Competition Prep

1. Math Kangaroo, Grades 1 to 6: counting shapes, mirrors and turns, cube nets, paths on a grid, balances, truth-tellers, line-ups, patterns and calendars.
2. Grades 3–4 and Grades 5–6: the word-problem types on state tests and credit by exam, each with its bar picture.
3. Grades 7–8 and Contest strategies: ratios, percents, rates, probability, and the ideas behind MATHCOUNTS and the AMC.
4. SAT: Algebra and data, Geometry, and AMC 10 / 12, for high school.

The Science section has ten levels shaped the same way: Physics for Grades 3 to 5 and 6 to 8, then Mechanics and Rotation, oscillations and fluids for high school; and Chemistry and Biology, each for Grades 3 to 5, 6 to 8 and 9 to 12.

Eighteen levels in all. The state-test levels follow common US standards rather than one state’s. Along the top, under Getting ready for a test? Pick it to see only its levels., a pill for each test shows only its levels: state tests, the SAT, MATHCOUNTS, AMC 8 / 10, AMC 12 and Math Kangaroo, and for science, state science tests, AP Physics 1, AP Chemistry, AP Biology and the Science, Physics, Chemistry and Biology Olympiads.

Each type opens with how to spot it, the words that give it away, its picture and its usual trap. Then Pip, the buddy, works one example on a chalkboard, the way a teacher would: it draws the problem, writes what we are told in blue and what we are finding in red, solves one part at a time, and writes each answer in green.

1. Tap Watch it on the board or Play to hear it, a step at a time.
2. Back and Next go through it by hand, at your child’s own speed.

In science, the usual mistaken idea about a type is shown only after the board example, never before it.

Every type has eleven problems of its own: a warm-up first, then problems at test level, then two stretch problems, the hardest a test at that level asks, then three challenges, new problems built on the ideas behind the hardest contest questions. Each one asks your child to pick the picture or the fact that unlocks it before solving, and each has three hints that never give the answer away.

Each level also has eleven mixed sets, one problem of every type, unlabeled, like a real test. Your child names the type first, then solves. The sets climb from warm-ups to challenges.

Every practice problem has its own chalkboard too. A note says Try it yourself first. Stuck? Then watch it worked on the board., and Watch it on the board opens it.

The pill marked Classic puzzles, after the test pills, opens the famous puzzles that turn up in contests and job interviews, for Grades 6 to 12, in groups. Most need no sums at all, just a careful idea.

Each puzzle has its statement and a picture of it, three hints, and a short narrated film of the answer. The film stops on pause and think before it gives anything away. The statements are in our own words, and settings a child should not meet are retold with the same logic.

Under the levels are the word problem sets from Pre-K to Grade 5, twenty problems in each of three tiers: Warm-up, Stretch and Olympiad.

Every problem has the same help ladder: a clue, then a strategy, then the first step, one tap at a time. The full solution appears after a correct answer.

Each tier prints as its own sheet, with the answers on a page of their own.

1. Choose the grade and the tier, then tap Print this set (PDF).
2. Press Print or save as PDF at the top of the sheet, then choose your printer or Save as PDF.

Every type’s chalkboard example is open to everyone, with no sign-in, and so is each classic puzzle’s statement and picture. The practice problems, the mixed sets, and the puzzles’ answers and films open when a grown-up signs in. Of the grade sets, the Warm-up tier is free at every grade. See Free week and membership for the rest.

They are written for Cogito, and every answer was solved twice: once by its writer and once by a separate check. The ideas behind contest problems belong to nobody; the wording of a real Kangaroo, MATHCOUNTS, AMC or SAT paper does belong to somebody, so none of it is here.