Learning

PSLE Math

Interactive notes for every PSLE Math topic — master the model method, then own the heuristics your marker rewards.

36 interactive notes · 4 themes · Free

The Model Method

14 notes

$A friendly flat-vector scene of a long bar split into coloured parts, with a few stacked counting cubes and a pencil, in IllumiTutor navy and amber on an off-white background.$ The Model Method

The Part-Whole Model

The foundation of the model method — drawing one bar, splitting it into parts, and finding the value of one unit to unlock the answer.

$A friendly flat-vector scene of two stacked bars of different lengths with a bracket marking the difference, beside a few counting cubes, in IllumiTutor navy and amber on an off-white background.$ The Model Method

The Comparison Model

Drawing two bars side by side to picture the difference, and using "times as many" to find the value of one unit.

$A friendly flat-vector scene of two bars labelled before and after with an arrow showing a piece moving from one to the other, beside a couple of coins, in IllumiTutor navy and amber on an off-white background.$ The Model Method

The Before-and-After Model

Drawing a before state and an after state, and spotting when a transfer keeps the total unchanged.

$A friendly flat-vector scene of two bars of different lengths with the same gap marked at both ends, beside a small calendar and birthday candle, in IllumiTutor navy and amber on an off-white background.$ The Model Method

The Constant-Difference Model

Why the gap between two ages never changes, and how to use that fixed difference to crack age problems.

$A friendly flat-vector scene of three stacked bars of different lengths, one with a small extra block on the end, beside a bowl of sweets, in IllumiTutor navy and amber on an off-white background.$ The Model Method

Combining Part-Whole and Comparison

Drawing a total and a comparison into one model, mixing equal units with extra known bits.

$A friendly flat-vector scene of a long bar cut into a shaded first part, with the leftover re-cut into smaller equal pieces, beside a slice of cake, in IllumiTutor navy and amber on an off-white background.$ The Model Method

The Remainder Model

Why the leftover becomes a new whole, and how re-cutting the bar into equal small units cracks "fraction of the remainder" problems.

$A friendly flat-vector scene of two bars of different lengths divided into equal small units that line up, beside two piggy banks, in IllumiTutor navy and amber on an off-white background.$ The Model Method

Making the Units Equal

Turning "a fraction of A equals a fraction of B" into a ratio by making the numerators match.

$A friendly flat-vector scene of two balance scales, one tipping with extra coins and one short of coins, beside a row of red packets, in IllumiTutor navy and amber on an off-white background.$ The Model Method

The Gap-and-Difference Method

Using a leftover in one plan and a shortfall in another to find a hidden count — the smarter successor to guess-and-check.

$A friendly flat-vector scene of two money bars with coins being added from outside, beside a shop till, in IllumiTutor navy and amber on an off-white background.$ The Model Method

External Change

What stays the same when amounts are added or removed from outside, and how to use that invariant.

$A friendly flat-vector scene of two ratio bars with one section locked the same size in both, beside a padlock, in IllumiTutor navy and amber on an off-white background.$ The Model Method

The Unchanged Quantity

Spotting the quantity that stays the same in a ratio problem and rescaling both ratios to match it.

$A friendly flat-vector scene of one bar split into labelled units and another into labelled parts, beside a balance scale, in IllumiTutor navy and amber on an off-white background.$ The Model Method

Units and Parts

Labelling the before-ratio in units and the after-ratio in parts, then solving them together when everything changes.

$A friendly flat-vector scene of two ratio bars joined at a shared middle section, beside a chain link, in IllumiTutor navy and amber on an off-white background.$ The Model Method

Repeated Identity

Joining two ratios that share a common quantity into a single three-way ratio.

$A friendly flat-vector scene of one bar labelled as a fraction, a ratio and a percentage at once, beside a pie chart, in IllumiTutor navy and amber on an off-white background.$ The Model Method

Ratio, Fraction and Percentage Bars

How fractions, ratios and percentages are the same idea in different clothes, all solvable with units.

$A friendly flat-vector scene of two bars drawn exactly the same length with different labelled pieces inside, beside an equals sign, in IllumiTutor navy and amber on an off-white background.$ The Model Method

The Equal-Stage Method

Drawing equal-length bars at the moment two quantities are the same, then solving for one unit.

Number & Algebra

10 notes

$A friendly flat-vector scene of large place-value blocks and number cards arranged in groups of three digits, beside a calculator, in IllumiTutor navy and amber on an off-white background.$ Number & Algebra

Whole Numbers

Reading numbers up to 10 million, the four operations, order of operations with brackets, and estimating answers to check your work.

$A friendly flat-vector scene of counters arranged into neat equal rows and arrays, with some numbers circled, in IllumiTutor navy and amber on an off-white background.$ Number & Algebra

Factors and Multiples

Factors, common factors, multiples, common multiples and prime numbers, and how to tell them apart.

$A friendly flat-vector scene of a pizza and a chocolate bar cut into equal fraction pieces, with a few pieces shaded, in IllumiTutor navy and amber on an off-white background.$ Number & Algebra

Fractions

Adding and subtracting unlike fractions and mixed numbers, multiplying fractions, finding a fraction of a set, and linking fractions to division.

$A friendly flat-vector scene of a long ribbon being cut into equal fraction lengths with scissors, with a few measured pieces, in IllumiTutor navy and amber on an off-white background.$ Number & Algebra

Dividing with Fractions

Dividing a whole number by a fraction, a fraction by a whole number, and a fraction by a fraction.

$A friendly flat-vector scene of coins, a price tag and a ruler showing tenths, with a decimal point highlighted, in IllumiTutor navy and amber on an off-white background.$ Number & Algebra

Decimals

The four operations on decimals, rounding to a chosen place, and converting between fractions and decimals.

$A friendly flat-vector scene of two jars of coloured sand in proportion next to mixing scoops, with a colon symbol between them, in IllumiTutor navy and amber on an off-white background.$ Number & Algebra

Ratio

Equivalent ratios, simplest form, ratios of two and three quantities, dividing an amount in a ratio, and relating ratio to fractions.

$A friendly flat-vector scene of a hundred-square grid with part shaded and a percent sign, beside coins, in IllumiTutor navy and amber on an off-white background.$ Number & Algebra

Percentage

Finding a percentage of a quantity, writing one amount as a percentage of another, and converting between percentage, fraction and decimal.

$A friendly flat-vector scene of a shop price tag with a sale sticker and a receipt showing a tax line, beside coins, in IllumiTutor navy and amber on an off-white background.$ Number & Algebra

Percentage Change, Discount and GST

Percentage increase and decrease, discount, GST, simple interest, and finding the original amount before a change.

$A friendly flat-vector scene of a tap filling a measuring jug and a printer producing pages, with a clock nearby, in IllumiTutor navy and amber on an off-white background.$ Number & Algebra

Rate

Rate as an amount per one unit, and finding the rate, the total, or the base from the other two.

$A friendly flat-vector scene of a balance scale with a mystery box labelled with a letter on one side and number blocks on the other, in IllumiTutor navy and amber on an off-white background.$ Number & Algebra

Algebra

Using a letter for an unknown number, writing and reading expressions, simplifying like terms, and evaluating by substitution.

Measurement & Geometry

10 notes

$A friendly flat-vector scene of a ruler, a weighing scale and a measuring jug, in IllumiTutor navy and amber on an off-white background.$ Measurement & Geometry

Measurement and Unit Conversions

How metric units of length, mass and volume fit together, converting between them, and handling compound units in PSLE word problems.

$A friendly flat-vector scene of a 24-hour digital clock and an analogue clock face, in IllumiTutor navy and amber on an off-white background.$ Measurement & Geometry

Time

Reading the 24-hour clock, finding durations, using timetables, and solving start-time and end-time word problems.

$A friendly flat-vector scene of coins, a few notes and a small receipt, in IllumiTutor navy and amber on an off-white background.$ Measurement & Geometry

Money

Calculating with dollars and cents, working out change, reading bills, and solving everyday money word problems.

$A friendly flat-vector scene of a rectangle and a triangle with a ruler marking their sides, in IllumiTutor navy and amber on an off-white background.$ Measurement & Geometry

Area and Perimeter

Area and perimeter of squares and rectangles, the area of a triangle, composite figures, and finding a side from the area.

$A friendly flat-vector scene of a circle with its radius and diameter marked, beside a semicircle, in IllumiTutor navy and amber on an off-white background.$ Measurement & Geometry

Circles

Radius and diameter, circumference, area of a circle, and working with semicircles, quarter circles and shaded composite figures.

$A friendly flat-vector scene of a cube and a cuboid tank partly filled with water, in IllumiTutor navy and amber on an off-white background.$ Measurement & Geometry

Volume of Cubes and Cuboids

Volume of cubes and cuboids, volume of liquid, base area times height, and finding an unknown edge from the volume.

$A friendly flat-vector scene of two crossing lines with marked angles and a protractor, in IllumiTutor navy and amber on an off-white background.$ Measurement & Geometry

Angles

Angles on a straight line, angles at a point, vertically opposite angles, and finding unknown angles in figures.

$A friendly flat-vector scene of three triangles, one with equal sides and one with a right angle, in IllumiTutor navy and amber on an off-white background.$ Measurement & Geometry

Triangles

Isosceles, equilateral and right-angled triangles, the angle sum of 180 degrees, and finding unknown angles.

$A friendly flat-vector scene of a square, a parallelogram and a trapezium, in IllumiTutor navy and amber on an off-white background.$ Measurement & Geometry

Quadrilaterals

Properties of the square, rectangle, parallelogram, rhombus and trapezium, and finding unknown angles in them.

$A friendly flat-vector scene of an unfolded cube net beside a folded cube and a pyramid, in IllumiTutor navy and amber on an off-white background.$ Measurement & Geometry

Nets of Solids

Nets of the cube, cuboid, prism, pyramid, cylinder and cone, and matching a flat net to its solid.

Statistics

2 notes

$A friendly flat-vector scene of a bar graph, a line graph and a pie chart beside a small data table, in IllumiTutor navy and amber on an off-white background.$ Statistics

Reading and Interpreting Data

How to pull the right numbers out of tables, bar graphs, line graphs and pie charts, compare them, and use them to solve word problems.

$A friendly flat-vector scene of three uneven stacks of counting cubes being levelled into equal stacks, beside a calculator, in IllumiTutor navy and amber on an off-white background.$ Statistics

Average (Mean)

The average formula and its three forms — finding the average, the total, or the number of items — plus word problems where a new value changes the average.