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How to learn Stage 5: Mathematics

Cambridge Primary, Lower Secondary and IGCSE: Mathematics, Stage 5

0 of 43 concepts ready to learn · Markdown, for your AI

1. Statistics and Probability · Probability

  1. Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability
  2. 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. Statistical Analysis Vocabulary: Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes
  2. Comparing measurements: 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

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. 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
  3. First Quadrant Coordinates: Describe positions on a 2-D grid as coordinates in the first quadrant

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

  1. Angle Sum Rules: Know that angles at a point sum to 360° (one whole turn), angles on a straight line sum to 180°, and vertically opposite angles are equal; use these facts to find missing angles
  2. Estimating Angles: Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size
  3. Translating and reflecting shapes: Draw and translate simple shapes on the coordinate plane; reflect shapes in the axes
  4. 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
  5. Understanding angles: Recognise angles as a property of shape or a description of a turn
  6. Measuring Perimeters: Measure the perimeter of simple 2-D shapes
  7. Perimeters of polygons: Solve problems involving perimeters of polygons: find perimeter from side lengths, find an unknown side length, and explore rectangles with same perimeter but different areas (or vice versa)
  8. Perimeter of Compound Shapes: Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
  9. Classifying shapes by properties: 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

5. Geometry and Measure · Time

  1. 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)
  2. Numbers on a number line: Solve word problems involving elapsed time by adding and subtracting time intervals in minutes, including using a number line
  3. Telling time to the minute (age 9+): Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days)
  4. 12-hour and 24-hour time: Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks

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. 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%
  3. 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
  4. 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
  5. 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
  6. Mixed numbers and improper fractions: Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5)
  7. Multiplying fractions (age 11+): Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150)

7. Number · Place value, ordering and rounding

  1. Decimal place value: Round decimals with one decimal place to the nearest whole number
  2. Decimal place value: Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy
  3. Place value of each digit: Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
  4. Place Value Problem-Solving: Solve number and practical problems involving place value with increasingly large positive numbers
  5. Decimal place value: Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6)
  6. Reading Decimal Places: Identify the value of each digit in numbers given to three decimal places (e.g. in 4.378, the 7 represents 7 hundredths)

8. Number · Integers and powers

  1. Tenths (age 8+): Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10
  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. Prime numbers: Know and use the vocabulary of prime numbers, prime factors, and composite numbers; establish whether a number up to 100 is prime; recall prime numbers up to 19
  4. Multiplying and dividing: Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000
  5. Order of operations: Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations
  6. Positive and Negative Numbers: Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances

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. What Multiplication Means: Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7)
  4. Negative Numbers: Count backwards through zero to include negative numbers