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How to learn Stage 3: Mathematics

Cambridge Primary, Lower Secondary and IGCSE: Mathematics, Stage 3

0 of 50 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. Simple Chance Experiments: Conduct simple probability experiments — flipping a coin, rolling a die, pulling coloured counters from a bag — record results, and compare experimental outcomes with expected theoretical outcomes

2. Statistics and Probability · Statistics

  1. Pictograms and tally charts: Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables
  2. Sorting Data into Categories: Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity
  3. 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. Describing Movements: Describe movements between positions as translations of a given unit to the left/right and up/down

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

  1. Calculating with measurements: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
  2. 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
  3. Understanding angles: Recognise angles as a property of shape or a description of a turn
  4. 2-D shapes: Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)
  5. 2-D shapes (age 6+): Identify and describe properties of 2-D shapes including the number of sides and line symmetry in a vertical line
  6. Sorting 2-D and 3-D shapes: Compare and sort common 2-D and 3-D shapes and everyday objects by their properties
  7. Measuring Perimeters: Measure the perimeter of simple 2-D shapes

5. Geometry and Measure · Time

  1. Sequence intervals of time: Compare and sequence intervals of time
  2. 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
  3. 12-hour and 24-hour time: Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks
  4. Comparing Time Durations: Compare durations of events and calculate the time taken by particular events or tasks

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

  1. 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
  2. Fractions of amounts: Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity
  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. 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
  6. Simple Fraction Sums: Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
  7. Adding Fractions (Same Denominator): Add and subtract fractions with the same denominator, including results greater than one whole (e.g. 5/8 + 6/8 = 11/8)
  8. Understanding fractions: Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2
  9. Fraction-Decimal Equivalents: Recognise and write decimal equivalents of 1/4, 1/2, and 3/4
  10. 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
  11. Unit fractions: Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
  12. Percentages (age 9+): Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole)

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. Place Value Problem-Solving: Solve number and practical problems involving place value with increasingly large positive numbers
  5. Place value understanding and number facts: Use place value understanding and number facts to solve problems

8. Number · Integers and powers

  1. Counting in 2s: Count in multiples of 2, 5, and 10 (skip counting)
  2. Number Words to 100: Read and write numbers to at least 100 in words
  3. Times tables: Recall and use multiplication and division facts for the 2, 5, and 10 multiplication tables
  4. What Multiplication Means: Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7)
  5. Properties of Operations: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
  6. Adding numbers: Add up to four two-digit numbers using strategies based on place value and properties of operations
  7. Reading and writing numbers to 1000: Read and write numbers to 1000 in numerals, number names, and expanded form

9. Number · Money

  1. Money Addition & Subtraction: Solve simple money problems involving addition and subtraction, including giving change
  2. Giving Change: Add and subtract amounts of money to give change, using both £ and p in practical contexts

10. Number · Counting and sequences

  1. Patterns & Sequences: Order and arrange combinations of mathematical objects in patterns and sequences
  2. Linear number sequences: Generate and describe linear number sequences, including those with negative and decimal steps; identify the term-to-term rule
  3. Odd and even numbers: Recognise odd and even numbers
  4. Counting forwards and backwards: Count forwards and backwards in steps of 3 from 0
  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
  6. Counting objects to 20: Count a set of objects to answer 'how many?' for sets up to 20 (arranged in lines, arrays, circles, or scattered)