How many triangles, squares or rectangles hide in the picture? Start with a few loose shapes and work up to crossing lines and grids. Six levels, a daily set and printable worksheets.
The question how many triangles are in this picture is one of the best-known puzzles for young maths contestants, because the obvious answer is almost always too small. A child sees the little triangles first and has to learn to look again for the bigger ones made of several small ones. This game trains that second look. It builds careful counting, the habit of counting in an order so nothing is counted twice or missed, and an early feel for how shapes are made of other shapes. It also teaches that a square is a kind of rectangle, which the rectangle questions say out loud each time. Children who count by pointing at random usually get a different number each time, so the puzzles gently push toward a method: count the smallest shapes, then the ones made of two, then three, and so on. The game counts toward the skill we call counting shapes, inside the spatial group of skills.
Level 1, Starter, shows between 5 and 9 loose shapes, triangles, squares and circles in mixed fills, and asks how many of one kind there are, from 2 to 5. Level 2 draws a triangle with one or two lines from its top corner, which hides 3 or 6 triangles, a 2 by 2 grid with 5 squares, or a triangle cut by three middle lines with 5 triangles. Level 3 uses fans of 3 or 4 parts with 6 or 10 triangles and grids where the child counts squares of every size, such as 14 in a 3 by 3 grid. Level 4 asks for every rectangle, squares included, in grids and rows, with answers from 9 to 18. Level 5 has the classic contest figures with answers from 10 to 20, such as a fan of 5 parts with 15 triangles or a triangle cut into 9 small ones with 13 triangles in all. Level 6 has crossing lines: a fan with a line across it hides 12 or 20 triangles, a triangle of 16 small ones hides 27, a 4 by 4 grid hides 30 squares, a 3 by 3 grid hides 36 rectangles, and a 2 by 2 grid with both diagonals hides 16 triangles. Some level 6 grids have two to four inner lines rubbed out, and three overlapping rectangles make a different count each time.
Every figure is a list of straight line segments, and the answer is found by counting in code, never typed in. A triangle is counted as any three segments that cross each other at three different points. A rectangle is counted as two across and two up segments whose four corners all lie on those segments. A square is a rectangle with equal sides. Lines that meet at one point, like the diagonals of a square, do not make a triangle by themselves, and the count handles that. Each figure is also turned or flipped at random, which never changes its count. The tests compare the engine with a second counting method that works from corner points instead of lines, with formulas such as a fan of k parts having k(k+1)/2 triangles and an n by n grid having 1 + 4 + 9 and so on squares, and with the numbers above. They run 500 puzzles at every level. A number puzzle has one right answer by nature, and the wrong ones are not shown.
The game moves up a level after 3 right answers in a row and down after 2 wrong answers in a row, and you or your child can pick a level yourselves. A wrong answer gets a gentle Try again, never a buzzer. After a second wrong try the game shows how the shapes add up, by size. Each day there is a set of 5 puzzles, the same for everyone with the same date on their device. To print, choose a level, 4, 6 or 8 puzzles and Letter or A4. The figures print as black lines, a child can colour each shape found, and the last page is the answer key with the count by size. Stars and progress are saved in this browser only. This game does not ask the child to tap or mark each shape on screen, it has no timer by default, and it does not replace a teacher. It gives one kind of puzzle, done many times, in short sessions.
Level 1 is meant for a 6 year old on the first day: loose shapes with an answer from 2 to 5. Levels 5 and 6 are hard for a 7 or 8 year old. The levels adjust on their own, so a younger or older child settles at a comfortable one within about 10 puzzles.
Yes, in the rectangle questions, and the question says so each time: a square is also a rectangle. In the square questions only squares are counted, of every size, including the big ones made of several small squares.
Count by size. Count the smallest shapes first, then the ones made of two small parts, then three, and write each number down. The answer after the puzzle shows the count by size in this order, for example 4 + 3 + 2 + 1 = 10 triangles.
The answer is counted by code from the drawn lines, and the tests count the same figures a second way and with formulas, for 500 puzzles at each level. A fan of 5 parts has 5 x 6 / 2 = 15 triangles, and a 3 by 3 grid has 14 squares.
Each figure is turned or flipped at random, and some grids have inner lines rubbed out. The count does not change when a figure is turned, so a child who learns the method can use it on every picture.
Yes. Pick a level, 4, 6 or 8 puzzles and Letter or A4. The figures print as black lines, and the last page is the answer key with the count by size.
No. Stars, levels and streaks are saved in this browser on this device. The page counts visits with Google Analytics, never answers or scores.