NVO Grade 4 Mathematics common mistakes
NVO Grade 4 Mathematics · Understand the traps and how to avoid them.
When evaluating a multi-step expression such as 3 × (8 + 4) − 6, the student works left to right regardless of grouping symbols, computing 3 × 8 = 24, then 24 + 4 = 28, then 28 − 6 = 22 instead of 30.
Grade 4 is the first year multi-step expressions appear, and students carry over the habit from single-operation arithmetic that reading order equals operation order. They have not yet internalized that parentheses mark a sub-expression to be evaluated as a single quantity.
What to do instead
Have the student circle and evaluate the parenthetical quantity first, writing its value above it (12), then rewrite the whole expression as 3 × 12 − 6 before continuing. Practice by rewriting the same expression with the parentheses moved and comparing results, so the student sees that grouping symbols change the value.
Given a multiplicative comparison such as 'Maya has 7 stickers; Leo has 4 times as many,' the student adds (7 + 4 = 11) or multiplies the wrong pair, rather than computing 4 × 7 = 28 and stating that Leo has 28.
Students conflate 'times as many' with 'more than' because both phrases signal increase. The language of multiplicative comparison is new in Grade 4 and there is no physical cue in the sentence distinguishing a multiplier from an addend.
What to do instead
Teach a two-column routine: identify the referent quantity (the '1 times' amount) and the multiplier (the 'times as many' number), then write an equation of the form multiplier × referent = unknown before computing. Pair each problem with a bar model showing one short bar and one bar that many times longer, and have the student label which bar is which.
When a word problem has an unknown in the middle, e.g. 'Sam had some marbles, won 15, and then had 42,' the student writes 42 + 15 = 57 instead of 42 − 15 = 27.
The student keys on the verb 'won' as a signal for addition without tracking the direction of change relative to the final amount. Signal-word strategies break down whenever the unknown is the starting quantity rather than the result.
What to do instead
Require the student to draw a start-change-result diagram and fill in the known values before choosing an operation, then solve by reasoning backward from the result. Have them check by substituting the answer into the story (27 + 15 = 42) so the operation is validated by the situation, not by a keyword.
The student identifies a number as prime when it is composite, most often calling 1 prime, calling 9 or 15 prime, or calling 51 prime because it 'looks odd.'
Students check only divisibility by 2 (even/odd) and stop, so any odd number appears prime. The special status of 1 as neither prime nor composite is also frequently misremembered.
What to do instead
Institute a divisibility checklist for every candidate: test 2, 3, 5, 7, and 11 in order and stop at the first divisor found. Explicitly drill that 1 has only one factor and is therefore neither prime nor composite, and have students list all factor pairs for numbers like 51 (1×51, 3×17) to confirm compositeness.
When comparing 4,507 and 4,570, the student says 4,507 is greater because '507 has more digits than 57,' or compares the hundreds digit before the thousands digit when the numbers have different lengths.
Students apply the rule 'more digits means larger' learned with whole numbers of different lengths, then overextend it to the digits within a number. They lack a stable place-value comparison procedure.
What to do instead
Have the student write both numbers in a place-value chart aligned on the right, then compare column by column from the left, stopping at the first difference. Reinforce with expanded form: 4,507 = 4,000 + 500 + 7 versus 4,570 = 4,000 + 500 + 70, so the tens column decides.
In a subtraction such as 5,003 − 2,468, the student subtracts the smaller digit from the larger in each column (e.g., 3 − 8 becomes 8 − 3 = 5) or borrows across a zero incorrectly, producing an answer larger than the minuend or off by hundreds.
Regrouping across one or more zeros requires a chain of borrows (from thousands to hundreds to tens to ones) that is hard to hold in working memory, so students substitute a column-by-column 'big minus small' shortcut that always yields a plausible-looking digit.
What to do instead
Use place-value blocks or a written chip diagram to physically decompose one thousand into ten hundreds, then one hundred into ten tens, before subtracting. Require an estimate first (5,000 − 2,500 ≈ 2,500) and have students reject any answer that falls outside the estimate or exceeds the starting number.
The student reads 3/8 as 'three and eight' or compares 3/8 and 3/5 by comparing denominators and concluding 3/8 is larger because 8 is larger than 5.
Whole-number magnitude reasoning is applied directly to the numerals in a fraction. Students have not yet built the idea that a larger denominator means smaller parts of the same whole.
What to do instead
Have students draw two identical bars, partition one into eighths and one into fifths, and shade three parts of each to see visually that 3/5 covers more. State the generalization aloud: for the same numerator, a larger denominator gives smaller pieces, so the fraction is smaller.
When adding 2/3 + 1/4, the student adds numerators and denominators to get 3/7, or adds numerators and keeps one denominator to get 3/3 or 3/4.
The additive procedure for whole numbers is transferred symbol by symbol to fractions. Students do not treat the denominator as a unit size that must be made common before counts can be combined.
What to do instead
Return to a length or area model: place a 2/3 bar and a 1/4 bar end to end and show that the total is close to 1, which 3/7 is not. Then partition both bars into twelfths so the student sees 8/12 + 3/12 = 11/12, and require the written step of renaming to a common denominator before any addition.
On a line plot of measurements in fractions of a unit, the student counts the X marks above a value and reports that as the measurement, or reads the scale by counting tick marks rather than interpreting the labeled intervals, giving a total like 5 instead of 5/8.
The student treats the plot as a frequency tally without connecting each mark to the value on the axis, and misreads an axis whose labels are fractions rather than whole numbers.
What to do instead
Have the student state the value of each tick aloud before counting, then record data as an explicit list (1/8, 3/8, 3/8, 5/8...) and transfer it to the plot. For questions about totals, require the multiplication step (number of marks × the axis value) to be written out rather than done mentally.
When finding the area of an L-shaped figure, the student multiplies the two longest outside dimensions and reports the area of the enclosing rectangle, or adds side lengths instead of multiplying them.
Students do not decompose composite figures into non-overlapping rectangles, and they confuse perimeter and area procedures because both are introduced together and both use the given side lengths.
What to do instead
Require the student to draw a single straight cut that splits the figure into two rectangles, label each rectangle's dimensions, compute each area, and add them, then verify that the two parts do not overlap and together cover the whole shape. Contrast with a perimeter calculation on the same figure to keep the two procedures distinct.
The student classifies a square as 'not a rectangle' or a rhombus as 'not a parallelogram,' and sorts shapes by visual appearance (e.g., a tilted square is not a square) rather than by properties.
Students form prototype-based categories in which a rectangle must be long and a square must sit on a flat side. The inclusive hierarchy of quadrilaterals, in which a square is a special rectangle, contradicts everyday naming.
What to do instead
Have students test shapes against a written property checklist (four right angles? opposite sides equal and parallel?) rather than against a picture in their head, and rotate shapes before judging. Build a hierarchy diagram showing that squares sit inside rectangles and rhombuses inside parallelograms, and ask 'must be true' versus 'could be true' questions.