Tasmania TCE Everyday Adult Standard - Mathematics common mistakes
Tasmania TCE Everyday Adult Standard - Mathematics · Understand the traps and how to avoid them.
When a percentage discount is followed by another percentage (e.g. 20% off then a further 10% off), the candidate adds the two rates and applies a single 30% discount to the original price.
Everyday language ('20% off plus another 10% off') sounds additive, and the candidate has practised single-step percentage calculations but never chained them, so the mental shortcut of summing rates feels natural.
What to do instead
Always work in money, not rates: take the first discount off the price, write the new price down, then take the second discount off that new price. Check with a quick estimate: a $100 item should land near $72, not $70.
On a GST question, the candidate finds 10% of the GST-inclusive price and calls that the GST component, rather than dividing by 11.
The familiar 'find 10%' move is over-learnt, and the candidate does not distinguish between 'GST added to a pre-GST price' and 'GST already inside a total price', which are two different operations.
What to do instead
Label every amount first as pre-GST or GST-inclusive before calculating. If the price already includes GST, divide by 11 to extract the GST; if it excludes GST, multiply by 0.1 to add it. Practise both directions on the same dollar figure so the difference is visible.
The candidate computes a unit rate (cost per gram, cost per sheet, kilometres per litre) but then compares the wrong pair of numbers, choosing the larger total price as better value or mixing units between products.
Unit-rate questions require holding two quantities in mind and matching units; under time pressure the candidate collapses the comparison into 'bigger number versus smaller number' and skips the unit alignment.
What to do instead
Write the rate with units attached (cents per 100 g, not just a number) before comparing, and convert both products to the same unit and same quantity basis first. State the rule aloud: lower cost per unit is better value, higher distance per litre is better value.
The candidate reads a scale drawing or map without checking the scale statement, measuring the diagram with a ruler and then reporting the drawn length as the real length.
The diagram is visually dominant and the scale is a small caption, so attention goes to the picture; students also confuse '1 cm represents 5 m' with '1:5'.
What to do instead
Before measuring anything, write the scale as a sentence and convert it to a single multiplier (1 cm = 5 m means multiply drawn centimetres by 500). Then convert the answer to sensible units (metres or kilometres) and sanity-check it against a known real-world distance.
The candidate calculates the area of a composite shape by multiplying the overall length by the overall width, double-counting the overlapping region or including a cut-out.
Composite shapes look like rectangles at a glance, and the candidate has not been taught to decompose the figure into non-overlapping parts before applying formulas.
What to do instead
Draw one or two straight split lines on the figure to break it into simple rectangles, label each part's dimensions, compute each area separately and add. For cut-outs, subtract the removed area. Verify the sum of part areas is less than the bounding rectangle's area.
When converting between units of area or volume, the candidate uses the linear conversion factor directly (e.g. treating 1 m² as 100 cm², or 1 m³ as 100 cm³).
The candidate has automatised 'multiply by 100 for metres to centimetres' and applies it to squared and cubed units without realising the factor must itself be squared or cubed.
What to do instead
Convert the linear dimensions first, then square or cube the factor: 1 m = 100 cm, so 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³. Anchor it with a sketch of a 1 m by 1 m square tiled with 100 cm squares.
The candidate computes a mean, median or range from a frequency table or grouped data by averaging the category labels or the frequencies themselves instead of the values.
Frequency tables present two columns of numbers with no obvious 'data list', and the candidate has only practised mean on raw lists, so they grab whichever column is more prominent.
What to do instead
Rebuild the raw data mentally (or write it out) by repeating each value its frequency number of times, then apply the usual formula. For grouped data, use the midpoint of each class as the value and weight it by frequency. Check the mean lies between the smallest and largest values.
The candidate misreads a graph's vertical axis, treating a non-zero baseline or a broken axis as starting at zero, and so overstates or understates differences between categories.
Visual height is read pre-attentively before the axis labels are examined, and truncated axes are common in media graphs the candidate has seen but never been taught to interrogate.
What to do instead
Before interpreting any graph, read both axes in full, note where the vertical axis starts, and check for a break symbol. If the baseline is not zero, describe comparisons as 'relative' and state the baseline in the answer.
On a two-way table or probability question, the candidate divides by the grand total when the question asks for a conditional probability (e.g. 'of the people who chose coffee, what fraction were female?').
The candidate has drilled 'probability = favourable over total' and does not register that the wording restricts the group being considered.
What to do instead
Underline the conditioning phrase ('of those who…', 'given that…') and circle the restricted group's total before dividing. Write the fraction as part/restricted-total, not part/grand-total, and check the answer is plausible for that subgroup.
The candidate sets up a multi-step problem (e.g. a quote comparison with a call-out fee plus an hourly rate) but stops after one operation, reporting an intermediate value as the final answer.
Working memory is overloaded by several given numbers, and the candidate treats the first computed number as the goal rather than tracking what the question actually asked for.
What to do instead
Before calculating, write the question's demand as a one-line target ('total cost for 3 hours, both quotes') and list the steps needed to reach it. After computing, reread the question and confirm the final number answers it, including units and a reasonableness check.