Estonian Basic-School Mathematics Exam common mistakes
Estonian Basic-School Mathematics Exam · Understand the traps and how to avoid them.
When multiplying or dividing an inequality by a negative number, the student keeps the inequality sign unchanged (e.g. solving −2x > 6 gives x > −3 instead of x < −3).
The rule is learned as a verbal add-on rather than derived from the number line, so it is forgotten under time pressure; students also over-generalise the 'do the same to both sides' habit and treat sign-flipping as optional.
What to do instead
Have the student verify every inequality answer by testing one number from the claimed solution set and one from outside it in the original inequality; also practise rewriting −2x > 6 as 0 > 6 + 2x and solving without dividing by a negative, so the flip emerges naturally.
When squaring or taking a square root in geometry and algebra, the student drops the ± case or squares each term separately, writing (a + b)² = a² + b² or √(a² + b²) = a + b.
The distributive habit from multiplication is applied to powers and roots, and the identity (a+b)² = a² + 2ab + b² is memorised as a shape rather than checked against a numerical example.
What to do instead
Require a quick numerical disproof check: with a = 3, b = 4, show 7² = 49 but 9 + 16 = 25. Then have the student expand (a+b)² by explicit double distribution until it is automatic, and in geometry always keep the Pythagorean step as c = √(a²+b²) with the sum computed before the root.
In multi-step word problems the student computes a correct intermediate number but answers a different question than the one asked, or leaves the answer without units or with mismatched units (minutes reported as hours, cm² reported as cm).
Attention is consumed by the arithmetic, so the final 'what is asked' check is skipped; unit conversions are treated as decoration rather than as part of the quantity.
What to do instead
Enforce a written three-line plan before calculating: given quantities with units, the operation chain, and the target quantity with its unit. Require the final answer sentence to restate the unit, and include one deliberate conversion step (e.g. 1.5 h = 90 min) in every practice set.
The student confuses perimeter and area formulas, or applies a linear scale factor to an area: doubling the sides of a rectangle is said to double its area, and a triangle's area is computed as base × height without the factor ½.
Formulas are memorised as strings of letters without the underlying picture, and the quadratic effect of scaling is counter-intuitive because length and area are not distinguished conceptually.
What to do instead
Have the student draw the figure, label the dimensions, and physically count unit squares for one example before using the formula. For scaling, compute areas for side lengths 1, 2, 3 and tabulate, so the factor-of-4 and factor-of-9 pattern is seen rather than told.
When reading a graph, the student reads the value at the wrong axis, treats the vertical intercept as the slope, or reads a value off a straight line by eye without checking it satisfies the equation.
Axis labels and scale markings are skimmed, and students do not connect the algebraic form y = mx + c with the visual features, so slope and intercept are not anchored to anything.
What to do instead
Use a fixed reading routine: name the horizontal quantity, name the vertical quantity, state the scale of each axis, then locate the point. Follow every graphical reading with a substitution check into the equation, and practise extracting m and c from three different graphs of the same line drawn at different scales.
The student mishandles negative numbers and order of operations in a single expression, for example evaluating −3² as 9, or computing 2 + 3 × 4 as 20.
The unary minus and the power bind in ways that are not visually obvious, and the left-to-right reading habit of written text competes with the precedence hierarchy.
What to do instead
Require bracketing of every substituted negative number, writing (−3)² versus −(3²) explicitly, and have the student mark the operation order above the expression before computing. Give short daily drills mixing powers, negatives and brackets so precedence becomes automatic.
The student sets up a proportional relationship with the quantities in the wrong order or inverted, producing an answer that is plausible in size but wrong, and does not notice because no estimate was made first.
Proportionality is applied as a template ('cross-multiply') without identifying which quantity corresponds to which, and the absence of a rough mental estimate removes the warning signal.
What to do instead
Have the student write the ratio as a labelled fraction (km over hours, not just numbers), then check that both sides of the proportion have the same labels in the same positions. Require a one-sentence estimate ('about 60 km, so around 1 hour') before solving, and compare the result against it.
In statistics tasks the student reports the mean of a data set as the typical value even when the data are skewed or contain an outlier, or computes the mean of already-grouped data by averaging the class midpoints without weighting by frequency.
Mean, median and mode are learned as three parallel procedures rather than as answers to 'what is typical here', and frequency weighting is an extra step that is easily skipped.
What to do instead
Present a data set with one extreme value and ask which average best represents it, requiring a justification in words. For grouped data, insist on a frequency column and the sum of frequency × value divided by total frequency, with the arithmetic shown.
The student gives a numerical answer with no reasoning, or writes a justification that merely restates the claim ('it is true because the calculation shows it'), so method marks for reasoning and communication are lost.
School practice often rewards the final number, so justification is treated as optional; students also lack sentence frames for mathematical argument and do not know what counts as sufficient.
What to do instead
Train a fixed four-part written solution: what is given, what is used (the rule or formula named), the working, and the conclusion with units. Provide sentence starters such as 'Because ... it follows that ...' and mark practice answers against a checklist of those four parts.
When solving a linear equation the student applies an operation to only one side, or drops a term while moving it across the equals sign, and then does not substitute the answer back to check.
The balance metaphor is understood in principle but the working is compressed into mental steps, so asymmetric operations go unnoticed; checking is seen as extra work rather than part of solving.
What to do instead
Require one operation per line with both sides written out, and make substitution of the found value into the original equation a compulsory final line. For a week, have the student mark each line with what was done to both sides, so asymmetry becomes visible.