1029 science project ideas, from class 1 to college.

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

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

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

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.

What it shows

A triangle cut from one end of a parallelogram and slid to the other end makes a rectangle of the same base and height, so the area of a parallelogram is base times height. Cutting the parallelogram along a diagonal gives two equal triangles, each with area half the base times the height.

You will need

• Two sheets of coloured card
• A ruler, set square and pencil
• Scissors
• A board with two card rails to slide the pieces
• Glue

Safety: An adult must help with the scissors for thick card.

Take it further: Cut a trapezium into two triangles and show that its area is half the sum of the parallel sides times the height.

What it shows

A cube of side 5 cm hinged along its edges opens flat into a net of six 5 cm squares, so its surface area is 6 times 25 = 150 square cm. A second box, 5 by 4 by 3 cm, opens to show three pairs of rectangles with total area 94 square cm.

You will need

• Thick chart paper or thin cardboard
• Cloth tape for hinges
• A ruler and pencil
• Centimetre grid paper glued on each face
• Scissors

Safety: An adult must help with cutting the cardboard.

Take it further: Make a cube with a lid to show that an open box has only five faces, 125 square cm for side 5 cm.

What it shows

A 10 cm arm pivots at the centre of a circle on a grid. At any angle, the height of its tip above the horizontal is 10 times the sine and the distance along the horizontal is 10 times the cosine, so at 30 degrees the tip is 5 cm up and 8.66 cm across.

You will need

• A 30 cm square board
• Centimetre graph paper glued to the board
• A stiff card or aluminium strip 10 cm long as the arm
• A split pin or a bolt with a nut as the pivot
• A protractor fixed round the centre
• Thread with a bead as a plumb line

Safety: An adult must drill the pivot hole if a bolt is used.

Take it further: Add a vertical tangent line at x = 10 cm and extend the arm to meet it: the height where it meets is 10 times tan of the angle.

What it shows

A rope with 13 knots at equal spacing is pulled into a triangle with sides of 3, 4 and 5 spaces. The angle between the 3 and 4 sides is exactly a right angle, because 3 squared plus 4 squared equals 5 squared, a trick used to lay out buildings for thousands of years.

You will need

• About 4 metres of thin rope or thick string
• A measuring tape
• Three pegs or three friends
• A set square to check
• Chalk to mark the ground

Safety: Peg the rope outdoors on soft ground, or hold it with fingers; never pull it tight near anyone's face.

Take it further: Use the rope to check whether the corners of your classroom are true right angles and report the error in centimetres.

What it shows

Beads falling through seven rows of nails bounce left or right at random at each nail. With eight collecting slots at the bottom, the expected share of beads in each slot follows Pascal's triangle, 1, 7, 21, 35, 35, 21, 7, 1 out of 128, which draws a bell-shaped curve.

You will need

• A plywood board 30 cm by 45 cm
• 28 small nails in a triangle of seven staggered rows
• Thin card strips for eight collecting channels
• A clear plastic sheet from an old folder as the front
• About 200 mustard seeds or 5 mm beads
• A funnel at the top
• Tape and glue

Safety: An adult must hammer the nails and check none pokes through the back.

Take it further: Bend some nails so beads go right with probability more than a half, and show the peak shifting to one side like a skewed distribution.

What it shows

Equal weights hung from a numbered beam at the data values balance only when the support is at the mean. Weights at 2, 3 and 7 balance at 4, their mean, and moving one weight from 7 to 13 shifts the balance point to 6, showing how an extreme value pulls the mean.

You will need

• A straight wooden scale or a 60 cm batten marked 0 to 20
• A triangular block or a pencil fixed to a base as the pivot
• Six identical washers or coins with thread loops
• A nail or hook at every number mark
• A small level or a straight edge

Safety: An adult must fix the hooks and make sure the beam cannot fall on fingers.

Take it further: Hang two washers at one value to show frequency, and find the mean of a frequency table on the beam.