Ontario MPT common mistakes
Ontario MPT · Understand the traps and how to avoid them.
On a fraction-division item, computes 3 ÷ 1/2 as 1.5 (multiplying by 1/2) or inverts the 3 instead of the 1/2, and cannot say whether the quotient should be larger or smaller than 3.
The candidate learned 'keep-change-flip' as a string of symbols with no referent, so under time pressure the operation and the inverted quantity are chosen by habit, and the magnitude check that would catch the error is never performed.
What to do instead
Before computing, restate the expression as a measurement question ('how many halves are in 3?') and predict whether the quotient is bigger or smaller than the dividend. Draw a number line or bar model split into halves to confirm. Practise mixed sets of multiplication and division by fractions, writing the prediction next to each answer.
Evaluates -3 - (-5) as -8, subtracting the magnitudes and keeping the negative sign, and answers -7 + 4 as -11.
The whole-number subtraction rule 'larger minus smaller, keep the sign of the larger' is over-generalised to integers, and the double-negative is read as 'more negative' rather than as the opposite of a negative.
What to do instead
Rewrite every integer subtraction as addition of the opposite first: -3 - (-5) = -3 + 5. Verify on a vertical number line or with a temperature/elevator context. Do 10 quick items where the first written step must be the rewrite, not the answer.
Evaluates -2^2 as 4 and 2 + 3 x 4^2 as 400, working strictly left to right through the expression.
Left-to-right reading habit from prose, plus the belief that a minus sign is part of the base; exponent notation is read as 'multiply by 2 twice' rather than 'base times itself'.
What to do instead
Before any computation, label each operation with its precedence order (brackets, exponents, x/÷, +/-) directly above the expression, and circle the base including or excluding the sign. Contrast (-2)^2 with -2^2 in writing and explain the difference aloud.
In a scaling question (recipe for 4 servings scaled to 12), adds the same amount to each ingredient instead of tripling, or sets up a ratio as part-to-part when the question needs part-to-whole.
Additive reasoning is developmentally prior and default under time pressure; the 'times as many' comparison is not made explicit by the wording, so the candidate falls back to difference thinking.
What to do instead
Force a unit-rate step: build a ratio table with a 'per 1' column before answering, and ask 'how many times as many?' explicitly. For part-whole items, label each quantity in the table as part or whole before forming the ratio.
Expands -(x - 3) as -x - 3, and solves 2(x + 3) = 10 by subtracting 3 from both sides before dividing by 2.
The negative sign is treated as a decoration rather than a factor of -1, and the order of inverse operations is chosen by what looks easiest rather than by reversing the order of operations.
What to do instead
Rewrite every subtraction of a bracket as multiplication by -1 before distributing. After solving, substitute the answer back and check both sides, and for expansion substitute x = 1 into the original and the expanded form to see whether they agree.
Converts 3 m^2 to cm^2 by multiplying by 100, giving 300 cm^2, and similarly converts volumes using the linear factor once.
The linear conversion factor is memorised as a number rather than derived from the relationship between the units, so the squaring of the factor is invisible.
What to do instead
Draw a 1 m by 1 m square subdivided into 100 cm by 100 cm and count the small squares to establish 1 m^2 = 10 000 cm^2, then convert one dimension at a time. Keep a reference card of area and volume conversion factors derived, not memorised.
On a 'what error is this student making?' item, selects the mathematically correct response (or a plausible-sounding misconception) instead of the error the work actually shows.
The candidate's reflex is to solve the problem rather than to read the student's steps, and the answer choices are written to make the correct mathematics look attractive.
What to do instead
Cover the answer choices, reproduce the student's work line by line, and mark the first line where it diverges from a correct solution. Name that divergence in words before uncovering the options, then match. Do this on 15 items in a row until the routine is automatic.
Asked which task best assesses conceptual understanding, chooses one answerable by a memorised procedure (e.g., 'calculate 3/4 x 2/3') rather than one requiring an explanation of why (e.g., 'explain why multiplying by a fraction less than 1 gives a product smaller than the starting number').
Candidates judge items by whether they are clear and easy to mark rather than by the cognitive demand the stem specifies; procedure and concept are treated as the same thing.
What to do instead
Before reading the options, classify the stem as procedural, conceptual or problem-solving, and write what evidence would show that kind of understanding. Then eliminate any option that can be completed by a rote rule with no reasoning.
Uses accommodation and modification interchangeably, e.g., describing a student who uses a calculator or has extra time as having a 'modified' program, and describing a student working on below-grade expectations as 'accommodated'.
The two terms are usually encountered in policy documents rather than in practice, and both are casually used to mean 'support' in everyday school talk.
What to do instead
Fix the distinction as a single sentence: accommodation changes how the student demonstrates learning, modification changes what or how much is expected. Sort a list of ten supports into the two columns and check that no item changes the grade-level expectation, then apply that test to each option.
Plans differentiation by lowering the numbers (2-digit instead of 4-digit multiplication) or by choosing an engaging game, while the stated expectation is unchanged.
Differentiation is associated with 'making it easier' and with engagement, so the candidate changes the difficulty or the fun level instead of changing access to the same expectation.
What to do instead
For each stem, write the expectation verbatim, then check that every chosen strategy keeps it intact while varying representation, entry point, or scaffolding. If the option removes the grade-level content, eliminate it.