How to learn Stage 2: Mathematics

Cambridge Primary, Lower Secondary and IGCSE: Mathematics, Stage 2

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1. Thinking and Working Mathematically

Generalising Patterns: Recognise and use repeated reasoning to generalise: spot calculation patterns, describe rules for sequences, and predict results using known mathematical facts

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

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

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
Turns & Directions: Describe movement and direction, including whole, half, quarter, and three-quarter turns
Position, direction, and movement: Use mathematical vocabulary to describe position, direction, and movement, including straight lines and distinguishing rotation as a turn in terms of right angles (quarter, half, three-quarter turns, clockwise and anti-clockwise)

Calculating with measurements: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
Measuring Perimeters: Measure the perimeter of simple 2-D shapes
Understanding angles: Recognise angles as a property of shape or a description of a turn
2-D shapes: Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)
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
Capacity and volume: Measure and begin to record capacity and volume using non-standard and standard units
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)
Edges, vertices, and faces: Identify and describe properties of 3-D shapes including the number of edges, vertices, and faces
Measuring & Plotting Lengths: Generate measurement data by measuring lengths to the nearest whole unit and display the data on a line plot
Comparing lengths by measuring: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit
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

Telling time to the minute: Measure and begin to record time in hours, minutes, and seconds
Telling Time: Hours and Half Hours: Tell the time to the hour and half past the hour, and draw clock hands to show these times
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
Days, Weeks, Months & Years: Recognise and use language relating to dates, including days of the week, weeks, months, and years
Number of minutes in an hour: Know the number of minutes in an hour and the number of hours in a day

What Is a Half?: Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity
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
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
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
Halves & Quarters of Shapes: Partition circles and rectangles into two and four equal shares and describe them using the words halves, fourths, and quarters

Rounding to 10, 100, 1000: Round any number to the nearest 10, 100, or 1000
Comparing and ordering numbers: Compare and order two-digit numbers using the symbols >, =, and <, based on place value understanding
Ordering Numbers to 1000: Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding
Adding numbers: Add up to four two-digit numbers using strategies based on place value and properties of operations

Adding money and giving change: Find different combinations of coins that equal the same amount of money
Coin Values: Recognise and know the value of different coins and notes

Counting in 2s: Count in multiples of 2, 5, and 10 (skip counting)
Multiplication as repeated addition: Understand multiplication as repeated addition and grouping equal sets
Times tables: Recall and use multiplication and division facts for the 2, 5, and 10 multiplication tables
Division as equal sharing: Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made)
Inverse: addition undoes subtraction: Recognise and use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems
Reading and writing numbers to 100: Read and write numerals from 0 to 100

Odd and even numbers: Recognise odd and even numbers
Rote counting to 100: Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones
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)