171 experiments found
Clear filtersA bulb glows only when the circuit is closed: an unbroken loop from the cell, through the bulb and back
Open up a torch and switch it on and off. Loosen a wire, add a second cell and try a broken bulb, and find out when current can flow and the bulb glows.
An object is at rest if it does not change its position compared with what is around it, and moving if it does; so rest and motion depend on what we compare with
Watch a passenger in a school bus, first from the roadside and then from a seat in the bus. Is the passenger moving? Is the tree? Find out why the answer depends on where you watch from.
At a mirror, the angle of reflection equals the angle of incidence
Shine a ray of light at a plane mirror at different angles, measure the angle of reflection, and compare a mirror with a rough surface.
Light travels in straight lines, so an opaque object blocks it and casts a shadow that grows as the light comes closer
Move a torch closer to and further from an object and watch its shadow on a screen grow and shrink. Try opaque, translucent and transparent objects.
Transparent materials let almost all light through, translucent materials let some through, and opaque materials let none through and cast shadows
Shine a torch through different materials, see how much light passes, and sort them into transparent, translucent and opaque.
Magnets attract iron, steel, nickel and cobalt; most other materials, including most metals, are non-magnetic
Test everyday objects with a magnet, find out what they are made of, and sort them into magnetic and non-magnetic materials.
Denser liquids sink below less dense liquids
Pour honey, dish soap, water and oil into a cylinder and watch them stack in layers by density.
Mass is the amount of matter and stays the same everywhere; weight is the pull of gravity and changes from place to place
Weigh objects with a beam balance and a spring balance on Earth, the Moon, Mars and Jupiter, and see which reading changes.
Read a ruler from the zero mark to the nearest millimetre, and subtract the starting mark if you cannot start at zero
Measure a pencil, an eraser and a leaf to the nearest millimetre, then learn to measure correctly with a ruler whose end is worn.
Read the bottom of the meniscus with your eye level with it
Read the volume of three liquids in a measuring cylinder at the bottom of the meniscus, and see why your eye must be level with it.
An object sunk in water pushes aside (displaces) its own volume of water
Lower a stone, a key, a marble and a toy into water and measure how much the water rises. Use an overflow can for a stone too big for the cylinder.
In a fair test we change only one thing (the variable we are testing) and keep everything else the same, so we know what caused the difference
Dip paper towels and a cloth in water and measure how much each soaks up. First see how an unfair test can fool you, then make it fair by changing only one thing at a time.
A lever balances when the clockwise and anticlockwise moments are equal
Hang a load on a metre-rule lever, push down on the other side, and find every way to balance it.
A ramp is a simple machine: a longer ramp needs a smaller push, but you push the load a longer way
Load a sack of rice onto a truck. Lift it straight up, then push it up ramps of different lengths, on a trolley or dragged, and see how much push each one needs.
Simple machines (lever, pulley, wheel and axle, inclined plane, wedge, screw) make work easier by changing the size or direction of a force
Look at how everyday tools and devices work, including a dhiki and a janto, and sort them into the six types of simple machine.
Sound is made when something vibrates; the faster it vibrates, the higher the note (pitch)
Blow across the top of a bottle and tap it with a spoon, with more and more water inside. Find what vibrates each time, and how the water changes the note.
Indicators change colour in acids and bases
Use red cabbage indicator to sort everyday liquids into acids, bases and neutral substances.
Natural fibres come from plants (cotton, jute, coir, flax) or animals (wool, silk, pashmina); man-made fibres such as nylon, polyester and acrylic are made from chemicals; plant fibres burn like paper, animal fibres smell of burning hair, and synthetic fibres melt
Look at twelve fibres, from cotton and jute to pashmina, silk and nylon. Find where each comes from and how a thread of it burns, then sort them into plant fibres, animal fibres and man-made fibres.
Evaporation turns liquid water into vapour; condensation turns vapour back into liquid
Heat salt water until the water evaporates and leaves salt behind, and watch water vapour condense on a cold lid.
The state of matter depends on how particles are arranged and how fast they move
Heat and cool water and wax, and watch how their particles are arranged and how fast they move in each state.
Physical changes can be reversed; chemical changes make new substances
Heat and cool ice, wax, sugar and egg white. Find out which changes can be reversed and which make a new substance.
Filtration separates insoluble solids from liquids
Filter muddy water and salty water. Discover what filter paper can and cannot remove.
Heavy insoluble particles settle, so the liquid above can be poured off
Stir sand into water, let it settle, then pour off the clear water without disturbing the sand.
A magnet separates magnetic materials from non-magnetic ones
Mix sand and iron filings, then use a magnet to pull the iron out. Find out why a magnet cannot separate salt from sand.
Some solids dissolve, and water can dissolve only a limited amount
Stir salt, sugar and sand into water. Find out which ones dissolve, and how much salt water can hold.
Heat, stirring and smaller pieces make a solid dissolve faster
Race sugar cubes and granulated sugar in cold and hot water, stirred and unstirred, and time how long each takes to dissolve.
Solids keep their shape, liquids flow and take the shape of their container, and gases spread out to fill any space
Test everyday materials for shape, flow and how they fill a container, then sort them into solids, liquids and gases.
Animals are grouped by what they eat: herbivores eat plants, carnivores eat other animals and omnivores eat both, and their teeth or beaks suit their food
Look at what each animal eats and at its teeth or beak, then sort the animals into herbivores, carnivores and omnivores.
Animals with a backbone (vertebrates) form five groups, told apart by their body covering, how they breathe and how their young are born
Check each animal's body covering, how it breathes and how its young are born, then sort it into fish, amphibians, reptiles, birds or mammals. Watch out for the bat, the whale and the penguin!
A balanced diet gives enough energy and protein and has every food group: cereals for energy, dal and milk for protein, vegetables and fruit for vitamins, minerals and roughage, with water
Plan a day's food from rice or roti, dal, milk or curd, vegetables and fruit. See how much energy and protein it gives against what an 11-year-old needs, and how many food groups are on the plate.
Iodine turns starch blue-black, copper sulphate with caustic soda turns protein violet, and fat leaves a see-through oily spot on paper; most foods are mostly one nutrient
Test twelve everyday foods, from rice and atta to egg white and ghee, with iodine, copper sulphate and a piece of paper, then sort them by the nutrient they are mostly made of.
Exercise makes our muscles need more oxygen and food, so we breathe faster and the heart beats faster; both slow down again as we rest
Count your heartbeats and breaths for 15 seconds while sitting still, then after walking, skipping and running, and again as you rest. See how hard your body works, and how quickly it calms down.
Living things carry out all the life processes; a thing that shows only one or two, like fire or a car, is not alive
Check things for the signs of life (moving, breathing, sensing, growing, reproducing, excreting and needing food) and sort them into living, once living and never alive.
Microorganisms are too small to see without a microscope; the main groups are bacteria, fungi, protozoa, algae and viruses, and some are useful while others cause disease
Look at prepared slides and microscope images of tiny living things, find out whether they are useful or harmful, and sort them into bacteria, fungi, protozoa, algae and viruses.
Flowering plants make flowers and seeds inside fruits; non-flowering plants never flower and make spores (ferns, mosses) or bare seeds on cones (pine, cycas)
Look for flowers and seeds on ten plants with a hand lens, then sort them into flowering and non-flowering plants. Does every plant have seeds?
Roots grow best in loose soil that holds some water and lets air in; too little or too much water slows them
Grow maize seedlings in clear pots of sandy, loamy and clay soil with different amounts of water, and measure the roots.
A seed contains a tiny plant (embryo) with a food store, protected by a seed coat; beans store food in two cotyledons, maize in its endosperm
Soak a bean seed and a maize grain, open them up, and label the seed coat, hilum, micropyle, cotyledons, plumule, radicle and endosperm.
A leaf has a stalk (petiole) and a flat blade (lamina) supported by a midrib and veins, with an edge (margin) and a tip (apex)
Examine a leaf with a magnifying glass and label its petiole, lamina, midrib, veins, margin and apex.
Leaves with a network of veins (reticulate) usually belong to plants with tap roots; leaves with parallel veins usually belong to plants with fibrous roots
Look closely at the veins in leaves from common Nepali plants, check their roots too, and sort them into reticulate and parallel venation.
Each part of a flowering plant has a job: roots take in water, the stem carries it, leaves make food, flowers make seeds, and fruits protect and spread them
Label the root, stem, leaf, flower, bud and fruit on a flowering plant, and find out the job each part does.
Seeds need water, warmth and oxygen (air) to germinate; light is not needed until the seedling grows
Set up dishes of bean seeds with and without water, warmth, air and light, and count how many germinate each day.
In a food chain every living thing depends on the others; taking one away upsets the balance of the whole pond
Watch the food chain in a village pond: water plants, insects, frogs and snakes. Catch frogs, or let soap or pesticide wash in, and see how the numbers of the others change.
Soil is a mixture of particles of different sizes and organic matter
Shake three soil samples with water and let them settle into layers of gravel, sand, silt and clay, with humus floating on top. Compare garden, river and clay soils.
Water quality can be compared using appearance, pH and hardness tests
Compare tap, well, river and pond water by appearance, pH and hardness, using distilled water as a control.
A computer takes in information through input devices, works on it in the processor, gives out results through output devices and keeps it in storage
Plug devices into a computer one by one and see what each does: does it send information in, give it out, work on it or keep it? Then sort them all.
Perimeter is the length around a shape and area is the space inside; the same perimeter can hold different areas
Shape a vegetable garden with a 24 m roll of fence and find which rectangle grows the most vegetables.
Split an irregular shape into rectangles and triangles and add their areas; for a curved shape, count the squares at least half inside
Find the area of an L-shaped room, a T-shaped courtyard, a field with a slanted side and a pond with a curved edge, by splitting them into rectangles and triangles or by counting squares on a 1 m grid.
The area of a shaded region is the area of the whole shape minus the area cut out of it
Pave a path round a rectangular lawn and dig a round pond in it, then work out the area of path to pave and the grass left to mow.
A point on a grid is named by an ordered pair (x, y): first how far along the x axis from the origin O, then how far up the y axis; the order matters
A village map is drawn on a grid. Move along the x axis and up the y axis to find the temple, the health post and the chautari, and see why (4, 3) is not the same place as (3, 4).
A scale such as 1 unit = 10 vehicles lets big counts fit on a graph: the height of each bar is the count divided by the scale, and a bar can be part of a unit
Pupils counted the vehicles passing their school in an hour: 75 motorbikes, 50 rickshaws, 45 cars, 30 bicycles and 20 buses. Draw the bar graph with different scales and see how many units tall each bar must be.
In a decimal, each place is ten times smaller than the one to its left; rounding looks at the next place to decide
Put 1 kg bags, 100 g packets and 10 g scoops of rice on a scale to build decimals, then round the weight for the bill.
An equation is a balance: x + 3 = 8 is true only when x = 5; if the left side is heavier, x + 3 > 8, and if it is lighter, x + 3 < 8
A bag of unknown weight x and some 1 kg weights sit on one side of a tarazu, and weights on the other. Try values of x until it balances, and see the inequality when it tips.
The LCM is the first common multiple and the HCF is the biggest common factor; prime factorisation finds both
Find when two buses leave the bus park together again (LCM), and how to cut two poles into the longest equal pieces (HCF).
A fraction, a decimal and a percentage can describe the same share of a whole
Cut a cake into equal pieces, take some, and see the same share as a fraction, a decimal and a percentage.
A function gives exactly one output for each input; a linear rule y = mx + c can be found from its table
Build a machine that turns plates of momo into a bill, then crack secret machines by comparing their inputs and outputs.
A power such as 2³ means the base 2 multiplied by itself 3 times: 2 × 2 × 2 = 8; the index tells how many times; any base to the power 1 is itself, and to the power 0 is 1
Choose a base and an index, see the power written as repeated multiplication, and find its value. Discover what an index of 0 or 1 means, and why powers of 10 make place value.
Adding a positive number moves right on the number line; adding a negative number moves left
Start from a morning temperature, warm up or cool down, and watch each change hop along the number line, including past zero.
Angles are measured in degrees: acute angles are less than 90°, a right angle is 90°, obtuse angles are between 90° and 180°, a straight angle is 180°, and reflex angles are more than 180°
Measure ten angles, from the hands of a clock to an open laptop and a pizza with a slice gone, compare each with a right angle, and sort them by type.
Each metric unit is 10 times the next smaller one, so converting means multiplying or dividing by 10, 100 or 1000
Walk up and down a staircase of metric units to convert road lengths, milk and rice between km, m, cm, L, mL, kg and g.
A prime number has exactly two factors, 1 and itself; crossing out the multiples of each prime in turn (the sieve of Eratosthenes) leaves only the primes, and a composite number has a smallest factor other than 1
Write the numbers from 1 to 100 in a grid, cross out the multiples of 2, 3, 5 and 7, and see the primes that are left. Count the primes up to a limit, and test whether numbers such as 91 and 97 are prime.
When each step adds the same amount a, the nth term of the pattern is an + b
Push tables together for a wedding feast, spot the pattern in the number of seats, and write the rule for any number of tables.
A polygon with n sides has angles adding up to (n − 2) × 180°; regular tiles fit round a point only if their angle divides 360°
Cut polygons into triangles to find their angle sums, then test which regular tiles cover a courtyard floor with no gaps.
When the selling price is more than the cost price there is a profit; when it is less there is a loss; profit or loss per cent = profit or loss ÷ cost price × 100
Buy things for your school fair stall and sell them. Change the cost price and the selling price, and find the profit or loss in rupees and per cent.
A quadrilateral has four sides and four angles adding up to 360°; its sides (equal or parallel) and angles (right or not) decide whether it is a square, rectangle, rhombus, parallelogram, trapezium or kite
Look at twelve four-sided shapes around you, from a carrom board to a Dhaka topi and a changa. Check their sides and angles, and sort them into squares, rectangles, rhombuses, parallelograms, trapeziums and kites.
A set is a well-defined collection; a set with no members is empty (∅), one with exactly one member is a singleton, one whose members can be counted to an end is finite, and one whose members never end is infinite
Write twelve sets in set notation, from the provinces of Nepal to the months with 32 days, count their members, and sort them by type.
n(A ∪ B) = n(A) + n(B) − n(A ∩ B), because the students in both sets are counted twice
Put every student of a class in a Venn diagram of football and cricket fans, and find how many like both, one or neither.
Volume = length × width × height counts the unit cubes inside; surface area adds up the six faces of the net
Shape a cuboid water tank, count the litres it holds, open it into its net and find the tank that needs the least metal.
distance = speed × time; on a distance–time graph a steeper line means a higher speed
Send a bus and a later motorbike along the 200 km highway, read a distance–time graph and find where the bike catches the bus.
A line of symmetry reflects a shape onto itself; rotational symmetry turns it onto itself before a full turn
Hold a mirror across tiles, a kite and the flag of Nepal, and turn them about their centre to find their lines and order of symmetry.
The three angles of any triangle add up to 180°
Turn the two rafters of a roof frame and see how the angle at the ridge always makes the three angles add up to 180°.
In the unitary method we first find the value of one unit by dividing, then the value of any number of units by multiplying
Rice, sugar, notebooks and eggs come in packs at a price. Find the price of one by dividing, then the price of as many as you want by multiplying.
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.