# Segundo ciclo (3.º–4.º): Mathematics

A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 30 concepts ready. In the app: https://ai.page/roadmap/es-primaria-mat-segundo-ciclo-3-o-4-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, Segundo ciclo (3.º–4.º)

## 1. A. Sentido numérico · 1. Conteo

- [Working with Large Numbers](https://ai.page/c/working-with-large-numbers/index.md): Solve number and practical problems involving reading, writing, ordering, comparing, and rounding whole numbers up to 1,000,000

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

- [Reading and writing numbers (age 9+)](https://ai.page/c/reading-and-writing-numbers-age-9/index.md): Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding
- [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
- [Adding Fractions (Unlike Denominators)](https://ai.page/c/adding-fractions-unlike-denominators/index.md): Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator

## 3. 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
- [Times tables (age 8+)](https://ai.page/c/times-tables-age-8/index.md): Recognise and use repeated reasoning to generalise: extend patterns in times tables and equivalent fractions, derive unknown facts from known facts efficiently, describe general rules
- [Addition and subtraction within 1000](https://ai.page/c/addition-and-subtraction-within-1000/index.md): Add and subtract within 1000 using concrete models, drawings, and strategies based on place value; understand composing and decomposing tens and hundreds

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

- [Comparing fractions (age 10+)](https://ai.page/c/comparing-fractions-age-10/index.md): Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks
- [Adding and subtracting (age 9+)](https://ai.page/c/adding-and-subtracting-age-9/index.md): Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

## 5. A. Sentido numérico · 5. Educación financiera

- [Estimating and comparing money](https://ai.page/c/estimating-and-comparing-money/index.md): Estimate, compare, and calculate different measures including money in pounds and pence

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

- [Measurable Attributes of Objects](https://ai.page/c/measurable-attributes-of-objects/index.md): Describe and identify measurable attributes of objects such as length, height, weight, and capacity; use comparative language (longer, shorter, heavier, lighter, more, less)
- [Calculating with measurements](https://ai.page/c/calculating-with-measurements/index.md): Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
- [Telling time to the minute (age 9+)](https://ai.page/c/telling-time-to-the-minute-age-9/index.md): Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days)

## 7. 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
- [Measuring with different units](https://ai.page/c/measuring-with-different-units/index.md): Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen

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

- [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

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

- [Sorting 2-D and 3-D shapes](https://ai.page/c/sorting-2-d-and-3-d-shapes/index.md): Compare and sort common 2-D and 3-D shapes and everyday objects by their properties
- [2-D shapes (age 10+)](https://ai.page/c/2-d-shapes-age-10/index.md): Draw 2-D shapes using given dimensions and angles, using a ruler and protractor accurately
- [2-D shapes (age 7+)](https://ai.page/c/2-d-shapes-age-7/index.md): Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them

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

- [Positional Language](https://ai.page/c/positional-language/index.md): Describe the position of objects using terms such as above, below, beside, in front of, behind, next to
- [Describing Movements](https://ai.page/c/describing-movements/index.md): Describe movements between positions as translations of a given unit to the left/right and up/down

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

- [Transformations on a Grid](https://ai.page/c/transformations-on-a-grid-maths/index.md): Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed
- [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

## 12. 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))

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

- [Pictograms and tally charts](https://ai.page/c/pictograms-and-tally-charts/index.md): Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables

## 14. 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)

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

- [Sorting Data into Categories](https://ai.page/c/sorting-data-into-categories/index.md): Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity

## 16. E. Sentido estocástico · 2. Incertidumbre

- [The Probability Scale](https://ai.page/c/the-probability-scale/index.md): Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible
- [Ordering Likelihoods](https://ai.page/c/ordering-likelihoods/index.md): Compare the likelihood of different events and order them from least to most likely — including situations with unequal outcomes such as a bag with more of one colour than another, or a spinner with sections of different sizes — and explain reasoning using informal language

## Health: 0 of 100

Of its 30 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):

- Working with Large Numbers comes before Reading and writing numbers (age 9+), which it needs
- Working with Large Numbers has no explanation yet
- Reading and writing numbers (age 9+) has no explanation yet
- Estimation to check answers to calculations has no explanation yet
- Adding Fractions (Unlike Denominators) has no explanation yet
- Ratio (age 10+) has no explanation yet
- Multi-step problems: choosing operations has no explanation yet
- Times tables (age 8+) has no explanation yet
- Addition and subtraction within 1000 has no explanation yet
- Comparing fractions (age 10+) has no explanation yet
- Adding and subtracting (age 9+) has no explanation yet
- Estimating and comparing money comes before Calculating with measurements, which it needs
- Estimating and comparing money has no explanation yet
- Measurable Attributes of Objects has no explanation yet
- Calculating with measurements has no explanation yet
- Telling time to the minute (age 9+) has no explanation yet
- Measuring length (age 7+) has no explanation yet
- Measuring with different units has no explanation yet
- Measurement Conversions has no explanation yet
- Sorting 2-D and 3-D shapes has no explanation yet
- 2-D shapes (age 10+) has no explanation yet
- 2-D shapes (age 7+) has no explanation yet
- Positional Language has no explanation yet
- Describing Movements has no explanation yet
- Transformations on a Grid has no explanation yet
- Shape patterns has no explanation yet
- Using Simple Formulae has no explanation yet
- Pictograms and tally charts has no explanation yet
- Expressions & Equations Vocabulary has no explanation yet
- Sorting Data into Categories has no explanation yet
- The Probability Scale has no explanation yet
- Ordering Likelihoods 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.