# Maths Learning Strands

Children in each year group work toward a set of learning objectives. We describe the learning objectives related to a particular ability as 'strands'. For example, being able to tell the time, understanding seconds, minutes and hours and being able to estimate the time all fall within the strand of measuring time.

*Materials presented on this page are the copyrighted property of Hook Junior School, unless otherwise stated. Permission is not granted for their use in any form without prior permission.*

### 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