NB Francophone G3 Math common mistakes
NB Francophone G3 Math · Understand the traps and how to avoid them.
When comparing or ordering whole numbers up to 1000, the student compares digit by digit from the leftmost digit but ignores place value, so they claim 89 > 120 because 8 > 1, or order 306 before 63 because 3 comes before 6.
The student treats numerals as strings of symbols rather than quantities and has not internalized that the number of digits (hundreds/tens/ones) determines magnitude first, then digits are compared place by place.
What to do instead
Have the student build each number with base-ten blocks or place-value cards and physically compare the hundreds, then tens, then ones; practice the rule 'fewest digits = smallest, same digits = compare from the left' with sets like 63, 306, 360, 630 until the comparison is automatic.
When subtracting a multi-digit number, the student subtracts the smaller digit from the larger in each column regardless of position, so 402 − 178 is computed as (4−1)(8−0)(8−2) = 386, or borrows without reducing the next column.
The student has memorized a column procedure but does not understand regrouping as exchanging one ten for ten ones, so they avoid the unfamiliar 'borrow' step by flipping the subtraction.
What to do instead
Demonstrate regrouping with physical bundles of ten straws being untied, do three or four examples fully with manipulatives, then require the student to say aloud 'I exchanged one ten for ten ones' at each regroup; follow with error-analysis tasks where they must find and correct a flipped-column subtraction.
The student interprets multiplication as repeated addition only for equal groups and cannot apply it to arrays or division, so they solve 4 × 6 by counting on fingers and answer 24 ÷ 6 by guessing or adding 6 repeatedly until reaching 24 without tracking the number of groups.
The operations were taught as separate procedures rather than as related inverse actions on the same array, so the student lacks a mental model linking them.
What to do instead
Use a single array (e.g., 4 rows of 6) to derive all four facts 4×6=24, 6×4=24, 24÷4=6, 24÷6=4, and have the student build and name the four facts for several arrays before practicing bare number sentences.
When comparing simple fractions with the same numerator (e.g., 1/3 vs 1/4) or same denominator, the student compares the denominators as if they were whole numbers, stating 1/4 > 1/3 because 4 > 3, or 1/5 > 2/5 because 1 < 2 is ignored and 5 is used.
The student applies whole-number comparison rules to fraction notation without understanding that the denominator names the size of the parts, so a larger denominator means smaller parts.
What to do instead
Have the student fold or shade identical paper strips into thirds and fourths and physically compare the shaded regions, then state the rule 'more parts = smaller parts when the numerator is the same'; follow with side-by-side bar diagrams for each comparison before moving to symbols.
The student relates fractions to decimals incorrectly, writing 1/2 as 0.2 or 1/10 as 0.1 but 3/10 as 0.3 while also writing 1/4 as 0.4, treating the denominator as the decimal digit rather than computing tenths and hundredths.
The student has seen 'tenths' written as one decimal place but overgeneralizes the pattern to all fractions, lacking the idea that a decimal names a fraction with denominator 10 or 100.
What to do instead
Use a hundred grid or metre stick where tenths are marked; have the student shade 3/10 and read 'three tenths = 0.3', then shade 1/4 and see it is 25 hundredths = 0.25, building a reference table of halves, fourths, and tenths as decimals.
When extending a growing pattern such as 2, 5, 8, 11, the student adds the previous term to itself or copies the last difference incorrectly, or when given a repeating pattern of shapes, they continue it by restarting the core unit at the wrong point (e.g., ABAB continued as ABB).
The student looks only at the most recent term instead of identifying the rule (add 3, or repeat the core AB), and has not been taught to state the rule explicitly before extending.
What to do instead
Require the student to write the rule in words first ('add 3 each time' or 'the core is AB') and to circle the repeating core; then have them extend at least three more terms and verify by checking the difference between consecutive terms.
When solving a simple equation with an unknown such as 7 + □ = 12, the student adds the two given numbers (19) or always subtracts the smaller from the larger without regard to the operation, and for □ − 4 = 9 answers 5 by subtracting instead of adding.
The student treats the equals sign as 'do the operation' rather than 'the two sides balance', and lacks a strategy for undoing an operation.
What to do instead
Model each equation on a balance scale or with counters in two rows, cover the unknown, and ask 'what must be on this side to balance?'; teach the inverse-operation routine (undo + with −, undo − with +) and check by substituting the answer back into the equation.
When measuring, the student chooses an inappropriate unit or tool (measuring a pencil in metres, a water bottle in grams, a room in centimetres) or reads a ruler from the end of the ruler rather than from the zero mark, producing lengths off by the ruler's margin.
The student has not built benchmarks for the size of a metre, kilogram, and litre, and has not been taught that measurement starts at zero on the scale.
What to do instead
Establish reference benchmarks (a metre is about a door width, a kilogram about a bag of sugar) and have the student sort objects by which unit fits; for rulers, practice measuring objects placed not at the end and confirm by counting the centimetre intervals rather than reading the numeral at the tip.
When finding the perimeter of a rectangle, the student counts the squares inside the shape (area) or adds only two sides (length + width) instead of all four, and when finding the perimeter of an irregular polygon they omit a side.
The student confuses perimeter with area and does not have a reliable procedure of tracing the boundary and marking each side as it is added.
What to do instead
Have the student trace the outline with a finger and mark each side with a tick as it is added, then write the sum of all side lengths; contrast with a shaded interior to distinguish perimeter from area, and use a rectangle to show perimeter = length + width + length + width.
When identifying 3-D objects, the student names a shape by its appearance rather than its attributes, calling a cube a square or a cylinder a circle, and when counting faces, edges, or vertices they count only visible ones, reporting a cube has 3 faces.
The student has not separated 2-D faces from the 3-D object and does not systematically count hidden parts, relying only on what is shown in a drawing.
What to do instead
Provide a physical cube, cylinder, and pyramid; have the student count faces by touching each one, then build a table of faces/edges/vertices and compare with the 2-D shape that forms each face; explicitly discuss hidden faces on a drawing.
When interpreting a pictograph or bar graph, the student counts the symbols or bar height as one each without applying the key (each symbol = 2 or 5), or reads the bar height to the nearest whole line when the bar ends between lines, and answers 'how many more' by giving the larger total instead of the difference.
The student reads the picture literally and has not been taught to check the key and axis scale first or to translate comparison questions into subtraction.
What to do instead
Before answering any question, require the student to state the key and the scale aloud; practice with keys of 2 and 5 and bars ending between gridlines, and for comparison questions have them write the subtraction sentence before computing.
When judging likelihood, the student says an event is 'impossible' merely because it is unlikely, or claims a coin that landed heads four times is 'due' for tails, and describes all non-certain events as '50-50'.
The student conflates probability with personal expectation and has no experience with the range from impossible through likely to certain, or with independent trials.
What to do instead
Sort events on an impossible–unlikely–likely–certain line with justification, then run repeated trials (e.g., 20 coin flips) and record results to show that past outcomes do not change the next flip while long-run frequencies approach the expected value.