Maths
At Hawthorn Tree School, we inspire all children to become confident and enthusiastic mathematicians, who are willing to take risks and are not scared of making mistakes but who learn from those mistakes. We aim to develop mathematical skills and to provide opportunities for their application in meaningful, real-life situations. We strive to provide the children with exciting and challenging questions, thereby increasing motivation and promoting a positive response to mathematics and developing the mastery approach through the use of the White Rose Maths curriculum.
Resilience
- Through Maths we teach the children to be resilient in their learning. With teacher encouragement, we nurture children to adapt their learning style to preserver when challenges become hard and not to give up. Children are encouraged to be flexible in their approach to Maths and by using RUCSAC (Read, Understand, Choose, Solve, Answer, Check) have a consistent approach towards problem solving throughout the school.
- At Hawthorn Tree School, we create a learning environment where children should not be afraid to make mistakes, but to learn from these errors and apply this to future work.
- Children are encouraged to talk about their understanding of Maths and question and debate the answers of others in order to work towards finding the most efficient way to complete tasks.
- Children are taught the tools of Maths, allowing them to find more than one way to answer questions and be able to link their understanding of the different areas of Maths.
Compassion
- Children are encouraged to have a growth mind set about Maths and to be taught that they all have the ability to succeed.
- Through intervention and pre-teaching, the worries and concerns of individuals are always taken into account, making sure their well-being is always considered throughout their Maths learning.
- Children are guided through areas of Maths that they have difficulties with through the PIXL therapies after completion of PIXL tests, allowing staff to make sure gaps in learning are addressed.
- Children are encouraged to be responsible for their own learning and to have compassion for those who don’t learn Maths in the same way as they do.
- Pupils are nurtured by staff to be successful Mathematicians and prepared for a life beyond school.
Innovation
- We provide children with a cross-curricular approach to learning, allowing them to see how Maths is embedded through the rest of the curriculum, preparing them for their future learning.
- Our curriculum helps the children to create a mathematical sense of the world, giving them regular opportunities to solve real life problems.
- The progressive nature of our curriculum allows pupils to develop a deeper understanding of Maths, with each objective building upon the next throughout the different areas of Maths.
- Through challenging tasks, children develop the ability to create their own Maths questions and satisfy their own curiosity with regards to number, shape and space.
Respect
- Children are taught to appreciate the Mathematical ideas of others and to understand that not all children learn in the same way.
- During explanations, children know that it is respectful to listen to both staff and their peers alike.
- Through discussion as to how to solve problems, children learn to appreciate the ideas of others even if methods suggested are not ones which they would use themselves.
- The learning styles of pupils are respected by all staff, enabling children to progress through the Maths curriculum in their own way.
Diversity
- Through our curriculum, we aspire to teach children to see how Maths is relevant to their lives and the lives of others. This allows the children to develop a sense of perspective and interact with their peers.
- Contextualising the questions that the children are working on to the pupil’s interests, where possible, allows them to relate to the work that they are completing, allowing them to see a value and reason to the tasks they are completing.
- Assessments given throughout the year provide children with a variety of response types for all learning styles.
Intent
- The mathematics curriculum is planned in a sequenced way based on the White Rose Maths Scheme of Learning to build knowledge, skills, understanding and mathematical vocabulary from EYFS to Year 6.
- Mathematics lessons will begin with a revision task or a skill which is embedded to ensure children return to previous knowledge or deep an understanding of mathematical fluency and are introduced to the concept essential to the lesson before applying that skill.
- The mathematics curriculum will equip children with a deep and embedded the understanding of mathematical reasoning, application and problem-solving skills for their time at Hawthorn Tree and life beyond.
Implementation
- The maths curriculum from EYFS to Year 6 builds on knowledge from one year to the next and well as intertwining skills within area of maths. Long term memory and any knowledge gaps are filled by cold maths activities and appropriate intervention where the need is identified by short, medium and long term assessment.
- Daily lesson plans show the key objectives for learning and from fluency practice and application activities mathematics lesson ensure children are clear about the mathematical knowledge to be acquired in that lesson.
- Teachers will plan lessons to create deep understanding of mathematical objectives. Concrete, pictorial and abstract resources will support children’s learning ensuring components are embedded.
Impact
- The impact of what has been taught is assessed daily through achievement of the objective, at the end of the unit through the White Rose End of Unit Test and at the end of each large term through the Rising Stars Optional Tests.
Maths Progression Map
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| EYFS | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | |||||
Place Value | Counting |
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Comparing numbers |
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Identifying, representing and estimating numbers |
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Reading and Writing numbers |
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Understanding place value |
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Rounding |
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Problem solving |
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Addition and Subtraction | Number bonds |
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Mental calculations |
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Written calculations |
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Inverse operations, estimation and checking |
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Problem solving |
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Multiplication and Division | Multiplication and division facts |
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Mental calculations |
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Written calculations |
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Properties of numbers |
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Order of operations |
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Inverse operations, estimating and checking |
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Problem solving |
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Fractions | Counting in fraction steps |
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Recognising fractions |
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Comparing fractions |
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Comparing decimals |
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Rounding including decimals |
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Equivalence of fractions, decimals and percentages |
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Addition and subtraction of fractions |
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Multiplication and division of fractions |
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Multiplication and division of decimals |
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Problem solving
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Ratio and Proportion | Solve problems involving the relative sizes of two quantities |
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Statements only appear in Year 6 but should be connected to previous learning, particularly fractions and multiplication and division
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Measurement | Compare and estimate |
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Measuring and Calculating |
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Geometry (properties of shape) | Identifying shapes and their properties |
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Drawing and constructing |
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Comparing and classifying |
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Angles |
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Geometry (position, direction and movement) | Position, direction and movement |
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Statistics | Interpreting, constructing and presenting data |
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Problem Solving |
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Algebra | Equations |
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Formulae |
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Sequences |
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Number: Number and Place Value
| Intent: COUNTING | ||||||||||||||||||||
EYSF | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||||||
Counts up to three or four objects by saying one number name for each item.
| count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number |
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| count backwards through zero to include negative numbers
| interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero | use negative numbers in context, and calculate intervals across zero
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Count actions or objects which cannot be moved.
| count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens | count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward
| count from 0 in multiples of 4, 8, 50 and 100;
| count in multiples of 6, 7, 9, 25 and 1 000
| count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 |
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Counts an irregular arrangement of up to 5 objects. | given a number, identify one more and one less
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| find 10 or 100 more or less than a given number
| find 1 000 more or less than a given number
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Counts out up to 20 objects from a larger group |
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Counts objects to 20. |
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Counts an irregular arrangement of up to 20 objects
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| Intent: COMPARING NUMBERS | ||||||||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||||||
Uses the language of ‘more’ and ‘fewer’ to compare two sets of objects. | use the language of: equal to, more than, less than (fewer), most, least
| compare and order numbers from 0 up to 100; use <, > and = signs
| compare and order numbers up to 1 000
| order and compare numbers beyond 1 000 | read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit (appears also in Reading and Writing Numbers) | read, write, order and compare numbers up to 10 000 000 and determine the value of each digit (appears also in Reading and Writing Numbers) | |||||||||||||||
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compare numbers with the same number of decimal places up to two decimal places (Fractions) | |||||||||||||||||||||
| Intent: IDENTIFYING, REPRESENTING AND ESTIMATING NUMBERS | ||||||||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||||||
Selects the correct numeral to represent 1 to 20 objects. | identify and represent numbers using objects and pictorial representations including the number line | identify, represent and estimate numbers using different representations, including the number line | identify, represent and estimate numbers using different representations
| identify, represent and estimate numbers using different representations |
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| Intent: READING AND WRITING NUMBERS (including Roman Numerals | ||||||||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||||||
Recognise some numerals of personal significance.
| read and write numbers from 1 to 20 in numerals and words. | read and write numbers to at least 100 in numerals and in words
| read and write numbers up to 1 000 in numerals and in words |
| read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit (appears also in Comparing Numbers) | read, write, order and compare numbers up to 10 000 000 and determine the value of each digit (appears also in Understanding Place Value) | |||||||||||||||
Recognises numerals 1 to 20. | tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks (Measurement)
| read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value. | read Roman numerals to 1 000 (M) and recognise years written in Roman numerals. | ||||||||||||||||||
| Intent: UNDERSTANDING PLACE VALUE | ||||||||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||||||
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| recognise the place value of each digit in a two-digit number (tens, ones)
| recognise the place value of each digit in a three-digit number (hundreds, tens, ones)
| recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones) | read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit (appears also in Reading and Writing Numbers)
recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents (Fractions) | read, write, order and compare numbers up to 10 000 000 and determine the value of each digit (appears also in Reading and Writing Numbers) | |||||||||||||||
find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as units, tenths and hundredths (Fractions) | identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1 000 where the answers are up to three decimal places (Fractions) | ||||||||||||||||||||
| Intent: ROUNDING | ||||||||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||||||
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| round any number to the nearest 10, 100 or 1 000
| round any number up to 1 000 000 to the nearest 10, 100, 1 000, 10 000 and 100 000 | round any whole number to a required degree of accuracy
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| round decimals with one decimal place to the nearest whole number (copied from Fractions)
| round decimals with two decimal places to the nearest whole number and to one decimal place (copied from Fractions)
| solve problems which require answers to be rounded to specified degrees of accuracy (copied from Fractions) | ||||||||||||||||
| Intent: PROBLEM SOLVING | ||||||||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||||||
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| use place value and number facts to solve problems | solve number problems and practical problems involving these ideas. | solve number and practical problems that involve all of the above and with increasingly large positive numbers
| solve number problems and practical problems that involve all of the above | solve number and practical problems that involve all of the above | |||||||||||||||
Addition and Subtraction
| Intent: NUMBER BONDS | ||||||||||||||||
EYFS | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | |||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||
| represent and use number bonds and related subtraction facts within 20 | recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 |
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| Intent: MENTAL CALCULATION | ||||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||
Finds the total number of items in two groups by counting all of them. | add and subtract one-digit and two-digit numbers to 20, including zero | add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
| add and subtract numbers mentally, including:
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| add and subtract numbers mentally with increasingly large numbers
| perform mental calculations, including with mixed operations and large numbers
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Says the number that is one more than a given number.
| read, write and interpret mathematical statements involving addition (+), subtraction (-)and equals (=) signs (appears also in Written Methods) | show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot |
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| use their knowledge of the order of operations to carry out calculations involving the four operations | |||||||||||
Finds one more or one less from a group of up to 20 objects.
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| Intent: WRITTEN METHODS | ||||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||
| read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs (appears also in Mental Calculation) |
| add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction
| add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
| add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) |
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| Intent: INVERSE OPERATIONS, ESTIMATING AND CHECKING ANSWERS | ||||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||||||||
Estimates how many objects they can see and checks by counting them. |
| recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. | estimate the answer to a calculation and use inverse operations to check answers
| estimate and use inverse operations to check answers to a calculation
| use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
| use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy. | |||||||||||
| Intent: PROBLEM SOLVING | |||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||
In practical activities and discussion, begin to use the vocabulary involved in adding and subtracting. | solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = * - 9 | solve problems with addition and subtraction:
| solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction
| solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why | solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why | solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
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solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change (Measurement) | Solve problems involving addition, subtraction, multiplication and division | |||||||
Multiplication and Division
| Intent: MULTIPLICATION & DIVISION FACTS | |||||||||
EYFS | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | ||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
| count in multiples of twos, fives and tens (Number and Place Value) | count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward (Number and Place Value) | count from 0 in multiples of 4, 8, 50 and 100 (Number and Place Value)
| count in multiples of 6, 7, 9, 25 and 1 000 (Number and Place Value)
| count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000 (Number and Place Value) |
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| recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers | recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
| recall multiplication and division facts for multiplication tables up to 12 × 12 |
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| Intent: MENTAL CALCULATION | |||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
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| write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods (appears also in Written Methods) | use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
| multiply and divide numbers mentally drawing upon known facts | perform mental calculations, including with mixed operations and large numbers
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| show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
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| recognise and use factor pairs and commutativity in mental calculations (appears also in Properties of Numbers) | multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 | associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3/8) (copied from Fractions) | ||||
| Intent: WRITTEN CALCULATION | |||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
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| calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
| write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods (appears also in Mental Methods) | multiply two-digit and three-digit numbers by a one-digit number using formal written layout
| multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers | multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
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| divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context | divide numbers up to 4-digits by a two-digit whole number using the formal written method of short division where appropriate for the context divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context | ||||
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| use written division methods in cases where the answer has up to two decimal places (Fractions (including decimals))
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| Intent: PROPERTIES OF NUMBERS: MULTIPLES, FACTORS, PRIMES, SQUARE AND CUBE NUMBERS | |||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
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| recognise and use factor pairs and commutativity in mental calculations (repeated) | identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers. | identify common factors, common multiples and prime numbers
use common factors to simplify fractions; use common multiples to express fractions in the same denomination (Fractions)
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know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers | ||||||||||
establish whether a number up to 100 is prime and recall prime numbers up to 19 | ||||||||||
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| recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3) | calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm3) and cubic metres (m3), and extending to other units such as mm3 and km3 (Measures)
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| Intent: ORDER OF OPERATIONS | |||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
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| use their knowledge of the order of operations to carry out calculations involving the four operations
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| Intent: INVERSE OPERATIONS, ESTIMATING AND CHECKING ANSWERS | |||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
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| estimate the answer to a calculation and use inverse operations to check answers (copied from Addition and Subtraction)
| estimate and use inverse operations to check answers to a calculation (copied from Addition and Subtraction)
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| use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy | ||||
| Intent: PROBLEM SOLVING | |||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
| solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher | solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts | solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects | solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects | solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes | solve problems involving addition, subtraction, multiplication and division
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| solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign |
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solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates | solve problems involving similar shapes where the scale factor is known or can be found (Ratio and Proportion) | |||||||||
Fractions (including Decimals and Percentages)
EYFS | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | ||||||||||
| Intent: COUNTING IN FRACTIONAL STEPS | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||||||||
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| Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number line (Non Statutory Guidance) | count up and down in tenths | count up and down in hundredths |
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| Intent: RECOGNISING FRACTIONS | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||||||||
In practical activities and discussion, begin to use the vocabulary involved in doubling, halving and sharing. | recognise, find and name a half as one of two equal parts of an object, shape or quantity
| recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity | recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators recognise that tenths arise from dividing an object into 10 equal parts and in dividing one – digit numbers or quantities by 10. | recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten
| recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
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| recognise, find and name a quarter as one of four equal parts of an object, shape or quantity |
| recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators |
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| Intent: COMPARING FRACTIONS | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||||||||
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| compare and order unit fractions, and fractions with the same denominators
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| compare and order fractions whose denominators are all multiples of the same number | compare and order fractions, including fractions >1
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| Intent: COMPARING DECIMALS | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||||||||
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| compare numbers with the same number of decimal places up to two decimal places | read, write, order and compare numbers with up to three decimal places | identify the value of each digit in numbers given to three decimal places | ||||||||||
| Intent: ROUNDING INCLUDING DECIMALS | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||||||||
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| round decimals with one decimal place to the nearest whole number
| round decimals with two decimal places to the nearest whole number and to one decimal place | solve problems which require answers to be rounded to specified degrees of accuracy | ||||||||||
| Intent: EQUIVALENCE (INCLUDING FRACTIONS, DECIMALS AND PERCENTAGES) | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||||||||
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| write simple fractions e.g. 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2. | recognise and show, using diagrams, equivalent fractions with small denominators
| recognise and show, using diagrams, families of common equivalent fractions
| identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
| use common factors to simplify fractions; use common multiples to express fractions in the same denomination
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| recognise and write decimal equivalents of any number of tenths or hundredths
| read and write decimal numbers as fractions (e.g. 0.71 = 71/100) | associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3/8) | ||||||||||
recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents | ||||||||||||||||
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| recognise and write decimal equivalents to 1/4; 1/2; 3/4
| recognise the per cent symbol (%) and understand that per cent relates to “number of parts per hundred”, and write percentages as a fraction with denominator 100 as a decimal fraction | recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. | ||||||||||
| Intent: ADDITION AND SUBTRACTION OF FRACTIONS | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||||||||
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| add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
| add and subtract fractions with the same denominator
| add and subtract fractions with the same denominator and multiples of the same number | add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
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| recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number (e.g. 2/5 + 4/5 = 6/5 = 11/5)
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| Intent: MULTIPLICATION AND DIVISION OF FRACTIONS | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||||||||
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| multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams | multiply simple pairs of proper fractions, writing the answer in its simplest form (e.g. 1/4 × 1/2 = 1/8) | ||||||||||
multiply one-digit numbers with up to two decimal places by whole numbers | ||||||||||||||||
divide proper fractions by whole numbers (e.g. 1/3 ÷ 2 = 1/6 )
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| Intent: MULTIPLICATION AND DIVISION OF DECIMALS | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||||||||
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| multiply one-digit numbers with up to two decimal places by whole numbers | ||||||||||
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| find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths |
| multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places | ||||||||||
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| identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places | ||||||||||
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| associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3/8) | ||||||||||
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| use written division methods in cases where the answer has up to two decimal places | ||||||||||
| Intent: PROBLEM SOLVING | |||||||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||||||||
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| solve problems that involve all of the above
| 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 | solve problems involving numbers up to three decimal places
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| solve simple measure and money problems involving fractions and decimals to two decimal places.
| solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those with a denominator of a multiple of 10 or 25. |
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Ratio and Proportion
Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 |
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| Implentation |
Statements only appear in Year 6 but should be connected to previous learning, particularly fractions and multiplication and division
| 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, of measures, and such as 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. | |||||
Measurement
EYFS | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 |
| Intent: COMPARING AND ESTIMATING | |||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation |
Orders two or three items by length or height.
Orders two items by weight or capacity. | compare, describe and solve practical problems for:
| compare and order lengths, mass, volume/capacity and record the results using >, < and =
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| estimate, compare and calculate different measures, including money in pounds and pence (also included in Measuring)
| calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes (also included in measuring) | calculate, estimate and compare volume of cubes and cuboids using standard units, including centimetre cubed (cm3) and cubic metres (m3), and extending to other units such as mm3 and km3. |
estimate volume (e.g. using 1 cm3 blocks to build cubes and cuboids) and capacity (e.g. using water)
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Orders and sequences familiar events. | sequence events in chronological order using language [e.g. before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening] | compare and sequence intervals of time
| compare durations of events, for example to calculate the time taken by particular events or tasks |
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| estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, hours and o’clock; use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight (appears also in Telling the Time) |
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| Intent: MEASURING and CALCULATING | |||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation |
Uses everyday language related to time.
Measures short periods of time in simple ways | measure and begin to record the following:
| choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels | measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
| estimate, compare and calculate different measures, including money in pounds and pence (appears also in Comparing)
| use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling.
| solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate (appears also in Converting)
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| measure the perimeter of simple 2-D shapes
| measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres | measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres | recognise that shapes with the same areas can have different perimeters and vice versa |
Beginning to use everyday language related to money | recognise and know the value of different denominations of coins and notes | recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value
| add and subtract amounts of money to give change, using both £ and p in practical contexts
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find different combinations of coins that equal the same amounts of money
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solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change | ||||||
Geometry: Properties of Shapes
EYFS | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | ||||
| Intent: IDENTIFYING SHAPES AND THIER PROPERTIES | |||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
Beginning to use mathematical names for ‘flat’ 2D shapes, and mathematical terms to describe shapes. | recognise and name common 2-D and 3-D shapes, including:
| identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line
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| identify lines of symmetry in 2-D shapes presented in different orientations
| identify 3-D shapes, including cubes and other cuboids, from 2-D representations
| recognise, describe and build simple 3-D shapes, including making nets (appears also in Drawing and Constructing) | ||||
Selects a particular named shape. | identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
| illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius | ||||||||
Beginning to use mathematical names for ‘solid’ 3D shapes and mathematical terms to describe shapes.
| identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
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| Intent: DRAWING AND CONSTRUCTING | |||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
Use familiar objects and common shapes to create and recreate patterns and build models. |
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| draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them | complete a simple symmetric figure with respect to a specific line of symmetry | draw given angles, and measure them in degrees (o) | draw 2-D shapes using given dimensions and angles | ||||
recognise, describe and build simple 3-D shapes, including making nets (appears also in Identifying Shapes and Their Properties) | ||||||||||
| Intent: COMPARING AND CLASSIFYING | |||||||||
| Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
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| compare and sort common 2-D and 3-D shapes and everyday objects |
| compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
| use the properties of rectangles to deduce related facts and find missing lengths and angles | compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
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distinguish between regular and irregular polygons based on reasoning about equal sides and angles
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| Intent: ANGLES | |||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
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| recognise angles as a property of shape or a description of a turn |
| know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles |
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| identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle | identify acute and obtuse angles and compare and order angles up to two right angles by size
| identify:
| recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles | ||||
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| identify horizontal and vertical lines and pairs of perpendicular and parallel lines |
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Geometry: Position and Direction
EYFS | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | ||||
| Intent: POSITION, DIRECTION AND MOVEMENT | |||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | ||||
Can describe their relative position such as ‘behind’ or ‘next to’. | describe position, direction and movement, including half, quarter and three-quarter turns. | use mathematical vocabulary to describe position, direction and movement including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise) |
| describe positions on a 2-D grid as coordinates in the first quadrant | 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 | describe positions on the full coordinate grid (all four quadrants)
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describe movements between positions as translations of a given unit to the left/right and up/down | draw and translate simple shapes on the coordinate plane, and reflect them in the axes. | |||||||||
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| plot specified points and draw sides to complete a given polygon |
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Statistics
EYFS | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 |
| Intent: INTERPRETING, CONSTRUCTING AND PRESENTING DATA | |||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation |
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| interpret and construct simple pictograms, tally charts, block diagrams and simple tables | interpret and present data using bar charts, pictograms and tables
| interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs | complete, read and interpret information in tables, including timetables | interpret and construct pie charts and line graphs and use these to solve problems
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| ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity |
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| ask and answer questions about totalling and comparing categorical data |
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| Intent: PROBLEM SOLVING | |||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | Implementation |
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| solve one-step and two-step questions [e.g. ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms & tables. | solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs. | solve comparison, sum and difference problems using information presented in a line graph
| calculate and interpret the mean as an average |
Algebra
Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | |||||
Intent: EQUATIONS | ||||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||||
solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = * - 9 (Addition and Subtraction) | recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems. (Addition and Subtraction) | solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction. (Addition and Subtraction)
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| use the properties of rectangles to deduce related facts and find missing lengths and angles (Geometry: Properties of Shapes) | express missing number problems algebraically | |||||
solve problems, including missing number problems, involving multiplication and division, including integer scaling (Multiplication and Division)
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| recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 (Addition and Subtraction) |
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| find pairs of numbers that satisfy number sentences involving two unknowns | |||||
represent and use number bonds and related subtraction facts within 20 (Addition and Subtraction)
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| enumerate all possibilities of combinations of two variables | |||||
Intent: FORMULAE | ||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||
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| Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit. (measurement) |
| use simple formulae | |||
recognise when it is possible to use formulae for area and volume of shapes (Measurement)
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Intent: SEQUENCES | ||||||||
Implementation | Implementation | Implementation | Implementation | Implementation | Implementation | |||
sequence events in chronological order using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening (Measurement)
| compare and sequence intervals of time (Measurement) |
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| generate and describe linear number sequences | |||
order and arrange combinations of mathematical objects in patterns (Geometry: position and direction)
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