A city built only from cubes, cylinders, cones and pyramidsTowers are cylinders and boxes, roofs are cones and pyramids. Shade the same side of every solid.
A right triangle inside the unit circle, legs labeled cosine and sineThe radius is the long side, length 1. Label the flat leg cos t and the upright leg sin t.
One quadrant of the unit circle enlarged, with its three triangles shadedDraw the 30°, 45° and 60° radius lines and drop a vertical from each to the x-axis. Shade each triangle.
The unit circle as a bicycle wheel with labeled spokesA spoke to each marked angle, the hub at the origin, and radius 1 written along one spoke.
The unit circle as a clock face, with angles where the hours go0° sits where the 3 would be and the angles run counterclockwise. One hand points at 45°.
The unit circle as a colour wheel, one hue per sectorOne hue per sector, running round from 0°. Put each point's coordinates in an outer ring.
The unit circle as a compass roseEast is 0° and north is 90°. The four long points sit on the axes and the short ones on the 45° lines.
The unit circle as a Ferris wheel with a car at every angleA car hangs at each marked angle. Label each car with its point: the top car is (0, 1).
The unit circle as a flower, a petal between each pair of anglesNarrow petals fill the 15° gaps and wide petals the 30° gaps. Write the angles along the petal edges.
The unit circle as a pizza, one slice for each marked angleCut at every marked angle, so slices come in two widths, 30° and 15°. Write each angle on the crust.
The unit circle as a planet with a moon in orbit at each angleThe circle is the orbit and the planet sits at the origin. Number the moons by their angles.
The unit circle as a porthole with the sea's horizon on the x-axisThe x-axis is the waterline. Mark the angles on the brass rim and sail a boat above 0°.
The unit circle as a rose window of coloured glassLead lines run from the centre to each marked angle. Give each quadrant's panes one family of colours.
The unit circle as a round table with a place set at each angleA plate at every marked angle, seen from above. Each place card carries that point's coordinates.
The unit circle as a ship's wheelEight handles on the axes and the 45° lines. Add the 30° and 60° marks as studs on the rim.
The unit circle as a spider web with labeled strandsStraight threads out to the marked angles, rings between them. Hang a label from the end of each thread.
The unit circle as a sun with a ray for each angleOne ray per marked angle. Make the four rays on the axes longest, where one coordinate is 0.
The unit circle as an orange cut across, segments for sectorsThe segment walls are the radius lines. Write degrees outside the peel and radians inside.
The unit circle unrolled into a sine waveMark the angles along a straight axis beside the circle. Carry each point's height across and join the dots.
Fibonacci and spirals 16
A bookcase whose shelves hold 1, 1, 2, 3, 5 and 8 booksSix shelves. Lean the lone books over and pack the eight upright.
A caterpillar whose segments grow by the sequenceCircles 1, 1, 2, 3, 5 and 8 squares wide in a row. The face goes on the smallest.
A daisy with 13 petals, then one with 21Both counts are Fibonacci numbers. Space the 13 by eye and see how crowded 21 becomes.
A galaxy drawn along the Fibonacci spiralDraw the spiral twice from one centre, the second turned halfway round. Dot the stars densest in the middle.
A necklace strung in groups of 1, 1, 2, 3, 5 and 8 beadsOne long curve of thread. Put a knot between the groups and change colour for each.
A patchwork blanket of Fibonacci squares, each with its own patternDots in the 1s, stripes in the 2, checks in the 3, and so on up. Stitch lines round each square.
A pine cone seen from its base, spirals traced in two coloursTrace the scales as spirals one way, then the other. Count each set and write the numbers beside it.
A rose seen from above, petals arranged along a spiralStart with a tight centre and wrap petals outward along a spiral, each one overlapping the last.
A skyline whose towers are 1, 1, 2, 3, 5, 8 and 13 floors tallEach tower is as tall as the two before it added together. Light one window per floor.
A snail whose shell is built from the Fibonacci squaresDraw the squares and the spiral first. Round the outside into a shell and add the snail below.
A spiral swung through the Fibonacci squares, a quarter circle in eachCompass point on a corner of each square in turn. Each arc crosses its square and carries on from the last.
A striped scarf with bands 1, 1, 2, 3, 5 and 8 squares wideCount squares on grid paper. Alternate two colours so the widening bands stand out.
A sunflower's seed head mapped as spirals turning both waysDraw one set of curves turning left from the centre and a second turning right. A seed sits at each crossing.
A tree that grows by the sequence: 1, 1, 2, 3, 5 branches per levelRule five faint levels. Count the branches crossing each one and adjust until the numbers match.
Fibonacci squares of 1, 1, 2, 3, 5 and 8 fitted into one rectangleOn grid paper. Two 1 squares side by side, a 2 along them, then 3, 5 and 8, each against the longest edge.
Fireworks that burst into 1, 1, 2, 3, 5 and 8 sparksSix bursts across a night sky. Count the sparks in each as you draw them.
Shapes and patterns 21
A butterfly finished from one half across a fold lineDraw one wing beside a ruled line. Measure each point's distance from the line and copy it across.
A castle front with one line of symmetry and three mistakes to findDraw the left half, mirror it, then change three things on one side. Rule the mirror line faintly.
A city built only from cubes, cylinders, cones and pyramidsTowers are cylinders and boxes, roofs are cones and pyramids. Shade the same side of every solid.
A cube unfolded into a cross of six squaresFour squares in a column and one each side of the second. Draw a different face on each square.
A family portrait of polygons, triangle to decagon, each with a faceEight shapes, from three sides to ten. Write the name and the number of sides under each.
A lion's mane with a tuft every 15 degrees, measured with a protractorMark every 15° round a full turn, which makes 24 tufts. Alternate long and short.
A pentagon with every diagonal drawn, and the star that appearsJoin each corner to the two corners it is not already joined to. A smaller pentagon sits in the middle.
A quilt block of squares and half-square trianglesA three-by-three grid. Cut some squares corner to corner and shade one half of each.
A robot built from every kind of quadrilateralSquare head, rectangle body, parallelogram arms, trapezoid feet, rhombus hands, kite antennas. Label each shape.
A scale drawing of your desk top, one square to two inchesMeasure the desk and what sits on it. Draw each thing from above on grid paper and write the scale in a corner.
A snake that bends through one acute, one right and one obtuse angleMark each bend with an arc, measure it, and label the three kinds.
A snowflake grown by adding a smaller triangle to every sideStart with a triangle. Swap the middle third of each side for two sides of a smaller triangle, twice over.
A snowman of three spheres with a cone nose and a cylinder hatShade one side of each sphere the same way. Name the three kinds of solid beside it.
A spiral of right triangles, each standing on the long side of the lastStart with a right triangle. Build the next one on its longest side with a short leg of the same length. Repeat.
A tessellating fish made by moving a bite from one side of a square to the otherCut a bite from one side of a paper square, tape it to the opposite side, and trace the shape in rows.
A tessellation of one triangle, flipped and repeatedDraw one triangle, flip a copy to sit against it, and carry on across the page. No gaps, no overlaps.
A triangle split into four, then its corners split againJoin the midpoints of the sides to make four triangles. Shade the middle one and repeat in the three corners.
One square cut into four equal parts in six different waysSix squares in a row. Strips, quarters and triangles are the easy three. Find three more and shade one part of each.
Squares inside squares, each touching the midpoints of the lastJoin the midpoints of a square's sides to make a smaller, turned square. Repeat until it is too small.
Three squares leaning together round a right triangleUse sides of 3, 4 and 5 grid squares. Count them: 9 small squares plus 16 equals the 25 in the largest.
Your name and its mirror image along a line of symmetryRule the mirror line. Write your name above it and its reflection below, letter by letter.
Numbers and graphs 25
A balance scale with x on one sideDraw a true equation: a box marked x and two weights on one pan, five weights on the other.
A bar chart of your week drawn as a row of buildingsOne bar per day, as tall as the minutes you read. Add windows and label both axes.
A clock face in Roman numeralsI to XII round the dial. Each numeral's foot points to the centre, so they turn as they go round.
A fraction wall: one whole, two halves, three thirds, four quartersFour rows the same length. Split the second in two, the third in three, the fourth in four.
A hundred chart with the multiples of 3 coloured inTen rows of ten. Colour every third number and look at the diagonal stripes that appear.
A magic square whose rows, columns and diagonals all add to 15A three-by-three grid of 1 to 9: 8, 1, 6 across the top, then 3, 5, 7, then 4, 9, 2. Decorate each cell.
A number line with a frog hopping in twosA line from 0 to 20 with a tick at each number. Arcs show the jumps: 0, 2, 4, 6.
A parabola plotted point by point, then turned into a valleyPlot y = x times x for x from -4 to 4 and join the points smoothly. Add a river along the bottom.
A pi skyline with towers 3, 1 and 4 floors tallPi is about 3.14, so the first three towers are 3, 1 and 4 floors. Carry on if you know more digits.
A picture hidden in coordinates: plot the points and join them in orderDraw a simple shape on a grid first. List its corners as (x, y) pairs and hand the list to a friend.
A pie chart of what is in your backpackCount what is inside by type. Give each type a slice in proportion and draw the item in its slice.
A pizza cut into halves, quarters and eighthsThree pizzas side by side. Label one slice of each: 1/2, 1/4, 1/8.
A place-value city of houses, apartment blocks and towersPick a three-digit number. Draw that many towers for hundreds, blocks for tens and houses for ones.
A sine wave turned into a sea with a boat on every crestDraw a smooth wave with even crests along an axis. Shade below it and sit a boat on each crest.
A thermometer number line that runs below zeroMark zero clearly and number down the stem into the negatives. Shade up to today's temperature.
A Venn diagram of two animals and what they shareTwo overlapping circles. Draw what only one animal has in each side and what both have in the middle.
An abacus set to your birth yearFour rods, for thousands, hundreds, tens and ones. Push up that many beads on each.
An infinity sign as a racetrackA figure eight on its side with a lane line down the middle and one small car.
Dominoes laid out as the three times tableSix tiles. Each shows 3 on one half and 1 to 6 on the other. Write the product under each tile.
Math symbols as repeating wallpaperPlus, minus, times, divide and equals in rows. Shift each row half a step and use two colours.
The numbers 0 to 9 turned into animalsKeep each digit readable. A 2 makes a swan, an 8 a snowman, and a 0 the body of an owl.
Prime dates ringed on a month's calendarRing 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31. Turn each ring into a small face.
Square numbers as squares of dots: 1, 4, 9, 16One dot, then a two-by-two block, three-by-three, four-by-four. Write the total under each block.
Tally marks that turn into a picket fenceGroups of four uprights with a slanted rail across each. Add a gate and a bird.
Triangular numbers as stacked cans: 1, 3, 6, 10One can, then a row of two under it, then three, then four. Write the running total beside each stack.
How it works
A unit circle project, a poster for the classroom wall, a notebook cover: these 80 math drawing ideas turn a rule into a picture. Each hint gives the construction, so the math stays right while the drawing gets decorated.
Read the full guide
Unit circle drawing ideas that keep the angles readable
Unit circle holds 18 disguises, such as a pizza, a Ferris wheel and a compass rose. Whatever the costume, keep three things in view: the angles at 30°, 45° and 60° in every quadrant, the radius of 1, and each point's coordinates.
Fibonacci drawing ideas start with squares
The sequence begins 1, 1, and every later number is the two before it added together: 2, 3, 5, 8, 13. Squares with those side lengths lock into one rectangle on grid paper. Fibonacci and spirals holds 16 built on that, from a skyline to a snail.
Work on grid paper in pencil, then ink. Most of these fail on one miscounted square.
Label as you go. With its numbers left off, a math drawing is only a drawing.
Questions and answers
What are some easy math things to draw?
Under More filters, Easy holds 39: a number line with a frog hopping in twos, square numbers as squares of dots, a robot built from every kind of quadrilateral. These three need only a ruler and a pencil.
Which mathematics drawing ideas suit a poster?
Pick one that reads from across a room: the unit circle as a sun with a ray for each angle, three squares leaning together round a right triangle, or a pi skyline. Letter the title large and the labels small.
How do I draw the Fibonacci spiral?
Draw the squares first: 1, 1, 2, 3, 5, 8. Then put a compass point on a corner of each square in turn and swing a quarter circle across it, so that each arc carries on from the last.