A class groups 38 counters into twenty-fives, fives and ones in order to write the number in base five. Which numeral do they write?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 004.
A dust grain is 4 × 10⁻³ cm wide. How long is a row of 6 × 10⁵ such grains laid side by side, in scientific notation?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 005.
A farmer bends 36 m of fence into a rectangular pen that is w meters wide. Which expression gives the pen's area in square meters?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 002.
A quilt block is a square whose area is 12 square inches. A student says its side "must be a fraction." What is true of the side?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 004.
Show all 44 questions (40 more)
Mathematical processes and number concepts, continued
A snowplow crew needs 7 tons of road salt to treat 4 miles of highway. At the same rate, how much salt treats 22 miles?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 003.
A student multiplies 47 × 36 by partial products and writes 1,200 + 210 + 42. Which partial product is missing?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 005.
A student reasons: "Every square is a rectangle. This figure is a rectangle. So this figure is a square." What is wrong with the argument?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 001.
A teacher wants the smallest number of pencils that can be bundled in groups of 18 or in groups of 24 with none left over. What is it?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 005.
After listing 3, 9, 15 and 21, a student conjectures that every multiple of 3 is odd. Which number is a counterexample?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 001.
Maya gives half of her stickers to Leo, then gives 6 stickers to Ana, and has 9 left. Working backward, how many stickers did she start with?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 002.
Six painters can paint a school in 8 days. Working at the same rate, how long would four painters take?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 003.
Which row of a class chart correctly matches a fraction, a decimal and a percent?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 004.
Patterns, algebraic relationships and functions 12
A cart starts from rest, and its speed in meters per second after t seconds is v = 3t. The distance it covers in the first 4 seconds equals the area under this line. What is that distance?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 010.
A class jar holds 31 coins, all nickels and dimes, worth $2.35 in all. How many dimes are in the jar?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 008.
A gardener has 40 m of fencing for a rectangular bed along a wall, so only three sides need fence. What is the largest area the bed can have?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 009.
A rain barrel drains through a hose. The gallons left after x minutes are y = 55 − 2.5x. In this model, what does the number −2.5 mean?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 008.
A recycling club collects 150 kg of paper in its first month and plans to raise the amount by 10% every month. By this plan, how much will it collect in the third month?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 010.
A student graphs f(x) = √(x − 4) on a graphing calculator. Where does the graph begin?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 007.
A student slides the parabola y = x² so that its vertex moves to (2, 3). Which equation describes the new graph?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 007.
A student tries to cover a tabletop edge to edge with copies of one regular polygon. With which shape will it work?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 006.
A teacher writes four relations as lists of (input, output) pairs. Which list fails the test for a function?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 007.
An art room kiln reads 70°F when it is switched on and 430°F forty minutes later, warming at a steady rate. Which equation gives its temperature y after x minutes?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 008.
At which point does the graph of y = x² − 8x + 13 turn?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 009.
One square table seats 4 people. Pushed end to end in a row, 2 tables seat 6 and 3 tables seat 8. How many people can sit at a row of 30 tables?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 006.
Measurement and geometry 10
A faucet drips 1 fluid ounce every 4 minutes. How many cups of water does it waste in one day? (1 cup = 8 fluid ounces)Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 011.
A kite flies on 41 m of string pulled tight. The kite is directly above a spot on level ground 9 m from the child holding the string. Taking the child's hand as ground level, how high is the kite?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 012.
A ramp crosses two parallel floor boards. It makes a 65° angle with the first board. What angle does it make in the matching position at the second board, and why?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 013.
A relay course is 0.75 mile long. How many yards is that? (1 mile = 1,760 yards)Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 011.
A sports field is a 20 m by 8 m rectangle with a half circle on each short end. What is its area, to the nearest whole number?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 012.
A wedge of cheese has two triangular faces and three rectangular faces. Unfolded flat, how many polygons does its net contain, and what is the solid called?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 012.
A wooden cube measures 4 cm on each edge and has a mass of 48 g. What is its density?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 011.
The diagonals of a quadrilateral bisect each other and are perpendicular, but they are not the same length. Which name fits the quadrilateral?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 013.
On a grid map, a scavenger hunt hides a clue exactly halfway between a tree at (−4, 7) and a bench at (6, −1). Where is the clue?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 014.
On a grid, a flag at (2, −1) is enlarged from the origin by a scale factor of 3, and the image is then flipped over the y-axis. Where does the flag's point end up?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 014.
Data, statistics, probability and discrete mathematics 10
A class logs minutes of reading on five days: 30, 32, 35, 38 and 40. A sixth day of 5 minutes is added. What happens to the mean and the median?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 015.
A line of best fit, y = 2.5x + 10, was built from data with x between 0 and 20. A student uses it to predict y when x = 60. What is this use of the line called, and why is it risky?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 016.
A pizza shop offers 6 toppings. How many different two-topping pizzas can be ordered if the order of the toppings does not matter?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 018.
A principal wants to know what all 600 students think of the lunch menu and surveys the first 50 students in the lunch line. What is the main weakness of the survey?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 016.
A spinner is half red and half blue. In 4 spins, what is the probability that red comes up at least once?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 017.
A stem-and-leaf plot shows 6 | 2 5, then 7 | 1 4 4 8, then 8 | 0 3. What is the median of the data?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 015.
Eight people meet, and each person shakes hands once with every other person. How many handshakes take place?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 018.
In a board game, a player rolls two fair dice and moves ahead only when the two numbers differ by exactly 1. What is the probability of moving ahead?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 017.
In a spinner game a player wins $5 with probability 1/4 and otherwise loses $1. What is the expected value of one play?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 017.
Six seedlings measure 3, 7, 7, 8, 10 and 13 cm. Which description of the heights is correct?Our own question, answer worked out twice (2026-10-16). Outline: MTTC Mathematics (Elementary) (089) test objectives, objective 015.
How this list was compiled: Our own questions, written to the test objectives of the Michigan Test for Teacher Certification (MTTC) field 089, Mathematics (Elementary), as the MTTC site prints them (https://www.mttc.nesinc.com/Content/STUDYGUIDE/MI_SG_OBJ_089.htm and the test page https://www.mttc.nesinc.com/TestView.aspx?f=HTML_FRAG/MI089_TestPage.html), read 2026-10-16: 80 multiple-choice questions in 2 hours 30 minutes, passing score 220; Subarea I Mathematical Processes and Number Concepts (objectives 001 to 005, 28%), II Patterns, Algebraic Relationships, and Functions (006 to 010, 28%), III Measurement and Geometry (011 to 014, 22%), IV Data Analysis, Statistics, Probability, and Discrete Mathematics (015 to 018, 22%). This bank holds 12, 12, 10 and 10, with two or three questions for each of the 18 objectives. Every numeric answer was worked out a second time by a script from the numbers in the question; the reasoning items rest on the definitions their explanations state. Licence: Questions, passages, choices and explanations are original work of this site.
How it works
Mathematics (Elementary), field 089, is the exam this MTTC Mathematics Elementary practice test is built on: 44 questions of our own and none from the real test. The page is unofficial and independent of the Michigan Department of Education and Pearson.
Read the full guide
MTTC Mathematics (Elementary) study guide: what field 089 weighs
By the test objectives read October 16, 2026: mathematical processes and number concepts 28%; patterns, algebraic relationships, and functions 28%; measurement and geometry 22%; data analysis, statistics, probability, and discrete mathematics 22%. This bank holds 12, 12, 10 and 10, two or three for each of the 18 objectives. Forty questions in 75 minutes, the timed run here, keeps the real pace of 80 in 150.
Calculator and formulas
A graphing calculator is expected: the test page tells candidates to bring one from its approved list, and says the formulas appear on screen during the test.
The objectives reach past the elementary classroom: linear programming, confidence intervals and the conceptual foundations of calculus are all named.
The test page says field 089 will last be given in 2029 and cannot be used for the Mathematics (5–9) endorsement.
Questions and answers
What is MTTC Mathematics (Elementary) 089?
The Michigan test for the Mathematics (Elementary) endorsement, code EX. Its field number, 089, is often written as 89. Every question on this page follows the objectives the MTTC site publishes for that field.
How many questions are on the MTTC Mathematics (Elementary) test?
Eighty, all multiple-choice, answered on a computer within 2 hours 30 minutes. The appointment runs 15 minutes longer, for a tutorial and a nondisclosure agreement.
What is the passing score for MTTC Mathematics (Elementary)?
A scaled 220, on a scale that runs from 100 to 300. Because the MTTC site derives that scale from the scorable questions answered correctly, a raw count cannot be turned into it, and this page gives no pass or fail.
Is there an official MTTC Mathematics (Elementary) 89 study guide?
The MTTC site publishes one for field 089, in four parts: the program, preparation advice, the objectives this page follows, and sample questions. Registered candidates also get an online practice test, and an interactive version is offered.