Ontario MPT No-Calculator Practice: Five Number Sense Questions

On the Ontario Mathematics Proficiency Test (MPT), the first five scored mathematics questions assess Number Sense without a calculator. EQAO provides an on-screen calculator for the other 45 scored mathematics questions. If you want to practise that opening block, put your calculator away and try the five questions below. Then use the worked answers to identify the first step you would change.

The EQAO MPT Framework, revised August 2026, places those five questions in the Knowledge and Understanding category. Its Number Sense blueprint covers operations with whole numbers, integers, decimals and fractions, as well as whole-number place value, exponents, square roots and order of operations. EQAO publishes the skills for Number Sense without specifying which five skills will appear in any sitting. The five below are original OpenExamPrep practice questions, selected to help you find gaps across that range.

Try five Ontario MPT questions without a calculator

Work them out before you read the key. For each answer, write one line that shows what you did first: a common unit, an operation, a rewrite or a quick estimate. Mark guesses with a question mark, even if you feel fairly sure. Leave the timer off on this first run; the useful part is finding out which steps are hard to reproduce.

1. Which is the expanded form of 408,205?

• A. 400,000 + 8,000 + 200 + 5
• B. 400,000 + 80,000 + 200 + 5
• C. 400,000 + 800 + 200 + 5
• D. 400,000 + 8,000 + 20 + 5

2. What is $-18 \div 3 \times 2 + 5$?

• A. 2
• B. 17
• C. −7
• D. −12

3. What is $3.06 - 0.478$?

• A. 2.628
• B. 2.592
• C. 3.538
• D. 2.582

4. What is $\frac{7}{8} \div \frac{21}{16}$ in simplest form?

• A. $\frac{147}{128}$
• B. $\frac{2}{3}$
• C. $\frac{3}{2}$
• D. $\frac{1}{3}$

5. What is $\sqrt{81} - 2^3 + (-2)^2$?

• A. 5
• B. −3
• C. 7
• D. 1

Worked answers: find the first step that went wrong

1. A — Keep the digit in its original place

The 4 is in the hundred-thousands place, the 8 is in the thousands place, the 2 is in the hundreds place and the 5 is in the ones place. The zero in the ten-thousands place tells you to skip that term; it does not move the 8 into that place. The zero in the tens place works the same way. Option B would build 480,205, which is already too large before you check the hundreds.

Quick check: Reassemble the number in chunks: 400,000 plus 8,000 is 408,000; the last three digits must therefore come from 205. If you missed this, name the place of each nonzero digit before you write its value. Try 507,032 next: the 7 contributes 7,000 and the 3 contributes 30.

2. C — Read division and multiplication from left to right

Divide first because division comes first in this expression. Then multiply: $-18 \div 3 = -6$ and $-6 \times 2 = -12$. Finally add 5 to get −7. If you got 2, you probably treated $3 \times 2$ as a single divisor. The expression would need brackets around that product for that to be correct.

Quick check: After the multiplication you are at −12, so adding 5 should move you five places toward zero. If the order caused the miss, work $24 \div 6 \times 2$ and $24 \div (6 \times 2)$ side by side. They give 8 and 2. If the sign caused it, go back to the two intermediate results: both should be negative.

3. D — Align place values before subtracting decimals

Write 3.06 as 3.060 so you can align the thousandths in both quantities. You can break the subtraction into two steps: subtract 0.400 to get 2.660, then subtract the remaining 0.078 to get 2.582. Option C gives the result of adding 0.478, so you can rule it out without doing any regrouping: a positive quantity was subtracted and the result should be below 3.06.

Quick check: $2.582 + 0.478 = 3.060$. An estimate also helps catch a misplaced decimal: 3.06 minus about 0.5 should land near 2.56. If regrouping is where you got stuck, use the same split on $4.2 - 0.367$. Write 4.200 first; the answer is 3.833.

4. B — Take the reciprocal of the divisor

Keep $\frac{7}{8}$ as written and replace division by $\frac{21}{16}$ with multiplication by $\frac{16}{21}$. In $\frac{7}{8} \times \frac{16}{21}$, cancel 16 against 8 and 7 against 21 to get $\frac{2}{3}$. Option A is the result of multiplying the two original fractions; it leaves the divisor unchanged.

Why does the reciprocal work? Division asks what number, multiplied by $\frac{21}{16}$, produces $\frac{7}{8}$. Multiplying both sides by $\frac{16}{21}$ undoes that multiplication. If you forget the shortcut, you can also rewrite $\frac{7}{8}$ as $\frac{14}{16}$: you are comparing 14 sixteenths with 21 sixteenths, so the quotient is $\frac{14}{21} = \frac{2}{3}$.

Quick check: The divisor is greater than 1, so the positive quotient must be smaller than $\frac{7}{8}$. Check the exact answer by multiplying $\frac{2}{3}$ by $\frac{21}{16}$: you get $\frac{7}{8}$ back. If you flipped the wrong fraction, write the divisor in words on your next attempt: “I am dividing by twenty-one sixteenths.”

5. A — Evaluate each root or power before you combine terms

$\sqrt{81} = 9$, $2^3 = 8$ and $(-2)^2 = 4$. That leaves $9 - 8 + 4 = 5$. Option B results if you treat the last term as −4. The brackets make the negative number the base, so the square is $(-2) \times (-2)$, which is positive.

Quick check: Compare $(-3)^2$ with $-3^2$ on paper. The first is 9 because the negative sign is inside the squared base. The second is −9 because the square applies to 3 before the minus sign is applied. This distinction also helps you keep the subtraction in front of $2^3$ separate from the exponent.

Use your first line of working to choose your next drill

Count an item as secure if you can explain its first step and reproduce it on a fresh question. A correct guess still gives you something to work on. If you got several wrong, start with the earliest step that failed, since a mistake there can make later calculations look worse than they are.

For example, suppose you picked 2 on Question 2 and wrote “multiply 3 by 2 first.” Write your correction as a short rule you can use again: “At the same priority, do the operation that comes first from the left, unless brackets group terms.” Then try the pair from the answer key. On another day, try a fresh pair: $36 \div 9 \times 3$ and $36 \div (9 \times 3)$. The results are 12 and $\frac{4}{3}$. If you can explain why they differ before calculating, you have fixed the step that produced the original mistake.

Use the whole numbers, integers and order of operations lesson for Questions 1–2, the decimal operations lesson for Question 3, the fraction operations lesson for Question 4, or the exponents lesson for Question 5. After reviewing, use the free Ontario MPT practice bank to find fresh questions on the same skill. Mix in a question you previously got right so you have to decide which method applies.

Rehearse reviewing the section before you submit

Once you can do a fresh set without notes, open the official EQAO MPT Practice Tests. EQAO offers two 75-question practice tests. Its practice instructions let you review answers within a section before submitting; once you submit and move on, you cannot return to that section. Rehearse that decision: use the review to confirm any answer you were unsure of, then submit. For an arithmetic question, check the sign, the size of the result or the inverse operation, whichever is most likely to catch your error.

The five scored no-calculator questions are only part of the mathematics component. The framework allocates 16 scored mathematics questions to Number Sense in total. That leaves 11 scored Number Sense questions on which you can use the calculator, so keep checking your setup and estimating even when a calculator is available. The framework separately lists four unscored field-test items that candidates cannot distinguish from the others. Give each question your best attempt.

After the practice test, compare the mistakes you made with and without the calculator. If you used the wrong operation in both settings, practise choosing the operation before entering anything. If your setup was right but only your handwritten calculation was wrong, repeat the short drill with new numbers. Keep these two kinds of errors separate so you can see which habit is improving.

There is no separate passing mark for the five-question block. The EQAO FAQ requires at least 70% in mathematics content and at least 70% in pedagogy on the same attempt. Use this drill to make your next practice session more specific; use a full practice test to see how you manage both components. For your next topic, see the Ontario MPT format and formula-sheet guide or review assessment and evaluation under Growing Success for the pedagogy component.