How to learn Segundo ciclo (3.º–4.º): Mathematics

Real Decreto 157/2022, enseñanzas mínimas de la Educación Primaria: Matemáticas (Mathematics), saberes básicos, Segundo ciclo (3.º–4.º)

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1. A. Sentido numérico · 1. Conteo

Working with Large Numbers: Solve number and practical problems involving reading, writing, ordering, comparing, and rounding whole numbers up to 1,000,000

Reading and writing numbers (age 9+): 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: Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
Adding Fractions (Unlike Denominators): Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator

Ratio (age 10+): Perform mental calculations including with mixed operations and large numbers, using strategies such as partitioning, compensation, and derived facts
Multi-step problems: choosing operations: 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+): 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: Add and subtract within 1000 using concrete models, drawings, and strategies based on place value; understand composing and decomposing tens and hundreds

Comparing fractions (age 10+): Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks
Adding and subtracting (age 9+): Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Estimating and comparing money: Estimate, compare, and calculate different measures including money in pounds and pence

Measurable Attributes of Objects: 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: 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+): Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days)

Measuring length (age 7+): 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: Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen

Measurement Conversions: Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts

Sorting 2-D and 3-D shapes: Compare and sort common 2-D and 3-D shapes and everyday objects by their properties
2-D shapes (age 10+): Draw 2-D shapes using given dimensions and angles, using a ruler and protractor accurately
2-D shapes (age 7+): Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them

Positional Language: Describe the position of objects using terms such as above, below, beside, in front of, behind, next to
Describing Movements: Describe movements between positions as translations of a given unit to the left/right and up/down

Transformations on a Grid: 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: 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

Using Simple Formulae: Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width))

Pictograms and tally charts: Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables

Expressions & Equations Vocabulary: 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)

Sorting Data into Categories: Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity

The Probability Scale: 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: 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