Maths Information Evening

“Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and all forms of employment. A high-quality education in maths therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of

the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.”

National Curriculum in England, Oct 2014

What are the main changes of the New Maths Curriculum?

• Greater emphasis on number and calculations, than other mathematical areas.

• Greater recall of number facts and greater fluency• Focus on reasoning and problem solving• Higher expectations in each year group. Many concepts and skills now taught in lower year groups, and added content in each year group.

Year 1- Look at multiplication and division in practical contexts.

Year 2- Recognise, find, name and write fractions (third, quarter, three quarters); find simple fractions of

amounts and recognise the equivalence of ½.

Year 3- Count up and down in tenths and recognise what tenths are; Column addition and subtraction;

Add and subtract fractions; Perpendicular and parallel lines; Roman numerals from I to XII

Year 4- Round decimals to the nearest whole number; Compare decimals with up to two decimal places;

Count up and down in hundredths and recognise what a hundredth is; Roman numerals to 100;

Multiplication and division facts to 12 x 12; Short, column method of multiplication.

Year 5- Powers of 10; Compare and order fractions with different denominators; Recognise and use

thousandths; Roman numerals to 1000; Prime numbers and prime factors; Square and cube numbers;

Long multiplication; Short division; Multiply fractions; Volume.

Year 6- Algebra; Construct pie charts; Long division; Divide fractions by whole numbers.

At St. Michael’s we aim to develop…

• A positive attitude towards mathematics and an awareness of the fascination of mathematics;

• An enjoyment and enthusiasm for mathematical learning through practical activity, exploration and discussion;

• Competence and confidence in mathematical knowledge, concepts and skills;• An ability to solve problems, to reason, to think logically and to work systematically and

accurately;• Initiative and an ability to work both independently and in cooperation with others;• An ability to communicate understanding through the language of mathematics;• An ability to use and apply mathematics in a range of contexts including across the

curriculum and in real life;• The ability to reason mathematically by following a line of enquiry and presenting

justification, proof and argument to demonstrate understanding;• A thorough knowledge and understanding of numbers and the number system, features of

shape and space, measuring skills in a range of contexts, and ways in which information can be gathered and presented.

Fluency

• Varied and frequent practice.

• Develop conceptual understanding.

• Recall and apply knowledge (number facts and relationships) rapidly and accurately.

• Efficient in their calculations and strategies.

• Flexible in their strategies.

• Procedurally and conceptually fluent- knowing how to use a strategy and why it works.

• Increasingly complex problems.

Reasoning

• Describing, explaining, convincing, justifying, proving.

• Follow a line of enquiry.

• Conjecture relationships and generalisations.

• Develop an argument, justification or proof.

• Use mathematical language.

• Select problem-solving strategies.

• Develop solutions and draw conclusions.

Problem Solving

• Apply their mathematics to a variety of problems and puzzles.• Using maths in everyday contexts- organising a party or spending a budget, games, • logic problems, • working systematically, • finding all possibilities, • visual problems, • rules and patterns• investigations

• Variety of problem skills involved.• Deciding upon strategies, breaking down a problem.• Trial and improvement• Working systematically• Pattern spotting• Visualising• Conjecturing• Generalising and proving• Concluding

Read Understand Choose Solution Answer Check

Key Stage One

• The principal focus is to develop confidence and mental fluency with whole numbers, counting and place value.

• Work with numerals, words and the four operations.

• Practical resources.

• Develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary.

• Use a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money.

Lower Key Stage Two

• The principal focus is to become fluent with whole numbers and the four operations.

• Develop efficient mental and written methods.

• Perform calculations accurately with increasingly larger whole numbers.

• Develop their ability to solve a range of problems.

• Simple fractions.

• Decimal place value.

• Pupils draw with increasing accuracy and analyse shapes and their properties.

• Use measuring instruments with accuracy and make connections between measures and number.

Upper Key Stage Two

• The principal focus is to extend their understanding of the number system and place value to include larger numbers.

• Develop the connections between multiplication and division with fractions, decimals, percentages and ratio.

• Develop their ability to solve a wider range of problems.

• Develop efficient written and mental methods of calculation for all four operations.

• Introduced to algebra.

• Classify shapes with complex geometric properties.

What does Maths at St. Michael’s look like?

• Taught on daily basis.

• Focus on one area for a week, fortnight or more.• Number and Place Value• Addition and Subtraction• Fractions• Geometry• Measurement• Multiplication and Division• Statistics • Algebra (Year 6)

• Opportunities for links within domains and across domains.

• Opportunities for all pupils to develop fluency, reasoning and problem solving skills.

• Cross-curricular links

• Everyday contexts, purposeful activities, real-life connections.

What does Maths at St. Michael’s look like?

• Practical activities, whole-class, group and paired discussions, problem-solving activities.

• Children ask, as well as answer, mathematical questions.

• High quality mathematical language used by pupils and adults,

• Variety of formal and informal calculation methods, appropriate to their age.

• Compare and discuss different methods.

• Choose appropriate strategies for different activities.

• Mental maths is incorporated throughout all lessons, and taught or practised explicitly when needed.

• Calculators are introduced in key stage two to support conceptual understanding and explore more complex number problems. They are not used to replace written or mental calculations.

• All pupils have access to a wide range of mathematical resources, and these are used on a regular basis within lessons.

ResourcesNumicon

Bead String

Hundred Square

Cubes

Dienes or Base Ten

Place Value CountersNumber Track

Number Line

Place Value Chart

Breadth and Depth

• The National Curriculum advises that pupils who grasp concepts rapidly should not be accelerated through new content. Instead, they should be challenged through rich and sophisticated problems.

• Activities are differentiated through the content, approach to complete, and use of resources.

• Given opportunities to choose the level of challenge of the activity.

• Spend longer on mathematical topics in order for all pupils to have a deeper, more accurate understanding.

Mastery

How you can support your child’s learning

Practise number facts and concepts as below regularly and continuously.

The aim is for pupils to recall these quickly and accurately, and have a secure understanding of

concepts and terms.

Year 1– Addition facts to 10 and subtraction facts from 10.

Addition facts to 20 and subtraction facts from 20.

Practice of simple addition, subtraction, multiplication (as groups

of) and division (as sharing). Practical practice of these is ideal.

Counting in steps of 2, 5 and 10 from 0.

Find one more and one less of numbers up to 100.

Counts to and across 100, forwards and backwards from any number.

 

  

Year 2- Addition facts to 20 and subtraction facts from 20.

Addition facts to 100 and subtraction facts to 100 (multiples of ten)

Multiplication and division facts for the 2, 5 and 10 times tables.

Odd and even numbers.

Counting in steps of 2, 3 and 5 forwards and backwards, from and to 0.

Count in steps of ten from any number,.

Year 3– Multiplication and division facts for the 3, 4 and 8 times tables.

Counts in steps of 4, 8, 50 and 100 forwards and backwards, from and to 0.

Finds 10 or 100 more or less than one, two and three-digit numbers.

 

 

Year 4– Multiplication and division facts for all the times tables up to 12 x 12.

Multiples, factors, factor pairs.

Understanding what a decimal number is.

Count in steps of 6, 7, 9, 25 and 1000 forwards and backwards, to and from 0.

Count beyond zero to include negative numbers.

Count in intervals of 10, 100 or 1000 from one, two, three and four-digit numbers.

Year 5– Multiples, factors, factor pairs, common factors, prime numbers, prime factors, composite

numbers, square numbers, cube numbers.

Multiply and divide whole numbers and decimal numbers by 10, 100 and 1000

Count forwards and backwards in powers of 10 from any number up to 1, 000. 000.

 

Year 6– Revision and practice of previous years.

 

http://www.mathplayground.com/games.html

http://www.topmarks.co.uk/maths-games

http://www.multiplication.com/games/all-games

http://www.bbc.co.uk/bitesize

http://www.primaryhomeworkhelp.co.uk/maths/

Calculation Strategies- Addition

Develop an understanding of number, counting and addition• Join in with songs, rhymes and stories.• Match sets of objects to written and spoken numbers.• Count on from different numbers.• Recognise that numbers relate to how many are in a set.• Record numbers and counting in words, symbols and

pictures

Calculation Strategies- AdditionDevelop a further understanding of addition• Understand that adding means the total of numbers or objects.• Practical addition with a variety of resources.

• Combine two groups of objects and count to total them. They start counting from 0.

• Then recognise that they can count from the larger set/number instead of starting from 0.

• Record additions as number sentences.• Add on number lines, number tracks and hundred squares.• Draw their own number lines to add.• Understand that addition can be done in any order.• Understand that addition and subtraction are inverses (opposites).• Find missing numbers in addition sentences.

Calculation Strategies- AdditionDevelop their addition fluency (facts they need to practise and learn)• Addition facts to 10 (expected by the end of year 1). 0 + 10 = 10, 9 + 1 = 10, 8 + 2= 10, 7 + 3 = 10...• Addition facts to 20 (expected by the end of year 2). 19 + 1 = 20, 18 + 2 = 20, 17 + 3 = 20, 16 + 4 = 20…• Add a series of one-digit numbers (e.g. 5 + 8 + 4) (expected by the

end of year 2).• Addition facts to 100 (multiples of 10) (expected by the end of year 2.) 10 + 90 = 100, 20 + 80 = 100, 30 + 70 = 100…• Use addition facts and place value to add multiples of 10 and 100

(e.g. 70 + 80, 900—400 etc.) (developed in years 2, 3 and 4).

Calculation Strategies- AdditionMental Methods of Addition• Bridging through tens

• What do you have to add to reach the next multiple of ten? How many more do we need to add?

• Do practically with a variety of resources (bead strings, cubes etc.)

• Then do on number tracks, number lines and hundred squares.

• Then draw their own number lines to complete on,• Then complete in their heads (with jottings if needed).• Move on to bridging hundreds.

Calculation Strategies- AdditionMental Methods of Addition• Adding near multiples of 10

• Explore how add 9 by adding 10 and then subtracting 1• Explore how add 11 by adding 11 and then adding 1• Can also look at other near multiples of 10 (e.g. 21, 39, 71 etc.)• Use the language- add a multiple of ten, then adjust

Calculation Strategies- AdditionMental Methods of Addition• Partitioning numbers to add

• Dienes and other resources can aid understanding• Partition both numbers and total.• Understand that they need to exchange when a place value

is greater than 9.• Can then partition the smaller number only and add them

to the larger number. Start on the ones to get used to the same order as in column addition.

Calculation Strategies- AdditionWritten Methods of Addition• Expanded Column

1. Label the columns with place value headings.2. Partition the first number and write in the correct column.3. Partition the second number and write underneath.4. Draw large equals sign.5. Add the ones, then tens, then hundreds etc.6. Write a final total beside or underneath.

Once confident, children can start to exchange when place value does not fit into that column.

Dienes can aid understanding and additions.

Once confident, progress to traditional short column method.

Calculation Strategies- Subtraction

Develop an understanding of number, counting and subtraction• Join in with songs, rhymes and stories.• Match sets of objects to written and spoken numbers.• Count back from different numbers.• Recognise that numbers relate to how many are in a set.• Record numbers and counting in words, symbols and

pictures

Calculation Strategies- SubtractionDevelop a further understanding of subtraction• Understand that subtracting means reducing a set or number, taking away and

working out how many are left, or finding the difference between two numbers or sets.

• Practical subtraction with a variety of resources.• Recognise that the most efficient way is to take away the smaller larger from the

larger number.

• Record subtractions as number sentences.• Subtract on number lines, number tracks and hundred squares.• Draw their own number lines to subtract.• Understand that subtraction cannot be done in any order.• Understand when counting back would be most efficient and when counting on

would be more efficient.• Understand that addition and subtraction are inverses (opposites).• Find missing numbers in subtraction sentences.

Calculation Strategies- SubtractionDevelop their subtraction fluency (facts they need to practise and learn)• Subtraction facts from 10 (expected by the end of year 1).

10—0 = 10, 10—1 = 9, 10—2 = 8, 10—7 = 3…

• Subtraction facts from 20 (expected by the end of year 2).

20—1 = 19, 20 –2= 18, 20—3= 17, 20—4=16…

• Subtract a series of one-digit numbers (e.g. 8—3—2) (expected by the end of year 2).

• Subtraction facts from 100 (multiples of 10) (expected by the end of year 2).

100—10 = 90, 100—20 = 80, 100—30 = 70…

• Use subtraction facts and place value to subtract multiples of 10 and 100 (e.g. 70 + 80, 900—400 etc.) (developed within years 2, 3 and 4).

Calculation Strategies- SubtractionMental Methods of Subtraction• Bridging through tens

• What do you have to subtract to reach the next multiple of ten? How many more do we need to subtract?

• Do practically with a variety of resources (bead strings, cubes etc.)

• Then do on number tracks, number lines and hundred squares.

• Then draw their own number lines to complete on,• Then complete in their heads (with jottings if needed).• Move on to bridging hundreds.

Calculation Strategies- SubtractionMental Methods of Subtraction• Subtracting near multiples of 10

• Explore how subtract 9 by subtracting 10 and then adding 1• Explore how subtract 11 by subtracting 11 and then subtracting

1• Can also look at other near multiples of 10 (e.g. 21, 39, 71 etc.)• Use the language- subtract a multiple of ten, then adjust

Calculation Strategies- SubtractionMental Methods of Subtraction• Partitioning numbers to subtract

• Dienes and other resources can aid understanding• Partition the smaller number and take away from the larger

number. Start on the ones to get used to the same order as in column subtraction.

• Understand that they need to exchange when they do not have enough to complete a subtraction.

Calculation Strategies- SubtractionWritten Methods of Subtraction• Expanded Column

1. Label the columns with place value headings.2. Partition the first number and write in the correct column.3. Partition the second number and write underneath.4. Draw large equals sign.5. Subtract the ones, then tens, then hundreds etc.6. Write a final total beside or underneath.

Once confident, children can start to exchange when they do not have enough to complete a subtraction.

Dienes can aid understanding and subtractions.

Once confident, progress to traditional short column method.

Calculation Strategies- Multiplication

Develop an understanding of number, counting and multiplication• Join in with songs, rhymes and stories.• Match sets of objects to written and spoken numbers.• Count on and back in steps of 1, 2, 5 and 10.• Recognise that numbers relate to how many are in a set.• Record numbers and counting in words, symbols and

pictures.• Group objects and count repeated groups.

Calculation Strategies- Multiplication

Develop a further understanding of multiplication• Understand that multiplying means the total of groups or lots of numbers and objects.• Practical multiplication with a variety of resources- creating groups.• Record multiplications as groups of or lots of sentences, before number sentences.• Draw arrays to show multiplications, and write multiplications from arrays.• Understanding doubling.• Multiply on number tracks, number lines and hundred squares.• Link multiplication and repeated addition.• Draw their own number lines to show multiplications.• Understand that multiplication can be done in any order.• Understand that multiplication and division are inverses (opposites).• Find missing numbers in multiplications.

Calculation Strategies- Multiplication

Develop their multiplication fluency (facts they need to practise and learn)•  2, 5 and 10 times tables (expected by the end of year 2).• 3, 4 and 8 times tables (expected by the end of year 3).• All times tables up to 12 x 12 (expected by the end of year 4).• The outcome of multiplying by 0 and 1 (All numbers are 0 when

multiplied by 0. All numbers stay the same when multiplied by 1) (expected by the end of year 4).

• The outcome of multiplying whole numbers by 10, 100, 1000 etc. (expected by end of year 4).

Calculation Strategies- Multiplication

Mental Methods of Multiplication• Partitioning numbers to multiply

• Dienes and other resources can aid understanding• Partition into place values. Start on the ones as the same

order as column multiplication.• Understand that they need to exchange when the place

value is greater than 9.

Calculation Strategies- Multiplication

Written Methods of Multiplication• Expanded Column

1. Label the columns with place value headings.2. Partition the first number and write in the correct column.3. Write the multiplier underneath4. Draw large equals sign.5. Multiply the ones, then tens, then hundreds etc.6. Write a final total beside or underneath.

Once confident, children can start to exchange when one of the place values is greater than 9.

Dienes can aid understanding and multiplications.

Once confident, progress to traditional short column method.

Children will also need to use the traditional long multiplication method when the multiplier is larger than a one-digit number.

Calculation Strategies- Division

Develop an understanding of number, counting and division• Join in with songs, rhymes and stories.• Match sets of objects to written and spoken numbers.• Count on and back in steps of 1, 2, 5 and 10.• Recognise that numbers relate to how many are in a set.• Record numbers and counting in words, symbols and

pictures.• Share objects into equal groups.

Calculation Strategies- Division

Develop a further understanding of division• Understand that dividing means sharing into equal groups.• Practical division with a variety of resources- splitting objects into groups and counting how

many are in each group.• Record divisions as shared into or groups of sentences, before number sentences.• Understanding halving.• Link division and repeated subtraction- counting back in steps.• Divide on number tracks, number lines and hundred squares by counting back in steps.• Draw their own number lines to show divisions.• Draw arrays to show divisions, and write divisions from arrays.• Understand division as how many fit into.• Introduce and understand remainders.• Understand that multiplication and division are inverses (opposites).• Find missing numbers in divisions.

Calculation Strategies- Division

Develop their division fluency (facts they need to practise and learn)• 2, 5 and 10 division facts (expected by the end of year 2).

• 3, 4 and 8 division facts (expected by the end of year 3).

• All division facts up to 144 ÷ 12 (expected by the end of year 4).

• The outcome of dividing by 0 and 1 (All numbers are 0 when divided by 0. All numbers stay the same when divided by 1) (expected by the end of year 4).

• Identify factor pairs and common factors (expected by the end of year 5).

• The outcome of dividing whole numbers by 10, 100, 1000 etc. (expected by the end of year 4).

Calculation Strategies- Division

Mental Methods of Division• Partitioning numbers to divide

• Dienes and other resources can aid understanding• Partition into known multiples of divisor.

Calculation Strategies- DivisionWritten Methods of Division

• Short Division (‘Bus stop’ method)• Can use dienes or other resources underneath to aid understanding and divisions.

• Can also partition the dividend to aid understanding and divisions.

• Traditional Long Division for larger divisors

Informal Workshops and Stations:

Times TablesEarly Years MathsProblem SolvingResourcesYear 6 SATsYear 2 SATs- In hall