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

In a right-angled triangle, the square on the longest side has the same area as the squares on the other two sides together (a² + b² = c²). Cut the two smaller squares into pieces and they fit exactly into the big one.

You will need

• Chart paper and coloured paper
• A ruler, a set square and scissors
• Glue
• A triangle with sides 3, 4 and 5 units is the easiest to start with

What it shows

Tear off the three corners of any paper triangle and place them side by side: they always make a straight line, which is 180 degrees.

You will need

• Paper triangles of different shapes
• Colours to mark each corner
• A protractor to check

What it shows

Cut a circle into many equal sectors and arrange them top to tail: they form a shape close to a rectangle with sides πr and r, so the area is πr².

You will need

• Coloured paper circles
• A compass, ruler and protractor
• Scissors and glue
• A chart to mount the pieces

What it shows

With only a few throws the results are uneven, but as the number of throws grows, the share of heads gets closer to one half and each face of a die to one sixth.

You will need

• Coins and dice
• A tally sheet
• Graph paper or a spreadsheet

What it shows

Measure the angle up to the top of a tree or building and your distance from its base. The height is the distance × tan(angle), plus the height of your eyes above the ground.

You will need

• A protractor
• A straw
• Thread and a small weight
• A measuring tape
• A calculator or tan table

Safety: Never look at the Sun through the straw.

What it shows

In the sequence 1, 1, 2, 3, 5, 8, 13 and so on, each number is the sum of the two before it, and the ratio of neighbours gets closer to about 1.618, the golden ratio. The spirals on sunflower heads and pine cones often come in Fibonacci numbers.

You will need

• Pine cones, sunflower heads or pineapples
• Coloured markers to count the spirals
• Graph paper
• A calculator

What it shows

Drop a needle of length L onto lines spaced d apart, with L no longer than d. The chance that it crosses a line is 2L ÷ (πd), so counting crossings over many drops gives an estimate of π.

You will need

• Toothpicks or matchsticks of equal length
• Chart paper ruled with parallel lines
• A tally sheet and a calculator

What it shows

Each rod of the abacus stands for a place: ones, tens, hundreds and thousands. Ten caps on one rod are worth exactly one cap on the next rod to the left, so the number 2,346 is 2 caps, 3 caps, 4 caps and 6 caps from left to right.

You will need

• A shoebox lid or a piece of plank for the base
• Four wooden skewers or pencils as rods
• 40 plastic bottle caps with a hole punched in the centre
• Four labels: ones, tens, hundreds, thousands
• Glue or clay to fix the rods
• A sketch pen

Safety: An adult must punch the holes in the caps with a hot nail or a drill, and cut the skewer points off so nobody is poked.

Take it further: Add a fifth rod for ten-thousands and show the population of your town or village on the abacus.

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

Adding is jumping forwards along the number line and subtracting is jumping backwards. The frog shows that 7 + 5 and 5 + 7 land on the same number, and that 12 take away 5 brings you back to 7.

You will need

• A string or rope 2 metres long tied between two chairs
• 21 clothes pegs numbered 0 to 20 with stickers
• A paper frog on a bent paper clip that slides along the string
• Number cards 0 to 10
• A dice

Safety: Keep the string at waist height so no child walks into it at neck level.

Take it further: Add pegs for negative numbers to the left of 0 and jump backwards past zero to show minus 3.

What it shows

Circles cut into 2, 3, 4, 6, 8 and 12 equal slices show that 1/2 is the same amount as 2/4, 3/6, 4/8 and 6/12, and that two slices of 1/3 plus one of 1/6 make 5/6, which is less than one whole pizza.

You will need

• Six paper plates or card circles of the same size
• A protractor and ruler
• Coloured sketch pens or paints
• A split pin or drawing pin for the spinner
• A cardboard arrow
• A tray or board to lay out the pieces

Safety: An adult must help with the split pin and the scissors.

Take it further: Add a circle cut into tenths and show 1/2 = 5/10 = 0.5 to link fractions and decimals.

What it shows

The digits of a number stay in order while the decimal point slides. Moving the point one place to the right multiplies by 10 (3.45 becomes 34.5) and one place to the left divides by 10 (3.45 becomes 0.345).

You will need

• A strip of thick cardboard 40 cm by 10 cm
• Six digit cards that slot into pockets
• A bright red bead or button on a thread as the sliding point
• Place labels: hundreds, tens, ones, tenths, hundredths, thousandths
• A ruler and glue

Take it further: Add a kilometre, metre, centimetre and millimetre scale under the boxes to show that 1.25 km is 1,250 m.

What it shows

Lattice multiplication breaks a product like 23 times 47 into four small products (8, 12, 14 and 21) written in split boxes, then adds along the diagonals to give 1,081. The machine makes the method quick enough to race a calculator.

You will need

• A square of thick cardboard 30 cm by 30 cm
• Chart paper for the 2 by 2 lattice with diagonals
• Four strips of card that slide in slots along the top and the right edge
• A whiteboard marker and a clear plastic sheet to write on
• A cutter and ruler

Safety: An adult must cut the slots with the cutter.

Take it further: Make a 3 by 3 lattice for three-digit numbers and multiply 123 by 456 to get 56,088.

What it shows

Each rod carries the multiplication table of one digit written in split boxes. Laying rods for 4 and 6 side by side and reading row 7 gives 7 times 46 = 322 by adding along the slanted lines, a 400-year-old calculating tool.

You will need

• 11 flat ice-cream sticks or card strips 2 cm wide
• A fine permanent marker
• A ruler
• A card frame with a numbered column 1 to 9 on the left
• A small box to store the rods

Take it further: Make a second set and use both to multiply numbers with repeated digits, such as 44 times 6.

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

Two plates joined at the centre open like a fan to show any angle from 0 to 360 degrees. The scale shows that a right angle is 90 degrees, a straight angle 180 degrees and a full turn 360 degrees, and the arm names each angle as acute, right, obtuse or reflex.

You will need

• Two paper plates of the same size in two colours
• A protractor
• A sketch pen
• Scissors
• A split pin (optional)

Safety: An adult must help with scissors for younger children.

Take it further: Use the plate to measure the angles of a triangle cut from card and show they add to 180 degrees.

What it shows

Rubber bands stretched round nails on a square grid make triangles, rectangles and other polygons in seconds. Counting the unit squares inside a shape gives its area, and a rectangle 3 by 4 always has area 12 and perimeter 14 wherever it is placed.

You will need

• A plywood board 25 cm by 25 cm
• 36 small nails with flat heads in a 6 by 6 grid, 4 cm apart
• Coloured rubber bands
• A pencil and ruler to mark the grid
• Dot paper for recording shapes

Safety: An adult must hammer the nails. File any sharp heads and keep rubber bands away from eyes.

Take it further: For class 9 and 10: count the boundary nails B and inside nails I of any shape and check Pick's formula, area = I + B/2 take away 1.

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 single mirror stood on a shape shows its line of symmetry: half a butterfly becomes a whole one. Two mirrors hinged together show more and more copies as the angle closes: at 90 degrees you see 4 copies in all, at 60 degrees 6 copies and at 45 degrees 8 copies, always 360 divided by the angle.

You will need

• Two small plastic mirrors or mirror tiles about 10 cm square
• Cloth tape for the hinge
• A protractor drawn on a card base
• Paper shapes: half a butterfly, letters, a coin
• Coloured beads or bindis

Safety: Use plastic mirrors, or tape the edges of glass mirrors, and an adult must handle any glass.

Take it further: Set the mirrors at 72 degrees and place a line segment between them to see a regular pentagon appear.

What it shows

A paper cone and a paper cylinder with the same base radius and the same height are filled with rice. Exactly three cones of rice fill the cylinder, showing that the volume of a cone is one third of pi r squared h.

You will need

• Chart paper or an old X-ray sheet
• A compass, ruler and protractor
• Tape
• About 1 kg of rice, sand or rajma
• A tray to catch spills
• A measuring cylinder or a kitchen scale to check

Take it further: Make a hemisphere of the same radius from a ball cut in half and show it holds two cone-fulls, giving the sphere formula four thirds pi r cubed.