168 experiments found
Clear filtersIn series one current flows through everything and resistances add; in parallel each branch gets the full voltage and the total resistance falls
Wire two or three bulbs in series and in parallel, compare their brightness and the current, take one bulb out, and calculate the total resistance.
Devices transform energy from one form to another; the main useful output tells us the transformation
Find out what energy goes into and comes out of everyday devices, from an electric kettle to a micro-hydro generator, and sort them by their main energy transformation.
A spring stretches in proportion to the force on it, so its stretch can measure force
Hang standard masses on a spring to see how it stretches, then use it as a spring balance to weigh an apple, a stone and a book.
A force can change an object's speed, direction or shape
Give a rolling ball a push forwards, backwards or sideways, and see how a force can speed it up, slow it down, change its direction or change its shape.
Wait until the liquid column stops moving, then read the top of the column at eye level
Measure the temperature of ice water, tap water, warm water and boiling water, waiting for the thermometer to settle before you read it.
Two plane mirrors at an angle θ form 360° ÷ θ − 1 images
Stand a toy in front of one mirror, then between two mirrors hinged together, and count the images as you open and close the angle between them.
A convex lens forms real, inverted images or virtual, magnified ones depending on where the object is; a concave lens always forms small, upright, virtual images
Move an object along an optical bench in front of convex and concave lenses, trace the rays, find the image, and measure the focal length.
Light bends towards the normal when it slows down entering a denser medium, and away from it when it leaves
Shine a ray into a glass block and a tank of water at different angles, measure how much it bends, and find the refractive index.
A coil carrying a current is a magnet; more turns, more current and an iron core make it stronger
Wind a coil around an iron nail, pass a current through it, and count how many paper clips it can lift as you change the turns, the current and the core.
Acceleration is how fast velocity changes: v = u + at, so a steadily accelerating bus gains the same speed every second and covers more distance each second
A bus leaves the stop and speeds up steadily. Read its speedometer and the distance it has gone every 5 seconds, then make it speed up harder or start already moving.
The air around us presses on everything; its pressure falls as you go higher
Travel from Biratnagar to the top of Everest with a barometer, a sealed snack bag and a glass of water held up by a card, and see how air pressure changes with height.
A liquid pushes up on an object with a force (upthrust) equal to the weight of liquid it displaces; an object floats if it is less dense than the liquid
Lower objects on a spring balance into fresh water, salt water and oil. Measure the upthrust and find out why some float and some sink.
Pressure applied to an enclosed liquid is passed on equally in all directions, so a big piston gets a big force
Push the small piston of a hydraulic lift and see how the pressure is passed through the oil to lift a car on the big piston.
Pressure = force ÷ area: a smaller area or a bigger force gives a bigger pressure
Stand bricks on a foam block on their flat side, their long side and their end, and see how the contact area and the force change the pressure.
Shaping a material into a hollow boat lets it push aside more water, giving enough upthrust to float
Drop a ball of plasticine into water, then shape the same plasticine into boats and load them with marbles until they sink.
In a fair test we change one variable at a time; for a pendulum only the length of the string changes the time of a swing, not the mass or a small swing
Time ten swings of a pendulum. Change the length of the string, the mass of the bob and how far you pull it back, one at a time, and find out which one really changes the swing.
Levers are grouped by what is in the middle: the fulcrum (class 1), the load (class 2) or the effort (class 3); mechanical advantage = load ÷ effort = effort arm ÷ load arm
Use a crowbar, scissors, a wheelbarrow, a nutcracker, tongs and a broom. Find the fulcrum, the load and the effort on each, see which is in the middle, and work out how much each one helps.
Rubbing two materials gives them opposite charges; like charges repel, unlike charges attract, a charged object pulls uncharged bits, and earthing lets the charge flow away
Rub balloons, combs, glass rods and plastic refills, bring them near each other, and sort twelve pairs into those that attract, those that repel and those where nothing happens.
An echo is sound reflected back; the speed of sound = 2 × distance ÷ echo time, about 340 m/s in air, and a little faster in warmer air
Clap in front of a cliff and time the echo. Stand nearer or farther, try a cold and a hot day, and work out how fast sound travels.
Sound needs a medium; it travels fastest in solids, slower in liquids and slowest in gases, and not at all in a vacuum
Send a sound along 1 km of air, water, wood and steel, time how long it takes, and see what happens in a vacuum.
The planets go round the Sun at different distances: the farther a planet, the longer its year; each planet's gravity is different, so the same mass weighs differently
Visit the eight planets. Find how long a year lasts on each, how long sunlight takes to get there, and what you would weigh, from little Mercury to giant Jupiter.
The pH scale from 0 to 14 measures how acidic or basic a solution is
Use universal indicator to measure the pH of seven household liquids, from lemon juice to limewater, and place each on the pH scale.
Air is matter: it takes up space, can be compressed, exerts pressure and expands when heated
Push the plunger of a sealed syringe full of air, then warm and cool a flask with a balloon on its neck.
Carbon dioxide turns limewater milky
Make carbon dioxide from marble chips and acid, then bubble it, your breath and fresh air through limewater to see which turn it milky.
Atoms join to form molecules; a molecule of an element has one kind of atom, and a molecule of a compound has two or more kinds
Build ball-and-stick models of common substances, count their atoms, and sort them into single atoms, molecules of elements and molecules of compounds.
Valency is the combining power of an atom, set by its outer electrons; atoms join so that their valencies balance, which the criss-cross rule turns into a formula
Join a metal with a non-metal. See each atom's electron shells, find its valency from its outer electrons, and build the formula: NaCl, MgO, Al₂O₃, CaCl₂ and water.
In electroplating the object is the cathode (−) and the coating metal the anode (+); the metal deposited is proportional to the charge passed, current × time
Hang a steel spoon in a solution of a metal salt and pass a current. Change the coating metal, the current and the time, and see how much metal is deposited and how thick the coat on the spoon grows.
Burning needs fuel, oxygen and heat (the fire triangle); take away any one and the fire goes out
Cover a burning candle with jars of different sizes and time how long it burns, then put the flame out by removing oxygen, heat or fuel.
Metals are shiny, malleable, sonorous and good conductors; non-metals are usually dull, brittle and poor conductors, with a few exceptions
Test elements for shine, hammering, ringing and electrical conduction, then sort them into metals and non-metals.
A microscope's magnification is the eyepiece's magnification times the objective's; the more it magnifies, the bigger and fewer the cells we see
Look at onion skin cells and cheek cells through a school microscope. Turn to stronger lenses and find out how magnification changes what you see.
Living things are classified into five kingdoms by their cells (one or many, with or without a nucleus) and how they get their food
Look at the cells of fifteen living things, from curd bacteria and amoeba to yarsagumba, rhododendron and frogs, find out how each gets its food, and sort them into the five kingdoms.
South Asian farmers grow kharif crops in the monsoon, rabi crops in the winter and zaid crops in the short summer between, because each crop needs its own temperature and water
Find out when twelve crops of India, Bangladesh and Nepal are sown and harvested, from paddy and jute to wheat, mustard and watermelon, and sort them into kharif, rabi and zaid crops.
Roots absorb water mainly through their root hairs, by osmosis; salty water stops absorption
Stand young plants in measuring cylinders of water sealed with oil, compare intact roots, damaged root hairs and cut-off roots, and try salty water.
Oviparous animals lay eggs and viviparous animals give birth to young; fertilisation happens inside the female (internal) or outside in water (external)
Find out how twelve animals, from the hen and the frog to the cow and the whale, have their young and where fertilisation happens, then sort them into egg-layers and those that give birth.
Pollen is carried to the stigma, a pollen tube carries the male gamete to the ovule, and after fertilisation the ovule becomes a seed and the ovary a fruit
Put the stages of pollination, fertilisation, seed and fruit formation and germination in the right order, and find out where in the flower each one happens.
A flower's stamens (anther and filament) are the male parts and its pistil (stigma, style and ovary with ovules) is the female part; petals and sepals attract and protect
Cut a flower in half, label its petals, sepals, stamens and pistil, and find out which parts are male and which are female.
An endangered species can recover when its habitat is protected and hunting stops; losing habitat and poaching can wipe it out
Follow 100 one-horned rhinos for 20 years. Protect them in a national park, add community guards, or let their forest be cut and poachers hunt them, and watch their numbers rise or fall.
Minerals are natural solids found in rocks; metallic minerals (ores) shine like metal and give metals such as iron and copper, while non-metallic minerals give materials such as cement, glass and talc
Test eleven minerals for lustre, streak and hardness, find out what each is used for in Nepal, and sort them into metallic minerals (ores) and non-metallic minerals.
Sunlight, wind and tides never run out; forests, wildlife, fish and groundwater grow back if used wisely; coal, petroleum, natural gas and minerals took millions of years to form, so once used they are gone
Find out how long twelve natural resources take to replace and what we use them for, from sunlight and wind to forests, groundwater, coal and petroleum, and sort them by whether they can run out.
The air quality index (AQI) turns the amount of fine particles (PM2.5) into a number from 0 to 500; India's scale has six bands, good, satisfactory, moderate, poor, very poor and severe, each with its own health advice
Change the amount of fine dust (PM2.5) in the air and watch the air quality index move from good to severe. Learn what each band means for your health and where the dust comes from.
Fine-grained soils with humus hold more water than sandy soils
Pour the same amount of water through sandy soil, garden loam and clay soil in funnels, and measure how much drains through each.
Biodegradable waste is broken down by decomposers into harmless substances; non-biodegradable waste stays in the environment for hundreds of years
Find out what happens to different kinds of waste buried in soil for three months, and sort household waste into biodegradable and non-biodegradable.
Settling and filtering remove particles; only disinfection makes water safe from germs
Clean muddy river water step by step: let it settle, filter it, then kill the germs by boiling or with a chlorine tablet.
An ATM is a digital system: it takes inputs (card, PIN, amount), checks them against the bank's computer, and only then gives outputs (cash, a new balance)
Put in a card, type a PIN and ask for cash. Watch the ATM check the PIN, the money in the account and the daily limit, then count out Rs 1000 and Rs 500 notes.
(x + a)(x + b) = x² + (a + b)x + ab, so factorising means finding two numbers with the right sum and product
Extend a square courtyard on two sides and see how (x + a)(x + b) breaks into x², x strips and unit squares.
Circumference = 2πr and area = πr²: a circle's slices rearrange into a rectangle πr by r
Cut a round roti-shaped circle into slices and lay them top to tail. With more slices they make a rectangle πr long and r tall, so the area is πr²; then see what doubling the radius does.
A regular polygon with n sides of length s has perimeter n × s and area ½ × perimeter × apothem
Split a regular pentagon, hexagon and polygons with more sides into triangles from the centre, find their perimeter and area, and see them get closer to a circle.
The four walls of a cuboid room unroll into one rectangle 2(l + b) long and h high, so their area is 2h(l + b); the floor is l × b, and the cost is the area × the rate
Your family wants to paint a room before Tihar. Change the room's length, breadth and height and the price of paint, find the area of the four walls and the cost, and see why the walls unroll into one long rectangle.
The back bearing points the opposite way: it is the bearing + 180° if the bearing is less than 180°, and the bearing − 180° otherwise; on a scale drawing, real distance = map distance × scale
Trek from a camp to a village on a bearing read from a map, then find the bearing that brings you back. Change the bearing, the length on the map and the scale, and find the back bearing and the real distance.
The perpendicular from the centre of a circle to a chord bisects the chord, so half the chord is √(r² − d²); the nearer the chord is to the centre, the longer it is, and through the centre it is a diameter
Draw a chord across a round chautari platform at different distances from the centre. See that the perpendicular from the centre cuts it in half, and use Pythagoras to find how long it is.
Each transformation changes coordinates by a rule: reflection in the x-axis (x, y) → (x, −y), in the y-axis (x, y) → (−x, y), rotation of 90° anticlockwise about O (x, y) → (−y, x), of 180° (x, y) → (−x, −y), and translation by (a, b) (x, y) → (x + a, y + b)
Move a point P on a grid by reflecting it in an axis, rotating it about the origin or sliding it. Read the coordinates of its image P′ and find the rule for each transformation.
2^m × 2^n = 2^(m + n), 2^m ÷ 2^n = 2^(m − n) and (2^m)^n = 2^(mn); 2^0 = 1 and 2^−n = 1/2^n
Fold, unfold and repeat folds of a sheet of paper to discover the laws of indices, and find out how thick the stack would get.
Simple interest is the same every year; compound interest earns interest on interest; depreciation takes a percentage of the value each year
Save money in a cooperative at simple or compound interest, watch the interest on interest grow, and see how a motorbike loses value.
A linear equation y = mx + c is a straight line; two lines meet at the solution of both equations
Plot two taxi fares as straight lines, read them at any distance and find where they cost the same.
When a transversal cuts two parallel lines, vertically opposite, corresponding and alternate angles are equal, while a linear pair and co-interior angles add up to 180°
A straight road crosses two parallel canals. Mark one angle where it meets the first canal, then find its vertically opposite angle, its linear pair, and the corresponding, alternate and co-interior angles at the second canal.
In base b each place is worth b times the place to its right (1, b, b², b³, …), and every digit is less than b; to convert, divide by b again and again and read the remainders upwards
Put a number on a place-value abacus in base 2 or base 5. See how many beads each rod gets, read the number in the new base, and check it by multiplying back.
Discount is a percentage of the marked price; VAT is a percentage of the selling price after the discount
Take a discount off a marked price, add 13% VAT to the selling price, and see when the bill ends up below the price on the tag.
The angle of each slice is its share of the total × 360°
Share out a family's monthly income between food, rent, school fees and savings, and draw the budget as a pie chart.
Probability = number of favourable cards ÷ 52, and P(not E) = 1 − P(E)
Shuffle a pack of 52 playing cards and draw one. Find the probability of a red card, a king, a face card or the ace of spades, and draw many times to see how often each really comes up.
Probability = favourable outcomes ÷ all equally likely outcomes, and the share seen in many trials gets close to it
Fill a lucky-draw bag with coloured balls, place the chance of winning on a scale from impossible to certain, and draw many times to test it.
In a right-angled triangle a² + b² = c²; when c² is not a perfect square, c is an irrational surd that may simplify to k√m
Cut a diagonal brace for a wooden gate: square the sides, add them, and find out when the brace is a whole number and when it is a surd.
A rational number can be written as p/q (q ≠ 0) and its decimal ends or repeats; an irrational number cannot, and its decimal never ends and never repeats; integers are rational too
Write twelve numbers, from √9 and 22/7 to π and √2, as decimals and as p/q, and sort them into integers, rational numbers and irrational numbers.
List every equally likely outcome; P(event) = favourable outcomes ÷ all outcomes
Lay out all 36 ways two dice can land, light up the outcomes you want, and test the probability with many rolls.
Any positive number can be written as a × 10ⁿ with 1 ≤ a < 10; n counts how many places the decimal point moves
Write the sizes of a virus, a hair, Mount Everest and the distance to the Sun in standard form, a × 10ⁿ, on a powers-of-ten ruler.
Two sets can be equal (the same members), one can be a proper subset of the other, they can overlap (some members in common) or be disjoint (none in common); sets with the same number of members are equivalent, even if their members differ
List twelve pairs of sets, from the letters of “follow” and “wolf” to the factors of 12 and 18. Find their members in common, compare how many members each has, and sort the pairs by how the sets are related.
Grouped data are counted in class intervals and shown as a histogram, whose bars touch because the classes follow on without gaps; the tallest bar is the modal class, and the class width decides how much of the pattern you can see
Thirty students got marks out of 50 in a maths test. Group the marks into classes 5, 10 or 25 marks wide, draw a histogram, and see which class width shows the pattern best and where the modal class is.
The three angles of a triangle add up to 180°, and an exterior angle equals the sum of the two interior angles opposite it
Change two angles of a triangle and watch the third. Carry one side on past a corner, and find that the angle outside it equals the two opposite angles inside put together.
If a job takes a hours, 1/a of it is done each hour; rates add when working together and a drain's rate is subtracted
Open two taps and a drain on a rooftop water tank and find how long it takes to fill, by adding the work done each hour.
Dynamic programming solves a big problem from the answers to smaller ones and remembers them: the ways to climb n stairs are the ways for n − 1 plus the ways for n − 2
You climb a staircase one or two steps at a time. In how many different ways can you reach the top? Build the answer up stair by stair from the answers before it, and see why remembering answers beats working them out again and again.
Halving the range each time finds any number from 1 to 100 in at most 7 guesses, because 7 halvings are enough to shrink 100 numbers to 1 (2⁷ = 128): the idea behind binary search
Think of a number from 1 to 100 and let the computer guess. It always guesses the middle of what is left, and each “too high” or “too low” throws half the numbers away. Count its guesses and find the number that makes it work hardest.
The work a program does grows with its input: one loop over n items takes about n steps, a loop inside a loop takes n × n, and halving n each time takes only about log₂ n; Big O names this growth
Count the steps three small programs take for the same n: one loop, a loop inside a loop, and a loop that halves n. Double n and see one count double, one grow four times and one hardly move: a first look at Big O.
Big O describes how an algorithm's steps grow with the size of its input n: O(1) stays the same, O(log n) grows by one when n doubles, O(n) doubles, O(n log n) a little more than doubles, and O(n²) quadruples
Race a hash lookup, binary search, linear search, merge sort and bubble sort as the number of items grows from 8 to 1024. See some lines barely rise while bubble sort shoots up past half a million steps, and learn the Big O names for how each one grows.
Breadth-first search (BFS) visits cells in order of distance using a queue, so its path is always a shortest one; depth-first search (DFS) follows one way as far as it can using a stack, so its path can be longer
Send a search through a maze, one cell at a time. Breadth-first search spreads out in rings with a queue and finds the shortest way; depth-first search dives down one corridor with a stack. Compare the paths they find and how many cells each one visits.
Bubble sort compares each pair of neighbours and swaps them when they are in the wrong order; each pass carries the largest number left to the end, and a pass with no swaps means the list is sorted
Watch bubble sort put a list of numbers in order, one comparison at a time. Count the comparisons and swaps, see the largest number bubble to the end after every pass, and compare a jumbled, a sorted and a reversed list.
A network of friends is a graph; when every link counts as 1, the shortest path is the fewest links, found by settling people in order of how many links away they are, nearest first
In a small network of friends, find how many links separate two people: a friend is 1 link away, a friend of a friend 2. A shortest-path search spreads out from one person, nearest friends first, and finds the fewest links, or shows that someone cannot be reached at all.
Linear search compares the target with each item in order; it needs 1 comparison at best and as many as there are items at worst, or when the target is missing
Search a list of test marks or shop prices for a number, checking one item at a time. Count the comparisons when the number is first, in the middle, last, or not in the list at all.
A greedy algorithm makes the best-looking choice at each step: for change, it gives the largest note that still fits, again and again, until nothing is left
A shopkeeper's program gives change in Nepali notes and coins. Run it for different amounts and watch the greedy rule at work: always give the largest note that still fits. Count the notes, and find out when being greedy is not the best plan.
Insertion sort keeps a sorted part on the left and inserts the next number into it by sliding it past every bigger number; on a list that is nearly sorted it does very little work
Watch insertion sort take each number in turn and slide it left into its place among the numbers already sorted, the way you sort cards in your hand. Count its comparisons and swaps, and compare it with bubble sort and selection sort on a jumbled, a sorted and a reversed list.
A number is prime when only 1 and itself divide it; a program tests divisors with %, stops at the first one that divides, and only needs to try divisors up to the square root, because any bigger factor comes with a smaller partner
Choose a number and watch a program try divisors 2, 3, 4 … with the remainder. It stops at the first divisor it finds, or as soon as the divisor times itself is bigger than the number. Count the tries and find out why it never needs to go further.
Binary search compares the target with the middle of a sorted list and throws away the half it cannot be in, so 16 items need at most 5 comparisons instead of 16; it only works on sorted input
Search 16 numbers two ways: one by one, and by halving the list at each step. Compare the comparisons each needs, then run binary search on a list that is not sorted and see it miss a number that is there.
Merge sort divides the list into halves until each part has one number, then merges sorted parts by always taking the smaller front number; its comparisons grow like n log n, far slower than the n² of bubble sort
Split a list of eight numbers in half again and again until every part holds one number, then merge the parts back, always taking the smaller front number. Count the comparisons and compare them with bubble sort and insertion sort on jumbled, sorted and reversed lists.
Selection sort looks through the unsorted part for the smallest number and swaps it into the next place at the front; it always makes the same number of comparisons, but at most one swap per pass
Watch selection sort put a list in order by finding the smallest number left and swapping it to the front, pass after pass. Count its comparisons and swaps, and compare it with bubble sort on a jumbled, a sorted and a reversed list.
Dijkstra's algorithm settles towns in order of their distance from the start; each settled town's distance is final, and trying the roads out of it can only make the other towns' distances shorter
Find the shortest way by road from Kathmandu or Pokhara to another town. Watch Dijkstra's algorithm settle the nearest town first, try the roads out of it, and keep the shortest distance it has found to every town.
An algorithm is a list of exact steps done in order; changing the order or one step changes the result, and debugging means finding the step where the plan breaks
Put move and turn blocks in order so a robot crosses a 5 × 5 grid to its battery. Run a broken plan to find the block where it bumps into a wall, fix it, and then find the shortest plan.
A Caesar cipher replaces each letter with the letter a fixed number of places (the shift) further along the alphabet, going round from Z back to A; shifting back by the same number decodes it
Hide a message by moving every letter the same number of places along the alphabet, then read it back by moving the other way. Watch the program code a word letter by letter, see what happens after Z, and crack a coded word.
A state machine is always in one of a few states and moves to the next state by a rule; a traffic light keeps its state in a variable and goes round red, green, yellow with (state + 1) % 3
Run a traffic light for a number of ticks. A loop moves it from red to green to yellow and back to red, using one variable for the state and % to go round again. Count each colour's turns and predict the light at any tick.
A big problem is easier when it is broken into small parts (decomposition); each part becomes a few steps, and a mistake in one part, such as one move too many, breaks the whole plan
Guide a robot through a 7 × 7 maze to its battery. Break the long route into short parts, find the block where a plan with a counting mistake breaks, and build the shortest plan.
A linked list stores each item in a node with a link to the next node; adding at the front is instant, but reaching node i means following i links from the head
Build a train where each carriage is hooked to the next one. Add a carriage at the front or after another, take one out, and find one, and count how many links you have to follow each time, because a linked list has no index to jump to.
A stack keeps items in a pile: push puts an item on the top, pop takes the top item off and peek only looks at it, so the last item in is the first one out (LIFO)
Push plates onto a stack, pop them off and peek at the top. See why the last plate you put on is always the first one you take off, and what happens when you try to pop from an empty stack.
A queue keeps items in a line: enqueue adds an item at the rear, dequeue takes the item at the front and front only looks at it, so the first item in is the first one out (FIFO)
Serve customers at a ticket counter with a queue: new people join at the rear, the person at the front is served first, and front shows who is next. See why a queue is fair, and what happens when nobody is left to serve.
In a binary search tree every number on a node's left is smaller and every number on its right is bigger, so a search throws away half the tree at each step, but only while the tree stays bushy and short
Insert seven numbers into a binary search tree, smaller ones to the left and bigger ones to the right. Search it with very few comparisons, print it in order, and see how numbers that arrive already sorted turn the tree into a long chain.
To check brackets, push each opening bracket on a stack; a closing bracket must match the bracket on top, which is popped; at the end the stack must be empty
Every ( needs a ), every [ a ] and every { a }, closed in the right order. Watch a program check an expression with a stack: push each opening bracket, pop it when the matching one closes, and stop at the first bracket that does not fit.
A hash table turns each key into a bucket number with a hash function; adding and finding a key look in that one bucket, so they stay fast however many keys there are, as long as collisions are few
Add names to a table of buckets, where a hash function works out each name's bucket from its letters. See two names land in the same bucket (a collision), find a name by looking in one bucket only, and change the number of buckets to spread the names out.
A list (array) keeps items in order; each item has an index, counted from 0, so a list of n items has indexes 0 to n − 1
Keep a shopping list in a program. Read an item by its index, change one, add and remove items, and find out what happens when you ask for an index past the end of the list.
A two-dimensional array is a list of rows, each a list of values; grid[row][col] picks one value, a loop along a row or down a column adds them up, and two nested loops visit every cell
Store a class's marks in a table with a row for each student and a column for each subject. Read one mark with grid[row][col], add up a student's row or a subject's column, and find the highest mark with a loop inside a loop.
A traversal visits every node of a tree once; pre-order visits a node before its children, in-order between its left and right children, post-order after them, and level order row by row with a queue
Build a binary search tree of seven numbers and walk it four ways: in-order, pre-order, post-order and level by level. See four different orders of the same numbers, why in-order comes out sorted, and how a queue walks the tree row by row.
An if / else statement checks a condition: when it is true the program runs the then part, otherwise the else part, never both
Change the chance of rain and run a small program that decides whether to take an umbrella. Watch the condition turn true or false, see which branch runs, and fix a condition that gives the wrong answer.
NOT turns true into false; AND is true only when both parts are true; OR is true when at least one part is true, so a long condition can be worked out one part at a time
Tell the program whether it is raining, whether your homework is done and whether it is a holiday, and watch it work out each part of the rule with NOT, AND and OR before it decides whether you can play outside.
Conditions can be joined with AND (all must be true) and OR (one is enough), and an if / else can sit inside another, so the program checks one question after another until one is true
Enter marks in maths, science and English and run a result program: it works out the total and the percentage, checks with AND that every subject is passed, and then uses nested if / else to give the division. Find the marks that reach each branch.
A year is a leap year when it divides by 4 and not by 100, or when it divides by 400; the remainder % tests divisibility and AND / OR join the rules into one condition
Choose a year and run a program that decides whether February has 29 days. See how the remainder operator % tests divisibility, and how AND and OR join three rules into one condition that gets 1900 and 2000 right.
A loop condition joined with AND stops as soon as either part is false: here when the PIN is right or when three tries are used up
An ATM gives you three tries to type your PIN. Choose the PINs typed on each try and run the program: a while loop keeps asking while the card is locked AND fewer than three tries are used, then either welcomes you or blocks the card.
A function keeps a rule in one place: to_fahrenheit(c) returns c × 9 ÷ 5 + 32, and every call gives it a new argument for its parameter c
Write to_fahrenheit(c) once and use it for Kathmandu, Jumla and Biratnagar. Change each town's temperature, watch every call get its own c, and see one rule give three answers.
Euclid's rule gcd(a, b) = gcd(b, a % b) makes the numbers smaller at every call, so a recursive function reaches its base case, b = 0, where the answer is a
Find the greatest common divisor (HCF) of two numbers with a function that calls itself: gcd(a, b) calls gcd(b, a % b), and the numbers shrink until the remainder is 0. Watch the call stack, count the calls, and see which pairs share no divisor but 1.
fib(n) = fib(n − 1) + fib(n − 2) with fib(0) = 0 and fib(1) = 1; because each call makes two more, the number of calls grows very fast, and the same answers are worked out many times
Work out Fibonacci numbers with a function that calls itself twice. Count the calls as n grows, watch the same small calls happen over and over on the call stack, and see why remembering answers is so much faster.
A function is a named set of steps written once and used many times: its parameters receive the arguments of each call, and return sends its answer back to where it was called
Define a function area(length, breadth) once and call it for a kitchen, a hall and a bedroom. Watch each call open a new frame with its own parameters, see the value it returns, and change the bedroom's size to reach a target area.
A recursive function solves a problem by calling itself on a smaller version of it; a base case answers the smallest version directly, so the calls stop and the answers come back up the call stack
Work out factorials with a function that calls itself. Watch the call stack grow one frame for every call down to the base case, then shrink as each call returns its answer, and see why a recursive function needs a base case.
To move n disks, move the top n − 1 out of the way, move the biggest, then move the n − 1 back on top; the same plan solves the smaller towers, so the moves double and add one each time: 2ⁿ − 1
Move a tower of disks from peg A to peg C, one disk at a time, never a bigger disk on a smaller one. A recursive plan solves it for any number of disks: watch the calls and the moves, and find the pattern 2ⁿ − 1.
In nested loops the inner loop runs all the way through for every turn of the outer loop, so a table of r rows and c columns has r × c products
Print a multiplication table with two loops, one inside the other: the outer loop chooses the row, the inner loop goes along it. Change the size of the table, count the products, and see how the inner loop starts again on every row.
n % 10 is the last digit of n and floor(n / 10) is n without it, so a while loop that repeats both until n is 0 visits every digit once
Choose a number and watch a while loop take it apart: % 10 gives the last digit, dividing by 10 drops it, and the loop adds each digit to a total until the number reaches 0. Count the digits on the way.
A loop can make a decision on every repeat: i % 3 == 0 is true when 3 divides i exactly, and in a chain of ELSE IFs the first true check wins, so the most special case must come first
Count from 1 to n, but say Fizz for multiples of 3, Buzz for multiples of 5 and FizzBuzz for multiples of both. Watch the remainder decide each number, and see why the order of the checks matters.
A loop repeats the same lines: a for loop runs once for each value of its counter, an accumulator adds something on every repeat, and a while loop repeats until its condition becomes false
Choose how many times a loop repeats, then run or step through it: watch the counter go up, each repeat light up and the running total grow, and learn when a while loop stops, and when it never does.
A while loop repeats its body as long as its condition is true, so the body must change something that makes the condition false in the end, or the loop never stops
Save the same pocket money every week until you have enough for something you want. A while loop keeps adding while the savings are less than the price: count the weeks, see the loop stop, and find out what makes a loop run forever.
In nested loops the inner loop runs completely for every turn of the outer loop; when the inner loop goes from 1 to row, row r prints r stars and n rows print n(n + 1)/2 stars
Run two loops, one inside the other, to print a triangle of stars. Change the number of rows, count how many times the inner loop runs, and work out how to turn the triangle into a square.
A variable is a named box that holds one value; an assignment works out the right-hand side and puts the answer in the box, replacing what was there, and the program uses the latest value
Buy notebooks at a shop with a small program: put in the price, how many and the money you pay, then step through it and watch each variable's box fill and change until the total and the change are printed.
Repeatedly dividing a number by 2 gives its binary digits as the remainders, from the last bit to the first; each remainder is placed one place further left
Choose a number and run the algorithm that turns it into binary: divide by 2, keep the remainder as the next bit, and repeat until nothing is left. Watch the bits build up from the right and count how many a number needs.
A string is a list of characters with indexes from 0; a loop can visit each one in turn, and two pointers moving in from both ends test a palindrome with only half as many comparisons
Go through a word one letter at a time: count its letters and its vowels, write it backwards, and test whether it is a palindrome by comparing letters from both ends at once.
Every atom is made of protons and neutrons in a tiny nucleus with electrons around it; the number of protons decides which element it is
Add protons, neutrons and electrons one by one and see the atom you make: its name, its mass and how its electrons sit in shells. Then turn carbon into nitrogen with a single proton.
NaHCO₃ + CH₃COOH → CH₃COONa + H₂O + CO₂: one mole (84 g) of baking soda gives one mole (44 g, about 24 L) of carbon dioxide and needs one mole (60 g) of acetic acid
Drop 2 to 20 g of baking soda into vinegar and blow up a balloon with the carbon dioxide. Use the equation and moles to find the mass and volume of the gas and how much vinegar the soda needs.
Solubility is the most of a substance that dissolves in 100 g of water at a given temperature; sugar's solubility rises steeply with temperature, but salt's hardly changes
Stir sugar or salt into water at different temperatures until no more dissolves. See how hot water dissolves far more sugar, while salt hardly changes, and why syrup for sweets is made hot.
Food spoils when microbes grow in it; microbes need water, warmth and time, so food keeps longer when we take the water out, keep it cold, heat it to kill the germs, or pickle it in acid or oil
Look at twelve kitchen foods, from sun-dried fish to mango achar, find out how long each keeps and what stops the microbes, and sort them by the way they are preserved: drying, cold, heat or pickling.
Dissolving salt makes water denser; an object floats when the liquid is denser than the object, so an egg floats once the salty water is denser than the egg
Drop an egg into a glass of water and stir in salt, a spoonful at a time, until the egg floats. Then try an old egg, which floats in plain water, and find out why cooks use this to test eggs.
Water boils when its vapour pushes as hard as the air above it; higher up the air pressure is lower, so water boils at a lower temperature (about 1 °C lower for every 300 m) and food cooks more slowly
Boil a pot of water at the seaside, in Kathmandu, Shimla, Leh and at Everest base camp. See how the boiling point falls as you climb, and why dal takes so much longer to cook up high.
A battery's capacity in mAh is the charge it holds: hours to charge = capacity ÷ charger current (plus about 20% losses), and energy in Wh = capacity (Ah) × voltage
Pick a phone battery of 3000, 4000 or 5000 mAh and a 1 A, 2 A or 3 A charger. Work out how long it takes to charge from empty, how much energy it stores and how many hours the screen can stay on.
An LED takes a fixed forward voltage (about 2 V for red, 3.2 V for blue and white); a resistor in series takes the rest, so by Ohm's law R = (supply − LED voltage) ÷ current
Light a red, green, blue or white LED from a 5 V, 9 V or 12 V supply. Work out the resistor that lets just the right current flow, and how much power the resistor turns into heat.
Electricity and fuel cost money and resources, and making them often pollutes the air; small habits, such as switching off, using LED bulbs and covering pots, save energy, while leaving things on or open wastes it
Look at twelve everyday habits, from switching off lights and cooking with a lid to leaving the TV on standby. Find out why each one saves or wastes energy, and sort them.
Energy = power × time: a 0.4 kW panel in 5 hours of sun gives about 0.4 × 5 × 0.8 = 1.6 kWh, after the losses of heat, dust and wiring
Put 2 to 10 solar panels on a roof and choose how many sunny hours a day it gets. See how many kilowatt-hours they make a day and a month, how many LED bulbs that lights for an evening, and how much CO₂ it saves against coal power.
Each fuel gives a fixed heat per gram, its calorific value, but a stove passes only part of it to the pot; grams burnt = heat needed ÷ (calorific value × efficiency), so a good fuel in a good stove burns far less
Boil 1, 2 or 5 litres of water on an LPG stove, a kerosene stove, a coal stove, an open wood fire or a dung-cake chulo. See the heat the water needs and how many grams of each fuel burn to give it.
On a spinner with equal sectors, P(colour) = sectors of that colour ÷ all sectors; the probabilities add up to 1, and the expected number of times = probability × number of spins
Colour the equal sectors of a spinner red, blue and green, and work out the chance of landing on each colour and how many reds to expect in 60 spins. Then make the game fair.
Batting average = runs ÷ times out (runs per dismissal); strike rate = runs ÷ balls faced × 100 (runs per 100 balls)
Change a batter's runs, balls faced and times out, and work out the batting average and the strike rate. Find out why one tells you how reliable a batter is and the other how fast they score.
Amounts in a recipe are in direct proportion to the number of people: each amount × (new number of people ÷ 4), so doubling the people doubles everything
A dal-bhat recipe feeds 4 people. Cook it for 2, 6, 8 or 10 people instead, and see how the rice, dal, water and salt all change by the same ratio.
In the Fibonacci sequence each number is the sum of the two before it (Fₙ₊₁ = Fₙ + Fₙ₋₁); the ratio of neighbours Fₙ₊₁ ÷ Fₙ gets closer and closer to the golden ratio φ = (1 + √5) ÷ 2 ≈ 1.618
Build the Fibonacci numbers 1, 1, 2, 3, 5, 8, … as a spiral of squares, and divide each by the one before. Watch the ratio swing above and below and settle on 1.618, the golden ratio found in sunflowers, pine cones and shells.
In a group of n people each person shakes n − 1 hands, but every handshake is shared by two people, so there are n(n − 1) ÷ 2 handshakes: the number grows much faster than the group
At a party everyone shakes hands with everyone else once. Change the number of people from 2 to 12 and count the handshakes, then find the rule that works for any group.
Each number in Pascal's triangle is the sum of the two above it; the k-th number of row n is C(n, k), the number of ways to choose k things from n, and row n adds up to 2ⁿ
Pick a row n and a place k in Pascal's triangle. Read the number C(n, k), see that it is the sum of the two above it, and find that every row adds up to a power of 2: the ways of choosing, of tossing coins and of walking a grid.
A loan is repaid in equal monthly instalments, EMI = P r (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), with r the monthly rate and n the months; a longer loan has a smaller EMI but much more interest
Borrow Rs 1 lakh to Rs 10 lakh at 8% to 12% a year and choose to pay it back in 1, 3 or 5 years. See the equal monthly instalment (EMI), the total you pay back and how much of it is interest.
A line of symmetry folds a shape into two halves that match exactly; some shapes have one, some have many, and some have none, even if they look balanced when turned
Look at twelve shapes from nature and daily life, from a butterfly and a snowflake to a shoe and a swirl. Find how many lines of symmetry each has, and sort them into one line, more than one, or none.
The minute hand turns 6° a minute and the hour hand 30° an hour plus 0.5° a minute, so the angle between them is |30h − 5.5m|, or 360° minus that if it is bigger than 180°
Set a clock to any time and work out the angle between its hands. Find the times when the hands make a right angle or a straight line, and see why the hour hand is never exactly on the number at half past.
With n people there are n(n − 1)/2 pairs, each with a 1 in 365 chance of sharing a birthday; the pairs grow so fast that the chance of a shared birthday passes 50% at 23 people: P ≈ 1 − e^(−n(n − 1)/730)
Fill a room with 5 to 70 people and find the chance that at least two of them share a birthday. See why a class of 23 already has an even chance, and why the number of pairs, not people, is the secret.
The nth triangular number is 1 + 2 + … + n = n(n + 1) ÷ 2, and a triangle with the one before it makes a square: Tₙ + Tₙ₋₁ = n²
Stack dots in rows of 1, 2, 3, 4 and more to build triangles. Count the dots in each triangle, find the rule n(n + 1) ÷ 2, and see how two neighbouring triangles fit together into a square.
Every measurement has a quantity (length, mass, volume or time) and a unit; we choose a unit that suits the size, so the number is neither huge nor tiny: kilometres for roads, millimetres for an ant
From the distance between two cities to a spoon of cough syrup, decide what each of twelve everyday things measures, length, mass, volume or time, and choose a unit that suits its size.
Body mass index compares mass with height: BMI = mass (kg) ÷ height² (m²); for adults 18.5 to under 25 is a healthy range, but children are still growing, so their BMI is checked on charts for their age and sex
Choose a mass and a height and work out the body mass index, BMI = mass ÷ height². See which adult band it falls in, and learn why doctors use age charts, not these bands, for growing children.
Energy used (kcal) ≈ MET × body mass (kg) × time (hours), where the MET says how many times harder than resting an activity is; harder play, a heavier body and longer play all use more energy
Choose a game or exercise, your body mass and how long you play, and work out how much food energy your body uses, in kilocalories and in rotis.
First aid is the help given before a doctor arrives: it keeps the person safe, stops things getting worse and gets them to proper care; some common habits, like ice on burns or sucking snake venom, harm or waste precious time
Twelve things people do for burns, cuts, nosebleeds, snake and dog bites, diarrhoea and someone who has fainted. Find out why each helps or harms, and sort the good first aid from the old habits that do damage.
Each case of a disease infects R₀ people when no one is immune; when more than 1 − 1/R₀ of people are vaccinated, each case infects fewer than one other and the disease dies out, protecting even those who cannot be vaccinated
Choose a disease, from flu to measles, and how many people in a town are vaccinated. See how many people each case infects now, how many must be vaccinated for herd immunity, and whether the disease dies out or keeps spreading.
Bacteria multiply by splitting in two; in warm food they can double every 20 minutes, so after n doublings one germ becomes 2ⁿ, which grows faster and faster
Start with one germ on a plate of food left out in the warm. Choose how often it doubles and how many hours pass, and watch one germ become thousands, then millions, which is why cooked food should not sit out for long.
The body loses water in sweat, breath and urine, so a child needs about 35 mL of water for every kg of body mass each day, more when playing hard and on hot days
Choose a body mass, the minutes of hard play and whether it is a hot day, and work out how much water a child needs in a day, in millilitres and in glasses.
Inherited traits are set by genes passed from parents to children; acquired traits are learnt or gained during life, from practice, injury or the surroundings, and are not passed on in the genes
Look at twelve traits, from eye colour and dimples to a scar, a suntan and the language you speak. Find where each comes from and whether your children could get it from you, then sort them into inherited and acquired traits.
A lack of one nutrient causes a deficiency disease: vitamin A night blindness, vitamin C scurvy, vitamin D rickets, vitamin B1 beriberi, iron anaemia and iodine goitre; foods rich in that nutrient prevent it
Twelve cards show a sign of poor diet, such as night blindness or a swollen neck, or a food that prevents one, such as carrots or iodised salt. Find out what each tells you, then sort them by the vitamin or mineral they are about.
Red cells may carry A, B and Rh antigens; a patient's blood attacks any A or B it lacks, and an Rh-negative patient reacts to Rh, so O− can give to everyone and AB+ can take from everyone
Check twelve donor and patient pairs, from O− to A+ and AB+ to O−. Find the antigens on the donor's red cells and the antibodies in the patient's blood, and sort each transfusion as safe or not safe.
Magnitude is a logarithmic scale: each step of 1 means 10 times the shaking on a seismograph and about 32 times (10^1.5) the energy
Pick two earthquakes by their magnitude, from a small 3 to a great 8, and see how many times more the ground shakes and how many times more energy the bigger one lets out. Find why the 7.8 Gorkha earthquake of 2015 was so much worse than a 5.
1 mm of rain on 1 m² of roof is 1 litre of water, so a roof collects area × rain × 0.8 litres (some splashes or soaks away): even a small roof can store a lot of water in the monsoon
Choose the size of a roof and the rain in a month, and work out how many litres of rainwater a family could collect in a tank, and for how many days it would give a family of five their water.
Gravity pulls a satellite towards the Earth and keeps it moving in a circle; in an orbit of radius r its speed is v = √(GM ÷ r), so higher satellites move slower and take longer to go round
Put a satellite in a low orbit like the International Space Station, in a GPS orbit, or in a geostationary orbit used for TV. See how far it is from the Earth's centre, how fast gravity makes it go and how long one trip round the Earth takes.
Light travels at about 299 792 km every second, so the time it takes is distance ÷ speed: a fraction of a second from a satellite, 8 minutes from the Sun and more than 4 years from the nearest star
Send light to us from a GPS satellite, the Moon, the Sun, Mars and the nearest star, and work out how long each journey takes. Find out why we see the Sun as it was eight minutes ago.
Light travels in straight lines, so a stick's shadow is its height ÷ tan(the sun's height): the lower the sun, the longer the shadow, and with the sun straight overhead there is no shadow at all
Stand a stick in the sun and move the sun from low in the morning sky to straight overhead. See how long the shadow is each time, and why shadows are long in the morning and evening and shortest at noon.
Trees take carbon dioxide from the air by photosynthesis and store the carbon in their wood: a grown tree takes about 21 kg of CO₂ a year, while a car gives out about 0.17 kg every kilometre
Plant 1, 10 or 100 trees and let them grow for 1 to 20 years. Find how much carbon dioxide they take from the air, and how many kilometres a car could drive to give out the same amount.
A scale model divides every size and distance by the same number: if the Earth were a 22 cm football, the Moon would be a 6 cm ball 6.6 m away and the Sun a 24 m ball 2.6 km away, so space is mostly empty
Shrink the Earth to a football, a cricket ball or a marble, and shrink everything else by the same scale. See how big the Moon and the Sun would be, and how far away they would sit.
Burning petrol and diesel gives carbon dioxide, a greenhouse gas: kg of CO₂ = km travelled × kg per km per person, so walking or cycling gives none, a shared bus gives little, and a car gives the most for each student
Choose how you get to school, how far it is, and for how many days. See how many kilograms of carbon dioxide the trips put into the air, and how many trees it would take a year to soak it up.
The Earth turns 360° in 24 hours, so 15° of longitude is 1 hour: places to the east see the sun first and their clocks are ahead; each country sets its standard time from a longitude near its middle
It is noon in Kathmandu. What time is it in London, Delhi, Tokyo or New York? Pick two cities and see how the turning Earth gives every country its own clock time, and why Nepal is 5 hours 45 minutes ahead of London.
Force = pressure difference × area: a fan that lowers the pressure under a car presses it onto the road
Switch on a fan that sucks the air out from under a sports car, and see how a small pressure difference over the car's floor gives a huge downforce, more grip and faster cornering. Then blow air in to make the car float, and fire thrusters to see when thrust beats weight and the car flies.
A stretched band stores elastic potential energy E = ½kx²; on release it becomes kinetic energy ½mv², so v = √(2E ÷ m), and at 45° the pellet flies about v² ÷ g: twice the stretch gives four times the energy and twice the speed
Stretch a rubber band and fire a paper pellet. Change the band, how far you stretch it and the pellet's mass, and see the energy stored in the band, the launch speed and how far the pellet flies.
A falling object speeds up until air drag equals its weight; then it falls at a steady (terminal) speed v = √(2mg ÷ (ρCA)), so a bigger canopy falls slower
Hang a 20 g, 50 g or 100 g toy under a canopy of 0.1 to 1 m², and find how fast it falls once air drag balances its weight, and how long it takes to drop 10 m.
Gear ratio = front teeth ÷ rear teeth: the back wheel turns that many times for each turn of the pedals, so a big ratio goes far and fast but is hard to push, and a small ratio is easy to push but slow
Change the front and rear gears of a bicycle and see how far one turn of the pedals takes you, and how fast you go at the same pedalling. Find the easy gear for a hill and the fast gear for a flat road.
Radioactive atoms decay at random, but in each half-life half of those left decay: after n half-lives 100% × (½)ⁿ remain, whether the half-life is hours or thousands of years
Watch a crowd of radioactive atoms decay. Choose an isotope used in hospitals or for dating old bones, let half-lives go by, and see what share of the atoms is left and how long that took.
Plants cannot move, so they spread their seeds away from the parent plant by wind, water, animals or bursting pods, and each seed or fruit has a shape that suits its way of travelling
Look closely at twelve seeds and fruits, from the dandelion's parachute to the coconut's husk and the burr's hooks, and sort them by how they travel: by wind, by water, by animals or by bursting pods.
Light arrives almost at once but sound travels only about 343 m a second, so the distance to lightning in km is the seconds from flash to thunder × 0.343
Count the seconds between a lightning flash and its thunder, and work out how far away the lightning struck. Find out why a short gap means you must go indoors at once.
Loudness is measured in decibels (dB): every 10 dB is ten times the sound energy; the level falls about 6 dB each time the distance doubles, and above 85 dB the safe listening time halves for every 3 dB more
Stand near a whisper, a conversation, busy traffic, a pressure horn or a firecracker. See the sound level in decibels, how it drops as you move away, and how long your ears can safely take it each day.
Hot things cool faster the hotter they are than the room: T = room + (start − room) × e^(−kt); a lid and a vacuum flask cut heat loss, giving a much smaller k
Pour tea at 90 °C into an open cup, a covered cup or a vacuum flask in a 25 °C room, and follow its temperature for an hour to see which keeps it hot and why.
Stopping distance = thinking distance (speed × reaction time) + braking distance (v² ÷ 2μg): doubling the speed doubles the first but four-times the second
A child steps onto the road 30 m ahead. Change the vehicle's speed, the driver's reaction time and the road, and find the thinking distance, the braking distance and whether it stops in time.
A scale shows how hard it pushes up on you: N = m(g + a), so you seem heavier when the lift speeds up upward, lighter when it speeds up downward, and weightless in free fall
Stand on a bathroom scale in a lift. See what it reads as the lift starts going up, moves steadily, starts going down, and, if the cable snapped, falls freely.