Maths Learning Strands

Geometry

• Compares and classifies triangles based on their properties and sizes
• Measure and calculate the perimeter of triangles (measure)
• Identify acute, obtuse and right angles and compare and order angles
• Complete a simple symmetric triangle with respect to a specific line of reflective symmetry
• Use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems
• Recognise where angles meet at a point on a straight line and find missing angles on the line

Measure Time

• Reads and writes the time from an analogue clock and 12-hour and 24-hour, including using Roman numerals from 1 to XII
• Know the number of seconds in a minute and the number of days in each month, year and leap year
• Estimate and read time, with increasing accuracy to the nearest minute, record and compare time in terms of seconds, minutes and hours, use vocabulary such as O’clock, AM/PM, morning, afternoon, noon and midnight.

Addition and subtraction

• Fluently recall and apply number bonds to 10
• Recognises the place value of each digit in a three-digit number (hundreds, tens and ones)
• Find 10 or 100 more or less than a given number
• Fluently can add all single digit combinations and their inverses
• Fluent recall of number bonds to 20 and the inverse
• Efficiently calculate number bonds to 100 mentally
• Round numbers to the nearest 10 and 100
• Adds and subtracts numbers mentally including: a three-digit number and ones; a three-digit number and tens; and a three-digit number and hundreds
• Record addition and subtraction calculations in a logical, structured format to demonstrate their reasoning with up to three-digit by three-digit numbers
• Measures, compares, adds and subtracts lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
• Adds and subtracts amounts of money to give change, using both £ and p in practical contexts

Statistics

• Solve one step and two step questions (for example ‘How many more?’ and ‘How many fewer’) using information presented in scaled bar charts, pictograms and tables (statistics objective)
• Presents data using bar charts and tables
• Read, interpret and construct pictograms with a range of scale/ multiples

Multiplication and division

• Fluent recall and application of the ten times table
• Solve word problems and missing number problems using known and derived facts for the tens times table
• Apply knowledge of multiples of 10 and 100 to convert between millimetres, centimetres and metres
• Fluent recall and application of the 2 and 5 times table
• Solve word problems and missing number problems using known and derived facts for the 2 and 5 times table
• Fluent recall and application of the 4 times table
• Solve word problems and missing number problems using known and derived facts for the 4 times table
• Read, interpret and construct pictograms with a range of scale/ multiples (statistic objective)
• Fluent recall and application of the 8 times table
• Solve word problems and missing number problems using known and derived facts for the 8 times table
• Fluent recall and application of the 8 times table
• Solve word problems and missing number problems using known and derived facts for the 8 times table
• Fluent recall and application of the 3 times table
• Solve word problems and missing number problems using known and derived facts for the 3 times table
• Fluent recall and application of the 6 times table
• Solve word problems and missing number problems using known and derived facts for the 6 times table
• Link x60 with time, converting between minutes and hours ; seconds and minutes
• Writes and calculates, using mental strategies (with jottings), mathematical statements for multiplication and division using the multiplication tables that are known including for two-digit numbers times one-digit numbers
• Fluent recall and application of all times table facts up to 10x10
• Recall all square numbers up to 10x10
• Solve problems involving scaling - a person twice as big is twice the height, feet twice the length etc. but not 4 arms, 4 legs etc.
• Solve correspondence problems in which n objects are connected to m objects e.g. 4 shirts, 2 trousers – how many different combinations?
• Fluent recall and application of the 8 times table
• Solve word problems and missing number problems using known and derived facts for the 8 times table
• Fluent recall and application of the 3 times table
• Solve word problems and missing number problems using known and derived facts for the 3 times table
• Fluent recall and application of the 6 times table
• Solve word problems and missing number problems using known and derived facts for the 6 times table
• Link x60 with time, converting between minutes and hours; seconds and minutes
• Writes and calculates, using mental strategies (with jottings), mathematical statements for multiplication and division using the multiplication tables that are known including for two-digit numbers times one-digit numbers
• Fluent recall and application of all times table facts up to 10x10
• Recall all square numbers up to 10x10
• Solve problems involving scaling - a person twice as big is twice the height, feet twice the length etc. but not 4 arms, 4 legs etc.
• Solve correspondence problems in which n objects are connected to m objects e.g. 4 shirts, 2 trousers – how many different combinations?

Fractions

• Recognise, find, name and write unit fractions, linking to both shape and quantity
• Order and compare unit fractions
• Add and subtract fractions with the same denominator
• Recognise equivalents of unit fractions
• Calculate fractions of amounts using known facts for unit fractions e.g. 1/5 of 25 = 5

Geometry

• Compares and classifies triangles and quadrilaterals based on their properties
• Measure and calculate perimeter of triangles and quadrilaterals in centimetres and metres
• Describe the positions on a 2D grid as co-ordinates in four quadrants
• Identify horizontal, vertical and diagonal lines and pairs of perpendicular (including intersection), opposite and adjacent sides and parallel lines
• Estimate and compare five angles (right angle, obtuse, acute, reflex and straight lines)
• Use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems for triangles, quadrilaterals and straight lines
• Identify lines of symmetry in quadrilaterals and triangles presented in different orientations and complete simple symmetric triangles and quadrilaterals with respect to a specific line of symmetry
• Use reflection in a variety of diagrams, including continuing to use a 2D grid and co-ordinates in the first quadrant, reflection should be in lines which are parallel to the axes
• Identify, describe and represent the position of a shape following a reflection or translation using the appropriate language and know that the shape has not changed (congruent)
• Calculate and compare the area of rectangles (including squares) an including using standard units of cm2 / sq.cm or m2/ sq.m
• Calculate the area of triangles

Measure

• Reads and writes the time from an analogue clock and 12-hour and 24-hour to the nearest minute (including using Roman numerals from 1 to XII)
• Convert between analogue and digital 12 and 24-hour clock
• Know the number of seconds in a minute and the number of days in each month, year and leap year
• Use vocabulary such as O’clock, AM/PM, morning, afternoon, noon and midnight
• Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days
• Calculate and compare durations of events (e.g. calculating time taken by particular events or tasks)
• Solve problems involving converting between different units of measure

Number and place value

• Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
• Orders and compares numbers beyond 1,000
• Rounds any number to the nearest 10, 100 or 1,000
• Counts backwards through zero to include negative numbers
• Compare and order numbers with the same number of decimal places up to two decimal places
• Counts up and down in hundredths, recognise that hundredths arise when dividing an object by hundred and dividing tenths by ten

Addition and subtraction

• Efficiently calculate number bonds to 100 mentally
• Adds and subtracts numbers mentally including: a three-digit number and ones; a three-digit number and tens; and a three-digit number and hundreds
• Derive number bond facts to 1000
• Adds and subtracts numbers with up to 4 digits using formal written methods of columnar addition and subtraction where appropriate
• Use and apply commutative and associative laws for addition
• Solves addition and subtraction two-step mixed word problems in context, deciding which operations and methods to use and why

Statistics

• Interpret and present discrete and continuous data using appropriate graphical methods including bar charts and time graphs
• Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs

Multiplication and division

• Fluent recall and application of the 6 times table
• Solve word problems and missing number problems using known and derived facts for the 6 times table
• Fluent recall and application of the 7 and 9 times table
• Fluent recall and application of all times tables up to 12x12
• Can derive times table facts for 12x, 13x etc.
• Recall square and square roots up to 12x12
• Recognise factor pairs, working in a logical and systematic order
• Find common factors of two numbers below 100
• Partition two and three-digit numbers to multiply and divide unknown facts by a single digit
• Apply known facts to determine remainders within problems with different divisors
• Solve problems in contexts (including two step problems), choosing the appropriate operation, working with increasingly harder numbers and scaling involving both relationships
• Use and apply commutative and associative laws for multiplication
• Use and apply distributive law for multiplication
• Use and apply doubling / halving of the multiplicand with halving / doubling of the multiplier
• Solve simple ratio problems

Fractions

• Add and subtract fractions with the same denominator
• Recognise and write decimal equivalents of any number of tenths or hundredths
• Recognise and show using diagrams, families of equivalent fractions for unit fractions
• Recognise and show using diagrams, families of equivalent fractions for non-unit fractions (including 3⁄4)
• Recognise 100%, 25%, 50% and 75% as 1, 1⁄4, 1⁄2 and 3⁄4
• Solves simple measure and money problems involving fractions and decimals to two decimal places
• Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number

Geometry

• Identify horizontal, vertical and diagonal lines and pairs of perpendicular (including intersection) and parallel lines
• Draw 2D shapes using given dimensions and angles
• Illustrate and name parts of circles, including radius, diameter and circumference and know that 2R=D
• Draw given angles and measure them in degrees
• Knows angles are measured in degrees, estimate and compare all six angles (acute, right angle, obtuse, straight line, reflex and around a point)
• Calculate and identify angles at a point and one whole turn, angles at a point on a straight line and half turn, other multiples of 90
• Recognise angles where they meet at a point, are on a straight line, or are vertically opposite and find missing angles
• Identify line of symmetry in 2D shapes presented in different orientations and complete a simple symmetric figure with respect to a specific line of symmetry
• Recognise, describe and build simple 3D shapes, including making nets

Measure

• Estimate and calculate volume (for example, using a 1cm3 blocks to build cuboids (including cubes) and capacity (for example, using water
• Measure and calculate the perimeter of simple 2D shapes and composite (compound) shapes
• Calculate and compare the area of rectangles (including squares) and including using standard units, square centimetres (cm2) and square metres (m2)
• Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days including time intervals
• Read and interpret timetables (statistic objective)

Multiplication and Division

• Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days including time intervals
• Read and interpret timetables (statistic objective)
• Identify multiples and factors including finding all the factor pairs of a number and the common factors of two numbers
• Know and use the vocabulary of prime numbers, prime factors and composite (non- prime) numbers
• Multiply up to 4 digits by a one digit number using a formal written method of short multiplication
• Multiply up to 4 digits by two digit number using a formal written method of long multiplication
• Divide numbers up to 4 digits by a 1 digit number, using the formal written method of long division and interpret remainders appropriately for the context
• Divide numbers up to 4 digits by a 2 digit number, using the formal written method of long division and interpret remainders appropriately for the context
• Solve problems involving multiplication and division including using a knowledge of factors and multiples, squares and cubes numbers
• To calculate simple word problems, involving ‘in every’ , ‘for every’ and the use of :
• Solve simple equations where one term is missing for all four operations

Addition and subtraction

• Add and subtract whole numbers with more than four digits, using formal written methods when appropriate (columnar addition and subtraction)
• Add and subtract decimal numbers with up to 3dp, using formal written methods when appropriate
• Solve addition and subtraction multi-step problems in context, deciding which opens and methods to use and why
• Add and subtract numbers mentally with increasingly large numbers (eg 12,462 - 2,300 = 10,162)
• Use rounding and knowledge of inverse to check answers to calculations and determine in the context of a problem, levels of accuracy.
• Derive number bond facts to 1000

Fractions

• Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number
• Identify and find equivalents of unit and non-unit fractions
• Compare and order fractions whose denominators are all multiples of the same number
• Add and subtract fractions with the same denominator and denominators that are multiples of the same number
• Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
• Solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25
• Solve problems involving multiplication and division, including scaling by simple fractions including fractions > 1

Statistic objectives

• Interpret and present discrete and continuous data using appropriate graphical methods including bar charts and time graphs
• Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and line graphs

Geometry

• Describe positions on the full co-ordinates grid (4 quads)
• Use reflection in a variety of diagrams, including continuing to use a 2D grid and co- ordinates in the four quadrants. Reflections should be in lines that are parallel to the axes
• Use translation (involving NSEW and as vectors) in a variety of diagrams including continuing to use a 2D grid and co-ordinates in the 4 quadrants
• Calculate missing co-ordinates within 2D shapes on a four-quadrant grid
• Compares and classifies geometric shapes based on their properties and sizes and finds unknown angles and missing lengths in any triangles, quads and regular polygons
• Use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems
• Draw and measure 2D shapes using given dimensions and angles
• Calculate the area of parallelograms and triangles
• Recognise when it is possible to use formulae for area and volume of shapes
• Estimate volume and capacity (measure objective)
• Calculate, estimate and compare volume of cubes and cuboids using standard units, including cm3, m3, mm3, and km3
• Solve problems involving similar shapes where the scale factor is known or can be found

Number and place value

• Read, write, order and compare numbers to 10,000,000 and determine the value of each digit
• Read, write, order and compare numbers with up to three decimal places, relating this to knowledge and understanding of “tenths”, “hundredths” and “thousandths”
• Interpret negative numbers in context and calculates intervals across zero
• Round any whole number to the nearest, 10, 100, 1000, 10,000, 100,000, 1,000,000
• Round decimals with 3 decimal places to the nearest whole number, 1dp and 2dp

Calculation

• Perform mental calculations, including with mixed operations and large numbers
• Identify common factors, prime factors, common multiples, prime numbers and composite numbers
• Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
• Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
• Multiply numbers with up to 2 decimal places by whole numbers
• Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders, fractions or by rounding as appropriate for the context
• Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
• Use knowledge of the order of operations to carry out calculations involving the four operations

Statistic Objectives

• Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days including time intervals
• Read and interpret timetables
• Interpret and present discrete and continuous data using appropriate graphical methods including bar charts and time graphs
• Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and line graphs
• Interpret and construct pie charts and line graphs and use these to solve problems

Measure

• Calculate and interpret the mean as an average
• Convert between miles and kilometres
• Understand and use approximate equivalences between metric units and common imperial units, such as inches, pounds and pints

Algebra

• Express and solve missing number problems algebraically
• Enumerate possibilities of combinations of two variables
• Find pairs of numbers that satisfy an equation with two unknowns
• Generate and describe linear number sequences
• Use simple formulae

Fractions

• Use common factors to simplify fractions (HCF); use common multiples to express fractions in the same denomination (LCM)
• Compare and order fractions including fractions >1
• Add and subtract fractions with different denominators using the concept of equivalent fractions
• Multiply simple pairs of proper fractions and mixed numbers, writing its answer in its simplest form
• Divide proper fractions by whole numbers
• Recalls and uses equivalences between simple fractions, decimals and percentages, including in different contexts
• 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 unequal sharing and grouping using knowledge of fractions and multiples
• Solves problems involving the calculation of percentages e.g. of measures and calculations such as 15 per cent of 360, and the use of percentages for comparison