Interactive Math & Computing Lessons

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

🔍 Explore📘 Learn✏️ Practise

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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!

Numbers & Place Value

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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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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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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Measurement, Time & Money

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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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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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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