Interactive Math & Computing Lessons

Self-paced, Singapore-Math style — Explore (hands-on) → Learn (step by step) → Practise (instant feedback). Academically rigorous. Free.

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📚 Fractions · CPA lessonmathprepai.com/learn
1 · Explore2 · Learn3 · Practice

Add the two parts together

½ +¼ =¾

Your turn

¼ + ½ = ?¾ ✓

🎉 Correct!

The secondary maths textbook — read it like a book

Every chapter of the Thai สสวท. curriculum with definitions, formulas and fully worked examples, cross-referenced to Common Core and Cambridge.

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A wooden desk laid out with base-ten blocks — unit cubes, ten-rods and a hundred-flat — beside a coloured-bead abacus and a notched wooden strip.

Numbers & Place Value

Vedic Maths — ten methods

Every method the Thai contest names, worked line by line on your own numbers.

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Place-Value Builder

Build numbers with base-10 blocks; read expanded form.

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Number Bonds

Split a whole into two parts (bonds to 10 & 20).

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Compare & Order Numbers

Use <, =, > by comparing place values.

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Rounding Numbers

Round to the nearest 10 or 100 on a number line.

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Skip Counting & Patterns

Count by 2s, 3s, 5s, 10s; spot patterns.

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Negative Numbers

Add and subtract integers on a number line.

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Ratio & Proportion

Simplify ratios and solve proportions.

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Counting to 20

Tap, count one-by-one, count on, and number order.

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Counting to 100

Hundred chart: down is +10, across is +1.

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Factors & Multiples

Factor pairs, common factors, HCF and LCM.

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Roman Numerals

Read & write I V X L C D M with add/subtract rules.

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Ordinal Numbers

1st, 2nd, 3rd — position words & the -st/-nd/-rd/-th rule.

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Number Line Intro

Read a 0–20 line; hop right to add, left to subtract.

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Divisibility Rules

Quick tests for ÷2, 3, 4, 5, 6, 9 and 10.

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Estimation Strategies

Round to estimate, then check if an answer is reasonable.

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Absolute Value

Distance from zero on the number line — always ≥ 0.

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Scientific Notation

Write big & small numbers as a × 10ⁿ.

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Square & Cube Numbers

See n² as an n×n grid and n³ as an n×n×n cube.

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Odd & Even Numbers

Pair two-by-two; use the last digit to tell them apart.

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Four carved wooden tiles showing plus, minus, multiplication and division symbols, surrounded by piles of coloured counters sorted into equal groups.

Operations

Addition Facts to 20

Add single digits fast with the make-ten trick.

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Subtraction Facts to 20

Count back, count up, and know your bonds fast.

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Mental Math Strategies

Round & adjust, split, and count up for 2-digit sums.

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Division with Remainders

The remainder — and round up, round down, or keep it.

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Two-Step Equations

Solve ax + b = c: undo +/− first, then divide.

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Multiplying & Dividing Integers

Sign rules: same signs +, different signs −.

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Distributive Property

Split hard multiplies: a×(b+c) = a×b + a×c.

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Word Problems: Choosing the Operation

Read the story, then pick + − × or ÷.

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Fact Families

Three numbers, four facts — how +/− and ×/÷ undo each other.

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Multiply & Divide by 10, 100, 1000

Digits slide across place-value columns, not 'add a zero'.

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Addition with Regrouping

Carry across columns with base-10 blocks.

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Subtraction with Regrouping

Borrow a ten with base-10 blocks.

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Multiplication Arrays

See multiplication as rows of dots.

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Times Tables & Patterns

Master facts 1–12 with memory tricks.

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Division as Equal Sharing

Share into equal groups; find the remainder.

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Long Division

Divide, multiply, subtract, bring down — step by step.

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Simple Equations

Balance the scale to solve for x.

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Prime Factors

Factors, primes, and factor trees.

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Order of Operations

Brackets, then ×÷, then +−.

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Exponents & Squares

Powers, perfect squares and square roots.

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Long Multiplication

Multiply big numbers with the area box model.

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Bar-Model Solver

Singapore bar models for word problems.

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A kitchen counter with a pie cut into equal slices and some lifted away, a chocolate bar broken along its scored lines, and a glass measuring jug filled part way.

Fractions, Decimals & Percent

What is a Fraction?

Equal parts of a whole; numerator & denominator.

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Equivalent Fractions

See why 1/2, 2/4 and 3/6 match.

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Simplifying Fractions

Reduce fractions to lowest terms with the GCF.

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Fractions on a Number Line

Place & read n/d on a line, even past 1.

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Adding & Subtracting Decimals

Line up the points, add or subtract column by column.

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Multiplying Decimals

Multiply as whole numbers, then count decimal places.

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Rounding Decimals

Round to whole, tenth, hundredth — round half up.

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Dividing Decimals

Shift both numbers so the divisor is a whole number.

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Fractions, Decimals & Percents

The FDP triangle — one amount, three ways.

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Percentage of an Amount

Find a percent of a quantity — 25% of 80 = 20.

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Percentage Increase & Decrease

New amount after a % change, and the % change itself.

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Decimal Place Value

Ones, tenths, hundredths, thousandths & expanded form.

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Compare & Order Decimals

Line up points, compare place by place: 0.45 < 0.5.

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Fraction Word Problems

Fraction of an amount + add/subtract in a story.

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Compare Fractions

Decide which fraction is bigger with <, =, >.

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Adding & Subtracting Fractions

Combine fractions, simplify the answer.

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Multiplying & Dividing Fractions

Multiply tops & bottoms; flip to divide.

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Mixed Numbers & Improper Fractions

Turn 7/4 into 1¾ and back.

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Fraction of a Quantity

Find a fraction of a group (3/4 of 12).

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Understanding Decimals

Tenths, hundredths, and decimal-fraction links.

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Percentages — Intro

Percent as per hundred; percent of a quantity.

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A wooden shelf with a brass balance scale and weights, an hourglass, a coiled tape measure and a round wall clock with a blank face.

Measurement, Time & Money

A drafting table with wooden geometric solids — a cube, sphere, cone and pyramid — beside a pair of compasses, a clear set square and a stand of coloured bars of different heights.

Geometry & Data

Area & Perimeter

Squares inside vs distance around a rectangle.

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Angles

Measure and classify angles in degrees.

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Types of Triangles

Classify triangles by sides and by angles.

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Classifying Quadrilaterals

Name shapes by parallel sides, equal sides & right angles.

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Parts of a Circle

Radius, diameter, circumference & area (π=3.14).

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Lines & Angles

Parallel, perpendicular & angle pairs on a line.

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Pythagorean Theorem

a² + b² = c² for right triangles.

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Reading Line Graphs

Read values, find peaks and trends on a line graph.

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Reflections on a Grid

Flip points across the x-axis, y-axis, and y = x.

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Rotations About the Origin

Turn a point 90°, 180°, 270° clockwise or anticlockwise.

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Polygon Interior Angles

Split polygons into triangles: (n−2)×180°.

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Reading Pie Charts

Read each slice as a fraction, percentage and count.

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Sorting 2D Shapes

Name shapes and count their sides and corners.

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Translations on a Grid

Slide points by a vector: (x,y) → (x+a, y+b).

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Tally Marks & Frequency

Record counts in fives, read a frequency table.

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Venn Diagrams

Sort into only A, only B, both & neither.

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2D Shapes & Symmetry

Sides, vertices and lines of symmetry.

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3D Solids & Nets

Faces, edges, vertices and unfolding nets.

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Coordinate Grid

Read and plot points (x, y) on a grid.

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Reading Bar Charts

Read values off the scale; compare bars.

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Reading Pictograms

One symbol equals a value — read the key.

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Mean, Median, Mode & Range

Four ways to summarise a data set.

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Basic Probability

How likely? From impossible to certain.

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A wooden table with a small round wheeled robot, a row of interlocking coloured blocks showing arrows in sequence, and a paper grid mat with a winding route drawn across it.

Computing & Coding

Algorithm Steps

An algorithm is an ordered list of steps — and the order matters.

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Binary Numbers

How computers count with 0 and 1 — flip the 16-8-4-2-1 bit switches.

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Loops & Repeat

A loop runs the same instructions again and again — count what it prints.

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Boolean Logic

Light a bulb through AND / OR / NOT gates, then read the truth tables.

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Trace the Output

Read Python-like code line by line and predict what it prints.

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Variables & Values

A variable is a named box that stores a value; assignment fills it, reassignment replaces it.

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If / Else Decisions

A program picks a different path depending on a condition.

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Flowcharts

Draw an algorithm with shapes and arrows, then follow it from Start to End.

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Hexadecimal & RGB Colour

Base-16 and how computers store colours as #RRGGBB.

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Find the Bug

Read a program and its wrong output, then spot the buggy line.

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What Is a Function?

Define a function with parameters, call it with arguments, and predict the value it returns.

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Nested Loops

A loop inside a loop — see why total iterations = outer × inner by tracing every (i, j) pair.

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ASCII & Text

How computers store letters as numbers — A=65, a=97. Turn letters into codes and shift them Caesar-style.

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Pattern Recognition

Find the rule in a sequence — add, multiply, or a repeating cycle — and predict what comes next.

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Sorting (Intro)

Order a list from smallest to largest and trace one bubble-sort swap step by step.

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A pendulum hanging from a wooden stand, a ball resting part way down a ramp, a spring with a weight on the end, and a glass prism casting a rainbow across the table.

Physics

Forces & Motion

Newton's 2nd law F = m·a, weight W = m·g, and resultant force — push a box and watch it accelerate.

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Energy, Work & Power

Work W = F·d, kinetic ½mv², potential mgh, power W/t — in joules & watts.

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Electric Circuits

Ohm's law V = I·R, series resistance and power P = V·I — with a live circuit you can tune.

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Waves & Sound

Change frequency and wavelength to see wave speed v = f × λ, plus period and wave types.

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Pressure & Density

Pressure P = F ÷ A and density ρ = m ÷ V — set the values live, then rearrange to find force or mass.

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Heat & Temperature

Heat energy Q = m·c·ΔT — set the mass and temperature of water, see the joules, and tell heat from temperature.

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Momentum & Collisions

Momentum p = m·v, and how it's conserved when two objects collide and stick together.

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Light & Optics

Change the angle of incidence to see the equal reflection angle live, plus refraction and the thin-lens equation 1/f = 1/dₒ + 1/dᵢ.

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Magnetism Basics

Poles rule (like repel, unlike attract), electromagnets, and the force on a wire F = B·I·L — with a live field you can tune.

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Circular Motion

Centripetal acceleration a = v²/r and force Fc = m·v²/r point INWARD; link ω and v with v = ω·r — watch a dot orbit.

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Static Electricity

Positive & negative charge, the like-repel / unlike-attract rule, charging by friction, and everyday sparks — with a charge sandbox you can rub.

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Gravitation

Weigh yourself on the Moon, Mars and Jupiter — W = m·g — and meet the inverse-square law F = G·M·m/r².

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Modern Physics

Photons E = h·f, the photoelectric effect, mass–energy E = m·c² and half-life — with a live decay you can step through.

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