BooksArithmetic
Arithmetic books
Kiselev’s Arithmetic, the other classic Russian arithmetic courses, and the problem books and mental-calculation books used with them. The courses prove every rule; the problem books give the practice.
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Arithmetic books: 14 books
Kiselev's Systematic Arithmetic
by A. P. Kiselev
US grades 5–8 · UK Years 6–9
Kiselev's definitive systematic arithmetic — the expanded companion to his classic arithmetic textbook. 207 pages, 264 numbered articles across seven divisions: whole numbers; concrete (denominate) numbers and the metric system; divisibility, primes, and factorisation; common fractions; decimal fractions with limits and repeating decimals; ratio and proportion; and a full course of word problems on proportional quantities. Includes elementary treatments most textbooks leave out — Euclid's proof of the infinitude of primes and the concept of a limit used to prove that 0.999… equals 1.
Vereshchagin's Arithmetic Problems
by I. P. Vereshchagin
US grades 4–8 · UK Years 5–9
The largest arithmetic problem collection of imperial Russia — 3,238 problems with the complete answer key, in English for the first time. Approved by the Ministry of Public Education for the Empire's secondary schools and teachers' seminaries, and separately for the girls' gymnasia of the Empress Maria department, it ran to eighteen editions. Three Parts and fifty-seven sections cover whole numbers and compound named numbers; divisibility; common and decimal fractions; the metric system; ratio and proportion; and the commercial rules — the rule of three, percentage, interest, discount, partnership and alligation. Vereshchagin insisted his data be real, so the problems run on railway timetables, the heights of Elbrus and Everest, the assay of the new silver ruble, and Eratosthenes measuring the earth between Syene and Alexandria. Translated from the seventh edition of 1891, with source-exact problem numbering.
Berezanskaya's Arithmetic Problems
by E. S. Berezanskaya
US grades 4–7 · UK Years 5–8
The iconic companion to Kiselev's Arithmetic — the problem collection Russian classrooms used side-by-side with Kiselev for over 70 years. 2,354 problems across eight chapters in the canonical order: numeration; the four operations on whole numbers; divisibility; common fractions; decimal fractions; ratio and proportion; percentages; and a concluding chapter of mixed problems drawing on everything before. Oral drills, written exercises, and word problems of real substance, sequenced from easy to demanding. The first complete, faithful English translation, with source-exact problem numbering.
Kiselev's Arithmetic
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The foundational arithmetic textbook used in Russian schools for over a century. 6 parts, 214 sections. Whole numbers through proportional quantities, with mathematical proofs for every operation.
Malinin & Burenin Problems
by A. Malinin & K. Burenin
US grades 5–8 · UK Years 6–9
3,807 problems with a complete answer key — the problem collection that accompanies Malinin and Burenin's arithmetic textbook, and the exercises Imperial Russian students worked through alongside the theory. First complete English translation from the original Russian edition.
Egorov's Arithmetic Problems
by F. I. Egorov
US grades 3–5 · UK Years 4–6
A graded problem book for the whole course of arithmetic in whole numbers, in first faithful English translation from the original Russian edition: 1,600 problems, with answers to 1,245 of them. It begins with numeration to a thousand, a million and beyond and with the meaning of the four operations, then works through written addition, subtraction, multiplication and division of multi-digit numbers, with its own sections on how a sum, difference, product and quotient change when their components change. Compound denominate numbers run alongside at every stage, followed by problems on time and on square and cubic measures, and a final set on all operations.
Malinin & Burenin
by A. Malinin & K. Burenin
US grades 5–8 · UK Years 6–9
A complete English translation of Malinin and Burenin's Imperial Russian arithmetic textbook. 11 chapters, 301 sections. Covers numeration, operations on whole numbers, divisibility, fractions, ratios, proportions, percentage, interest, and Diophantine problems.
Rashevsky's Arithmetic
by K. N. Rashevsky
US grades 5–8 · UK Years 6–9
A complete course in arithmetic in nine sections, in first faithful English translation from the original Russian edition. The four operations on whole numbers with the written methods set out in full; named and metric quantities; areas and volumes worked from drawings; tests for divisibility, primes, greatest common divisor and least common multiple; common and decimal fractions, including repeating decimals; ratio, proportion and proportional division; percentage and mixing problems; and plans, diagrams and graphs. Long divisions and column multiplications are printed digit under digit, so the reasoning stays visible on the page.
Malinin's Mental Calculation
by A. F. Malinin
US grades 2–7 · UK Years 3–8
First faithful English translation from the original Russian edition. 1,963 problems arranged from short numerical exercises to demanding multi-step work with fractions, money, weights, measures, and proportions. Preserves Malinin's original numbering and five-part progression.
Perelman's Entertaining Arithmetic
by Ya. I. Perelman
US grades 4+ · UK Year 5+
The classic of Russian popular mathematics. Puzzles, riddles, and curiosities that make arithmetic genuinely entertaining.
Rachinsky Solutions
by Valery Manokhin
US grades 4–8 · UK Years 5–9
The essential companion to Rachinsky's 1001 Problems — every problem solved, every error corrected. Step-by-step arithmetic reasoning for all 1,001 problems in the 1899 collection, with 12 errata corrections to misprints in the original answer key (problems #188, #410, #454, #468, #519, #563, #705, #779, #796, #836, #889, #892 — independently verified). Includes a complete conversion table for pre-revolutionary Russian units (puds, funts, zolotniks, sazhens, arshins, vershoks, desyatinas, chetveriks). 257 pages, professionally typeset. Solutions organised by problem number to match the companion problem book exactly.
Berman's Calculation Techniques
by G. N. Berman
US grades 6–10 · UK Years 7–11
Three parts covering mental calculation, written calculation, and approximate calculation — the practical arithmetic skills the Russian school tradition treated as foundational. A short, dense book on how to compute well without a calculator.
Rachinsky's 1001 Problems
by S. A. Rachinsky
US grades 4–8 · UK Years 5–9
1,001 carefully selected problems from the village schoolteacher whose students were depicted in Bogdanov-Belsky's famous 1895 painting "Mental Arithmetic."
Amenitsky's Arithmetic Games
by N. N. Amenitsky
US grades 4+ · UK Year 5+
Four mathematical games — the racing game, guessing numbers, the Tower of Lucas and the game with a needle — that turn place value, doubling, parity and a first experiment in probability into play, in first faithful English translation from the original Russian edition. A short 31-page reading edition with four illustrations, for curious students, teachers and readers of recreational mathematics. No prerequisites beyond arithmetic.