Start where the counting starts.

What the requirement actually is

A Brazilian public-school mathematics book has to satisfy a stack of documents, and they are not the same document.

Document	What it binds
Lei de Diretrizes e Bases, Lei 9.394/1996, as amended	The structure of basic education: preschool, nine years of elementary school (ensino fundamental), three years of high school. Minimum annual hours: 800 in elementary school, 1,000 in high school.
Base Nacional Comum Curricular, homologated 2018	The mandatory learning. Ten general competencies for all of basic education. Eight competencies specific to mathematics in elementary school, five in high school. Under those, the skills.
Lei 14.945/2024 and Resolução CNE/CEB nº 2/2024	High school was reorganized. The common core (formação geral básica) went back to at least 2,400 hours across the three years, and mathematics is again a required subject in every year. The 43 BNCC skills were not replaced. Pathways (itinerários) shrank to at least 600 hours. Technical programs have a different split.
State and municipal curricula	They may add, exemplify, or reorder. They may not delete a BNCC skill. A local addition gets a suffix on the code. This map is the national floor, not São Paulo's pacing guide or any other state's.
PNLD, the national textbook program	How a book gets bought and delivered to public schools. Alignment with the BNCC is necessary and not sufficient. A school may use other material tomorrow. Entering the official distribution is a multi-year public call, with a rights-holder who can print.

Preschool is part of the curriculum and not part of the textbook. The BNCC organizes it as rights and fields of experience, not as subjects. The mathematical root sits in one field, Espaços, tempos, quantidades, relações e transformações. Children count, sort, and talk about before and after. A textbook series that begins at 1st grade is already standing on that. The map includes the twelve objectives that the later skills actually use.

How a skill code works

EF01MA05 reads from the left. EF is elementary school. 01 is the year. MA is mathematics. 05 is the fifth mathematics skill written for that year. High school drops the year: EM13MAT303 is high school, the skill is tied to specific competency 3, and it is the third skill under that competency. The 13 means the whole three-year stage, not grade 13. Schools, not the BNCC, decide which year of high school teaches it. That is why the map places high-school concepts in one column.

Elementary mathematics has five thematic units, kept visible from the 1st grade on purpose. Algebra in the 1st grade is sorting and patterns. It is not x. Probability in the 1st grade is the words certain, maybe, and impossible. It is not a fraction. Treating the unit names as the content of that year is the usual way to overshoot.

Unit	What it is doing in the early years
Números	The jobs of a number, the count, place value, the four operations, then fractions, decimals, integers, rationals, reals.
Álgebra	Pattern first, then equality as sameness, then proportion, then a letter, then equations, then functions.
Geometria	Position from a stated reference, solids in ordinary objects, plane figures, angles, constructions, similarity, Pythagoras.
Grandezas e medidas	Comparison before units. Then the fact that the number changes when the unit changes. Area, volume, time, money, temperature.
Probabilidade e estatística	Chance in words, then a survey and a graph, and only then a probability that is a fraction. Later: mean, sample, and a misleading axis.

There are 247 elementary skills and 43 high-school skills. The wording on the map is the official wording, taken from the open dataset bncc-dados, which traces each record to the MEC spreadsheet and to a page of the homologated PDF. I did not re-proof every character against that PDF. A spot check of the skills this argument depends on did match.

The year is not the dependency

The BNCC publishes no prerequisite arrows. A skill in the 3rd grade is not, by that fact, built on every skill in the 2nd. Some skills in the same year depend on each other, and the code number hides it. The 82 concepts on the map are a pedagogical inference. Each of the 138 solid arrows is a gate: the later idea is unfinished without the earlier one. Each dashed arrow is support: the earlier idea helps, and a careful teacher can start without it. Every arrow has a written reason. None of this is a line in the official document, and the map says so on every panel.

1. Comparing numbers does not require place value.EF01MA05, “which of these two numbers is larger,” can be answered from the count: the later number is the larger one, on a cord or a line. Place value (EF01MA07, then the hundreds in the 2nd grade) is a better tool later. Teaching “more digits means bigger” works for 8 and 15 and fails for 99 and 100.
2. A decimal needs place value and it needs fractions.The positions to the right of the ones are the same ten-for-one rule. A tenth is also the fraction 1/10. Without both, 0.1 is two whole numbers and a dot.
3. A numerical probability waits for the fraction.From the 1st grade through the 4th, chance stays in words. In the 5th grade the probability is favorable outcomes over possible outcomes. That is a fraction. The words are not a warm-up that can be skipped, and the fraction is not a notation pasted on at the end.
4. Irrationals come after Pythagoras, not before.EF09MA01 says that, once a unit is fixed, some segments have no rational length, and it points at diagonals. EF09MA13 asks for a demonstration of Pythagoras by similarity of triangles. The theorem forces the new number. Using the real numbers to justify Pythagoras turns the dependency around.

The same discipline runs along the main number thread. This is the spine the first book is cut from. The full graph, including geometry, measure, and statistics, is the map.

1. Preschool: say the count out loud and match it to things. EI02ET07, EI03ET07
2. A number counts, or it orders, or it is only a name. EF01MA01 — written
3. Count each thing once. The last word is the size of the collection. Estimate, then pair. The count reaches 100 in groups of ten. EF01MA02, EF01MA03, EF01MA04 — written
4. Who comes later in the count is larger, through two-digit numbers, on the line and off it. EF01MA05 — written, still without requiring place value
5. Beside that, not under it: break numbers into sums. That is the start of place value. EF01MA07 — written
6. Basic addition facts, then the actions: join, add on, separate, take away. Compare and complete arrive in the 3rd grade. EF01MA06, EF01MA08 — written; EF03MA06 is not
7. Hundreds, and zero as an empty position. Then the same rule through the thousands. 2nd to 4th grade
8. Multiplication as equal groups, then as an array, then as a rate. Division undoes it, remainder included. 2nd to 4th grade
9. Fractions, from fair shares and from parts of shapes. Decimals, from place value and from tenths. Percent, as those fractions said per hundred. 4th to 6th grade
10. Integers, when take-away does not stop at zero. Rationals as one number with two writings. Powers and roots. 7th and 8th grade
11. Cross from geometry: similarity, then Pythagoras. 9th grade
12. Some lengths are not rational. The real line. EF09MA01, EF09MA02

High school does not start a new arithmetic. It uses this spine. An affine function is the first-degree equation allowed to vary, drawn on the plane, with direct proportion as the line through the origin. Compound interest is a percent applied again to the new amount, which is why it waits on both percent and the exponential. A misleading graph waits on having read an honest one, and on knowing a sample from a census.

Using it in place of a bought book

A school can name this work as the material for a skill the student book and the teacher book finish. It cannot name the work as the mathematics textbook of a whole year until every skill of that year is finished. The adoption minute is generated from that rule. A private school records it in the pedagogical proposal. A public school whose network adhered to the PNLD still has to use the books the FNDE sent. This work is not a PNLD book, and the minute says so.

The mastery record describes how a teacher would know which assumption a child used. Each option is one hypothesis. A correct reason is evidence for the concept and for the prerequisites that reason actually uses, with the chance of a guess written beside it. “12, because it has more digits” is that false rule. It is not a gap in place value, and it does not block later topics, because place value is not what the question was asking. Not knowing which number is said first is different: that is a missing count, so comparison is blocked and place value, which was not asked, is blocked without being marked wrong. The published site does not store the record. A child’s name is not sent to the host.

What was written, and what was not

The 1st grade is written: twelve units, student book and teacher book, one for every mathematics skill of the year. The class is a fictional municipal school. Unit 1 still stops at 20 on purpose. Unit 2 is where the count reaches 100, where 28 and 31 are compared, and where a number is broken into different sums. The student index lists the order, which follows the dependencies rather than the numeric order of the codes.

The student pages are in Portuguese, at read-aloud length, because a Brazilian 1st grader is still learning to read. There is an English gloss on each lesson so you can judge the mathematics without guessing.

Years 2 through 9, and high school, are mapped and not written. A PNLD teacher manual would also reprint every student page with the answers in the margin. These two web books are linked instead of duplicated, and the note on the two books says what the official format would still require.