68: 48 questions of our own in its four multiple-choice subareas. It is unofficial and not affiliated with, endorsed by or sponsored by the Massachusetts Department of Elementary and Secondary Education or Pearson.
Read the full guide
The four subareas
By the test objectives: number systems and operations, 30% of the score; algebraic thinking and relations, 20%; geometry, 15%; measurement, data and probability, 15%. This bank holds 18, 12, 9 and 9, in that order.
The clock in exam mode
The MTEL site gives 4 hours of testing time for the whole test and no separate time for its multiple-choice questions, so exam mode here is untimed.
The two open-response assignments are not practiced here. The MTEL site says they may be handwritten and scanned.
Questions and answers
How many questions are on the MTEL elementary math test?
The MTEL site lists 100 multiple-choice questions and 2 open-response assignments. It adds that tests may include questions that do not count toward the score.
What is the passing score for MTEL Elementary Mathematics?
The MTEL site gives a qualifying score of 240. Multiple-choice questions are 80% of the score and the open-response assignments 20%, so the number right on this page is not a prediction.
Can you use a calculator on the MTEL elementary math test?
Only the one the test supplies. The MTEL site says standard four-function calculators are provided on screen.
Is MTEL Elementary Mathematics the same as the General Curriculum math subtest?
No. The MTEL tests list shows Mathematics (Elementary) (68) and General Curriculum (178/278) as separate tests. General Curriculum’s second subtest (278) covers mathematics, science and technology/engineering. This page follows the objectives of field 68 only.