NL Grade 6 Math common mistakes
NL Grade 6 Math · Understand the traps and how to avoid them.
When dividing a whole number by a fraction such as 3 ÷ 1/4, the student divides by the numerator instead of multiplying by the reciprocal, giving 3/4 or 12/4 instead of 12.
Students memorize 'invert and multiply' as a chant without understanding why division by a number less than 1 yields a larger quotient, so they reach for the familiar operation of dividing by the top number.
What to do instead
Have the student model the problem with fraction strips or a number line: count how many 1/4 pieces fit in 3 wholes, then write the matching equation 3 × 4 = 12 and connect it to 3 × 4/1. Require a sketch before every division-by-fraction computation until the reciprocal rule is anchored in the model.
When comparing or ordering decimals such as 0.6 and 0.58, the student says 0.58 is larger because 58 is greater than 6, or orders by counting digits after the decimal point.
Students transfer whole-number place-value reasoning ('more digits means bigger') to decimals and do not treat tenths as the largest decimal place value.
What to do instead
Have the student write both numbers with the same number of decimal places (0.60 and 0.58) and place them on a marked number line between 0 and 1. Practise with grids shaded to hundredths so the student sees 60 hundredths exceeds 58 hundredths before comparing symbols.
When adding or subtracting fractions with unlike denominators, the student adds the numerators and the denominators (1/2 + 1/3 = 2/5) or adds numerators while keeping one original denominator.
The student treats numerator and denominator as independent whole numbers rather than as parts of a single quantity, and has not internalized that the units must match before combining.
What to do instead
Use fraction strips or two same-size rectangles divided into halves and thirds to show that 1/2 and 1/3 are different-sized pieces. Have the student rename both with the least common denominator and state aloud, 'I have 3 sixths plus 2 sixths, so 5 sixths,' writing the common unit each time.
When finding a percent of a quantity, such as 15% of 60, the student multiplies 15 × 60 = 900 and reports that as the answer, or computes 15/60.
The student recognizes 'of' as multiplication but omits the division by 100 that converts the percent to a decimal or fraction, because percent has not been connected to hundredths.
What to do instead
Build a 10-by-10 hundredths grid and shade 15 squares to show 15% means 15 out of 100. Then have the student write 15% as 0.15 and as 15/100 before multiplying, and check reasonableness: 15% of 60 must be less than 60, closer to 9.
When writing or extending a pattern rule, the student describes the relationship recursively ('add 3 each time') when asked for a rule relating term number to term value, or misidentifies the starting term as term 0.
Students see the sequence as a running list rather than a function of position, and they count terms from zero or from the first visible number without checking which term number the question asks about.
What to do instead
Have the student build a two-column table with term number and term value, then test a rule such as 'multiply the term number by 3 and add 1' against at least three rows. Require the student to state the rule in words and verify it by predicting a far term (e.g., term 20) and checking by repeated addition.
When solving a one-step equation such as x + 7 = 12, the student adds 7 to both sides or performs the operation written rather than its inverse, producing x = 19.
The student focuses on the visible symbol instead of the goal of isolating the variable, and has not practised the balance model enough to choose the inverse operation deliberately.
What to do instead
Use a balance-scale diagram and have the student ask, 'What is being done to x, and what undoes it?' before writing anything. Require substitution of the answer back into the original equation as a routine final check, and give mixed add/subtract equations so the inverse must be chosen each time.
When calculating the area of a triangle, the student multiplies base × height and stops, omitting the division by 2, or uses a slanted side as the height.
The rectangle formula is overlearned and applied by default, and students do not distinguish the perpendicular height from a side length that merely looks vertical.
What to do instead
Have the student place two congruent triangles together to form a parallelogram or rectangle, showing that one triangle is half the area. Require drawing and labelling the perpendicular height with a right-angle square on every diagram before computing, and include triangles drawn in non-standard orientations.
When converting between units such as 3.5 m to centimetres, the student multiplies by 1000 or divides by 100, moving the decimal point the wrong number of places or the wrong direction.
Students memorize 'move the decimal' without attaching it to the metric prefixes and their relative sizes, and they do not check whether the answer should be larger or smaller than the starting number.
What to do instead
Have the student build a metric staircase (km, m, cm, mm) and state the direction and factor aloud before computing. Add a magnitude check: converting to a smaller unit must give a larger number, so 3.5 m must become more than 3.5 cm.
When reporting the mean of a data set, the student divides by the number of distinct values rather than the number of data points, or reports the median or mode when the mean was requested.
The three measures of centre are taught together and their names and procedures blur; the student also forgets that repeated values each count as separate data points.
What to do instead
Have the student list every data point, including duplicates, cross each off while adding, and write 'sum ÷ number of points' explicitly before dividing. Give a set with a repeated value and ask for all three measures side by side so the differing procedures are contrasted in one task.
When reporting probability, the student writes a ratio of favourable outcomes to favourable outcomes, or gives a count such as '3' instead of a probability between 0 and 1, for example saying the probability of rolling an even number on a die is 3.
The student counts successes without forming the part-to-whole relationship, and has not internalized that probability compares favourable outcomes to all equally likely outcomes.
What to do instead
Have the student list the full sample space first (1 to 6), circle the favourable outcomes, and write the probability as favourable over total, then check that the value lies between 0 and 1. Repeat with spinners and bags of coloured counters so the whole is always identified before the part.