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How to learn Stage 4: Mathematics

Cambridge Primary, Lower Secondary and IGCSE: Mathematics, Stage 4

0 of 44 concepts ready to learn · Markdown, for your AI

1. Statistics and Probability · Probability

  1. Likelihood Language: Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible

2. Statistics and Probability · Statistics

  1. Sorting Data into Categories: Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity
  2. Sorting into categories (age 6+): Interpret categorical data by asking and answering questions about totals, how many in each category, and how many more or less one category has than another

3. Geometry and Measure · Position and transformations

  1. Transformations on a grid: 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
  2. First Quadrant Coordinates: Describe positions on a 2-D grid as coordinates in the first quadrant
  3. Describing Movements: Describe movements between positions as translations of a given unit to the left/right and up/down
  4. 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

4. Geometry and Measure · Geometrical reasoning, shapes and measurements

  1. Understanding angles: Recognise angles as a property of shape or a description of a turn
  2. Types of angles: Identify acute and obtuse angles; compare and order angles up to two right angles by size
  3. Estimating Angles: Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size
  4. 2-D shapes (age 8+): Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry
  5. Nets of 3-D Shapes: Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net
  6. Edges, vertices, and faces: Identify and describe properties of 3-D shapes including the number of edges, vertices, and faces
  7. Measuring Perimeters: Measure the perimeter of simple 2-D shapes

5. Geometry and Measure · Time

  1. Telling time to the minute (age 7+): Tell and write time from analogue and digital clocks to the nearest five minutes, using a.m., p.m., and 12-hour and 24-hour notation
  2. 12-hour and 24-hour time: Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks
  3. Converting measurement units: Convert between different units of measure (e.g. kilometre to metre, hour to minute, minute to second, year to month, week to day)

6. Number · Fractions, decimals, percentages, ratio and proportion

  1. Decimal & Percent Notation: Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value
  2. Fraction Notation: Read, write, and use fraction notation correctly — fraction, numerator, denominator, unit fraction, non-unit fraction, proper fraction, improper fraction, mixed number, equivalent fraction, simplest form — and understand what each term describes, including the roles of the numerator and denominator in expressing parts of a whole
  3. Fractions on a number line: Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line
  4. Comparing fractions: Compare and order unit fractions, and fractions with the same denominator
  5. Understanding Percentages: Understand the per cent symbol (%); know that per cent means ‘number of parts per hundred’; write percentages as a fraction with denominator 100 and as a decimal
  6. Fraction Addition Concepts: Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way
  7. Adding fractions (different denominators): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
  8. Unit fractions: Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
  9. Fractions of a whole: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b
  10. Percentages as Fractions: 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%

7. Number · Place value, ordering and rounding

  1. Place value of each digit: Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
  2. Rounding to 10, 100, 1000: Round any number to the nearest 10, 100, or 1000
  3. Ordering Numbers to 1000: Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding
  4. Comparing Large Numbers: Order and compare numbers beyond 1000
  5. Place Value Problem-Solving: Solve number and practical problems involving place value with increasingly large positive numbers
  6. Decimal place value: Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy
  7. Multiplying and dividing: Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000

8. Number · Integers and powers

  1. All times tables to 12×12: Recall multiplication and division facts for multiplication tables up to 12 × 12
  2. Factors, multiples, and primes: Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems
  3. Reading and writing numbers to 1000: Read and write numbers to 1000 in numerals, number names, and expanded form
  4. Properties of Operations: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
  5. Adding numbers: Add up to four two-digit numbers using strategies based on place value and properties of operations

9. Number · Counting and sequences

  1. Square and cube numbers: Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
  2. Linear number sequences: Generate and describe linear number sequences, including those with negative and decimal steps; identify the term-to-term rule
  3. Patterns & Sequences: Order and arrange combinations of mathematical objects in patterns and sequences
  4. Reasoning with Equivalences: Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms
  5. Tenths (age 8+): Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10