1029 science project ideas, from class 1 to college.

What it shows

To multiply 97 by 96, write how far each is below 100 (3 and 4). Subtract crosswise, 97 minus 4 = 93, and multiply the deficits, 3 times 4 = 12, to get 9,312. The slider lines up the two numbers and their deficits so the answer appears in two steps.

You will need

• A card strip 50 cm long with two sliding windows
• A number strip from 90 to 110
• A marker
• A calculator for checking
• Glue and a cutter

Safety: An adult must cut the windows in the card.

Take it further: Make a base-1,000 strip for numbers like 997 times 994, where the deficit product is written with three digits: 991,018.

What it shows

Slicing a cone with a flat cut gives a circle when the cut is parallel to the base, an ellipse when tilted, a parabola when parallel to the slanting side, and a hyperbola when steeper than the slanting side. Four clay cones, each cut one way, show the four curves side by side.

You will need

• About 1 kg of air-dry clay or plaster of Paris in four paper cone moulds
• A thin wire or a fishing line with handles to cut
• A protractor and card to set the cut angles
• Four display bases
• Poster colours to paint the cut faces

Safety: An adult must handle the cutting wire; plaster must be mixed outdoors and never poured down a drain.

Take it further: Shine a torch at a wall at different angles: the edge of the light patch traces the same four curves.

What it shows

Threads joined between two scales at right angles, the first point on one to the last on the other and so on, form no curve themselves, yet their edges outline a smooth parabola. The curve is the envelope of the lines, touched by every one of them.

You will need

• A square of plywood or thick card 30 cm across
• 40 small nails or pins
• Coloured thread
• A ruler and pencil
• A hammer or a pushpin tool

Safety: An adult must hammer the nails and cover the points at the back with tape.

Take it further: Put nails round a circle and join each nail n to nail 2n to see a cardioid envelope appear.

What it shows

A loop of string round two pins and a pencil draws an ellipse, because the pencil keeps the sum of its distances to the two pins constant. With pins 6 cm apart and a loop giving a major axis of 10 cm, the minor axis comes out as 8 cm and the eccentricity as 0.6, exactly as the formulas predict.

You will need

• A soft board or thick cardboard 30 cm square
• Two drawing pins
• A loop of thread tied to a measured length
• A pencil and a ruler
• Graph paper to draw on

Safety: Drawing pins are sharp; keep them in a closed box.

Take it further: Draw a hyperbola with a ruler pivoted at one focus and a string tied at the other, keeping the difference of distances constant.

What it shows

Four land areas joined by seven bridges cannot be walked in one trip crossing every bridge once, because every land area has an odd number of bridges. Lifting any one bridge off the board leaves only two odd areas and the walk becomes possible, starting at one odd area and ending at the other.

You will need

• A board painted as a river with two banks and two islands
• Seven removable card bridges with velcro or pegs
• A toy figure to walk the route
• A dry-erase sheet to draw the graph
• Labels A to D for the land areas

Take it further: Draw the map of your school corridors as a graph and find a route that walks every corridor exactly once, or prove there is none.

What it shows

You can find a distance you cannot measure directly by measuring a baseline and two angles. The sine rule in the triangle then gives the width.

You will need

• A measuring tape or a 10 m rope marked in metres
• A protractor and a plumb line, or a clinometer app on a phone
• Two sticks or flags for the ends of the baseline
• A flat piece of cardboard 30 cm by 30 cm for a sighting board
• A straw taped along its edge for sighting
• A pencil and graph paper
• A calculator with sin

Safety: Keep well away from the water edge. An adult must come along and stay with the group. Do not climb trees or walls to take readings.

Take it further: Use two landmarks to measure the distance between them across the water using two baselines.

What it shows

The height of a point on a turning wheel, measured above the centre, follows a sine curve in time. Tracing it on moving paper gives amplitude, period and a smooth wave.

You will need

• A cardboard disc of radius 10 cm
• A pushpin or a nail through the centre to a board
• A pencil or a coloured pen as a pointer
• A long strip of paper, 60 cm by 10 cm, or a roll of receipt paper
• A ruler and a protractor
• A set square
• A second sheet of graph paper for plotting
• Tape

Safety: An adult must help with the pin or the nail so that fingers are not pricked.

Take it further: Fix two pens at 90 degrees on the disc to trace sine and cosine waves together on the same paper.

What it shows

Two measurements on the same person can be linked. Collecting data for a class and drawing a scatter plot, a line of best fit and a correlation shows how statistics finds a pattern in data.

You will need

• A measuring tape or a metre stick with a long string
• A wall with a chalk mark for height
• Data from 30 or more classmates with their permission
• Graph paper or a spreadsheet
• A calculator
• A table for name code, height and arm span
• A transparent ruler

Safety: Take measurements with the person standing straight and use only first names or code numbers on the sheet. Ask permission before measuring anyone.

Take it further: Compare the line for boys and girls separately and for different age groups.

What it shows

The area of an odd shape can be estimated by throwing random points on a square that contains it. The share of points that land inside the shape estimates the share of the square it covers.

You will need

• A flat leaf such as peepal or banyan
• A sheet of graph paper with 1 mm or 2 mm squares
• A pencil and a ruler
• A die or two for random coordinates, or a calculator with random numbers
• A table of results
• A 10 cm by 10 cm square drawn on a card
• A phone with a calculator or a spreadsheet

Safety: No special safety. Take leaves only from the ground or with permission, and do not pick from protected trees.

Take it further: Find the area of the map of your state on a printed outline using the same method.

What it shows

In the three-door puzzle, switching wins two times out of three, though many people feel that it is a fifty-fifty choice. Playing it many times and listing all the outcomes shows why.

You will need

• Three paper cups
• One coin or small ball to hide
• A partner to act as the host
• A tally table with two columns: stay and switch
• Paper and pencil
• A tree diagram on a chart
• A calculator

Safety: No special safety. Play fairly and do not peek.

Take it further: Write a small program or a spreadsheet formula that plays 10,000 games and shows the two win rates.

What it shows

The number of turns to finish a game is random but has a stable average. Playing or simulating many solo games gives the mean game length and shows how the snakes and ladders change it.

You will need

• A snakes and ladders board
• A die and a counter
• A tally table of 100 game lengths
• Graph paper for a histogram
• A calculator or a spreadsheet
• A second board without snakes and ladders, drawn on paper
• A pencil

Safety: No special safety.

Take it further: Find the chance that a game ends in under 20 throws from the simulation and compare it with the hand data.

What it shows

The point where the three medians of a triangle meet is its centroid, and a flat triangle balances there. Its coordinates are the average of the three vertex coordinates.

You will need

• A sheet of thick cardboard
• Graph paper to glue on it
• A pencil, ruler and scissors
• A sharp pencil tip or a blunt needle stuck in an eraser as a pivot
• Glue
• A compass
• Calculator

Safety: An adult must supervise cutting. Keep the needle covered and use a blunt point for balancing.

Take it further: Cut a cardboard map of India and find its balance point by hanging it from two points and drawing plumb lines.

What it shows

On a street grid you cannot travel diagonally, so the distance is the sum of the horizontal and vertical steps. With this rule a circle looks like a diamond, which shows that geometry depends on how distance is defined.

You will need

• A large sheet of graph paper or a chalk grid on the floor
• Coloured pens
• String
• A ruler
• A small toy or cap as a taxi
• A map of a nearby town with a grid-like area
• Paper for tables

Safety: If you draw on a floor or playground, do it away from traffic and use washable chalk.

Take it further: Define an ellipse and a parabola in taxicab geometry and sketch them.

What it shows

A ball that bounces back to a fixed fraction of its previous height gives a geometric sequence of heights. The total distance travelled until it stops is the sum of a geometric series.

You will need

• A rubber or tennis ball
• A metre stick fixed upright on a wall
• A hard floor
• A phone to record slow-motion video
• A table for bounce heights
• Graph paper, preferably semi-log
• Calculator

Safety: Use a ball that is soft enough not to break things and keep it away from windows and glass.

Take it further: Calculate the time between bounces and show that it also forms a geometric sequence, with ratio equal to the square root of r.

What it shows

Cutting equal squares from the corners of a sheet and folding it gives a box. The volume rises and then falls as the cut grows, and calculus predicts exactly where it is greatest.

You will need

• 6 sheets of square card, 24 cm by 24 cm
• Scissors and a ruler
• Tape
• Rice or sand to measure volume
• A measuring cup or a 250 ml container
• Graph paper
• A calculator

Safety: An adult must supervise the use of scissors. Wash hands after handling the rice.

Take it further: Find the shape of a cylinder-shaped tin with the least metal for a fixed volume of 500 ml and compare it with a real tin.

What it shows

The area under a curve can be approximated by many thin strips. The more strips used, the closer the sum is to the definite integral.

You will need

• Graph paper with 1 mm squares
• A pencil and ruler
• Coloured pencils
• A calculator
• A table of values for y = x squared
• Scissors and glue for a cut-out comparison
• A thin card to cut out the shape

Safety: An adult should supervise the use of scissors for younger students.

Take it further: Repeat for y = sin x from 0 to 180 degrees, with x in radians, and see that the area is exactly 2.

What it shows

The slope of a distance-time graph at a point is the instantaneous speed, which is the derivative of distance with respect to time. A car on a ramp that speeds up gives a curve whose tangents get steeper.

You will need

• A toy car
• A wooden plank or board about 1.5 m long, propped at a small angle
• A metre tape
• A phone for slow-motion video with a clock or timer app
• Chalk to mark each 10 cm along the ramp
• Graph paper
• A transparent ruler

Safety: Do the experiment on the floor, away from stairs. Keep fingers clear of the car and the ramp end.

Take it further: Increase the ramp angle and show that the acceleration changes with the sine of the angle.

What it shows

A chain hanging under its own weight forms a catenary, while a cable carrying a load spread evenly along the horizontal, as in a suspension bridge, forms a parabola. The two curves look alike but have different equations.

You will need

• A light bead chain or a thin metal chain, 1 m
• Two nails or drawing pins on a board
• A pegboard or a notice board covered with graph paper
• A string, 1 m, and 11 equal washers or nuts
• Sticky tape, a ruler and a plumb line
• A phone to photograph the curves square on
• A spreadsheet or a calculator with cosh

Safety: An adult must help with nails and pins. Use a cork board and keep the board flat or upright so nothing falls on feet.

Take it further: Invert a photo of the hanging chain and build the arch from card strips to show that it stays up under load.

What it shows

When you know which colour was drawn, you can work backwards to the chance of which bag it came from. The experiment shows how new information updates a probability.

You will need

• Two opaque cloth bags or cups
• 3 red and 1 blue bead for bag A, 1 red and 3 blue beads for bag B (or coloured paper pieces)
• A coin to choose the bag
• A tally table
• A tree diagram on chart paper
• A calculator
• A pencil

Safety: Keep small beads away from young children and do not put them in the mouth.

Take it further: Apply the same rule to a medical test that is 95 per cent accurate for a disease affecting 1 per cent of people, and compute the chance of disease given a positive test.

What it shows

For a projectile launched at the same speed from ground level, the range is proportional to sin 2 theta, which is greatest at 45 degrees. Equal ranges occur for angles that add up to 90 degrees.

You will need

• A ruler catapult: a ruler pivoted on a pencil with a rubber band, or a simple spring launcher
• A soft foam or paper ball
• A protractor and a cardboard ramp to set angles
• A tape measure on the floor
• Chalk
• A table of angle and range
• Graph paper and a calculator

Safety: Use only soft balls and launch in an open area with no one in front. Wear eye protection and never aim at anyone.

Take it further: Use the slope to calculate the launch speed and check it by timing the ball over a short flat distance.

What it shows

Stacking identical boxes shows that volume is repeated cubic units, while joining them hides some faces and reduces the total surface area. It is also a useful desk organiser.

You will need

• 12 empty matchbox trays and sleeves
• Glue or double-sided tape
• Coloured paper to cover the outside
• Small beads as drawer knobs
• A ruler
• A notebook

Safety: Use only empty matchboxes with no matches inside. An adult must remove any leftover heads and strikers.

Take it further: Rearrange 12 boxes into 2 by 3 by 2 and 1 by 3 by 4 and find which shape needs the least wrapping paper.

What it shows

Circles packed in a hexagon pattern leave less gap than circles in a square grid. The pen stand lets you compare the two packings by measuring the wasted space.

You will need

• Seven identical small tins or cardboard tubes (free)
• Strong glue or tape
• Coloured paper
• A ruler
• A sheet of graph paper
• Compasses

Safety: An adult must check the cut edges of tins and cover them with tape. Wear gloves when handling sharp edges.

Take it further: Test with marbles in a box: pack them in a square then hexagonal way and see how many fit.

What it shows

A four-sided frame can collapse but a triangle cannot change shape without changing the length of a side. A dome of triangles is strong and light.

You will need

• About 40 drinking straws
• A packet of pipe cleaners or thread
• Scissors (adult help)
• A ruler
• A square of straws for comparison
• A tray

Safety: An adult must cut the straws. Cut pipe cleaner ends are sharp, so bend them in.

Take it further: Check Euler’s formula V minus E plus F equals 2 for your dome.

What it shows

Landing on a square means answering a multiplication fact. Repeated practice helps children learn tables and see the patterns in them.

You will need

• A flattened cereal box about 40 cm square
• Markers and a ruler
• Bottle caps as tokens in different colours
• A die made from a folded paper cube
• Coloured paper for snakes and ladders
• Scissors (adult help)

Safety: An adult must cut the card. Keep bottle caps away from small children.

Take it further: Make a division board using the same facts in reverse.