ai.page · roadmaps

How to learn Key stage 2: Mathematics

The national curriculum in England: Key stages 1 and 2 framework document, Key stage 2

0 of 56 concepts ready to learn · Markdown, for your AI

1. Number – addition, subtraction, multiplication and division

  1. Order of operations: Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations

2. Number – fractions (including decimals and percentages)

  1. 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)
  2. Multiplying and dividing (age 10+): Multiply and divide numbers by 10, 100, and 1000 giving answers up to three decimal places, understanding that digits shift position in the place-value chart

3. Number - addition and subtraction

  1. Mental addition and subtraction (age 7+): Mentally add and subtract a three-digit number and ones
  2. Mentally adding tens to 3-digit numbers: Mentally add and subtract a three-digit number and tens
  3. Mentally adding hundreds to 3-digit numbers: Mentally add and subtract a three-digit number and hundreds
  4. Adding and subtracting (age 7+): Add and subtract numbers with up to three digits using formal written methods of columnar addition and subtraction
  5. Estimating by rounding: Estimate the answer to a calculation and use inverse operations to check answers; apply to increasingly large numbers using rounding and inverse reasoning
  6. Missing number problems (age 7+): Solve addition and subtraction problems including missing-number problems, using number facts, place value, and more complex methods
  7. Adding and subtracting (age 8+): Add and subtract numbers with up to four digits using formal written methods of columnar addition and subtraction
  8. Two-step addition and subtraction problems: Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

4. Number - fractions

  1. Tenths: Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and from dividing one-digit numbers or quantities by 10
  2. Unit fractions: Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
  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. Equivalent fractions: Recognise and show, using diagrams, equivalent fractions with small denominators
  5. Simple Fraction Sums: Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
  6. Comparing fractions: Compare and order unit fractions, and fractions with the same denominator
  7. Comparing fractions (age 7+): Solve problems involving counting in tenths, fractions of quantities, equivalence, fraction addition/subtraction, and fraction comparison

5. Geometry - properties of shapes

  1. 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
  2. Understanding angles: Recognise angles as a property of shape or a description of a turn
  3. Right Angles & Turns: Identify right angles; recognise that two right angles make a half-turn, three make three-quarters, and four make a complete turn
  4. Parallel and perpendicular lines: Identify horizontal and vertical lines and pairs of perpendicular and parallel lines

6. Measurement

  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 Perimeters: Measure the perimeter of simple 2-D shapes
  3. Giving Change: Add and subtract amounts of money to give change, using both £ and p in practical contexts
  4. 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
  5. Estimating answers (age 7+): Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, and hours
  6. Time Units and Calendar Facts: Know the number of seconds in a minute and the number of days in each month, year, and leap year
  7. Comparing Time Durations: Compare durations of events and calculate the time taken by particular events or tasks

7. Number - multiplication and division

  1. Times tables (age 7+): Recall and use multiplication and division facts for the 3, 4, and 8 multiplication tables
  2. Written Multiplication & Division: Write and calculate mathematical statements for multiplication and division using known tables, including two-digit × one-digit, using mental and progressing to formal written methods
  3. Multi-Step Multiply & Divide: Solve problems involving multiplication and division, including scaling problems and correspondence problems where n objects are connected to m objects
  4. All times tables to 12×12: Recall multiplication and division facts for multiplication tables up to 12 × 12
  5. Mental multiplication and division: Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 1, and multiplying together three numbers
  6. Factor Pairs & Commutativity: Recognise and use factor pairs and commutativity in mental calculations
  7. Written Multiplication: Multiply two-digit and three-digit numbers by a one-digit number using formal written layout
  8. Multiply & Add Problems: Solve problems involving multiplying and adding, including using the distributive law, integer scaling problems, and harder correspondence problems

8. Number - number and place value

  1. Skip Counting (4s, 8s, 50s, 100s): Count from 0 in multiples of 4, 8, 50, and 100
  2. The three digits of a three-digit number: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones
  3. 10 or 100 More or Less: Find 10 or 100 more or less than a given number up to 1000
  4. Ordering Numbers to 1000: Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding
  5. Representing Numbers: Identify, represent, and estimate numbers using different representations including the number line
  6. Reading and writing numbers to 1000: Read and write numbers to 1000 in numerals, number names, and expanded form
  7. Place Value to 1000: Solve number problems and practical problems involving place value of numbers up to 1000
  8. Counting in 6s: Count in multiples of 6, 7, 9, 25, and 1000
  9. Place value of each digit: Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
  10. 1000 More or Less: Find 1000 more or less than a given number
  11. Negative Numbers: Count backwards through zero to include negative numbers
  12. Numbers to 10,000: Identify, represent, and estimate numbers up to 10,000 using different representations
  13. Comparing Large Numbers: Order and compare numbers beyond 1000
  14. Rounding to 10, 100, 1000: Round any number to the nearest 10, 100, or 1000
  15. Place Value Problem-Solving: Solve number and practical problems involving place value with increasingly large positive numbers
  16. Roman numerals to 100: Read Roman numerals to 100 (I to C) and understand that the numeral system changed over time to include zero and place value

9. 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