Maths Information Evening Foundation & Key Stage 1 Wednesday 24 th April 2013

What is the Maths Framework? The Maths Framework follows on from the success of the Numeracy Strategy It is structured to enable children to spend more time on a particular area and to make links in their learning The Maths Framework incorporates seven strands of learning that are organised into blocks

The seven mathematics strands of objectives - 1 Using and applying mathematics [including problem solving] Knowing and using number facts Calculating Counting and understanding number Handling data Understanding shape Measuring

Block A Counting, partitioning and calculating Block B Securing number facts, understanding shape Block C Handling data and measures Block D Calculating, measuring and understanding shape Block E Securing number facts, relationships and calculating Using and applying mathematics Counting and understanding number Calculating Using and applying mathematics Knowing and using number facts Understanding shape Using and applying mathematics Measuring Handling data Using and applying mathematics Calculating Measuring Counting and understanding number Knowing and using number facts Calculating Understanding shape

Block C Unit 3 Block D Unit 3 Block E Unit 3 Block A Unit 3 Block A Unit 2 Block A Unit 1 Block A Counting, partitioning and calculating Block B Unit 3 Block C Unit 2 Block B Unit 2 Block B Unit 1 Block B Securing number facts, understanding shape Block E Unit 2 Block E Unit 1 Block E Securing number facts, relationships and calculating Block D Unit 2 Block D Unit 1 Block D Calculating, measuring and understanding shape Block C Unit 1 Block C Handling data and measures Term 1 Term 2 Term 3

Block C Unit 3 Block D Unit 3 Block E Unit 3 Block A Unit 3 Block A Unit 2 Block A Unit 1 Block A Counting, partitioning and calculating Block B Unit 3 Block C Unit 2 Block B Unit 2 Block B Unit 1 Block B Securing number facts, understanding shape Block E Unit 2 Block E Unit 1 Block E Securing number facts, relationships and calculating Block D Unit 2 Block D Unit 1 Block D Calculating, Measuring and Understanding shape Block C Unit 1 Block C Handling data and measures

The Teaching and Learning Cycle Review – Teach – Practise – Apply – Review The cycle constitutes four teaching and learning foci: Focus A: Review prior learning and introduce new learning Focus B: Practice and Consolidate learning Focus C: Apply, secure and extend learning Focus D: Review and evaluate progress in learning

Examples of teaching sequences over a Unit (10 lessons) Focus A Review prior learning/ introduce new learning (2 lessons ) Focus B Practise and Consolidate (2 Lessons) Focus C Apply, secure and extend learning (3 Lessons) Focus D Review and evaluate progress in learning (1 Lesson) Foci B, C (1 Lesson) Focus D Review and evaluate progress in learning (1 Lesson) Focus A Review prior learning/ introduce new learning (1 lesson ) Focus B Practise and Consolidate (2 Lessons) Focus C Apply, secure and extend learning (4 Lessons) Focus B Practise and Consolidate (1 Lesson) Focus C Apply, secure and extend learning (1 Lesson) Focus D Review and evaluate progress in learning (1 Lesson) or

Developing an understanding of number When children arrive in Reception we work to develop their knowledge of numbers 1-10 (before moving on to numbers to 20) by: -singing number songs and nursery rhymes (e.g. 10 green bottles, 5 currant buns) -reading number stories (e.g. The Three Pigs, Goldilocks) -playing number games when matching numerals and objects in practical situations in class and the outside area.

Experience, Language, Pictures, Symbols (ELPS) (Liebeck, 1984) Firstly the children are first exposed to learning to add, subtract, double and halve through experiences with objects which is when they begin to develop some mathematical language. They are then gradually encouraged to record their working out. Initially this is by mark making, drawing pictures, or moving images on the interactive white board. They then write numbers and eventually symbols (number sentences, for example 3+2=5).

An example of addition using ELPS in the context of toy cars 1) Experience and Language: The children are encouraged to develop mathematical vocabulary such as ‘altogether’, ‘more’, ‘makes’ and ‘adding’ in practical contexts when counting objects in 2 or more groups. Example: Whilst the children are playing with various amounts of cars each. An adult asks the children ‘How many cars have you got each / altogether? Who has got the most? How many more do you have than ‘Child A’?’

2) Pictures: Once a child has started to develop their understanding of counting objects. An adult would encourage them to record their working out either by; mark making, tally charting or drawings of cars or shapes. They would also be encouraged to work with images on the interactive white board or paper instead of counting objects. Once a child has developed recognition of number they are also introduced to number lines when counting objects to help with the concept of ‘counting on’. 3) Symbols: A child would then be encouraged to record how many cars there are by matching numeral cards to objects / writing numerals. At a later developmental stage the child would record their working out using a number sentence e.g. Child A has 2 cars and Child B has 3, so Child A writes 2+3=5.

An example of subtraction using ELPS in the context of money. 1) Experience and language: Similar to addition, the children are encouraged to develop mathematical vocabulary such as ‘take away’, ‘less’ ‘left’ and ‘fewer’ in practical contexts when subtracting one or more from a group. Example: Child B is pretending to be a shopkeeper who has pretend price tagged fruit. Child A is pretending to be a customer, he/she has counted ten penny coins into her bag: Child A: ‘I would like an apple please.’ Child B: ‘That’s 3p please.’ (Child A counts out / subtracts 3p from her 10p and passes it to Child B) Adult intervenes: ‘Child A, how much money do you have left now? Can you buy anything else from Child B?’

2) Pictures: Once a child has started to develop their understanding of taking away objects, similar to addition an adult would ask a child to move / take away images on the interactive white board or on paper. Example: A child has images of 10 pennies on the interactive white board / paper. When asked to pay for a 3p apple, he/she subtracts 3p by crossing off 3 images of coins and counting how many coins are left. Once a child has developed recognition of number they are also introduced to number lines when subtracting objects to help with the concept of ‘counting back’. 3) Symbols: The child is then encouraged to record how many coins they have by writing numerals / selecting numeral cards. At a later developmental stage they would record their working out using a number sentence e.g. 10p - 3p = 7p.

Multiplication The children learn to count in 2s and 10s by singing songs and counting with actions. They also learn about doubling. This is introduced as ‘adding on the same amount again’. The children use the following mathematical language: ‘add’, ‘double’, ‘more’, ‘and’, ‘altogether’, ‘same amount’.

An example of doubling using ELPS in the context of plastic bears 1) Experience and language: Discussion about doubling objects: Adult: Can you make double 3 by counting out these bears? (child makes two groups of 3 bears). Adult: How much is double three? / How many bears are there altogether? (Child counts all of the bears in two groups) 2) Pictures: Once a child is familiar with doubling objects, they double pictures on the interactive white board and double numbers on the number line by circling the number they are doubling and counting on. 3) Symbols: The child would then record double of a number by writing number sentences e.g. 3+3=6 (In Year 2 they start to write the symbol for division when writing number sentences).

Division The children’s first introduction to division is through being taught sharing and halving. This is introduced as ‘sharing in to two or more equal groups / parts’. They halve an object as an introduction to halving number. The children use the following mathematical language: ‘take away’, ‘halve’, ‘share’, ‘equal’, ‘fair’.

An example of halving using ELPS in the context of an apple and buttons 1) Experience and language: Discussion about halving an object: Adult: How can I cut this apple in half? Child: You can cut it down the middle. Adult: How do I know that the apple is in half now? Child: Because it is in two equal bits. Then a child would develop an understanding of sharing an amount of buttons in half between themselves and another child. 2) Pictures: On the interactive white board the child would then share out images of buttons into two equal groups. 3) Symbols: The child would then record their groupings by writing numbers. (In Year 2 they start to write the symbol for multiplication when writing number sentences.)

Shape, Space and Measures We talk about, recognise and recreate simple patterns We use language such as ‘greater’, ‘smaller’, ‘heavier’ or lighter to compare quantities We use language such as ‘circle’ or ‘bigger’ to describe the shape and size of solids and flat shapes We use developing mathematical ideas and methods to solve practical problems

Theory into Practise Year 1

Counting and Understanding Number Most children: Read, count and write numerals from 0-20 (then beyond) Use knowledge of place value to order numbers Say the number that is one more and one less than a given number

Knowing and Using Number Facts Number bonds to 5 and 10 Simple addition to at least five Count on and back in 1, 2, 5, and 10’s Know doubles of all numbers to at least 10

Calculating Most children learn to: Use the vocabulary related to addition and subtraction and the symbols to describe and record Relate addition to counting on and understand that addition can be done in any order Understand as take away and find the difference by counting up Apply these skills solving practical problems

Understanding Shape Most children learn to: Name common 2D shapes and 3D solids and describe their features Use them to make patterns, pictures and models Use everyday language to describe position, direction and distance

Measure and Data Handling Most children learn to: Estimate, measure weigh and compare objects, choosing and using suitable uniform non-standard units and measuring instruments Answer a question by recording information in lists, tables, pictograms and graphs

Writing number stories and number sentences

Writing and solving word problems

Number line 100 square

Counting in 2s 5s and 10s to understand values of coins

Repeated subtraction as division

Theory into Practise Y2

Counting and Understanding Number Most children learn to: Count up to 100 objects by grouping them and counting in tens, fives and two’s (aerobics) Explain what each digit in a two digit number represents, including numbers where 0 is a place holder (partitioning) Add two digit numbers using the partitioning strategy

Knowing and Using Number Facts Most children learn to: Derive and recall all addition and subtraction facts for each number to at least ten (number bonds) Understand that halving is the inverse of doubling, derive and recall doubles of all numbers to 20 and the corresponding halves Derive and recall multiplication facts for the 2, 5, and 10 times tables and the related division facts

Calculating Most children learn to: Add or subtract mentally a one digit number or a multiple of ten from a two digit number Use practical and informal written methods to add and subtract two digit numbers Repeated addition and arrays as multiplication and sharing and grouping as division

Understanding Shape Most children learn to: Name common 2D and 3D solid shapes, sort make and describe shapes referring to their properties Identify reflective symmetry in patterns and 2D shapes and draw lines of symmetry in shapes Follow and give instructions involving position, direction and movement

Measuring and Handling Data Most children learn to: Estimate compare and measure length, weights and capacity using standard units (m,cm,kg,litre) Use units of time (seconds, minutes, hours and days) and know the relationship between them To read the time to the quarter hour, half past and on the hour Answer a question by collecting and recording the data Use ICT to organise and present data

Addition- Partitioning method = T: = 50 U: = = 59 Some children might prefer to use a number line or a 100 square to support them with each step of the addition. Most will be able to add a single digit to a multiple of 10 mentally.

Subtraction- Number line 36 – 14 =

Multiplication- Repeated addition

Division- Repeated subtraction

Homework and Top Tips The homework set is to reinforce the learning that has taken place during the week It will not contain any new strategies or concepts You can help by working on the 2, 5, 10 and 3 times tables beyond that they will learn the 4 and 6’s Research shows that children learn best through practical experiences that they can relate to the world around them So let your children buy the newspaper or ask them to work out how many apples you will need for pack lunches next week If you are feeling really adventurous get cooking with them and let your child weigh and measure the ingredients