Key Stage 2: Math

Key Stage 2 (KS2) Mathematics in the UK covers Years 3, 4, 5, and 6 (ages 7-11) and aims to develop a deep understanding of mathematical concepts, alongside fluency in fundamental skills and the ability to reason mathematically and solve problems. The curriculum is structured around three core aims: fluency, reasoning, and problem-solving.

Here's a summary of what's expected in KS2 Math:

1. Number:

  • Number and Place Value:

    • Counting and Reading Numbers: Children learn to count in increasingly larger steps (e.g., 6s, 7s, 8s, 9s, 25s, 1000s) and with negative numbers. They read, write, order, and compare numbers up to 10,000,000.

    • Place Value: Understand the value of each digit in numbers up to 10,000,000. They learn to identify the value of each digit in numbers with up to three decimal places.

    • Rounding: Round numbers to the nearest 10, 100, 1000, 10,000, 100,000, 1,000,000, and to a specified number of decimal places or significant figures.

    • Roman Numerals: Read Roman numerals to 100 (C) and then to 1000 (M), and understand how over time, the numeral system changed to include the concept of zero and place value.

  • Addition, Subtraction, Multiplication, and Division (The1 Four Operations):

    • Mental Calculation: Develop strong mental calculation strategies for all four operations, including mixed operations.

    • Formal Written Methods: Become proficient in formal written methods for addition and subtraction of numbers with up to 4 or more digits.

    • Multiplication: Master formal written methods for multiplication, including short multiplication (up to 4-digit by 1-digit or 2-digit) and long multiplication (up to 4-digit by 2-digit).

    • Division: Master formal written methods for division, including short division (up to 4-digit by 1-digit) and long division (up to 4-digit by 2-digit), interpreting remainders appropriately (as whole number remainders, fractions, or by rounding).

    • Multiplication and Division Facts: Know all multiplication and division facts up to 12×12 and apply them to larger numbers and problems.

    • Order of Operations: Understand and use the order of operations (BIDMAS/BODMAS) in calculations involving the four operations.

    • Common Factors and Multiples: Identify common factors, common multiples, and prime numbers.

    • Problem Solving: Solve multi-step problems in contexts, deciding which operations and methods to use and why.

  • Fractions (including Decimals and Percentages):2

    • Understanding Fractions: Recognise, find, and write fractions of a discrete set of objects and quantity. Understand equivalent fractions and simplify them.

    • Comparing and Ordering: Compare and order fractions with different denominators.

    • Calculations with Fractions: Add and subtract fractions with the same denominator and then with different denominators. Multiply simple pairs of proper fractions. Divide proper fractions by whole numbers.

    • Decimals: Understand the relationship between fractions and decimals. Read, write, order, and compare numbers with up to three decimal places. Multiply and divide numbers by 10, 100, and 1000, giving answers up to three decimal places.3

    • Percentages: Recognise the percentage symbol (%) and understand that it relates to "number of parts per hundred". Write percentages as a fraction with denominator 100, and as a decimal. Solve problems4 involving the calculation of percentages5 of whole numbers or measures.

    • Equivalences: Know and use equivalences between simple fractions, decimals, and percentages.

2. Ratio and Proportion (Year 6):

  • Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.

  • Solve problems involving the calculation of percentages [for example, 15% of 360] and the use of percentages for comparison.

  • Solve problems involving similar shapes where the scale factor is known or can be found.

  • Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

3. Algebra (Year 6):

  • Use simple formulae expressed in words.

  • Generate and describe linear number sequences.

  • Express missing number problems algebraically.

  • Find pairs of numbers that satisfy an equation with two unknowns.

  • Enumerate possibilities of combinations of two variables.

4. Measurement:

  • Units of Measure: Convert between different units of metric measure (e.g., kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre). Understand and6 use approximate equivalences between metric units and common imperial units7 (e.g., inches, pounds, pints).

  • Perimeter, Area, Volume: Calculate and compare the perimeter of rectilinear shapes. Find the area of rectilinear shapes by counting squares and then calculating using formulae (rectangle, square). Estimate volume and capacity. Calculate the volume of cuboids.

  • Money: Solve problems involving calculating with money, including converting between pounds and pence.

  • Time: Tell and write the time from an analogue clock, including using Roman numerals and 12-hour and 24-hour clocks. Convert between8 units of time (e.g., hours to minutes, minutes to seconds, years to months, weeks to days). Solve problems involving converting units of time and calculating durations.

5. Geometry:

  • Properties of Shapes:

    • 2-D Shapes: Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.9 Identify properties of 2-D shapes (e.g., parallel and perpendicular lines, types of angles). Draw 2-D shapes using given dimensions and angles.

    • 3-D Shapes: Identify 3-D shapes, including cubes and other cuboids, from 2-D representations. Recognise, describe, and build simple 3-D shapes, including making10 nets.

    • Angles: Identify acute, obtuse, and reflex angles. Know that angles on a straight line add up to 180∘, angles at a point add up to 360∘, and angles in a triangle add up to 180∘. Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

  • Position and Direction:11

    • Coordinates: Describe positions on a 2-D grid as coordinates in the first quadrant, then all four quadrants.

    • Translation and Reflection: Describe movements between positions as translations of a given unit to the left/right and up/down. Plot specified points and draw sides to complete a given polygon. Describe positions on the full coordinate grid (all four quadrants). Draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

6. Statistics:

  • Interpreting Data: Interpret and present discrete and continuous data using a variety of graphs and charts, including bar charts, pictograms, tally charts, tables, line graphs, and pie charts.

  • Solving Problems: Solve comparison, sum, and difference problems using information presented in these types of graphs and charts. Calculate and interpret the mean as an average.

Throughout KS2, there's a strong emphasis on mathematical reasoning (e.g., explaining thinking, proving ideas, making generalisations) and problem-solving (e.g., applying mathematical knowledge to solve real-world and abstract problems, breaking down problems into smaller steps). Children are expected to articulate their understanding and justify their mathematical choices.