Caleb Gattegno’sapproach to math focuses on the process for generating mathematics in the mind. While many believe that math is the skill of a few gifted people, he believed that every student is capable of functioning like a mathematician. By taking abstract concepts and representing them in visible and tangible ways, he found that students can gain mathematical competence well beyond their designated grade levels.
If you already have a set of Algebricks rods (a.k.a. Cuisenaire Rods) at home and are looking for the most effective way to use them, then this Book Set is designed for you. These books are reprints of Dr. Caleb Gattegno's classic series of texts.
This Book Set includes:
Gattegno Mathematics Textbook 1: Qualitative Arithmetic - The Study of Numbers up to 20
Gattegno Mathematics Textbook 2: Study of Numbers up to 1,000 - The Four Operations
Mathematics with Numbers in Colour Book VI: Applied Mathematics
Mathematics with Numbers in Colour Book VII: Algebra and Geometry
Now Johnny Can Do Arithmetic: A Handbook on the Use of Colored Rods (for parents)
*Please note that Gattegno Mathematics Textbook 3: Applied Arithmetic is not included. This book is not necessary for a modern curriculum, as it focuses on outdated units of British measurement.
1 Sessions of free play Unstructured playtime allows children to develop familiarity with the various sizes and colors of the rods.
2 Qualitative work with the rods Students discover equivalence, trains, patterns, inequalities, staircases, complementarities, trains of one color, transformations, and odd and even lengths.
3 Literal work Students are introduced to:
color name notation for rods
signs for addition, difference and equivalence
equations (such as r + g = y)
brackets and parentheses
multiples
names of fractions and equivalent expressions
4 Number measure study of numbers up to 10 Children use a unit of measure to generate number names for rods and are introduced to the four operations with numbers up to 5, and later to 10.
5 Applications Children work on word problems involving operations on numbers up to 10.
6 Study of numbers up to 20 Students work on problems involving all four operations, odd and even numbers, prime and composite numbers, series, ordinal numbers, zero, and short division.
1 Study of numbers from 1 to 100 Problems involve multiples, first milestones, tables of products, factors, primes, composites, squares, common factors, and highest common factor.
2 Vertical notation Addition and subtraction, equivalent subtractions, multiplication, and division are written in vertical form.
3 Clock Children work on challenges involving reading the clock, finding the remaining minutes within the hour, counting the time from one hour to another, travel, the 24 hour day, and other time related questions.
4 Numbers up to 1000 Problems involve:
equivalent crosses (rods)
towers of three
milestones: multiples of 100, transformations using towers, other multiples of 100, doubles providing milestones
HTU: hundreds, tens, units
completing naming numerals up to 1000
sequences through doubling, equivalent products, distribution and multiplication
towers of four, preparing for quick mental calculations multiplying by 25, vertical notation, quick calculations, multiples of 11, 3, 6, 9,
criteria of divisibility
more about squares, square of a sum or difference, product of a sum and a difference
curiosities from Pythagoras1 school
5 Days and weeks Children learn about such things as the calendar year, seasons, making a model for the calendar, and leap years.
6 Reading and writing of numbers Students learn about another way of naming numbers — “the number array,” as well as place value and zero as a place holder, and jumping from hundreds to millions and beyond.
7 Procedures, algorithms for the four operations Topics include:
addition and equivalent additions
families of equivalent subtractions and best equivalent subtractions
speeding up the operations
multiplication and casting out 9’s
milestones again: doubling, quicker and safer divisions, application to long division
a very simple calculating machine
8 Grouping, cost price, selling prices, profit Units such as dozens, grosses, and scores are covered as well as time, buying and selling, profit, and price.
9 Perimeters, area, volume Students learn about rectangles, cubes and cuboids, and their perimeters, area, total area, volume, and units of volume.
1 Fractions as operators Operators, inverse operators, composition of operators, and equivalent operators are explored.
2 Study of fractions Students become knowledgeable about: ordered pairs, families of equivalent ordered pairs, first element of a family of equivalence, equivalent expressions for pairs, equivalent fractions, reciprocals, addition and subtraction of pairs, addition and subtraction of fractions, cross multiplication and equivalences, inequalities, transformation of pairs, ratios and proportions, fractions of fractions, division of fractions, mixed numbers, and operations on mixed numbers.
3 Study of decimal fractions Students work on defining a decimal fraction, translating one notation for another, operating on decimals, operating on hundredths and thousandths, operating on powers of ten, and applying this knowledge in various ways.
4 Percentages The new notation (%) and various forms of writing percentages are explored in conjunction with fractions, decimals, and applications.
1 The formation of numbers Students explore place value and powers of ten, largest and smallest number of n figures, index notation, horizontal and vertical notation, equivalent subtractions, growth of numbers, multiplication of numbers.
2 Different bases of numeration Polynomials, the binary scale, scales of three, seven and twelve, and the four operations in any scale are covered.
3 Divisibility and prime numbers Students use the Eratosthenes sieve, find criteria of divisibility, find (all) prime factors, do exercises and further explore prime numbers.
4 HCF and LCM HCF -highest common factor, decomposition into prime factors, and LCM - lowest common multiple are worked on.
5 Squares, cubes, and cube roots Students learn about the square of a sum, the formation of a table of squares, the square of a difference, the formation of a table of cubes, the cube of a difference, square roots, approximations, calculating square roots, and square roots to a certain approximation.
6 The set of integers In this area, students learn about infinite sets, equivalent sets, partition of the set of integers, equivalence of (1) and one of its parts, other partitions of (1), how to think about infinite sets, the infinite nature of the set of prime numbers.
1 Length, area and volume Topics include: the centimeter and its multiples, conversions, multiples and submultiples, errors and approximations, absolute and relative errors, the cubic centimeter, volumes of various bodies, areas and approximation of areas, figures reducible to rectangles, tables of units and applications.
2 Capacity and volume of round bodies The liter and its multiples and submultiples, round bodies, and solids of revolution are explored.
3 Weight, mass and density Students learn about weights and balances, how to weigh an object, finding a fraction of a weight, units of weight, making a box of weights, mass and weight, density, and applications.
4 Measures, their formalization Dimensional formulae, measuring a length, isometric measures, measuring an area, transformation of a figure, measuring a volume, properties of measure, other magnitudes, and scalar and vector quantities are covered.
5 The C.G.S., M.K.S., and M.T.S. Systems of units historical notes, fundamental and derived units, the systems
6 Proportions and mixtures Students explore areas including sharing, films and tapes, the post office, conversions of units, discounts, and the compound unitary method.
7 Problems depending on measurements & Problems in economics Problems may include building a road, building a site, dividend and interest, budgets, consumer goods, and travel.
8 Problems on speed Topics include: speed, paths/routes, speeds in various units, comparing actual speeds, relative measurements, graphical representation, and acceleration.
9 The perpetual calendar Students explore the use of remainders in division by 7, days in the year, the number code for the months, days in different years, some historical dates worked out, and historical notes.
1 Simultaneous equations about directed numbers Topics include: finding a pair through knowledge of another pair, formalization of the solution, a word about algebra, a class of equivalence, and generalizations.
2 Permutations and combinations Students are introduced to permutations, transpositions and substitutions, combinations, computation of permutations and combinations.
3 Sets and subsets algebra of sets Sets and elements, the null set, relationships between sets, inclusion, equivalence of sets, operations on sets, and analogy between operations on sets and on products are explored.
4 Arithmetic progressions and geometric progressions Students learn about arithmetic progressions, powers and their algebra, geometric progressions, sum of the terms of a G.P., and applications to decimal numbers.
5 The geometry of the Geoboards Challenges on the nine-pin rectangular lattice Geoboard the regular polygon boards are worked on.
Why do some children struggle with mathematics, while others seem to be naturally gifted? In this book, Caleb Gattegno examines the obstacles that keep students from succeeding in math, and provides a clear solution. Using Algebricks colored rods, parents and teachers can make arithmetic visible, tangible, and rewarding for their learners. Through exploring and playing with the materials, children absorb essential mathematical knowledge, while parents and teachers discover the astounding learning capacity and inventiveness of their children.
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