1029 science project ideas, from class 1 to college.

What it shows

Strips cut into halves, thirds, quarters and smaller parts show which fractions are equal (2/4 is the same as 1/2) and which fraction is bigger.

You will need

• Coloured paper strips of equal length
• A ruler and scissors
• A board

What it shows

A single matchstick is one, a bundle of ten is a ten, a flat of ten bundles is a hundred and a box of ten flats is a thousand. Seeing the sizes side by side shows why 1,000 is so much more than 100.

You will need

• About 1,200 used matchsticks or broom sticks (free)
• Rubber bands or thread for bundling
• Ten flat cardboard sheets 12 cm by 12 cm
• A small carton for the thousand
• Glue
• Labels

Safety: Use burnt or headless matchsticks only, or broom sticks, so there is nothing to strike.

Take it further: Use the flats to show decimals: let a flat be one whole, a bundle one tenth and a stick one hundredth.

What it shows

On a 10 by 10 chart of 1 to 100, counting in twos, fives and tens makes straight columns, counting in nines makes a diagonal and counting in threes makes slanting stripes. Patterns appear because the chart has ten numbers in each row.

You will need

• A chart paper ruled into a 10 by 10 grid, numbers 1 to 100
• Transparent plastic sheets from old folders
• Coloured permanent markers
• Tape or clips to hold the overlays
• A ruler

Take it further: Make an overlay that colours only the prime numbers and count them: there are 25 primes below 100.

What it shows

Join the last digits of a multiplication table in order on a circle marked 0 to 9: the two times table draws a pentagon, the three times table a ten-pointed star, the five times table a single line, and the nine times table traces the one times table backwards.

You will need

• A square of plywood or thick cardboard 25 cm across
• Ten drawing pins or nails arranged round a circle
• Coloured wool or thread
• A protractor to space the pins 36 degrees apart
• Labels 0 to 9

Safety: An adult must hammer the nails or press the pins, and the finished board should have the points covered with tape at the back.

Take it further: Make a 12-point circle and see which tables now draw a star; it is the tables that share no factor with 12.

What it shows

The seven tangram pieces are cut from one square. The two large triangles are each one quarter of the square, the medium triangle, the square and the parallelogram are each one eighth, and the two small triangles are each one sixteenth, so the fractions add up to one whole.

You will need

• A square of thick card or foam sheet 16 cm by 16 cm
• A ruler and pencil
• Scissors or a cutter
• Coloured paper or paint for the seven pieces
• A chart for the fraction table

Safety: An adult must use the cutter if the card is thick.

Take it further: Cut a second set from a 32 cm square and show that doubling the side makes every area four times as big.

What it shows

Only five solids can be made with every face the same regular polygon and the same number of faces at every corner: the tetrahedron (4 triangles), cube (6 squares), octahedron (8 triangles), dodecahedron (12 pentagons) and icosahedron (20 triangles). Each is folded from a flat net.

You will need

• Cereal-box cardboard or thick chart paper
• A ruler, compass and protractor
• A blunt knife or an old pen for scoring folds
• Glue or tape
• Paints in five colours

Safety: An adult must help with scoring and cutting.

Take it further: Make the cube and octahedron so one fits inside the other with vertices touching face centres: they are dual solids.

What it shows

A piece cut from one side of a square and slid to the opposite side still tiles the plane with no gaps, because the square itself tiles. Repeating the trick on the other pair of sides gives a tile shaped like a fish or a bird that covers a whole chart with no overlaps.

You will need

• A square of stiff card 6 cm by 6 cm
• Scissors and tape
• A large chart paper
• A pencil and colours

Safety: Use round-tipped scissors; an adult must help if the card is thick.

Take it further: Start from a regular hexagon instead of a square and slide pieces between opposite sides for a honeycomb-based design.

What it shows

A survey of 30 classmates is shown as coloured bottle caps on a circle. If 12 chose cricket, cricket gets 12 out of 30 of the circle, which is 144 degrees, and the slices of the pie add up to the full 360 degrees of the class.

You will need

• About 30 bottle caps in four colours, or caps painted
• A card circle of radius 15 cm
• A protractor and ruler
• Glue
• A survey sheet and a tally
• A bar chart on graph paper for comparison

Take it further: Survey a second class and make a pie of the same size, then compare the slices for each game.

What it shows

Paper cups stacked in a triangle carry Pascal's numbers: each cup holds the sum of the two cups above it. Row sums double each time (1, 2, 4, 8, 16, 32), the second diagonal counts 1, 2, 3, 4, and the third diagonal holds the triangular numbers 1, 3, 6, 10, 15.

You will need

• 55 paper cups for ten rows
• A marker
• Coloured stickers for odd and even numbers
• A board or a wall space and tape
• A calculator to check the big numbers

Take it further: Read each row as a number (1, 11, 121, 1331, 14641) and show these are powers of 11 until carrying spoils it at row 5.

What it shows

Squares of side 1, 1, 2, 3, 5, 8 and 13 cm fit together into a rectangle of 13 cm by 21 cm, and a quarter circle in each square joins into a spiral. The ratio of the sides, 21 divided by 13, is about 1.615, close to the golden ratio 1.618, and the ratio gets closer as more squares are added.

You will need

• Chart paper and coloured paper
• A compass, ruler and set square
• Scissors and glue
• A calculator
• A board 30 cm by 40 cm

Safety: Keep the compass point capped when not in use.

Take it further: Measure the ratio of your height to the height of your navel and of several objects in the room, and see which come near 1.6.

What it shows

In a magic square every row, column and both diagonals add to the same total. The 3 by 3 square using 1 to 9 always totals 15 and has 5 in the centre; the 4 by 4 square 16, 2, 3, 13 / 5, 11, 10, 8 / 9, 7, 6, 12 / 4, 14, 15, 1 totals 34 in every line, in each corner 2 by 2 block and in the centre block too.

You will need

• Two card boards with 3 by 3 and 4 by 4 grids
• Number tiles from bottle caps or card squares
• A marker
• Velcro dots or a shallow lip so tiles stay in place
• A card with blank grids for visitors

Take it further: Build a 5 by 5 magic square with the Siamese method (start at the top middle, move up and right, drop down when blocked); its total is 65.

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.