160 experiments found
Clear filtersCurrent flows only around a complete, unbroken circuit; more cells push a bigger current
Connect cells, a switch and a bulb, close and open the switch, add a second cell and break a wire to see when current flows.
Conductors let electric current flow and insulators do not; metals and graphite conduct, while plastic, rubber, glass and dry wood insulate
Put different materials into the gap in a simple circuit, see whether the bulb lights, and sort them into conductors and insulators.
The current through a socket is the sum of the currents of everything plugged into it; a fuse melts and breaks the circuit when the current is more than the wiring can safely carry
Plug a TV, a kettle, a heater and an iron into one extension board. Watch the current add up, see the fuse blow when it gets too big, and learn why a fuse keeps your home safe.
Acceleration increases with force and decreases with mass (a = F ÷ m)
Pull a trolley with different forces and loads, read its ticker tape, and discover how force and mass change its acceleration.
Rougher surfaces and heavier objects give more friction
Pull a wooden block across glass, wood, sandpaper and oiled wood with a spring balance, and find the force that just starts it moving.
Dark surfaces absorb more of the Sun's radiation than light or shiny ones; a reflector sends in more sunlight and a glass lid traps the heat
Heat a pot of water in a box solar cooker. Try a black, a white and a shiny pot, add a foil reflector and a glass lid, and find out how to make the water boil with sunlight alone.
Heated liquid expands, becomes less dense and rises; cooler, denser liquid sinks to take its place
Drop a purple dye crystal into a beaker of water, heat one corner, and follow the dye as the convection current carries it round.
Metals are good conductors of heat; glass and wood are poor conductors (insulators)
Stand rods of copper, aluminium, iron, glass and wood in hot water with wax beads stuck along them, and watch how fast the heat travels.
A plane mirror forms an upright, same-size, laterally inverted virtual image as far behind the mirror as the object is in front
Stand a letter card in front of a mirror at different distances and find where its image is, how big it is and which way round it faces.
Light travels in straight lines, so rays from a candle cross at the pinhole and make an upside-down image on the screen
Point a pinhole camera at a candle. Move the candle, make the box longer and the hole bigger, and see how the upside-down image on the screen changes.
Like poles repel and unlike poles attract; the force gets weaker as the magnets move apart
Bring the poles of two bar magnets together in different pairs and at different distances, and find the rule for attraction and repulsion.
Average speed = total distance ÷ total time
Time a walker, a runner, a cyclist, a bus and a tortoise over measured distances and calculate their average speeds.
Motion can be linear, circular, rotational, oscillatory or random, depending on the path an object follows
Watch the path of moving things, from a falling stone to a spinning prayer wheel and a swinging ping, and sort them by their type of motion.
Practical work is safe when we follow the lab rules, protect our eyes and skin, and understand the hazard symbols on chemicals
Before practical work, think about what could happen with each habit in the science lab, then sort them into safe and unsafe. Learn the hazard symbols on the bench.
Pulleys change the direction of a force, and more supporting strands reduce the effort needed
Lift loads with a fixed pulley, a movable pulley and a block and tackle, and compare the effort, mechanical advantage and efficiency.
Sound is made by vibrations; frequency sets the pitch and amplitude sets the loudness
Pluck a string on a sonometer, change its length, tightness and how hard you pluck it, and watch the sound wave on an oscilloscope.
The Earth's axis is tilted, so as it goes round the Sun, Nepal leans towards the Sun in summer (long days, high Sun) and away from it in winter (short days, low Sun)
Move the Earth round the Sun and see how long the day is in Kathmandu, how high the Sun climbs at noon and how long a stick's shadow is in June, September, December and March. Then imagine an Earth with no tilt.
The Sun always lights half of the Moon; as the Moon goes round the Earth in about 29.5 days, we see more or less of that lit half, which gives the phases
Move the Moon round the Earth, day by day through its month, and watch how much of it we see lit from Nepal, from Aunsi (new moon) to Purnima (full moon) and back.
Gas, a new solid or a colour change can show a chemical reaction
Mix kitchen substances and look for evidence that a new substance has formed: gas bubbles or a new solid.
Iron rusts when both water and oxygen are present; salt speeds it up and coatings prevent it
Leave iron nails in six test tubes with different conditions for several days and find out what rusting needs, and how paint and zinc protect iron.
Natural materials come from plants, animals or the ground; synthetic materials are made in factories, mostly from petroleum, and behave differently when burnt and in the soil
Find out where eleven everyday materials come from, from Dhaka cloth and pashmina to nylon and plastic bags, test a thread of each in a flame, and sort them into natural and synthetic.
An element has one kind of atom, a compound has different atoms chemically joined in fixed amounts, and a mixture has substances mixed but not joined
Look at particle models of everyday substances, test whether they can be separated, and sort them into elements, compounds and mixtures.
Several separation methods can be combined to separate a mixture
Use dissolving, filtration and evaporation one after another to separate salt from sand and collect salt crystals.
Invertebrates have no backbone; they are grouped by their body plan, such as jointed legs (arthropods), a soft body often with a shell (molluscs) or a body of rings (annelids)
Look at the body, the legs and the covering of fifteen invertebrates, from butterflies and crabs to snails, leeches and starfish, then sort them into their groups.
Plant and animal cells both have a nucleus, cytoplasm, cell membrane and mitochondria; only plant cells have a cell wall, chloroplasts and a large central vacuole
Label the parts of a plant cell and an animal cell, find out what each part does, and discover which parts only plant cells have.
Organs that work together to do one big job form a body system, such as the digestive system, which breaks down food
Find sixteen organs on the body, read what each one does, and sort them into the digestive, respiratory, circulatory, nervous, excretory and skeletal systems.
Organisms have adaptations, special features that help them survive in their habitat
Study the body features of plants and animals, from a yak to a lotus, and match each one to the habitat it is adapted to.
Water travels up the stem in xylem tubes, pulled by water evaporating from the leaves
Stand celery stalks in red-dyed water, with and without leaves, in a warm sunny place and a cool shady one, and track how high the dye climbs.
Plants use light energy to make glucose from carbon dioxide and water, giving off oxygen; light, carbon dioxide and temperature can each limit the rate
Shine a lamp on pondweed and count the oxygen bubbles. Change the light distance, the light colour, the carbon dioxide and the temperature to find what limits photosynthesis.
Stomata are tiny pores, mostly on the underside of leaves, opened and closed by a pair of guard cells to let gases in and out and control water loss
Look at a peel from the underside of a leaf under the microscope and label the epidermal cells, guard cells, chloroplasts and open and closed stomata.
Plants lose water vapour through stomata in their leaves; it is faster in warm, bright, windy and dry conditions
Stand a leafy shoot in water under a plastic bag and measure how much water it loses in light and dark, still and windy, dry and humid air, and with its leaves greased.
Many plants make new plants from a stem, a root or a leaf, without seeds; this vegetative propagation gives plants exactly like the parent, quickly
Find which part of twelve plants, from potato, ginger and sugarcane to sweet potato and bryophyllum, is planted to grow a new plant, and sort them by stem, root or leaf.
Energy flows from producers through consumers in a food chain; only about a tenth of the energy passes to each next level
Build a food chain from organisms found around a Nepali paddy field, place each at its feeding level, and follow how energy is lost at every step.
Decomposers such as bacteria and fungi break down dead organic matter fastest when it is warm and moist; plastic is not biodegradable
Leave fruit peel, leaves, paper and plastic in sealed jars of soil, change the moisture and temperature, and measure how much decomposes over four weeks.
The Sun drives the water cycle of evaporation, condensation and precipitation
Shine a lamp on water in a covered tank with ice on the lid. Watch evaporation, condensation and rain happen in a small model of the water cycle.
Weather records of the highest and lowest temperatures and the rainfall, averaged over many years, describe a place's climate; the mean temperature is (highest + lowest) ÷ 2 and the range is highest − lowest
Read the weather records of Delhi, Mumbai, Kolkata, Dhaka, Kathmandu and Chennai in January, May and July: the highest and lowest temperatures, the daily range, the mean and the rainfall. Compare the cool winter, the hot dry summer and the wet monsoon.
A computer stores numbers as bits that are either on (1) or off (0); each bit is worth twice the one to its right, and the number is the sum of the bits that are on
Four bulbs are worth 8, 4, 2 and 1. Switch them on and off to make numbers, and find out how a computer stores every number with just ones and zeros.
A password is safer when it is long and mixes letters, digits and symbols, because the number of possible passwords to try grows enormously
A computer tries a million passwords every second. Make a password longer, add letters and symbols, and see how long it would take the computer to try them all.
(a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b², which can be seen as areas of squares and rectangles
Build a square of side a + b from four tiles and see why (a + b)² = a² + 2ab + b². Then cut strips from a square of side a to see (a − b)² = a² − 2ab + b².
Area of a triangle = ½ × base × height, wherever the top corner is; its perimeter is the sum of its three sides
Draw a triangle inside a rectangle with the same base and height, slide its top corner along and see that its area is always half the rectangle, even when the triangle leans over.
A bearing is a direction measured clockwise from north, written with three figures (045°); on a scale drawing, real distance = distance on the map × the scale
Draw the way from your school to a village on a map. Change the scale, the length on the map and the bearing, and find the real distance and direction.
The circumference of any circle is π × diameter, and its area is π × radius²
Unroll a wheel's rim along the road to discover π, cut the wheel into slices to find its area, and work out how far it rolls.
Congruent figures have the same shape and the same size; similar figures have the same shape (equal angles, sides in the same ratio) but can be different sizes; every congruent pair is also similar
Compare ten pairs of figures, from a page and its photocopy to a small and a large map of Nepal. Check their sides and angles, and sort the pairs into congruent, similar or neither.
Reflections, rotations and translations move every point by a rule on its coordinates and keep the shape congruent
Flip, turn and slide a rangoli motif on a coordinate grid and watch where every corner lands.
An inequality such as x > 2 has many solutions, shown on a number line by a shaded arrow; an open circle means the boundary is not included (> or <), and a filled circle means it is (≥ or ≤)
Choose an inequality such as x > 2, see its solutions shaded on a number line, and test numbers to find out whether they are solutions. Learn when the circle is open and when it is filled.
For the same base, aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ and (aᵐ)ⁿ = aᵐⁿ
Multiply, divide and raise powers of 2. See each written out in full, then find the shortcut: add the indices, subtract them or multiply them.
The product of two integers with the same sign is positive and of two with different signs is negative: (+) × (+) = +, (−) × (−) = +, (+) × (−) = − and (−) × (+) = −
A lift is at floor 5. It moves up or down a number of floors each minute. Find where it will be in a few minutes, or where it was a few minutes ago, and discover the rules for multiplying positive and negative numbers.
An equation stays balanced when the same thing is done to both sides
Rice bags of unknown weight sit on a taraju. Take weights off both pans and share them out to find what one bag weighs.
When a transversal crosses parallel lines, corresponding and alternate angles are equal and co-interior angles add up to 180°
Turn a diagonal road across two parallel streets and compare the angles it makes at both crossings.
The volume of a cuboid is length × breadth × height and its total surface area is 2(lb + bh + hl); a cube is a cuboid with all edges equal
Change the length, breadth and height of a cardboard box. Find how much it holds (volume) and how much cardboard it needs (surface area), and see that boxes with the same volume can need different amounts of cardboard.
Profit or loss = SP − CP, and its percentage is worked out on the cost price; commission is a percentage of the selling price
A farmer sells a crate of oranges through a dealer: set the cost, the selling price and the dealer's commission, and see the profit or loss.
Two mixtures taste the same when their ratios are equal, whatever the amount
Pour cups of syrup and water to match a 1 : 3 recipe, then scale it up for more guests without changing the taste.
A rational number is p/q with q ≠ 0; to place it, cut each unit into q equal parts and count p parts from 0, to the right if p/q is positive and to the left if it is negative; equivalent fractions such as 1/2 and 2/4 share one point
Choose a numerator p and a denominator q, positive or negative, and see where p/q sits on the number line: split each unit into q equal parts and count p of them. Find its decimal, the integers it lies between, and fractions equal to it.
The universal set U holds every member we are talking about; A is a subset of B (A ⊆ B) when every member of A is also in B, and the complement A′ is everything in U that is not in A
The universal set is the numbers 1 to 12. Choose two sets from it, see their members in a Venn diagram, and find out when one set is a subset of the other.
A solid has faces (flat surfaces), edges (where faces meet) and vertices (corners); for every solid with flat faces like these, Euler's formula says F + V − E = 2
Build seven solids from straws and clay: a cube, a cuboid, prisms, pyramids, a tetrahedron and an octahedron. Count their faces, vertices and edges, and find the number that F + V − E always gives.
The side of a square is the square root of its area; a square root lies between the roots of the nearest perfect squares
Choose the area of a square carpet and find how long its sides are; estimate square roots that are not whole numbers.
The mean shares the total out equally, the median is the middle value, and one unusual value moves the mean far more than the median
Drag the stacks of tomato crates sold each day and watch the mean, median, mode and range change.
The interior angles of a polygon with n sides add up to (n − 2) × 180°; a regular polygon tessellates on its own only if its interior angle divides 360° exactly, as for triangles, squares and hexagons
Fit regular triangles, squares, pentagons, hexagons and octagons round a point. Find each polygon's angle sum and interior angle, and discover which ones tessellate with no gaps.
When the work is fixed, the number of workers and the number of days are inversely proportional: workers × days stays the same, so twice the workers take half the days
A wall needs 60 worker-days of work. Change the number of workers and find how many days the job takes. Then try harvesting a field.
The cube of a number n is n × n × n = n³, the number of unit cubes in a cube with n along each edge; the cube root ∛ undoes it, so ∛64 = 4 because 4³ = 64
Build cubes from small unit cubes, 1, 2, 3 and up to 6 along each edge. Count the cubes, the squares on the outside and the cubes hidden inside, and find cube roots.
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.