Maths
Maths projects for class 6 to 8: 51 ideas.
Each project below opens to its own page with what it shows, the science behind it, the materials, safety, step-by-step instructions, what you should see and viva questions. Many can be made from things at home; where a kit helps, the page links one.
Other subjects for class 6 to 8: Physics, Chemistry, Biology, Earth and space, Electronics and robotics, Environment, Computing and coding.
Fraction wall
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.
Pythagoras theorem model
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.
The angles of a triangle add up to 180°
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.
Area of a circle by cutting sectors
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.
Fraction pizza circles with a spinner that matches equal parts
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.
Sliding decimal point board for tenths and hundredths
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).
Lattice multiplication machine with sliding digit strips
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.
Napier's bones multiplication rods made from ice-cream sticks
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.
Times-table string art on a ten-point circle
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.
Paper plate angle maker with a sliding arm and degree scale
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.
Nail and rubber-band geoboard for shapes, perimeter and area
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.
Tangram set with a fraction and area table for each piece
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.
Five Platonic solids folded from cardboard nets
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.
Tessellating animal tile made by the cut-and-slide method
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.
Hinged mirror pair that shows symmetry and how many images appear
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.
Cut-and-slide board that turns a parallelogram into a rectangle
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.
Unfolding cube that shows surface area is six squares
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.
Knotted 3-4-5 rope for making right angles like builders
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.
Measure a tree's height from shadows and similar triangles
At the same moment the Sun makes the shadow of a tree and the shadow of a metre stick in the same proportion. If a 1 metre stick casts a 1.5 metre shadow and the tree casts a 9 metre shadow, the tree is 9 divided by 1.5, which is 6 metres tall.
Fair and unfair spinners: predicted versus observed outcomes
A spinner with four equal sectors lands on each colour about a quarter of the time. A spinner with sectors of 180, 90, 45 and 45 degrees lands on the big colour about half the time and on each small colour about one eighth, showing that probability is the share of the circle.
Bottle-cap pie chart built from a class survey of favourite games
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.
Balance beam that finds the mean of a data set
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.
Pascal's triangle cup pyramid with hidden number patterns
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.
Measure pi by rolling lids of five different sizes
Rolling a round lid exactly one turn along a ruler marks out its circumference. For every lid, from a bottle cap to a steel plate, dividing the distance rolled by the diameter gives the same number, about 3.14, which is pi.
Clothes-hanger balance that solves x + 3 = 7 with marbles
A hanger with a cup on each side stays level only when both sides weigh the same. A sealed bag of marbles stands for x; with 3 loose marbles beside it balancing 7 on the other side, removing 3 from each side keeps the balance and reveals that the bag holds 4.
Coordinate battleship game played on all four quadrants
Players hide paper ships on a grid running from minus 8 to 8 on both axes and call shots as ordered pairs like (minus 3, 5). Reading x before y and keeping the signs straight is the only way to win, so the game drills plotting points in every quadrant.
Magic square boards: the 3 by 3 Lo Shu and the 4 by 4 of Durer
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.
Matchstick Nim game board with its unbeatable strategy
Two players take 1, 2 or 3 sticks in turn from a pile of 21 and the player who takes the last stick wins. Whoever leaves a multiple of 4 after their move (20, 16, 12, 8, 4) can always win, so the second player wins a game of 21 by always making the two moves in a round add to 4.
Tower of Hanoi from bottle caps with the 2 to the n minus 1 rule
Discs of different sizes must be moved from one peg to another, one at a time, never putting a larger disc on a smaller one. The least number of moves is 1, 3, 7, 15, 31 and 63 for 1 to 6 discs, which is 2 to the power n minus 1, so 64 discs would take more than 18 quintillion moves.
Geared clock hands model that measures the angle between hands
The minute hand turns 6 degrees per minute and the hour hand half a degree per minute, so the angle between them at any time is the difference of 30 times the hours and 5.5 times the minutes. At 3:00 the angle is 90 degrees and at 3:30 it is 75 degrees, not 90, because the hour hand has moved on.
Vedic maths flip board for squaring numbers ending in 5
To square a number ending in 5, multiply the tens digit by the next number up and write 25 after it: 35 squared is 3 times 4 = 12 followed by 25, so 1,225. The flip board shows each step and the algebra behind it: (10a + 5) squared = 100a(a + 1) + 25.
Nikhilam slider that multiplies numbers near 100 in one line
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.
Matchbox drawer organiser that explains volume and surface area
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.
Tin-can pen stand that shows the best packing of circles
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.
Ice-cream stick fraction wall for halves, quarters and eighths
Equal parts of the same whole can be compared by length. The wall shows that one half equals two quarters and four eighths.
How much does rice swell? Water ratio and volume maths
Rice soaks up water and swells, and the amount of cooked rice depends on the ratio of rice to water. By measuring in cups you practise ratio and volume and see how much bigger the rice becomes.
Which paper towel or tissue soaks up the most? A fair test with maths
You compare tissue papers or paper towels for absorbency and cost by measuring grams of water held per sheet and per rupee. It is a practice in fair testing, averaging and unit costs.
Best buy at the kirana shop: unit price of five everyday items
The cheapest looking pack is not always the best buy. Dividing the price by the weight or volume gives the unit price, which lets you compare packs of different sizes fairly.
The discount puzzle: 20 percent off then 10 percent off
Two successive discounts do not add up to one big discount. A 20 percent off followed by 10 percent off is worth 28 percent, not 30. You test this with real prices from a sale and learn to calculate discounts correctly.
Scaling a recipe: ratios, fractions and measuring cups
A recipe is a set of ratios, so halving or doubling it means multiplying every amount by the same number. You rewrite a simple recipe for 2, 4 and 10 people and practise fractions and unit conversion.
How many tiles for the floor? Area, wastage and cost by newspaper model
The number of tiles needed depends on the area of the room divided by the area of a tile, plus some extra for cutting. You model a room with newspaper sheets as tiles and then work out the count and cost for a real room.
Dot rangoli: patterns with lines and symmetry on dots
Joining dots makes patterns that have symmetry. Both halves of the drawing look the same, like a rangoli.
Paper tiles that fit together: which shapes leave no gaps?
Some shapes, like squares, triangles and hexagons, can cover a floor without gaps. Others, like circles, leave gaps. This is why floors are tiled with certain shapes.
Paper money class shop: buy, sell and give change
Money is used to buy things, and shopkeepers give back change. Playing shop teaches adding prices, counting notes and finding change.
Weekly pocket money chart: save, spend and share
Money can be saved, spent or shared. Writing it in a chart shows where it goes and helps children plan.
Two paper triangles that fit together to prove area is half base times height
Any triangle, copied and turned upside down, joins its twin to make a parallelogram with the same base and height. So the triangle has exactly half the area, which is why area = 1/2 times base times height.
Trapezium area from two copies that form a parallelogram
Two identical trapeziums, one turned upside down, fit together into a parallelogram whose base is the sum of the two parallel sides. This shows that the area of a trapezium is half of the sum of the parallel sides times the height.
Walk a polygon on the ground: exterior angles always add to 360 degrees
If you walk around any polygon and turn at each corner, the turns add up to one full turn of 360 degrees. From this the angle sum of an interior polygon, (n minus 2) times 180 degrees, follows.
Straw and hinge model of parallel lines cut by a transversal
Two parallel straws cut by a third straw make eight angles, and the model shows that corresponding angles and alternate angles are equal while co-interior angles add up to 180 degrees. Turning one straw so the lines are no longer parallel breaks these rules.
Twenty-four cubes: which box shape has the smallest surface area?
The same 24 sugar cubes or dice can be stacked into several boxes with the same volume, but their outside areas differ a lot. The box closest to a cube, 2 by 3 by 4, has the smallest surface area, which is why packing and animal shapes matter.
One 40 cm thread loop, many shapes: which encloses the most area?
A closed loop of thread of fixed length can be made into a triangle, rectangle, square, hexagon or circle. The enclosed area grows as the shape gets more regular and is largest for the circle, so for a fixed perimeter the area can be very different.