For parents

Math Detours is a set of printable math sheets for curious kids, organised by grade. Grades 5 to 12 (ages 10 to 18) are live. This is work in progress. The aim is two things. Make school math feel easy by going one notch past it. And show the ideas just around the corner, the ones that make a child decide math is interesting.

The site was created by an applied mathematician with three school-age daughters. Everything here is open. There is no paywalled content.

How to use it

• Start with the Start here page for your grade (grade 5, grade 6, grade 7, grade 8, grade 9, grade 10, grade 11, grade 12). It lists a first thirty nights in a sensible order.
• One sheet a night, ten to fifteen minutes. Print it before dinner. Each sheet is a short idea, one worked example, four exercises (up to six in grade 6), and a starred stretch problem.
• Answers print on the last page. Fold it under or keep it. Checking their own work is part of the point, so let them see it once they have tried.
• The stretch is meant to be hard. Not getting it is normal. Ten minutes of honest struggle on a stretch problem is worth more than the rest of the sheet.
• Mix the tracks. A Sharpen sheet on a school night, an Around the corner sheet at the weekend, a Connections sheet when they are tired, works well.
• The demos are for the screen. They are short interactive toys that go with specific sheets. A few minutes each.

What is on the sheets

Every grade has the same three tracks. Sharpen follows that year's school course, explains why each method works, and sets exercises a bit harder than typical homework. Around the corner covers ideas usually met later or never, chosen so that nothing needs more than that grade's arithmetic. Connections are sheets with more reading and less calculation, on where the math shows up in the world.

• Grade 5 (ages 10 to 11): place value, decimals, fractions and volume with pictures; then cube nets, a logic grid, the fake coin and a game you cannot lose.
• Grade 6 (11 to 12): ratios, percentages, negative numbers and simple equations; then primes, binary, Pascal's triangle, infinity and the Monty Hall problem.
• Grade 7 (12 to 13): proportion, two-step equations, circles and chance; then pentominoes, fair division, sorting and a triangle with no area.
• Grade 8 (13 to 14): lines and slope, systems, exponents and Pythagoras; then Euclid's algorithm, the birthday paradox and a cube in four dimensions.
• Grade 9 (14 to 15): factoring, parabolas and trigonometric ratios; then proof with letters, shortest paths, the Game of Life and logic gates.
• Grade 10 (15 to 16): the quadratic formula, logarithms and circle theorems, all derived; then induction, RSA, complex numbers as rotations and a first look at calculus.
• Grade 11 (16 to 17): radians, the sine and cosine rules, log scales and vectors; then the cubic formula, Buffon's needle, max flow and fractal dimension.
• Grade 12 (17 to 18): calculus, vectors and probability, derived; then eigenvectors, gradient descent, the halting problem, and the math of rockets, clinical trials and climate.

The map of mathematics goes the other way: it lists all 534 sections of the subject classification mathematicians use, says which ones the sheets already reach, and suggests an elementary way into each of the rest.

Why the sheets are built this way

The design choices (answers on every sheet, mixed tracks, one worked example, a hard stretch, parents nearby) follow the learning-science literature. The research page lists the studies, with designs and effect sizes, and the claims that did not hold up.

Printing

Use the Print button at the top of any sheet, or your browser's print command. Sheets are laid out for Letter and A4, black and white, with ruled space for working. Turn on "background graphics" in the print dialog if the shaded example box comes out blank.

Suggestions and mistakes

If you spot an error in an answer, or want a topic covered, open an issue at github.com/microprediction/mathdetours. The whole site is plain HTML, so corrections are quick.