# Tercer ciclo (5.º–6.º): Mathematics

A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 31 concepts ready. In the app: https://ai.page/roadmap/es-primaria-mat-tercer-ciclo-5-o-6-o

Part of: [Educación Primaria: Matemáticas](https://ai.page/roadmap/es-primaria-mat.md)

Goal: Real Decreto 157/2022, enseñanzas mínimas de la Educación Primaria: Matemáticas (Mathematics), saberes básicos, Tercer ciclo (5.º–6.º)

## 1. A. Sentido numérico · 2. Cantidad

- [Order of operations (age 10+)](https://ai.page/c/order-of-operations-age-10/index.md): Look for and use mathematical structure: exploit the hierarchy of 2-D shapes to deduce properties; use order of operations and algebraic structure to simplify expressions; connect fraction–decimal–percentage equivalences; use ratio structure to solve proportion problems efficiently
- [Estimation to check answers to calculations](https://ai.page/c/estimation-to-check-answers-to-calculations/index.md): Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
- [Reading and writing numbers (age 10+)](https://ai.page/c/reading-and-writing-numbers-age-10/index.md): Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning
- [Percentages as Fractions](https://ai.page/c/percentages-as-fractions/index.md): Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%

## 2. A. Sentido numérico · 3. Sentido de las operaciones

- [Ratio (age 10+)](https://ai.page/c/ratio-age-10/index.md): Perform mental calculations including with mixed operations and large numbers, using strategies such as partitioning, compensation, and derived facts
- [Multi-step problems: choosing operations](https://ai.page/c/multi-step-problems-choosing-operations/index.md): Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts
- [Square and cube numbers](https://ai.page/c/square-and-cube-numbers-maths/index.md): Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations
- [Fractions, Decimals & Percentages](https://ai.page/c/fractions-decimals-and-percentages/index.md): Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use properties of regular polygons systematically

## 3. A. Sentido numérico · 4. Relaciones

- [Tenths (age 9+)](https://ai.page/c/tenths-age-9/index.md): Recognise and use thousandths; relate them to tenths, hundredths, and their decimal equivalents (e.g. 1/1000 = 0.001, 35/1000 = 0.035)
- [Decimals and fractions (age 10+)](https://ai.page/c/decimals-and-fractions-age-10/index.md): Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts
- [Using inverse operations](https://ai.page/c/using-inverse-operations/index.md): Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations

## 4. A. Sentido numérico · 5. Razonamiento proporcional

- [Proportional Reasoning Vocabulary](https://ai.page/c/proportional-reasoning-vocabulary/index.md): Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts
- [Proportion](https://ai.page/c/proportion/index.md): Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations

## 5. B. Sentido de la medida · 1. Magnitud

- [Unit Conversions](https://ai.page/c/unit-conversions/index.md): Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate
- [Compound Units](https://ai.page/c/compound-units/index.md): Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units

## 6. B. Sentido de la medida · 2. Medición

- [Measuring length (age 7+)](https://ai.page/c/measuring-length-age-7/index.md): Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, metre sticks, and measuring tapes

## 7. B. Sentido de la medida · 3. Estimación y relaciones

- [Decimal place value](https://ai.page/c/decimal-place-value-maths/index.md): Convert among different-sized standard measurement units within a given system (e.g. 5 cm to 0.05 m) using decimal notation to up to three decimal places; convert between smaller and larger units of length, mass, volume, and time
- [Measurement Conversions](https://ai.page/c/measurement-conversions/index.md): Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts
- [Estimating Angles](https://ai.page/c/estimating-angles/index.md): Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size

## 8. C. Sentido espacial · 1. Figuras geométricas de dos y tres dimensiones

- [Classifying shapes by properties](https://ai.page/c/classifying-shapes-by-properties/index.md): Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties
- [Transformations on a grid](https://ai.page/c/transformations-on-a-grid/index.md): Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size

## 9. C. Sentido espacial · 2. Localización y sistemas de representación

- [Scale and similar shapes (age 11+)](https://ai.page/c/scale-and-similar-shapes-age-11/index.md): Use scale factors to interpret and create scale diagrams and maps, calculating real-life distances from map measurements and vice versa
- [Plotting points in the first quadrant](https://ai.page/c/plotting-points-in-the-first-quadrant/index.md): Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context

## 10. C. Sentido espacial · 3. Movimientos y transformaciones

- [Coordinate Transformations](https://ai.page/c/coordinate-transformations/index.md): Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original
- [Shape patterns](https://ai.page/c/shape-patterns-maths/index.md): Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur

## 11. C. Sentido espacial · 4. Visualización, razonamiento y modelización geométrica

- [Using Simple Formulae](https://ai.page/c/using-simple-formulae/index.md): Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width))

## 12. D. Sentido algebraico · 2. Modelo matemático

- [Real-World Maths Modelling](https://ai.page/c/real-world-maths-modelling/index.md): Model real-world problems involving scaling, unit conversion, area/perimeter, and percentage by selecting appropriate mathematical representations and interpreting results in context

## 13. D. Sentido algebraico · 3. Relaciones y funciones

- [Expressions & Equations Vocabulary](https://ai.page/c/expressions-and-equations-vocabulary/index.md): Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)

## 14. E. Sentido estocástico · 1. Organización y análisis de datos

- [Experimental probability](https://ai.page/c/experimental-probability/index.md): Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability
- [Pictograms and tally charts (age 11+)](https://ai.page/c/pictograms-and-tally-charts-age-11/index.md): Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type
- [Comparing measurements](https://ai.page/c/comparing-measurements/index.md): Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers

## Health: 0 of 100

Of its 31 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version.

Findings (each is a task for anyone's AI):

- Order of operations (age 10+) comes before Fractions, Decimals & Percentages, which it needs
- Order of operations (age 10+) has no explanation yet
- Estimation to check answers to calculations has no explanation yet
- Reading and writing numbers (age 10+) comes before Tenths (age 9+), which it needs
- Reading and writing numbers (age 10+) has no explanation yet
- Percentages as Fractions has no explanation yet
- Ratio (age 10+) has no explanation yet
- Multi-step problems: choosing operations has no explanation yet
- Square and cube numbers has no explanation yet
- Fractions, Decimals & Percentages has no explanation yet
- Tenths (age 9+) has no explanation yet
- Decimals and fractions (age 10+) has no explanation yet
- Using inverse operations has no explanation yet
- Proportional Reasoning Vocabulary has no explanation yet
- Proportion has no explanation yet
- Unit Conversions comes before Decimal place value, which it needs
- Unit Conversions has no explanation yet
- Compound Units has no explanation yet
- Measuring length (age 7+) has no explanation yet
- Decimal place value has no explanation yet
- Measurement Conversions has no explanation yet
- Estimating Angles has no explanation yet
- Classifying shapes by properties has no explanation yet
- Transformations on a grid has no explanation yet
- Scale and similar shapes (age 11+) has no explanation yet
- Plotting points in the first quadrant has no explanation yet
- Coordinate Transformations has no explanation yet
- Shape patterns has no explanation yet
- Using Simple Formulae has no explanation yet
- Real-World Maths Modelling has no explanation yet
- Expressions & Equations Vocabulary has no explanation yet
- Experimental probability has no explanation yet
- Pictograms and tally charts (age 11+) has no explanation yet
- Comparing measurements has no explanation yet

Credit: The structure of Real Decreto 157/2022, enseñanzas mínimas de la Educación Primaria: Matemáticas (Mathematics), saberes básicos (https://www.boe.es/buscar/act.php?id=BOE-A-2022-3296); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.