Botswana PSLE Mathematics common mistakes
Botswana PSLE Mathematics · Understand the traps and how to avoid them.
When subtracting, the learner subtracts the smaller digit from the larger digit in each column regardless of which number is on top, so 52 − 27 is worked as 7 − 2 = 5 in the ones column and 5 − 2 = 3 in the tens column, giving 35 instead of 25.
The learner has memorised subtraction as 'take away the smaller from the bigger' from early single-digit work and has no procedure for borrowing. Because every column produces a non-negative answer, the method feels safe and is never self-corrected.
What to do instead
Teach regrouping with concrete bundles of ten sticks: exchange one ten for ten ones before subtracting, and record the exchange with a crossed-out digit and a small '1'. Then have the learner check every subtraction by adding the answer back to the number subtracted, so an incorrect 35 + 27 = 62 exposes the error immediately. Practise five regrouping items daily for two weeks.
The learner writes the answer to a division or fraction problem as a decimal or fraction without checking whether the remainder must be interpreted, e.g. answering 4 remainder 1 as '4.1' or giving 4.5 when 4 full buses leave 1 child behind and a fifth bus is needed.
Remainders are learned as a notation to copy rather than as a quantity with meaning. Learners do not connect the written remainder to the real situation described in the word problem.
What to do instead
Use a two-column routine: write the division, then write a sentence stating what the remainder represents in the story. Sort a set of word problems into 'round up', 'round down' and 'give the remainder as a fraction' using the sentence test. Insist on the final answer being stated in words with units.
The learner performs operations strictly left to right in expressions such as 8 + 4 × 3 and gets 36, or works 20 − 6 ÷ 2 as 7, ignoring the order of operations and brackets.
Earlier schooling rewards reading order, and the learner has not yet internalised that multiplication and division bind more tightly than addition and subtraction. Brackets are treated as decoration rather than instruction.
What to do instead
Have the learner underline or circle the multiplication and division parts first, then rewrite the expression with those values computed before adding or subtracting. Use a bracket drill: give the same numbers with and without brackets and compare answers. Require the working to be shown line by line so the order is visible.
When converting between units the learner multiplies where division is needed or vice versa, for example converting 3.5 metres to centimetres by dividing by 100 and getting 0.035 cm, or converting 2500 g to kilograms by multiplying by 1000.
The learner remembers 'times 100' or 'divide by 100' as a rule attached to a pair of units without a sense of whether the number should grow or shrink. There is no mental benchmark for how large a metre or a kilogram is.
What to do instead
Anchor each conversion in a physical referent: a metre stick marked in 100 cm, a 1 kg mass beside a 1000 g pile. Teach the direction test: 'Am I going to a smaller unit? Then I need more of them, so multiply.' Have learners predict whether the answer will be bigger or smaller before calculating, then check the prediction.
The learner reads a clock or calculates a time interval incorrectly, for example stating that a lesson starting at 10:45 and lasting 40 minutes ends at 11:25 rather than 11:25 is correct but writing 10:85, or treating 1 hour 30 minutes as 1.30 hours and adding it as a decimal.
Base-60 time is confused with the base-10 place value system used everywhere else. The learner applies decimal thinking to minutes, and the carry from minutes to hours is missed.
What to do instead
Use a number line marked in five-minute jumps to count on from the start time to the end time, crossing the hour boundary explicitly. Contrast 1 hour 30 minutes with 1.5 hours using a clock face and a fraction of a full turn. Give mixed exercises where some quantities are in minutes and some in decimal hours so the learner must convert deliberately.
When finding the perimeter or area of a compound shape, the learner adds all the labelled side lengths and ignores unlabelled sides, or counts a shared internal edge twice, producing a perimeter that is too small or an area that double-counts a rectangle.
The learner treats perimeter as 'add up the numbers I can see' rather than as a closed boundary. For area, the split into rectangles is done without marking which region belongs to which rectangle.
What to do instead
Require the learner to trace the boundary with a finger or coloured pencil before writing any numbers, and to write in every missing side length first using the property that opposite sides of a rectangle are equal. For area, shade each rectangle a different colour and label its dimensions inside the shape before multiplying. Check by asking whether the total area is plausible compared with a bounding rectangle.
The learner identifies a shape by its orientation or by one feature only, calling a square rotated 45 degrees a diamond and therefore not a square, or labelling any four-sided figure a square because it 'looks regular', and misclassifying a rhombus or trapezium.
Shape names are learned from prototypical pictures in one orientation, so the visual template dominates over the defining properties of equal sides, right angles and parallel sides.
What to do instead
Sort a varied set of cut-out quadrilaterals, including rotated and elongated examples, using a property checklist (four equal sides? four right angles? one pair of parallel sides?). Have the learner justify each classification with a measured or marked property rather than appearance. Include non-examples deliberately.
The learner reads values from a bar chart or pictogram using the top of the bar rather than the axis scale, or ignores a key such as 'one symbol represents 5 learners', reporting 3 learners instead of 15.
The learner looks at the picture as an illustration rather than as a scaled measurement. The key is treated as a caption, and uneven axis numbering is not checked.
What to do instead
Before answering any question, have the learner state aloud what one square or one symbol is worth and what the axis steps are. Practise with charts whose axis starts at zero and steps by 2, 5 or 10, and with pictograms using half symbols. Ask a comparison question as well as a reading question so the scale must be used twice.
The learner finds the mean by adding the values and dividing by the number of different values listed rather than the number of data items, or reports the mode when the mean was asked for, for example giving 5 as the mean of 4, 4, 4, 5, 8 because 4 appears most often.
The three averages are learned as three procedures without distinct meanings, so the labels blur. The learner also miscounts items when values repeat, treating a repeated value as one entry.
What to do instead
Teach the mean as 'share the total equally' using counters shared into piles, and the mode as 'most common', median as 'middle when lined up'. Give mixed questions that name the average required and require the learner to write the definition before calculating. Always have them count the data items explicitly with tally marks.
When continuing a number pattern the learner adds a constant difference even when the pattern is multiplicative or alternates, for example continuing 1, 3, 9, 27 with 29, or continuing 2, 5, 4, 7, 6 with 8 because they saw only the first difference.
The learner checks only the first pair of terms and assumes the rule is uniform. Alternating and two-rule patterns are not tested against all the given terms.
What to do instead
Require the learner to test a proposed rule against every consecutive pair before writing the next term, and to write the rule in words, e.g. 'multiply by 3 each time' or 'add 3, subtract 1, repeat'. Provide patterns with alternating rules and with rules expressed in terms of position, such as 'double the position number plus one', so the general rule is found rather than one step guessed.