Free Ontario Mathematics Proficiency Test Practice Questions

Sample Practice Questions

Try these 10 sample questions from the Ontario Mathematics Proficiency Test practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1Which sum gives the standard place-value expansion of 608,407?

   1. A.600,000 + 8,000 + 400 + 7Correct answer: A
   2. B.600,000 + 800 + 400 + 7
   3. C.600,000 + 8,000 + 40 + 7
   4. D.600,000 + 8,000 + 400 + 70

   Explanation: The curriculum notes that “A number can be represented in expanded form” to show place value. In 608,407, the nonzero digits represent 600,000, 8,000, 400 and 7, totalling 608,407. B places the 8 in the hundreds instead of the thousands; C places the 4 in the tens instead of the hundreds; D places the 7 in the tens instead of the ones.

   Reference: Ontario Curriculum, Grades 1–8 Mathematics: Grade 6 Number Sense — B1.1, Teacher supports, expanded form

2. 2In Grade 9 mathematics, what is the purpose of descriptive feedback in relation to a learning goal?

   1. A.Provide students with precise information needed to reach the goal.Correct answer: A
   2. B.State the intended learning that the lesson is designed to address.
   3. C.Describe the criteria by which success will be recognized.
   4. D.Select a problem to introduce the intended mathematical concept.

   Explanation: The curriculum states, “The use of descriptive feedback involves providing students with the precise information they need in order to reach the intended learning goal.” Thus A is correct. B describes the learning goal, C describes success criteria, and D describes selecting a problem-solving task; these are different instructional functions.

   Reference: Ontario Curriculum, Grade 9 Mathematics: Some Considerations for Program Planning — Instructional Approaches in Mathematics, High-Impact Practices

3. 3In the number 44,000, how does the value of the 4 in the ten-thousands place compare with the value of the 4 in the thousands place?

   1. A.It is 10 times as great.Correct answer: A
   2. B.It is 100 times as great.
   3. C.It is the same value.
   4. D.It is one-tenth as great.

   Explanation: Ontario's curriculum states that “each column to the left has a value that is 10 times as great as the one to its right.” The two 4s represent 40,000 and 4,000; 40,000 ÷ 4,000 = 10. B incorrectly uses a two-place factor, C ignores place value, and D reverses the comparison.

   Reference: Ontario Curriculum, Grades 1–8 Mathematics: Grade 4 Number Sense — B1.7, Sample tasks, decimal place value

4. 4Which classroom practice most directly develops assessment as learning?

   1. A.Students monitor their progress and identify their next learning steps.Correct answer: A
   2. B.The teacher summarizes completed learning in a final report.
   3. C.The teacher uses a diagnostic result to plan a new lesson.
   4. D.Students receive a final grade for a completed assignment.

   Explanation: Growing Success says that teachers engage in assessment as learning by helping students “set individual goals, monitor their own progress, determine next steps, and reflect on their thinking and learning.” A develops this student self-monitoring. B and D summarize or report achievement, while C uses evidence to guide the teacher's next instruction.

   Reference: Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools — Chapter 4, p. 28, Policy

5. 5Among these four fractions with denominator 11, which is greatest?

   1. A.3/11
   2. B.7/11Correct answer: B
   3. C.5/11
   4. D.2/11

   Explanation: The curriculum says, “If two fractions have the same denominator, then the numerators can be compared.” All denominators are 11, and 7 is greater than 5, 3 and 2. Thus 7/11 is greatest; each other choice has a smaller numerator with the same positive denominator.

   Reference: Ontario Curriculum, Grades 1–8 Mathematics: Grade 6 Number Sense — B1.3, Teacher supports, comparing fractions

6. 6A student's organization habits are not part of a particular curriculum expectation. Under Growing Success, how should the teacher normally handle their evaluation when determining the student's grade?

   1. A.Evaluate the habits separately from the subject grade, where possible.Correct answer: A
   2. B.Include the habits in the grade as part of the curriculum expectation.
   3. C.Include the habits in the grade only during final evaluation.
   4. D.Include the habits in the grade when reporting progress to parents.

   Explanation: Growing Success states, “To the extent possible, however, the evaluation of learning skills and work habits, apart from any that may be included as part of a curriculum expectation in a subject or course, should not be considered in the determination of a student’s grades.” The stem excludes the curriculum-expectation exception. B assumes the excluded condition, while C and D add grade contributions for timing or reporting that do not change the stated separation.

   Reference: Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools — Chapter 2, p. 10, Policy

7. 7Which of these integers lies farthest left on the number line?

   1. A.−4
   2. B.−9Correct answer: B
   3. C.−2
   4. D.−6

   Explanation: The curriculum states, “When comparing negative integers, the least number is the negative integer with the greater magnitude.” The magnitudes are 4, 9, 2 and 6, so −9 is least. The other integers have smaller magnitudes and lie to its right on the number line.

   Reference: Ontario Curriculum, Grades 1–8 Mathematics: Grade 6 Number Sense — B1.3, Teacher supports, comparing integers

8. 8Which approach does Learning for All describe as providing broad principles for planning instruction and learning environments for a diverse group of students?

   1. A.Universal Design for LearningCorrect answer: A
   2. B.Differentiated instruction
   3. C.The tiered approach to intervention
   4. D.Assessment for learning

   Explanation: Learning for All states that “UDL provides teachers with broad principles for planning instruction and designing learning environments for a diverse group of students.” B addresses specific skills and difficulties; C organizes interventions of increasing intensity; D gathers information to improve learning. These serve related but different purposes.

   Reference: Learning for All: A Guide to Effective Assessment and Instruction — Instructional Approaches, pp. 12–13

9. 9Which of the following positive fractions has the smallest value?

   1. A.5/8
   2. B.5/12Correct answer: B
   3. C.5/6
   4. D.5/4

   Explanation: The curriculum states, “If two fractions have the same numerators, then the denominators can be compared.” With equal positive numerators, larger denominators give smaller parts; 12 is the largest denominator. Therefore 5/12 is smaller than 5/8, 5/6 and 5/4.

   Reference: Ontario Curriculum, Grades 1–8 Mathematics: Grade 6 Number Sense — B1.3, Teacher supports, comparing fractions

10. 10Which approach uses frequent progress monitoring and assessment data to plan interventions of increasing intensity?

    1. A.Universal Design for Learning
    2. B.Differentiated instruction
    3. C.The tiered approach to interventionCorrect answer: C
    4. D.Assessment of learning

    Explanation: Learning for All says the tiered approach “is based on frequent monitoring of student progress and the use of assessment data” to plan interventions of increasing intensity. A provides broad accessible design principles, B adapts instruction to learners' differing characteristics, and D summarizes learning achieved.

    Reference: Learning for All: A Guide to Effective Assessment and Instruction — Instructional Approaches, p. 24, The Tiered Approach