38 experiments found
Clear filtersPerimeter 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.
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.